Report on integration of modelling tools with test ... - SERIES

SEVENTH FRAMEWORK PROGRAMME Capacities Specific Programme Research Infrastructures Project No.: 227887

SERIES SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES

Workpackage [WP13] Deliverable [D13.3] – Report on integration of modelling tools with test equipment and on virtual model development

Deliverable/Editor: EUCENTRE, UNITN Reviewer: UNITN Revision: Final

February, 2013

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development

ABSTRACT The main objective of this report that covers the research activities of Task JRA2.4 is the presentation of recent advances in system identification and model updating, in order to develop virtual models of test equipment-specimen-instrumentation systems. Use of virtual models, along with the latest advances in control to reduce the number of experimental substructures of calibration pre-tests, optimizes the location and number of sensors and improves the quality of results. In greater detail, the following topics and objectives are treated: -

Use of modelling tools, data processing software and databases to improve the design of testing equipment and set-ups.

-

Identification of testing equipment by means of system identification and model updating.

-

Modelling in tests using reduction techniques on substructures.

-

Integration of testing equipment and specimen model to build virtual models.

Keywords: System identification, model updating, hysteretic systems, substructure modelling, shaking tables

i


ii


ACKNOWLEDGMENTS The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under grant agreement n° 227887. The contribution of Politecnico of Torino for the issuing of both Chapter 2 and 3 is gratefully acknowledged. This work has been developed by the partners of the JRA2 activity.

iii


iv


DELIVERABLE CONTRIBUTORS EUCENTRE Alberto Pavese Igor Lanese Simone Peloso ITU Alper Ilki Medine Ispir TUIASI Gabriela M. Atanasiu Vasile Horga UNITN Oreste S. Bursi Giuseppe Abbiati Zhu Mei Md. Shahin Reza Alessia Ussia

v


vi


CONTENTS List of Figures ................................................................................................................................ ix 1

Study Overview .......................................................................................................................1

2

State of the Art on System Identification...............................................................................2 2.1 Introduction ....................................................................................................................2 2.1.1 Linear identification...........................................................................................2 2.1.2 Non‐linear identification ...................................................................................3 2.1.3 By‐passing non‐linearities .................................................................................4 2.1.4 Parametric approaches......................................................................................5 2.1.5 Non‐parametric approach .................................................................................5 2.1.6 Approaches based on instantaneous estimation..............................................5 2.1.7 Identification of hysteretic and evolutive/degrading systems .........................6 2.1.8 Identification of hysteretic and evolutive/degrading systems .........................7 2.2 Concluding Remarks ....................................................................................................10

3

Model Updating and Data Assimilation ...............................................................................12 3.1 Introduction ..................................................................................................................12 3.2 Model‐Driven vs. Data‐Driven Approaches .................................................................12 3.2.1 Model‐driven approaches ................................................................................12 3.2.2 Modal reduction and expansion ......................................................................13 3.2.3 Direct methods and sensitivity methods ........................................................13 3.2.4 Parameterization of a model ...........................................................................14 3.2.5 Comparison between identified and analytical data: MAC and COMAC.......15 3.3 Data‐Driven Approaches .............................................................................................16 3.4 Conclusion ....................................................................................................................16

4

System Identification to Improve the Design of Testing Equipment and Set‐ups..............17 4.1 Introduction ..................................................................................................................17 4.2 Identification based on a visual optical system ...........................................................17 vii

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 4.2.1 Basic steps for the usage of a visual system ...................................................17 4.2.2 Limits of the vision system ..............................................................................18 4.3 Identification of Hysteretic Systems Based on Kalman Filter.....................................19 4.3.1 Kalman filter ....................................................................................................19 4.3.2 Application of Unscented Kalman Filter to a damper ....................................21 4.4 Identification of MDoF Hysteretic Systems ................................................................26 4.4.1 A modified Bouc‐Wen model ..........................................................................27 4.4.2 The model for a two storey system .................................................................29 4.4.3 The model for a four storey system ................................................................33 5

Test Modelling with Substructuring Including Experimental and Numerical Uncertainties39 5.1 Introduction ..................................................................................................................39 5.2 Modelling in the Case of Uncertainties........................................................................39 5.3 Modelling of a Piping System for Real‐time and Pseudo‐dynamic Tests...................40 5.3.1

FE modelling and modal analysis of the piping system under investigation .40

5.3.2 Analysis of the piping system under seismic loading .....................................42 5.3.3 Substructuring of the piping system ...............................................................44 5.3.4 Model reduction of the PS ...............................................................................46 5.3.5 Results from experimental tests .....................................................................47 6

Integration of Testing Equipment and Specimen Model in order to Build a Virtual Model 49 6.1 Introduction ..................................................................................................................49 6.2 Advanced Methods Applied in Updating Structural Computational Models .............49 6.2.1 The advanced method .....................................................................................49 6.2.2 Implementation of the methods .....................................................................50 6.3 Integration of Testing Equipment and Specimen Model for Shaking Tables ............53 6.3.1 Hardware and software architecture ..............................................................54 6.3.2 The implemented real‐time algorithm ...........................................................55 6.3.3 Tuning of the hybrid testing system ...............................................................55

7

Summary ...............................................................................................................................59

References .....................................................................................................................................60 viii


List of Figures Fig. 2. 1 An unknown system with input and output ...................................................................... 7 Fig. 2. 2 Component and interaction diagram of a shake table system .......................................... 8 Fig. 2. 3 Test –analysis comparison ................................................................................................ 8 Fig. 2. 4 NEES-SCSD LHPOST with a full-scale seven-storey full-scale R/C building slice, 19.2m high mounted on it ................................................................................................. 9 Fig. 2. 5 Mechanical sub-system of NEESUCSD LHPOST .......................................................... 9 Fig. 2. 6 Conceptual mechanical model of the table with model parameters Me, Ke, Ce and Fμe to be identified through periodic, earthquake, and white noise tests .............................. 10 Fig. 4. 1 A sample of marker locations ......................................................................................... 18 Fig. 4. 2 A view of each marker displacements in x- and y- directions........................................ 18 Fig. 4. 3 Comparison between the displacements measured from the visual optical system and that from transducer ...................................................................................................... 19 Fig. 4. 4 Comparison of hysteretic cycles ..................................................................................... 22 Fig. 4. 5 Comparison of displacement .......................................................................................... 22 Fig. 4. 6 Comparison of velocity .................................................................................................. 23 Fig. 4. 7 Comparison of restoring force ........................................................................................ 23 Fig. 4. 8 Estimation of BoucWen parameters ............................................................................... 23 Fig. 4. 9 Control and acquisition instrumentation setup in TT1 Test Rig .................................... 24 Fig. 4. 10 Comparison between experimental and numerical data ............................................... 26 Fig. 4. 11 A slip function .............................................................................................................. 27 Fig. 4. 12 Slip and BoucWen springs in series for a SDoF system .............................................. 28 Fig. 4. 13 A two-story frame ......................................................................................................... 29 Fig. 4. 14 Plan view of the prototype structure tested at JRC and concentrically braced frame .. 31 Fig. 4. 15 Amplitude of x2 (t ) ....................................................................................................... 32 Fig. 4. 16 Instantaneous values of βi and γi for different values of PGA...................................... 33 Fig. 4. 17 A chain like four-storey frame...................................................................................... 34 Fig. 4. 18 Layout of the specimen................................................................................................. 34 Fig. 4. 19 Interstorey drift vs. Restoring force .............................................................................. 35 Fig. 4. 20 Comparison of displacements and forces at first floor ................................................. 36 Fig. 4. 21 Comparison of displacements and forces at second floor ............................................ 36 Fig. 4. 22 Comparison of displacements and forces at third floor ................................................ 36 Fig. 4. 23 Comparison of displacements and forces at fourth floor .............................................. 37 Fig. 4. 24 Instantaneous coefficients for the stiffness matrix ....................................................... 37 Fig. 4. 25 Instantaneous frequencies of the degrading model from estimated instantaneous coefficients .................................................................................................................... 38 Fig. 5. 1 The reference piping system under investigation ........................................................... 41 Fig. 5. 2 Specifications and boundary conditions of the piping system ....................................... 41 Fig. 5. 3 Mode 1 and Mode 2 of the piping system model ........................................................... 42 Fig. 5. 4 Finite element model of the support structure ................................................................ 42 Fig. 5. 5 Measurement points of accelerograms on the support floor........................................... 42 Fig. 5. 6 The reference earthquake for experimental tests ............................................................ 43 ix

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Fig. 5. 7 Moment in the piping system without damping ............................................................. 43 Fig. 5. 8 Shear in the piping system without damping.................................................................. 43 Fig. 5. 9 Moment in the piping system with Rayleigh damping (0.5%) ....................................... 44 Fig. 5. 10 Shear in the piping system with Rayleigh damping (0.5%) ......................................... 44 Fig. 5. 11 The physical and numerical substructures of the piping system .................................. 45 Fig. 5. 12 Dimensions and actuator position................................................................................. 45 Fig. 5. 13 Actual test set-ups for hybrid tests ............................................................................... 45 Fig. 5. 14 Displacement history of coupling node 1 in direction x ............................................... 46 Fig. 5. 15 Displacement history of coupling node 2 in direction x ............................................... 46 Fig. 5. 16 Rotations of the two end nodes of Elbow #1 at SLTC ................................................. 47 Fig. 5. 17 Horizontal accelerations of Coupling Node #1 at SLTC .............................................. 48 Fig. 5. 18 Horizontal displacements of Coupling Node #1 at SLTC ............................................ 48 Fig. 6. 1 2D shear type model ....................................................................................................... 50 Fig. 6. 2 Process of iterative optimization for model updating ..................................................... 51 Fig. 6. 3 Process of iterative optimization for model updating ..................................................... 51 Fig. 6. 4 Process of iterative optimization for model updating based on output only-deterministic method........................................................................................................................... 52 Fig. 6. 5 Process of iterative optimization for model updating based on output-stochastic method ....................................................................................................................................................... 53 Fig. 6. 6 Implemented RTDHT system ......................................................................................... 54 Fig. 6. 7 Eucentre Bearing Testing System (Left) and BTS horizontal actuator (Right) ............. 54 Fig. 6. 8 Vertical and lateral thrust bearings of BTS table ........................................................... 55 Fig. 6. 9 Simulink experimental model: main window ................................................................. 55 Fig. 6. 10 Proposed assessment procedure; step # ........................................................................ 56 Fig. 6. 11 Simulink experimental model: delay estimation .......................................................... 57 Fig. 6. 12 Pseudo-random displacement signal and simulated constant delay feedback with noise ....................................................................................................................................................... 57 Fig. 6. 13 Imposed and estimated delay (noisy feedback) ............................................................ 57 Table 4. 1 Numerical and estimated values of BoucWen parameters .......................................... 23 Table 4. 2 Initial values of stiffness parameters ........................................................................... 38 Table 4. 3 Final values of stiffness parameters ............................................................................. 38 Table 5. 1 Some design parameters of the support structure ........................................................ 42 Table 5. 2 Maximum moment, M max and stress,  max without damping ...................................... 44 Table 5. 3 Maximum moment, M max and stress,  max with damping............................................ 44 Table 5. 4 Maximum shear,  max in the straight pipe ..................................................................... 44 Table 5. 5 Hybrid test program ..................................................................................................... 47 Table 6. 1 Initial model’s characterization ................................................................................... 50 Table 6. 2 Results of model’s charateristics ................................................................................. 51 Table 6. 3 Results of model’s characteristics................................................................................ 51 Table 6. 4 Model updating results of output only – deterministic method ................................... 52 Table 6. 5 Model updating results of output only-stochastic method ........................................... 52

x


1

Study Overview

The scope of the Task JRA2.4 is the improvement in design of testing equipment and set-ups and of interpretation of experimental results, using modelling tools: FE codes, data processing software and databases. Techniques employed were based on experimental/numerical data to identify testing equipment and specimens by combining observational data with the state of the dynamic system that was partly unknown. Using sophisticated concepts derived from optimal control and Kalman filters, virtual model of the equipment/test facility can be briefly built, also with updating techniques. This will allow for reducing the number of calibration pre-tests, optimising the number and location of sensors and improving the quality of results. More specifically, this task entailed: – Use of modelling tools, data processing software and databases to improve the design of testing equipment and set-ups. – Identification of testing equipment by means of system identification and model updating. – Modelling in tests using reduction techniques on substructures. – Integration of testing equipment and specimen models to build virtual models.

1


2

State of the Art on System Identification

2.1

INTRODUCTION

System identification refers to the development of structural models from input and output measurements performed on a real structure using sensing devices. Dynamic system identification is a major tool for monitoring and diagnosis of structures: experimental results from dynamic testing provide knowledge about global structural behaviour and can be used for calibrating numerical models, for forecasting the response to dynamic and earthquake loading and for helping in the evaluation of safety conditions (Natke et al 1993, Ghanem & Shinozuka 1995, Maia & Silva 1998). Even if the age of virtual prototyping has already started (Auweraer Van Der 2002), experimental testing and system identification still play a key role, because they help the structural dynamicist to reconcile numerical predictions with experimental investigations. The term ‘system identification’ is sometimes used in a broader context in the technical literature and may also refer to the extraction of information about the structural behaviour directly from experimental data, i.e., without necessarily requesting a model (e.g., identification of the number of active modes or the presence of natural frequencies within a certain frequency range). 2.1.1 Linear identification Linear system identification is a discipline that has evolved considerably during the last 30 years (Soderstrom and Stoica 1989). Experimental modal analysis is by all means the most popular approach to performing linear system identification in structural dynamics. The model of the system is expressed in the form of modal parameters, namely the natural frequencies, mode shapes and damping ratios. The popularity of modal analysis stems from its great generality; modal parameters can describe the behaviour of a system for any input type and any range of the input. The field of linear identification now offers a vast range of effective techniques. In recent years, time domain techniques have been used rather successfully, thanks to the great spectral resolution offered and to their modal uncoupling capability (Masri et al 1982, Shinozuka et al 1982, Natke & Yao 1986, Safak 1991, Safak & Celebi 1991, Peeters & DeRoek 1999, Loh et al 2000). One of the basic shortcomings of these methods is that they often produce spurious modes, whose true nature, however, can usually be identified by means of simple modal form correlation indicators (Ewins 2000), or, as an alternative, with the aid of numerical models. An important family of time domain methods makes use of time series autoregressive models and exploits the theoretical results coming from research in the field of system control (Ljung 2

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 1999). These techniques provide a very general and attractive formulation, and are frequently applied to civil structures. The most critical aspect resides in the computational complexity associated with applications to multi-degree-of-freedom (M-DOF) systems. The extension of the parameter estimation techniques to stochastic multi-variate models, in fact, is far from being trivial, and additional difficulties arise from local minimum points and algorithmic instabilities (Fassois & Lee 1993). Among the deterministic methods, in addition to the historic Ibrahim Time Domain (Ibrahim and Mikulcik 1977), we should mention the Eigensystem Realisation Algorithm (ERA) (Juang & Pappa 1984), which, based on a Single Value Decomposition (SVD) of Hankel's matrix, has been closely studied in the literature (e.g. Lew et al 1993), and the Polyreference Time Domain (PRTD) stemming from a generalisation of Prony's method (Vold 1982, Deblauwe and Allemang 1985). Since the beginning of the nineties, there has been an increasing interest in so-called Stochastic Subspace Identification methods, in which statistical, algebraic and numerical concepts and algorithms cooperate, leading to user-friendly software for linear system identification (Zeiger & McEwen 1974, James et al 1995, Peeters & DeRoek 1999). Contrary to classical algorithms, subspace algorithms do not suffer from the problems caused by a-priori parametrizations and non-linear optimizations. Van Overschee and De Moor (1996) studied three different subspace algorithms for the identification of combined deterministic-stochastic systems. This comparison is done through the introduction of a unifying theorem, of which the three algorithms are special cases. For a description and classification of various input-output modal analysis techniques the reader may consult specialized texts (Heylen et al., 1997; Maia and Silva, 1997; Ewins, 2000). Unification of the theoretical development of modal identification algorithms was also attempted (e.g. in Allemang and Brown, 1998 and Allemang and Phillips, 2004), which is another sign of the maturity of this research field. Different is the situation with modal analysis algorithms that, being conceived to work with output data (output-only or input-unknown techniques), are of special interest for structures exposed to natural vibration (bridges, towers, buildings etc.). These issues in the nineties gave rise to a new research area, officially inaugurated in a special session of IMAC-XIV organised by Felber and Ventura (1996), which today is often referred to as “in operation” (or improperly “operational”) modal analysis (e.g. Cunha and Caetano 2007, Brincker and Moller 2007, Reynder et al 2008, Giraldo et al 2009). In ambient vibration conditions, there is still a need to determine to what extent the use of these techniques in non-ideal conditions, as is in the typical case, can be deemed acceptable, or whether it proves necessary to resort to techniques specially conceived for dealing with non-stationarity. Inherently non-stationary techniques include stochastic approaches (e.g. Yuen et al 2002), time-frequency instantaneous estimators (e.g. Ceravolo 2004) or time-varying estimators (e.g. Poulimenos and Fassois 2008, Du and Wang 2009). 2.1.2 Non‐linear identification Though the word non-linearity has a tautological character, a classification of possible sources of non-linearity might still retain a practical interest in structural dynamics. A drawback in using this term in a survey is rather due to the vast range of problems and techniques that deserve a proper coverage. This section on non-linear identification is not intended as a comprehensive review by any means. In fact, such a review already exists in the form of the textbook 3

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Nonlinearity in Structural Dynamics: Detection, Identification and Modelling by Worden and Tomlinson (2001) and in several comprehensive state-of-the-art papers. For a much more comprehensive overview the reader is directed to these and other documents. The present survey is intended to illustrate the use of a small number of vibration-based methods of direct or potential interest for the Project, hence it will inevitably reflect the tastes of the authors. A first category includes identification methods using various strategies to by-pass non-linearity. Other methods can be framed respectively in the parametric and the non parametric approach: in the former case, a priori selection of a specific model for the dynamic behaviour of the system is needed and the identification process consists of determining the coefficients for such model. Non parametric methods, instead, do not require any assumption on the type and localisation of structural non-linearities but, generally, the quantities identified cannot be directly correlated to the equation system of motion. 2.1.3 By‐passing non‐linearities Traditional techniques for analysing the dynamics of nonlinear structures are based on the assumptions of weak nonlinearities and of a non-linear modal structure that is similar or a small perturbation of the underlying linearised system. Caughey in 1959 proposed to replace a nonlinear oscillator with external Gaussian excitation by a linear one with the same excitation such that the mean-square error between the actual nonlinear and linearised systems is minimised in a statistical sense. The procedure, known as equivalent linearisation, operated directly on the equations of motion. Many developments have been proposed since the work of Caughey (Roberts and Spanos, 1990). This commonly used approach has proved useful in most applications, particularly for the random vibration analysis of systems where the nonlinear restoring force is hysteretic. For experimental applications, the extraction of a linear model requires the knowledge of the functional form of the restoring force, which is generally not the case. Hagedorn and Wallaschek (1987) have developed an effective experimental procedure for doing precisely this. This work triggered the development of the concept of equivalent linear systems with random coefficients which has enjoyed some success for system identification of nonlinear systems (Soize and Le Fur, 1997; Bellizzi and Defilippi, 2003). The harmonic balance method described by Nayfeh (1981) can be also employed for linearising nonlinear equations of motion with harmonic forcing. This method has been the basis of several nonlinear system identification techniques (among others see Yasuda et al 1988; Benhafsi et al 1992; Meyer et al 2003; Ozer et al 2005). For multiple degree of freedom (MDOF) systems a suggestive way to make a transition between linear and nonlinear dynamics is through the extension of the concept of normal mode of classical linear vibration theory to nonlinear systems. In particular conditions, the concept of nonlinear normal mode (NNM) has been introduced by Rosenberg (1966) and developed by Vakakis (1997). The identification of individual NNMs may represent a limitation when considering the arbitrary motion of a nonlinear system; in this case, the NNMs are bound to interact. Several authors have used other types of non-linear modes for the identification of nonlinear systems from free vibration (Bellizzi et al 2003, Hasselman et al 1998, Hemez and Doebling 2001).

4

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 2.1.4 Parametric approaches Apart for linearization techniques, that usually are parametric, a very direct strategy to obtain a typically parametric identification algorithm consists of extending the use of time series models (Ljung 1999) to non-linear systems. A suggestive extension is represented by NARMAX (Nonlinear ARMA with eXogeneous input) model proposed by Leontaritis and Billings (1985). The NARMAX structure is general enough to admit many forms of model including neural networks, although the estimation problem becomes nonlinear and the orthogonal estimator will not work (Billings et al., 1991). In fact, the application of NARMAX to structures is extremely complex an no relevant applications to real structures are reported to date. 2.1.5 Non‐parametric approach The Volterra series representation of the input/output relationship is one of the principal tools for studying weakly non-linear systems is: in this theoretical framework the problem of identification is the determination of the higher-order frequency response functions, in the frequency domain, or higher-order impulse response functions, in the time-domain, from experimental data. Usually, methods based on Volterra series representation are classed as nonparametric, like all those making use of non-linear functionals. The structures can be tested applying loads deterministic (i.e. stepped-sine test) or stochastic in nature. In the latter case, there is quite an extensive literature about the techniques for identifying Volterra systems: one of the first attempts to determine the linear and quadratic frequency response functions of a quadratic system was performed by Tick (1961), under the assumption that system excitation is white Gaussian noise. The hypothesis of gaussianity greatly simplifies the problem of identification but can lead to unrealistic results. This difficulty has been overcome with the formulation of identification methods which can be applied in conditions characterised by excitation with arbitrary spectral properties, defined both in the time domain (e.g. Koukoulas and Kalouptsidis, 2000) and in the frequency domain (e.g. Kim & Powers 1993). All these methods require the calculation of higher order statistical moments: in structural engineering applications it is not possible to obtain a number of experimental measurements large enough as necessary to get a consistent estimate of the statistical moments of interest. The availability of a limited number of experimental data can be obviated through the time-frequency representation of the signals and the definition of instantaneous estimators of the mechanical properties to be identified (Demarie et al 2005). We underline that a vast majority of identification techniques, especially non-parametric ones, variously admit heuristic versions. In this connection we shall mention neural networks, because of their universal approximation features, and neuro-fuzzy models, because of their semantic transparency (e.g. Juditksy et al. 1995, Sjo¨ berg et al. 1995, Chassiakos and Masri 1996, Kosmatopoulos et al. 2001, Riche Le et al. 2001, Song et al. 2004, Liang et al. 2001, Fan and Li 2002). 2.1.6 Approaches based on instantaneous estimation This class of methods was already considered in the 1960s for problems in acoustics and vibrations (Priestley, 1967), but it is only from the 1990s that it gained widespread popularity 5

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development within the structural dynamics community. A survey of the analysis of non-stationary signals using time–frequency methods is available in Hammond and White (1996), Hammond and Waters (2001). Feldman showed how to use the traditional definition of the analytic signal and the time-domain Hilbert transform in order to identify nonlinear models of SDOF systems. The FREEVIB approach proposed in (Feldman, 1994a) is based on free vibration whereas the FORCEVIB approach proposed in (Feldman, 1994b) deals with forced vibration. These approaches can be used to construct the instantaneous damping and stiffness curves for a large class of nonlinear systems, but are only suitable for monocomponent signals. We mention that a method for the decomposition of signals with multiple components into a collection of monocomponents signals, termed intrinsic mode functions (IMFs), was proposed in Huang et al. (1998) and is now referred to as Huang– Hilbert transform in the time-frequency literature. The IMFs are constructed such that they have the same number of extrema and zero-crossings, and only one extremum between successive zero-crossings. As a result, they admit a well-behaved Hilbert transform. The method now enjoys several applications in structural dynamics including linear system identification (Yang et al 2003) and damage detection (Yang and Lin 2004). Other time–frequency representations are is also suitable for the analysis of nonlinear oscillations. Linear representations have been used for instance by Spina et al (1996) and Demarie et al (2005). An overview of the use of the wavelet transform in nonlinear dynamics can be found in Staszewski (2000), while among others interesting applications are reported by Newland (1999) and Erlicher and Argoul (2007). Quadratic representations which include the Wigner– Ville distribution and the Cohen-class of distributions have also received some attention (Feldman and Braun, 1995; Bonato et al 1997; Wang et al., 2003a). 2.1.7 Identification of hysteretic and evolutive/degrading systems Several contributions of the last three decades were concerned with the identification of hysteretic models, in particular the Bouc-Wen (BW) model. Due to its great simplicity, related to the absence of an elastic domain, the BW model has been extensively used in the seismic analysis, both deterministic , e.g. Foliente (1995), and stochastic, e.g. Casciati (1989). Chassiakos et al. (1995) and Smyth et al. (2002) proposed a parametric method in which the parameters of the BW model are identified through an adaptive procedure, based on the application of least square techniques of estimation. An alternative approach is due to Kyprianou et al. (2001), who introduced a differential evolutive method for the identification of the parameters, whose formulation in many respects comes close to that of genetic algorithms. Classical non-parametric methods are based on the extension of the restoring force surface method: Benedettini et al. (1995) approximated the surface of the time derivative of the internal restoring force on a polynomial basis, by assuming as state variables the force itself and velocity; Masri et al. (2004) extended this approach by proposing a polynomial base approximation of the restoring force as a function of velocity, displacement and the excitation. A similar approach may be also used to define instantaneous estimators of the system dynamic properties (Ceravolo et al 2007). In the frame of non-parametric approaches, Pei et al. (2004) used a special type of neural network, which showed good performances in the identification of hysteretic systems. Saadat et al. (2004) formulated a hybrid approach that combine in a single identification procedure the potentials of both the parametric and the non parametric approaches.

6

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Finally, we should mention the recent work of Wu and Smyth (2008), who have successfully applied the Unscented Kalman Filter for identifying the parameters of hysteretic systems. 2.1.8 Identification of hysteretic and evolutive/degrading systems System identification is a general term to describe mathematical tools and algorithms that build dynamical models from measured data. If we are given an unknown system, to which we can give any input we want and observe the output, the process of identifying the unknown parameters of the system by analyzing the input and the output is called system identification. Generally, for a dynamic system, the parameters to be identified are the mass, stiffness and damping. Fig. 2.1 shows a schematic of the input (x), output (y) and unknown system.

Fig. 2.1 An unknown system with input and output

System identification is extensively used in the field of dynamics and control. In adaptive control, system identification is used to design the controller so that it can adjust its properties when the system undergoes any change. Identification can be done off-line: for example, executing a series of measures from which to calculate an approximated mathematical model, typically its transfer function or matrix. Such identification from the output, however, cannot take account of unobservable dynamics. Sometimes the model is built directly starting from known physical equations: for example, in the case of a mass-spring-damper system the governing equation of motion is known as, Ma + Cv + Kx = 0, where M, C, K are mass, damping and stiffness respectively, and a, v, x are acceleration, velocity and displacement respectively. Even assuming that a "complete" model is used in designing the controller, all the parameters included in these equations (called "nominal parameters") are never known with absolute precision; the control system will have to behave correctly even when connected to physical system with true parameter values away from nominal. Some advanced control techniques include an "on-line" identification process. The parameters of the model are calculated ("identified") while the controller itself is running: in this way, if a drastic variation of the parameters ensues (for example, if the robot's arm releases a weight), the controller will adjust itself consequently in order to ensure the correct performance. A good number of literatures can be found on the application of system identification in control theory, e.g., (Ravn, 2000, Saravanakumar, 2006). System Identification is very useful in civil engineering applications. Identification of the unknown parameters of a shake table is very important; because to test a structure, either full scale of scaled-down, we need to know the parameters of the shake table to properly build a model which will allow working with the numerical model. A number of literatures have been recently published on the identification of the mechanical subsystem of a shake table (Ozcelik et el. 2006, Ozcelik et el. 2007, Ozcelik et el. 2008).

7

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Ozcelik et el. (2006) have developed a virtual model of the UCSD-NEES shake table. This virtual model included the following subsystems: a virtual replica of the controller, nonlinear servo-valve model, single-ended actuator model with internal volume change, and simplified models of the mechanical subsystems, namely a rigid platen, horizontal stiffness provided by the hold-down struts, and dissipative/friction force mechanisms. The complex dynamics of large shaking table systems emanated from multiple dynamic interactions and nonlinearities among various system components. An interaction diagram of the subsystems of the LHPOST is shown in Fig. 2.2

Fig. 2.2 Component and interaction diagram of a shake table system

Comparison of feedback platen accelerations obtained from the actual tests and the simulation model is given in Fig. 2.3. It was observed that the actual and simulated feedback acceleration records were in good agreement.

Fig. 2.3 Test –analysis comparison

Ozcelik et el. (2007) proposed a simple conceptual mathematical model for the mechanical components of the NEES-UCSD large high-performance outdoor shaking table and focused on the identification of the parameters of the model by using an extensive set of experimental data. An identification approach based on the measured hysteresis response was used to determine the fundamental model parameters including the effective horizontal mass, effective horizontal stiffness of the table, and the coefficients of the classical Coulomb friction and viscous damping 8

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development elements representing the various dissipative forces in the system. The effectiveness of the proposed conceptual model was verified through a detailed comparison of analytical predictions with experimental results for various tests conducted on the system. Fig. 2.4 shows the shake table with a full scale seven-storey building mounted on it, and Fig. 2.5 shows the model of the mechanical subsystem of the shake table.

Fig. 2.4 NEES-SCSD LHPOST with a full-scale seven-storey full-scale R/C building slice, 19.2m high mounted on it

Fig. 2.5 Mechanical sub-system of NEESUCSD LHPOST

Although the parameters of the model considered in this work had been identified by using the response during periodic sinusoidal and triangular excitations, it had been shown that the resulting model was also capable of representing the more common shake table tests involving earthquake ground motions and white noise excitations. Later, the same authors (Ozcelik et el., 2008) published a paper in which they developed the method of identification of mechanical subsystem of the NEES-UCSD shake table using least squares method. The first objective of this study was to test the applicability of a parameter identification approach based on the standard least squares method for shake table tests with very different excitations including periodic tests, white noise tests, and seismic tests. Of primary interest was the robustness of the parameter estimates across different types of tests. A second objective was to compare the results of the least-squares identification approach with those obtained by consideration of the hysteresis loops for periodic tests. A third objective of the study was to further validate the model and identify parameters by detailed comparisons with experimental data from different types of tests. Finally, the steady-state frequency response of the shake table mechanical subsystem to commanded harmonic displacement of the shake table was examined. This analysis provides an additional verification of the nonlinear damping model used in the study, and illustrates the response of the table in the vicinity of the characteristic frequency of the mechanical subsystem. Fig. 2.6 shows the conceptual mechanical model of the shake table.

9


Fig. 2.6 Conceptual mechanical model of the table with model parameters Me, Ke, Ce and Fμe to be identified through periodic, earthquake, and white noise tests

where Fact(t)=total effective actuator force applied on the pistons of the two horizontal actuators; Me=effective mass of the platen (including the mass of the moving parts of the horizontal actuators and a portion of the mass of the hold-down struts); Ke = total effective horizontal stiffness provided by the two hold down struts; Ce = effective viscous damping coefficient; Fμe = effective Coulomb friction force due to various sources; and ux(t) = total horizontal displacement of the platen along the longitudinal direction. According to this simplified model, the equation of motion of the shake table can be written as 

M eux (t )  K eu x (t )  [Ce u x (t )  Fe ]sign[u x (t )]  Fact (t )

(0.1)

The parameters Me, Ke, Ce, Fμe of the mathematical model given in the above equation are identified by use of the linear least-squares method for a given value of α. The main finding of the paper is that the least-squares approach appears to be equally capable of identifying the key system parameters from scaled earthquake tests, and periodic sinusoidal and triangular tests. For white noise tests, the least squares approach leads to the correct effective mass, and the correct total friction force if the viscous damping coefficient is constrained. Identification of unknown parameters of testing equipments is an essential requirement to carry out experimental tests. In this respect, system identification is a very useful tool and its application in shaking table and control theory has been proved to be very useful. 2.2

CONCLUDING REMARKS

1° Issue: Linear identification and structural testing 1.A : Further checks needed on the accuracy afforded by output-only techniques; 1.B : In the same connection, the use of ambient vibration should be considered also for lab tests. 2° Issue: Non-linear identification and structural testing 2.A : Need for validating experimentally non-linear identification techniques. In fact, most of the existing non-linear identification methods have not been tested yet on real structures. 2.B : Exploitation of consolidated non-linear identification techniques to account for weak non-linearity (e.g. geometrical non-linearity, non-linear damping, etc.) in testing structures and devices. 3° Issue: Identification of evolutive systems

10

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 3.A : The development of identification techniques for evolutive systems is beneficial to performance-based engineering and to testing control. 3.B : Non-linear identification techniques can characterize degrading hysteretic systems under cyclic or pseudo-dynamic testing (“rate independent” damping only). In dynamic tests, there is still a need to separate various dissipation phenomena.

11


3

Model Updating and Data Assimilation

3.1

INTRODUCTION

There are two main complementary approaches to the calibration of a model: a model-driven and a data-driven approach. Also the nature of the problem changes depending on the type of approach which is pursued. In the case of the model-driven methods the parameters of the model (or at least part of them) are unknown and must be obtained from measured data. In this case, a version of the model is constructed using physical laws based on first principles. Then, the model parameters are changed by means of some optimisation techniques to fit measured data. This procedure is commonly known with the name of Model Updating (MU). The data-driven approach consists in a forward evaluation problem and it is treated as a Statistical Pattern Recognition (SPR) problem. In its broader sense pattern recognition consists of labelling a sample of measured data according to a series of pre-defined classes. Pattern recognition finds applications in several engineering, economic and social fields. 3.2

MODEL‐DRIVEN VS. DATA‐DRIVEN APPROACHES

3.2.1 Model‐driven approaches The model updating is a technique that has been developing through the last years. In various fields of the engineering the usage of numerical models to evaluate the behaviour of a physical system is frequent. The accurate representation of a system depends of the type of numerical model used to represent the elements of the system and on the properties of this model (e.g. in a structural application the elasticity modulus, boundary conditions, et cetera). The discrepancies between the behaviour of a numerical model and the real system can be significant as reported by (Zhang Q.W. 2001) and (Brownjohn J.M.W. 1999). Inverse methods are commonly used to improve the quality and reliability of a model. They combine an initial (generally finite element) model of the structure, whose parameters can be derived by specific characterisation tests or simply guessed, and measured data expressed in the form of modal properties or frequency response function.

12

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 3.2.2 Modal reduction and expansion Model Reduction There are different types of modal reduction. The so-called static reduction or Guyan’s reduction (Guyan R. 1965) allows calculating a transformation matrix T which reduces the mass and the stiffness matrices to the terms related to the useful degrees of freedom. The dynamic reduction is an extension of the Guyan’s method, accounting of the inertial terms for a particular frequency. In this case is possible to reach higher precision respect to the static reduction. (Zhang N. 1995) An Improved reduction system (IRS) has been introduced by O’Callahan (O'Callahan 1989) which improves the static reduction method through the introduction of inertial terms as pseudostatic forces. O’Callahan and others have developed also the System Equivalent Reduction Expansion Process (SEREP) which utilizes the computation of eigenvectors to produce the transformation between master and slave coordinates. (J. O'Callahan 1989) Model Expansion Modal expansion is a procedure strictly related to modal reduction, and is possible to look at it as an inverse reduction. The easier way to expand data is to substitute the unknown eigenvector values with the values calculated from the analytical model but using this procedure both analytical and measured modal shapes have to be normalized in the same way. It is possible to expand data using the stiffness and mass matrices. This procedure is dual to the dynamic reduction. (Zhang N. 1995) An alternative method is to use modal data coming from the finite element analysis. The identified modes are treated as a linear combination of the analytical modes and in this way it is possible to calculate a transformation matrix T. This procedure is strictly linked to the SEREP procedure. (O'Callahan J. 1989) 3.2.3 Direct methods and sensitivity methods Model updating methods may be classified as direct or sensitivity methods. Direct methods try to reproduce the measured data from the structure by applying little changes to the stiffness and mass matrix which are difficultly associable to the parameters of the model. Indeed, the main drawback of direct methods is that their results are characterised by a lack in the physical meaningfulness. More details about these methods can be found in (Friswell M.I.1995) (Berman A.1983) (Caesar B.1986) (Baruch M. 1978) (Wei F.S. 1990) (Minas C. 1988) (Gladwell G.M.L. 1986). Sensitivity-based methods have seen a larger widespread compared to direct methods because of their capability to calibrate the model taking the influence of the updating parameters of the different structural elements into account. They offer a wide range of parameters to update that have physical meaning and allow a degree of control over the optimization process. All these parametric methods rely on the definition of a so-called penalty function which is computed as the quadratic norm of the differences between the measured and the numerical quantities. The discrimination among the methods is based on the choice and the number of parameters to compute the objective function and the optimisation technique used to minimise it. Recently heuristic techniques like Simulated Annealing (Kirkpatrick S. 1983) (Johnson D.S. 1989), 13

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Genetic Algorithms (Srinivas M. 1994) and Evolutionary Strategies (Dack T.B. 1991) and probabilistic approaches have supplanted traditional methods to solve non-linear problems like Newton-Raphson. New developments in optimisation techniques consent different approaches to the problem, such an optimisation through all the Pareto set of solution, performing a multiobjective minimization. (Christodoulou K. 2008) 3.2.4 Parameterization of a model The choice of the structural parameters that have to be updated is influenced on the typology of the modelled structure and on the uncertainty level which affects the model. Once the model is defined the most important task in a model updating procedure is the choice of the parameter to update. The sensibility to a single generic parameter θ, according to Wittrick (Wittrick W.H. 1962) and Fox-Kapoor (Fox R.L. 1968) is given by: [ K ]   j  [ M ] 

  j 

 [K ]   [ M ]  j    j   [ M ]   j     

(3.1)

It is possible to rearrange this formula in order to calculate the sensibility of the single eigenvector. In particular types of problems it may be useful to calibrate different part of the model. Generally, several elements sharing the same properties are merged into a single macroelement in order to reduce the number of parameters to update and to ease the research of the optimal solution. In this case is possible to update single parts of the stiffness and mass matrices: n

M   M 0    i  M i

(3.2)

K   K 0    i  K i

(3.3)

i 1 n

i 1

where [M] and [K] are the global matrices and [M]i and [K]i are the matrices of the group of elements that needs update. In the case that the parameter θ assumes the aspect of a physical quantity as the elastic modulus, the volumetric mass or the Poisson’s modulus is impossible to apply (8) and (9), because the linearity between parameter and matrices is not guaranteed anymore. The Young’s modulus and the moment of inertia of the most uncertain elements are usually considered because they are directly related to the stiffness of the elements. In this case is possible to expand in Taylor series obtaining: n M   M 0     M   d j (3.4) j 1

 j

K   K 0     K   d j n

j 1

(3.5)

 j

14

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 3.2.5 Comparison between identified and analytical data: MAC and COMAC The measurement data used to compute the objective function may belong to the frequency or modal domain. Time domain data are generally disregarded because measured time-series are affected by noise and their volume of data is difficult to handle. Data compression is performed to obtain FRF data, which are less affected by random noise because averaged but suffer little loss of information in the passage from time to frequency domain. Model updating methods based on modal parameters like natural frequencies, mode shapes and damping ratios exploit a further reduction in the number of data points but they have to cope with the reduction of accuracy in the modal parameters estimation. Furthermore, mode shapes are valuable parameters to be implemented in a model updating procedure because they allow to pair the analytical and experimental modes but their precise estimation is difficult to reach and changes due to damage are often smaller than the error bounds on corresponding measurements. In literature is possible to find many functional indexes that consent to compare measured and numerical data. Among the most used there is the MAC (Modal Assurance Criterion), defined as:

MAC jk



Tj   a k    a Tk   a k   m Tj   m  j  2

m

(3.6)

where {Φa}k is the theoretical eigenvalue corresponding to the kth mode, and mj is the measured eigenvalue, corresponding to the j-th mode. The MAC can vary between 0 and 1, and the comparison could be considered satisfied with a MAC value superior to 0.8. The COMAC (Co-ordinate MAC) quantifies the correlation between identified and analytical modal shapes referring to a particular degree of freedom: N

COMAC ( j ) 

      i 1

a

T ji

m

ji

(3.7)

N  N 2   2     a  ji      m  ji   i 1   i 1 

where i is the i-th modal shape and j is the j-th degree of freedom. Many authors use a Weighted MAC (WMAC) which utilises a weight matrix [W]. The weights can depend from the reliability of certain data (due to the distribution or the accuracy of the sensors). It is possible also to remind: • • • • • • •

Partial Modal Assurance Criterion (PMAC); Modal Assurance Criterion Square Root (MACSR); Scaled Modal Assurance Criterion (SMAC); Modal Assurance Criterion using Reciprocal Vectors (MACRV); Modal Assurance Criterion with Frequency scales (FMAC); The Enhanced Coordinate Modal Assurance Criterion (ECOMAC); Inverse Modal Assurance Criterion (IMAC);

15

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development For a review of all the MAC-derived criteria and a complete bibliography, consult (Allemang R.J. 2002). Another approach is to compare, instead of the modal shapes, the frequency response functions, with the same principle of the MAC. This comparison is feasible in the case of experimental tests performed with a vibrodina. In this case it is called Frequency Response Assurance Criterion (FRAC). The Complex Correlation Coefficient (CCF) and the Frequency Domain Assurance Criterion (FDAC) derive from the previous. 3.3

DATA‐DRIVEN APPROACHES

Differently from the model-driven methods, in the forward approach the knowledge of the phenomena ruling the structural behaviour is not derived from physical laws implemented in a model but is extracted directly from the data or based on a priori information, if available. The PR algorithm is trained to recognise the correspondence between samples of data and type classes (Bonato P. 1997). Two different types of learning do exist. In the supervised learning several sets of training data are presented along with the corresponding class they belong to. Both the uniqueness of the correspondence between a set of measurements and its class and the exhaustiveness in the presentation of all the possible classes are fundamental requirements. The availability of patterns concerning the state of the structure represents the major obstacle for this type of learning. Unsupervised learning does not require a prior information about the state of the structure; only data from the normal operating condition of the structure are needed to create a model of normal condition which is compared with all the new acquired data samples to detect changes. Two sources of data can be exploited: numerical modelling or experiment. The former presents the same drawbacks of the inverse problem approach. They are related to the dependence on a model of the structure whose properties may be uncertain, the constitutive laws of the materials not accurately defined and the analyses excessively time-consuming. On the other hand, the collection of training sets from experiments is even harder to accomplish because it requires several replica of the same system according all the possible scenarios which might affect the structure. (Mares C. 2006) (Xiong Y. 2009) 3.4

CONCLUSION

The calibration of numerical models, through experimental data, has been a breakthrough advancement in the field of numerical simulation. The advantage of distributed model in producing distributed predictions provided by updating is in contrast with traditional experimental testing, which allowed to characterise the model of a structure only locally. A need exists for the use of confidence levels which may be assigned to quantified mesh, or test data, uncertainties. In the field of model updating, one of the main research branches is the stochastic model updating, which may compensate in some way a possible lack of data (Goller B., 2009, Govers Y. 2009). This type of approach provides a suitable safeguard against severe underestimation of the variability of parameters derived from a small sample set.

16


4

System Identification to Improve the Design of Testing Equipment and Set‐ups

4.1

INTRODUCTION

System identification refers to the development of structural models from input and output measurements performed on a real structure using sensing devices. Dynamic system identification is a major tool for monitoring and diagnosis of structures: experimental results from dynamic testing provide knowledge about global structural behaviour and can be used in calibrating numerical models, in forecasting the response to dynamic and earthquake loading and can help in evaluating safety conditions (Natke et al 1993, Ghanem & Shinozuka 1995, Maia & Silva 1998). Even if the age of virtual prototyping has already started (Auweraer Van Der 2002), experimental testing and system identification still play a key role because they help the structural dynamicist to reconcile numerical predictions with experimental investigations. The term ‘system identification’ is sometimes used in a broader context in the technical literature and may also refer to the extraction of information about the structural behaviour directly from experimental data, i.e., without necessarily requesting a model, e.g., identification of the number of active modes or the presence of natural frequencies within a certain frequency range. 4.2

IDENTIFICATION BASED ON A VISUAL OPTICAL SYSTEM

In order to develop the visual optical system, the Istanbul Technical University (ITU) aimed at enabling tracking displacements of a specimen during a test. The visual optical system consists of hardware and software components. The hardware components include high-resolution camera, lens, metric calibration plate and I/O card (USB). Software component includes a graphic interface for measurement preparation and related modules and measurement/reporting modules. 4.2.1 Basic steps for the usage of a visual system The basic steps needed to be followed are summarized herein: • Determination of marker locations on the specimen as shown in Fig. 4.1 a, b • Drawing a rectangle around each marker, large enough to accommodate the displacement of the marker during tests 17

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development • Camera calibration which is needed to calibrate the intrinsic camera parameters as shown in Fig. 4.1 a, b • Estimation of the 2D pose of the test specimen which is extrinsic to camera parameters • Acquire a sample image before test • Grab images for a predefined period of time • Automatically detection and tracking the marker locations across consecutive images see Fig. 4.1 b • Conversion pixel displacements to metric displacements by making use of intrinsic and extrinsic camera parameters see Fig. 4.2 • Reporting results

(a)

(b) Fig. 4.1 A sample of marker locations

Fig. 4.2 A view of each marker displacements in x- and y- directions

4.2.2 Limits of the vision system The capability of the vision system is limited in several aspects. The displacements can be tracked in 2D. The system is calibrated for two camera-to-specimen distances, 1.5 and 2.5 m, and operating with a precision less than 0.1 mm. Utilizing this system, the deformations occurring in 18

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development an area of 500x 500 mm2 can be observed. It should be noted that it is possible to calibrate the system for different camera-to-specimen distances and different areas, which results from low precisions. In order to assess the displacement measurements of the visual optical system, these measurements are compared with displacements measured with transducers in as presented in Fig. 4.3. It shows that the visual system measurements are in good agreement with the transducer measurements. 30

Visual system Transducers

25

Compressive load (kN)

20

15

10

5

0 0

2

4

6 Displacement (mm)

8

10

12

Fig. 4.3 Comparison between the displacements measured from the visual optical system and that from transducer

4.3

IDENTIFICATION OF HYSTERETIC SYSTEMS BASED ON KALMAN FILTER

The non-linear hysteretic behaviour is quite common in civil/mechanics systems subjected to cyclic load, such as earthquakes, wind or wave; under this type of excitations the structural response can be characterized by repeated cycles in the inelastic range. Consequently, both stiffness and strength may deteriorate and the dissipation of energy will induce a hysteretic behaviour characterised by stiffness deterioration and strength degradation. The exact nature of deterioration/degradation is a function of both materials and configuration of the system itself, and it varies from system to system. So, the identification of hysteretic behaviour of a non-linear system is quite important. 4.3.1 Kalman filter The Kalman filter is an algorithm that produces estimation of unknown variables. In detail, the following discrete-time dynamic system, with the state vector ∈ and the measurements vector ∈ is considered. Its evolution in the state space and its input/output non-linear relation ship are: xk  f ( xk 1,uk 1, wk 1 ) (4.1)

yk  h( xk 1, vk )

(4.2)

where and are process and measurement noises governed by Gaussian probability distributions. It is assumed that the noises are white, zero mean and uncorrelated with each other:

19


p( w)

N (0, Q)

(4.3)

p (v )

N (0, R)

(4.4)

and are unknown. However, we can approximate both the state vector and the In practice, measurement vector by considering the noise to be zero.

xk  f ( xˆk 1,uk 1, 0)

(4.5)

y k  h( xk 1, 0)

(4.6)

where xˆk 1 is the state estimation a posteriori. Conventionally for the linear case, it is assumed that the distribution of the state xk is Gaussian. However, in the non-linear case, the distribution does not have a general shape and generally is no longer of normal type. One of the most known methods for the estimation of non-linear systems is the Extended Kalman Filter (EKF); it applies the traditional Kalman filter to non-linear systems simply linearizing the equations of the system around the point at the k th instant. However, there is no theoretical guarantee that the estimator is the optimal one and that it is correct, since it is only an approximation. Moreover, the implementation of EKF turns out to be much costly from the computational point of view, because the gain and covariance matrices must be calculated at each step together with the Jacobian matrix Ak and H k . The Unscented Kalman Filter (UKF) is an alternative to the EKF. The basic component of the UKF is the Unscented Transformation (UT); it uses a set of points appropriately weighed to parameterize the mean and the covariance of the probability distributions (Gaussian) of the system random variables. A brief introduction of UKF is presented in the following part: Let’s consider the discrete non-linear system of equations: 1

, ,

;

(4.7)

;

(4.8)

where is the n-dimensional state, is the input vector, is the q-dimensional Gaussian process noise, is the observations vector and is the Gaussian measurement noise. It is assumed that and have zero mean and covariance: (4.9) (4.10) 0, ∀ ,

(4.11)

The UKF prediction and update steps can be written in matrix form: 1. Prediction equations:  Definition of sigma points: 20

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development …

√ 0

 Propagate sigma points into the process non-linear equation: ,

X  Compute the predicted mean:

;

1

X  Compute the predicted covariance: ,

2. Update equations:

X

X

 Compute the a priori sigma points: …

√

0

,

,

 Propagate sigma points into the measurement non-linear equation: ,

;

 Compute the predicted observation: ̅  Compute innovation variance (the measurement noise is considered additive and independent): ,

 Compute the cross-correlation matrix:  ,

Then the filter gain, the state mean and the covariance: 

,

,

;

 

̅ ; ,

,

,

.

(4.12)

4.3.2 Application of Unscented Kalman Filter to a damper

The state estimation The application of the UKF (Sarkka S., 2011) is presented herein to estimate the state of a SDoF non-linear system characterized by a hysteretic behaviour which is reproduced by means of the well know BoucWen model (Ortiz G.A., Alvarez D.A, 2013). The dynamic system is governed by the following expressions:

21


(4.13)

| |

in which w(t ) is Gaussian process white noise and u (t ) is the known sinusoidal input with frequency varying from 0.1 Hz and 2Hz. The second equation in (4.13) is the BoucWen model for the hysteretic behaviour of the system. Assuming that the acceleration and the external excitation are known, the equation of measurement results to be: (4.14) where v is the Gaussian measurement white noise. Hence, the dynamic system in state space form reads: x     1   x   (cx  K 0 x  z )  u  w  m  (4.15) X  f ( X , u , w)     n    z (t )   A  z (   sign( zx ))  x    041   and the measurements equation reads: 1 (4.16) Y  h( X , v)   (cx  K 0 x  z )  v m Assuming that the model has the unitary mass, c  0.3 Ns / m , K 0  9 N / m , A  1 ,   2 ,   1 ,and n  2 . The state vector is defined as X  [ x, x, z, A,  ,  , n] with the initial conditions X  [0, 0, 0, 0.7,1.5, 0.5,1.5] . Both the process noise w(k ) and the measurement noise v(k ) have

RMS equal to 106 . The filter parameters read 10 , 2, and 5, respectively. In this respect, Fig. 4.4 -Fig. 4.7 show results in term of comparison between numerical and estimated hysteretic cycles, displacements, velocity and restoring force, respectively.

Fig. 4.4 Comparison of hysteretic cycles

Fig. 4.5 Comparison of displacement

22


Fig. 4.6 Comparison of velocity

Fig. 4.7 Comparison of restoring force

The accuracy of the estimations is very high and the estimation error of hysteretic parameters has an average value of about2.58% and a maximum value of 4.61%, respectively. The numerical, initial and estimated results of BoucWen parameters and the error of estimation are shown in Table 4.1 and Fig. 4.8. Table 4.1 Numerical and estimated values of BoucWen parameters

PARAMETERS Exact value Initial value Estimated value Error (%)

A 1 0.7 1.0027 0.27

β 2 1.5 1.9078 4.61

γ 1 0.5 0.9751 2.49

N 2 1.5 1.9410 2.95

Fig. 4.8 Estimation of BoucWen parameters

23

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Experimental application by means of the TT1 Test Rig

Tests on the parameters identification took place in the Materials and Structural Testing Laboratory of the University of Trento. The set-up is presented in Fig. 4.8 and was used to identify the device non-linear behaviour; in addition the set-up was useful to identify the currentdamping force relationship. Actually, this is a SDoF system that reproduce the dynamic of the numerical model. The TT1 test rig was equipped with: - The mass; - the Magneto Rheological (MR) rotational damper with a current maximum limit of 6A and electrical resistance of 3.6 Ω; it consists of a disk-type MR damper produced by Maurer Söhne Gmbh with MR fluid MRB10; - the current regulator IASP Gmbh type CR 603 which is designed to energize the electrical component starting from a voltage set-point; the changing speed of the current, for a unit step function, is only a few milliseconds; - the load cell AEP TS of 200 kg (LC3) placed in axis with the gear beam and its analog transducer AEP TA/2; the measured force is defined as fm; - the dSPACE® platform which is used for both measurement acquisition and signal control; - 2 load cells AEP TC4 of 2500 kg (LC1-LC2); - 2 optical displacement transducers, Opto-NCDT 1402-200 from MicroEpsilon; - The accelerometer PCB 393B12 with sensitivity 10 V/g and acceleration range of ±5 m/s2 and the accelerometer PCB 393C with sensitivity 1 V/g but acceleration range of ±25 m/s2 Also, two springs will be added in order to experimentally reproduce the complete SDoF system previously analyzed. Fig. 4.9 shows the input/output working outline for the dSPACE® instrumentation. Acceleration, force and displacement measurements are input for the controller. Furthermore the current driver uses a channel to send feedback of both the actual current and voltage. Output signals, instead, come from the controller: in particular Matlab/dSPACE® sends the displacement reference signal to actuators and the voltage set-point to the current driver in order to regulate voltage/current. The sampling frequency is 1 kHz.

Fig. 4.9 Control and acquisition instrumentation setup in TT1 Test Rig

In view of the Kalman filter estimation, a preliminary identification of the MR damper was made by using the optimization toolbox (OPTIMIZATION) made available by Matlab. The damper was firstly been modeled by means of the classical BoucWen model (Dyke et al., 1996), which 24

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development consists of a differential equation that describes the hysteretic damper response. Assuming for simplicity, a symmetric hysteresis equations reads, f   z  c0 x  f 0

(4.17)

n

z  Ax   x z   z x z

n 1

(4.18)

where, f , the damping force designed as the sum of three components: the hysteretic term  z ,the linear viscous dash-pot c0 x , the static off-set term f 0 ; where, c0 , viscous damping coefficient; x , damper top velocity;  , hysteretic scaling factor; z , hysteretic variable; f 0 , damping force that embodies an initial displacement or force offset; A ,  ,  , BoucWen parameters. With regard to the model to hand, Spencer et al. (Spencer B.F., 1997) suggested the following linear relationship: (4.19)    a  bv c0  c0 a  c0b v

(4.20)

where, parameters were chosen to be  a  0.35 N/mm,  b  2.8 N/mmV, c0 a  0.3 Ns/mm and c0b  0.42 Ns/mmV, respectively. In order to define parameters, we have to minimize the residual between the measured force and that provided by the adopted model. The objective function used here reads, J 

f est (t )  f m (t ) f m (t )

2

(4.21)

2

in which, f est (t ) is estimated damping force and f m (t ) is the force measured by the load cell on the damper. A sinusoidal displacement input with frequency of 1.5Hz and amplitude of 14mm was considered, whist the sampling rate was chosen to be 1kHz. As a result, through the optimization process, we identified the following values: A  40  16 ,   1.1  0.08 mm-2 and   1.1  0.08 mm-2 . Good agreements between experimental and numerical data were achieved as illustrated in Fig. 4.10.

25

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Damper force - sin reference, f 1.5 Hz, A 14 mm 1500

Measured Experimental

Force[N]

1000 500 0 -500 -1000 -1500 0

5

10

15

Time [s]

(a) Force vs. Time Damper force - sin reference, f 1.5 Hz, A 14 mm 1500


1000 500 0 -500 -1000 -1500 -15


1000 Force[N]

Force[N]

Damper force - sin reference, f 1.5 Hz, A 14 mm 1500

500 0 -500 -1000

-10

-5 0 5 Displacements [mm]

10

(b) Force vs. Displacement

15

-1500 -150

-100

-50

0 50 Velocity [mm/s]

100

150

(c) Force vs. Velocity

Fig. 4.10 Comparison between experimental and numerical data

4.4

IDENTIFICATION OF MDOF HYSTERETIC SYSTEMS

The current baseline of dynamic earthquake engineering testing, consisting of classical few point/local measurements in seismic testing, cannot serve the current needs of Performancebased Earthquake Engineering which emphasises structural damage. In this context, recent advances in optical fibres, optical sensors, wireless communication, Micro-Electro Mechanical Systems (MEMS) and information technologies software frameworks, databases, visualisation, Internet/grid computations are destined to significantly enhance seismic testing of complex structural systems. This progress is expected to be compensated by equally sophisticated behavioural models for structures that take into account non-linear and evolutionary (e.g. hysteretic) responses. The identification of complex dynamic features, such those caused by structural degradation or seismic devices, often requires a set of instantaneous parameters to be identified and calls for special signal processing tools. In this context, structural identification is expected to play an important role in hybrid testing (Blakeborough et al 2001) and in shaking table test design and control, especially for virtual modelling. Molina et al (1999) of ELSA – JRC proposed time-domain methods specifically tailored for large structures seismically tested by using the pseudo-dynamic method. They also compared the results of such identification methods applied to a 3-storey steel-concrete composite building and to a 2-storey seismically retrofitted reinforced concrete building. If a few dynamic features of tested structures may result from an experimental modal analysis, it is also evident that nonlinear identification techniques should be developed and tested in the future to capture the global dynamic response at the ultimate limit states. Herein, novel identification techniques are 26

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development proposed to identify and model a two storey structure (Bursi et al, 2009, Bursi et al, 2012). Moreover a preliminary identification of a four storey structure is presented too. 4.4.1 A modified Bouc‐Wen model When subject to intense earthquake excitation, structural systems typically dissipate energy through hysteretic effects. In this context the Bouc-Wen model is often used to describe the hysteretic behaviour of structural systems because of its compact and continuous representation of hysteresis (Bouc, 1971; Wen, 1976; Bonelli and Bursi, 2004). Several studies on this model were proposed during recent decades, to understand its properties; see Erlicher and Point (2008) and Erlicher and Bursi (2008), among others. Other studies mainly focused on rendering the model capable of capturing some specific behaviour of engineering materials; for instance, Li et al. (2004) and Sivaselvan and Reinhorn (2000), where emphasis was given to pinching, stiffness deterioration and strength degradation. As here we deal with the hysteretic response of a steelconcrete composite structure (Bursi et al., 2004), the so-called pinching or slip model suggested by Li et al. (2004) is appropriate enough. Along this line (Li et al., 2004) and in order to account for the slip, the following relationship

xs  f   s

1  e 1  e

 s  f  s  f

 

(4.22)

Was introduced in Ceravolo et al. (2011), where f defines a spring force, s the amount of slip and μs a coefficient that controls the inverse of the tangent near the origin. This function is depicted in Fig. 4.11, which in agreement with Li et al. (2004) and Sivaselvan and Reinhorn (2000), s precisely defines only half of the total slip.

Fig. 4.11 A slip function

This slip spring is assumed to operate in series with a Bouc-Wen hysteretic spring, i.e. x  xs  xBW

(4.23)

This assumption is illustrated in Fig. 4.12.

27


xs xs

xBW xel

xnl

 s,s

A

  n

x

ü(t) m A

s s

Fig. 4.12 Slip and BoucWen springs in series for a SDoF system

From Equation (4.22), the inverse of the tangent stiffness k s ( f ) associated with slip is defined as: dx  f  2s s 1 (4.24) e s f  0  s  s f 2 ks  f  df 1 e





and the tangent stiffness of the Bouc-Wen model is: k BW  f ,sign  x BW  f    A     sign  x BW  f     f

n

(4.25)

So, the equivalent stiffness of the springs in series, k , becomes:

   2  s s  f k  f ,sign  x  f     e 2 k s  f   k BW  f ,sign  x  f    1  e  f   k s  f  k BW  f ,sign  x  f

s

s



1 A    sign  x  f    

  n f  

1

(4.26) To sum up, the differential system for a SDoF model takes following form, mx  f   mu     f  k  f , sign  x  f    x

(4.27)

If we define k as the equivalent stiffness that we would obtain by excluding hysteresis from Equation (4.26), it can be proven that system (4.27) is equivalent to  mx  f  mu   f  k  f  x  xnl   1  xnl   p  f ,sgn  x   xBW A   1 1 1     k  f  A ks  f 

(4.28)

28

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development with

   f  p  f ,sgn  x      sgn  xf

n

(4.29)

and x BW  x  xs  x 

f

(4.30)

ks  f 

which is easier to generalize to the Two-DoF with respect to (4.27).

4.4.2 The model for a two storey system With reference to the two-storey system shown in Fig. 4.13 and in accordance with Equation (4.23), global displacements can be expressed in terms of flexibility, by summing both linear and nonlinear components. 1  xnl ,1  f1  f 2   x1   k11 k12   f1              (4.31)          x2   k12 k22   f 2   xnl ,2  f 2   xnl ,1  f1  f 2   el where K el can be defined as,

 k11 K el     k12

k12    k22  el

(4.32)

K el represents the condensed stiffness matrix of the underlying linear system, that will be time

variant during the identification process; xnl ,1 and xnl ,2 define the non-linear displacement contributions of the two storeys.

m

2

m

1

x

x

2

1

Fig. 4.13 A two-story frame

Therefore the equations of motion associated with the frame system assume the following form:  g  M   x  f  M  u     f   x (4.33)  f  K  -1 -1 -1 K    f   K el + K s 29

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development where K ( f ) is the tangent stiffness matrix of the coupled linear and slip springs. K s 1 is the form of non-linear flexibility matrix which can be expressed as:  2e ks ,1  f1  f2  k s1s1  2  1  e ks,1  f1  f2   K s 1    2e ks ,1  f1  f2  k s s ,1 1  2  k f f   1  e s,1 1 2  

 



k s ,1  f1  f 2 

  k f f  1  e s,1  1 2    k f k f f 2e s,2 2 k s ,2 s2 2e s,1  1 2  k s ,1s1    2 2 k s,1  f1  f 2  ks ,2 f 2  1 e 1 e  2e



 

k s ,1s1



2

 

(4.34)



K s can be defined as the tangent stiffness matrix related to the slip function. Like SDoF system, (4.34) can be modified as follows:

 g M   x  f  M  u     f    x  x  f  K nl  -1 -1   K  f   K el + K s-1   x  K   f 1  β p  f , sign  x    x  nl



(4.35)



where the matrix βp defines the hysteretic part of the restoring force vector f . In greater detail, it can be expressed as follows:

 fp  f1  f2 ,sign  x1    fp  f2 ,sign  x2  x1    fp  f2 ,sign  x2  x1     βp  f ,sign  x        fp  f2 ,sign  x2  x1   fp  f2 ,sign  x2  x1    

(4.36)

where fp denotes a BoucWen type of hysteresis:

fp  f ,sign  x     f

ni

  i sign  f  x    i 

(4.37)

Additional information about the properties of the BoucWen model can be found in Ikhouane et al. (2007), Erlicher and Point (2008), and Erlicher and Bursi (2008). This parametric identification was applied to a 3D structure depicted in Fig. 4.14.

30

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 400 700

Concentrically braced frame MR-PS Frame

HEB 260

00 x8

HEB 260 L

3000

12800

HEB 260

00 x8

HEB 260 50 x1 L

700

7400

Effective width [EC8]

x8 00 x1 50

HEB 260

IPE 240

L

Braced Frame

IPE 240

Flexible thin plate

8 0x 10

Simply supported secondary beam

x 50

Orientation of ribbed steel deck 1400

IPE 240

L

Concentrical Bracing

HEB 260

IPE 240

50 x1

Concentrical Bracing

3000

Fig. 4.14 Plan view of the prototype structure tested at JRC and concentrically braced frame

The identification algorithm described at length in the paper (Ceravolo et al., 2010, Ceravolo, 2009) minimized the objective function Q(t , p) . In greater detail, Q(t , p) was extended to a twoDoF system as follows: 2

Q  j,p  = 

N -1

  SPEC x   j,k; p  - SPEC x   j,k 

i 1 k=0

where

γ

γ

i

im

    p id  t = j  t  = arg  min Q  j,p   , , j= j  p  

p = {k11 , k12 , k22 , 1 , 2 ,  1 ,  2 , n1 , n2 , s1 , s2 , s1 , s 2 }

(4.38) defines the vector of linear, hysteretic

   and slip parameters, respectively. SPEC x   j , k  and SPECx  j, k ; p are values of computed i im

and measured spectrogram, respectively. The acceleration signals were characterised by a sampling frequency of 100 Hz and duration of 20 s. Hence the computed spectrograms used the whole information contained in signals, with a Hanning window of 100 samples. A Pattern Search algorithm available in the software package MatLab (2010) was used to minimise Q(t , p) . Moreover, Δt=0.1s and Δf=0.05 Hz were adopted. The entailing results of the parametric identification show that experimental and identified hysteretic loops well agree with each other. Nonetheless, we can appreciate differences between dissipated energies of experimental and identified hysteretic loops relevant to two storeys for higher PGA levels. In order to better appreciate the evolution of some Bouc-Wen model parameters including slip, we introduce an analytic representation of real-valued response signals (Worden and Tomlinson, 2001) which retrieves the positive frequency components of the Fourier transform of signals, with no loss of information. Therefore, we define the amplitude A  t  of a generic signal x  t  :

A  t   xa  t   x 2  t   xˆ 2  t  ,

(4.39)

where ˆx  t  denotes the Hilbert transform of x  t  and xa  t  indicates the analytic signal. In time domain, the Hilbert transform ˆx  t  is defined as: xˆ  t  

1



p.v.



u  

 t   d

(4.40)

31


Equation (4.39) was applied to the upper storey displacement x2 (t ) , see Fig. 4.15 that well reflects a significant amount of nonlinearity activated in the two-DoF system. From Fig. 4.16, a careful reader can observe the instantaneous variation of  i and  i . As expected, for higher levels of PGA nonlinearity is evident, and therefore, Bouc-Wen model parameters exhibit a small variation or, in other words, they tend to stable values. 0.25

Signal Amplitude [m]

0.1 g

0.25 g

1.4 g

1.8 g

0.2 0.15 0.1 0.05 0

0

10

20

30

40 Time [s]

50

60

70

80

Fig. 4.15 Amplitude of x2 (t ) 30 0.1 g

25

0.25 g

1.4 g

1.8 g

1

20 15 10 5 0

0

10

20

30

30 0.1 g

25

40 Time [s]

0.25 g

50

60

1.4 g

70

80

1.8 g

2

20 15 10 5 0

0

10

20

30

(a)

i

40 Time [s]

50

60

70

for different values of PGA

32

80

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 30 0.1 g

20

0.25 g

1.4 g

1.8 g

1

10 0 -10 -20 -30

0

10

20

30

30 0.1 g

20

40 Time [s]

0.25 g

50

60

70

1.4 g

80

1.8 g

2

10 0 -10 -20 -30

0

10

20

30

(b)

40 Time [s]

50

60

70

80

 i for different values of PGA

Fig. 4.16 Instantaneous values of βi and γi for different values of PGA

4.4.3 The model for a four storey system In this subsection, the modified Bouc-Wen model will be extended to chain-like frame systems. With reference to the four-storey system shown in Fig. 4.17 and in accordance with Equation (4.23), one can express the global displacements in terms of flexibility, by summing both linear and nonlinear components. First, the nonlinearity caused by slip was introduced: 1 xs ,1 ( f1  f 2 )   x1   k11 k12 k13 k14   f1          x (f  f ) x (f  f ) s ,1 1 2   x2    k21 k22 k23 k24  .  f 2    s ,2 2 3 (4.41)  x3   k31 k32 k33 k34   f3   xs ,3 ( f3  f 4 )  xs ,2 ( f 2  f3 )           x4   k41 k42 k43 k44   f 4   xs ,4 ( f 4 )  xs ,3 ( f3  f 4 )  where,  k11 k12  k k K el   21 22  k31 k32   k41 k42

k13 k23 k33 k43

k14   k24  k34   k44 

(4.42)

represents the condensed stiffness matrix of the underlying linear system, which will be time variant during the identification process; xs ,1 and xs ,2 define the non-linear inter-storey drifts at the first and second storey, respectively. Therefore, the equation of motion associated with the frame system reads, 33


 g x  f  M  u M    f  K  f  x  x nl   1  x nl  K el  p  f ,sgn  xBW   x BW  1 1 1 K  f   K el  K s  f 

(4.43)

1 where x BW  x  x s  x  K s f  f , K f  is the inverse of the nonlinear flexibility matrix K s-1 owing to the slip contribution. The matrix K s is defined as,

 k s11  k Ks   s 21  k s 31   k s 41

k s12

k s13

k s 22

k s 23

k s 32

k s 33

k s 42

k s 43

k s14   k s 24  k s 34   k s 44 

(4.44)

and the matix  p defined the hysteretic part of the restoring force vector f,  fp1  f1 , xBW 1      fp 2  f 2 , xBW 2  xBW 1  0 0   fp 2  f 2 , xBW 2  xBW 1     fp 2  f 2 , xBW 2  xBW 1       f p 3  f3 , xBW 3  xBW 2  0   f p 2  f 2 , xBW 2  xBW 1   p  β   f p 3  f 3 , xBW 3  xBW 2     f  f , x  p3 3 BW 3  xBW 2      0  f p 3  f 3 , xBW 3  xBW 2   f p 4  f 4 , xBW 4  xBW 3        f p 4  f 4 , xBW 4  xBW 3      f , x   f , x     0 0 f x f x      p 4 4 BW 4 BW 3 p 4 4 BW 4 BW 3  

Fig. 4.17 A chain like four-storey frame

Fig. 4.18 Layout of the specimen

34

(4.45)

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development The tests were performed in the ELSA laboratory of the Joint Research Centre. The general layout of the full scale reinforce concrete test structure is shown in Fig. 4.18. It is a four-storey, high ductile, framed structure. Dimensions in plan are 10mx10m, measured from the column axis. Interstorey heights are 3.0 m, except for the ground storey with 3.5 m. The structure is symmetric in one direction (that of testing) with two equal spans of 5.0 m. The interstorey drift and restoring force diagrams on bare frames obtained from the pseudo-dynamic test are shown in Fig. 4.19. This preliminary analysis showed a clear degrading behaviour in stiffness. At higer loading levels, hysteresis and pinching phenomena are observed in Fig. 4.19. 1.5

x 10

6

1.5

6

1 Restoring Force [N]

Restoring Force [N]

1

x 10

0.5 0 -0.5

0.5 0 -0.5

-1

-1

-1.5 -0.1

-0.05

0 0.05 Interstorey Drift [m]

0.1

-1.5 -0.1

-0.05

(a) First floor 1

x 10


0.1

(b) Second floor

6

8

x 10

5

Restoring Force [N]

Restoring Force [N]

6

0.5

0

-0.5

4 2 0 -2 -4 -6

-1 -0.06

-0.04

-0.02 0 0.02 Interstorey Drift [m]

(c) Third floor

0.04

0.06

-8 -0.04

-0.02


0.04

(b) Fourth floor

Fig. 4.19 Interstorey drift vs. Restoring force

A low-level test has been firstly performed on the frame with the reference signal scaled by 0.4. The resulting nominal peak ground acceleration corresponds to 0.12g and it was thought not to cause significant yielding inside the structure. Comparisons of the displacements and forces between the identified and numerical results are shown in Fig. 4.20 to Fig. 4.23. One can see that a quite good agreement is achieved. The identification procedure proposed in Bursi et al. (2012) was applied in order to identify the tangent stiffness matrix. The identified instantaneous coefficients for the stiffness matrix are shown in Fig. 4.24 and the initial and final values of stiffness parameters are shown in Table 4.2 and Table 4.3. Fig. 4.25 shows the instantaneous frequencies of the degrading model from estimated instantaneous coefficients. From Fig. 4.24, one can see that degradation is actually detected by the identification technique, so the instantaneous values estimated by the algorithm for linear parameters ma by considered reliable.

35

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 0.015

2

x 10

5

0.01 1 f1 [N]

x1 [m]

0.005 0

0

-0.005 -1 -0.01 -0.015

0

2

4 6 Time [s]

8

-2 0

10

2

4 6 Time [s]

8

10

0.03

3

0.02

2

0.01

1

f2 [N]

x2 [m]

Fig. 4.20 Comparison of displacements and forces at first floor

0 -0.01 -0.02

x 10

5

0 -1

0

2

4 6 Time [s]

8

-2 0

10

2

4 6 Time [s]

8

10

8

10

Fig. 4.21 Comparison of displacements and forces at second floor 0.04

3

x 10

5

0.03 2 0.01

f3 [N]

x3 [m]

0.02

0

1 0

-0.01 -1

-0.02 -0.03

0

2

4 6 Time [s]

8

10

-2 0

2

4 6 Time [s]

Fig. 4.22 Comparison of displacements and forces at third floor

36

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 0.04

3

x 10

5

2 0.02 f4 [N]

x4 [m]

1 0

0 -1

-0.02 -2 -0.04

0

2

4 6 Time [s]

8

-3 0

10

2

4 6 Time [s]

8

10

Fig. 4.23 Comparison of displacements and forces at fourth floor

3

x 10

K11

8

-1.4

2.5

-1.5

2

-1.6

x 10

K12

8

2.5

x 10

K13

7

-1

2

1.5

0

2

4

6

8

-1.7

0

2

Time [s] -1.2

x 10

6

8

1.5

2.6

x 10

0

2

4

6

8

-2

0

2

Time [s]

K22

8

K14

6

-1.5

Time [s]

K21

8

4

x 10

-1.1

-1.4

2.4

-1.2

-1.6

2.2

-1.3

x 10

K23

8

4

6

8

6

8

6

8

6

8

Time [s] 1.4

x 10

K24

7

1.2

-1.8

0

2

4

6

8

2

0

2

Time [s] 2.5

x 10

K31

7

4

6

8

-1.4

0

2

Time [s] -1.15

x 10

K32

8

4

6

8

1

0

2

Time [s] 2.2

x 10

K33

8

4

Time [s] -7

-1.2

2.1

-1.25

2

-9

-1.3

1.9

-10

x 10

K34

7

-8

2

1.5 0

2

4

6

8

0

2

Time [s] -1.2

x 10

K41

6

4

6

8

0

2

Time [s] 1.6

x 10

K42

7

4

6

8

2

-0.95

x 10

K43

8

4

Time [s] 9

-1.4

x 10

K44

7

8 1.4

-1

1.2

-1.05

-1.6 -1.8

0

Time [s]

7

0

2

4

Time [s]

6

8

0

2

4

Time [s]

6

8

0

2

4

Time [s]

6

8

6

0

2

4

Time [s]

Fig. 4.24 Instantaneous coefficients for the stiffness matrix (no constants on off-diagonal terms were introduced for computational reasons)

37

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 12 1 2 3 4

Frequency [Hz]

10

8

6

4

2

0

0

1

2

3

4

5

6

7

8

9

Time [s]

Fig. 4.25 Instantaneous frequencies of the degrading model from estimated instantaneous coefficients

Table 4.2 Initial values of stiffness parameters

2.83e8 -1.64e8 2.10e7 -1.60e6

-1.68e8 2.59e8 -1.31e8 1.39e7

2.34e7 1.31e8 2.13e8 1.00e7

-1.77e6 1.46e7 -1.00e7 8.66e7

Table 4.3 Final values of stiffness parameters

2.00e8 -1.25e8 2e7 -1.25e6

-1.6e8 2.2e8 -1.2e8 1.5e7

2e7 -1.2e8 1.95e8 -9.7e7

-1.2e6 1.2e7 -8e7 0.7e8

38


5

Test Modelling with Substructuring Including Experimental and Numerical Uncertainties

5.1

INTRODUCTION

Pseudo-dynamic and real-time test with dynamic substructuring are novel hybrid experimental techniques and are applicable in testing several types of nonlinear structures/systems. In a hybrid test, a heterogeneous model of the emulated system is created by combining a Physical Substructure (PS) and a Numerical Substructure (NS). Generally, the critical part of a structure which is difficult to be numerically modelled is chosen as the PS and is experimentally tested, while the NS is modelled in a computer. By the interaction of these two substructures, the overall response of a structure is obtained. In this chapter, the modelling theory in case of uncertainties is briefly introduced; and the process of implementations of hybrid test techniques on a typical petrochemical piping system subjected to seismic loading is presented. Finally, some of the results from the hybrid tests are provided. All experimental tests confirmed a quite good seismic performance of the piping system and of its components under earthquake levels suggested by Standards.

5.2

MODELLING IN THE CASE OF UNCERTAINTIES

In real-time hybrid simulation, structural responses under earthquakes are replicated through integrating physical testing of PS and NS. To ensure the structural response to be truthfully replicated, the desired responses computed by a numerical algorithm have to be imposed accurately onto experimental substructures in a real-time manner. Experimental studies however indicated that actuator delay-induced tracking errors are often inevitable even when a sophisticated actuator delay compensation technique is applied. This poses a great challenge for reliability assessment of real-time hybrid simulation results since exact structural response is often not available for an immediate comparison. In general, the transmission mechanism has been modelled as a rigid component, by ignoring the compliance between the power source and a remote site. To enhance mechanical performance, most researchers have focused on the power driving end or the controlled end of the transmission system Cheng C.C., (1998), Menon K. (1999), Yao B. (1997), etc. However, the compliance mechanism between these two ends usually causes difficulties in designing controller based on rigid dynamic models. With respect to the compliance property, Ortega and Spong (1989) explored the flexible problem of the robotic system and introduced two nonlinear control techniques for flexible robots. McAskii and Dunford (1988) proposed a self-tuning pole 39

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development placement method for the positioning control of a manipulator with flexible joints. Er et al. (1996) proposed a multirate output and input PID controller for a two-link flexible-joint robot by using a digital-signal-processor (DSP). Ider (1999) developed an inverse dynamic control algorithm to achieve position and force control in constrained flexible joint robots. In order to reduce the complexity of controller design, a nonlinear system can be easily analyzed using singular perturbation analysis (SPA) (Kokotovic P.V., 1986), since the controlled system can be theoretically characterized by fast-mode dynamics and slow-mode dynamics. Recently, Lee et al. (Hunag L., Ge S.S., Lee T.H., 2006) have studied the problem of adaptive position/force control of an uncertain constrained flexible-joint robot using the singular perturbation approach without the assumption of weak-joint robots’ flexibility. To overcome the difficulty of precision positioning in a transmission system with variable compliance, a hybrid control strategy consisting of singular perturbation analysis and adaptive robust control (ARC) is proposed to guarantee transient performance and final positioning accuracy without force measurement feedback. This method showed better transient and steadystate responses with variable compliance.

5.3

MODELLING OF A PIPING SYSTEM FOR REAL‐TIME AND PSEUDO‐DYNAMIC TESTS

The objective of pseudo-dynamic and real time tests is to investigate the behaviour of a piping system and its critical components, mainly pipe elbows, Tee joints, bolted flange joints, etc., under seismic events. For instant, the pipe elbow, which is a curved pipe segment, is very flexible and is one of the most critical components of a piping system. Due to the presence of geometrical discontinuity, stress is intensified in an elbow and a higher probability of failure exists in this component (Karamanos et al., 2011; Nayyar, 2007; Suzuki and Abe, 2005). In fact, results of experimental activities carried out by the Gresnigt et al., (2012) show that the behaviour of pipe elbows under cyclic loading is very complex. Instead of performing typical slow cyclic tests, dynamic tests on pipe elbows which take into account the inertial effects are implemented to observe their performance under actual seismic loading. These tests can potentially simulate shaking table tests by the use of actuators, controllers and appropriate software.

5.3.1 FE modelling and modal analysis of the piping system under investigation The piping system to be experimentally tested is a typical industrial piping system, as the one shown in Fig. 5.1. Dimensions and other geometrical properties of the piping system are taken from (DeGrassi et. al., 2008). The piping system initially contained 8 and 6 inch straight pipes, several elbows and a T-joint, see Fig. 5.1. Characteristics and boundary conditions of the piping system are presented in Fig. 5.2. .

40


Fig. 5.1 The reference piping system under investigation

(a) Specifications of the piping system

(b) Boundary conditions of the piping system

Fig. 5.2 Specifications and boundary conditions of the piping system

In order to perform required preliminary analysis, a three dimensional finite element model of the piping system is developed in SAP2000 software (2004). All pipes including elbows are modelled using straight elements with the section of pipes. However, the flexibility of these straight elbow elements are adjusted to have the equivalent flexibility properties found from an FE analysis on corresponding elbows carried out in ABAQUS software (Hibbit H.D., 2003). Various dynamic characteristics, such as eigenfrequencies, of the piping model can be found by modal analysis. The stiffness and mass matrices of the model that we need in Matlab and Simulink can also be extracted by SAP2000. We are interested about the response in x direction because the earthquake loading will be applied on the piping system in this direction. It can be seen from the first 20 modes we obtained that the 1st and 2nd mode are the main two modes which excites about 36% and 12% masses respectively in the x directions. The 1st and 2nd mode shapes are presented in Fig. 5.3.

41


(a) Mode 1- Frequency: 5.18Hz; Mass participation in x: about 36%

(b) Mode 2 – Frequency: 6.32Hz; Mass participation in x : about 12%

Fig. 5.3 Mode 1 and Mode 2 of the piping system model

5.3.2 Analysis of the piping system under seismic loading In order to perform a numerical investigation of the seismic response of the piping system, we carried out time history analyses on the piping system using SAP2000 software. To carry out the earthquake time history analysis, it was necessary to find a realistic input seismic loading. The piping system is placed on a typical industrial piping support structure which is designed for generating the input earthquake acceleration. The support structure is a three dimensional frame structure whose geometry is illustrated in Fig. 5.4. Some of the design parameters of the support structure are shown in Table 5.1.

Fig. 5.4 Finite element model of the support structure

Fig. 5.5 Measurement points of accelerograms on the support floor

Table 5.1 Some design parameters of the support structure

Location PGA q factor Ground type Return Period Importance Class *

High Seimic-prone Region 0.33g 3.2 C 712y Ⅲ*

Industries with dangerous activities, Vr  50  1.5 42

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development We worked with a uniform excitation at the bare of the support structure, and we recorded acceleragrams at different pipe rests coming from time-history analyses. The measurement points on the support floor are shown in Fig. 5.5. The 1940 EL Centro earthquake signal was applied in the base of the support structure. The acquired signals of different points stated that the accelerograms were quite similar except that at point (7) which corresponds to the top floor node. For our purpose, we choose the accelerogram at point (1). The reason we choose this accelerogram is that, in this point, there is a vertical support of the piping system and most of the pipes stay in the first floor. The time history and response spectra of the chosen earthquake are shown in Fig. 5.6.

Fig. 5.6 The reference earthquake for experimental tests

The reference seismic excitation for the hybrid tests is now defined which corresponds to a Safe Life Limit State. During our tests, we planned to use different levels of PGA corresponding to the limit states set by codes, i.e. Operational Limit State, Damage Limit State and Collapse Limit State, in order to analyse performances of the piping system at those levels of earthquake loading. The time history analyses with selected input earthquake loading are carried out both considering damping and without considering it. In our analysis, the Rayleigh damping model was considered with a 0.5% damping. The earthquake loading was applied to the piping system in the horizontal direction (along the x axis). Envelopes of moment and shear in the piping system under the reference earthquake without and with damping are shown in Fig. 5.7 to Fig. 5.10.

Fig. 5.7 Moment in the piping system without damping

Fig. 5.8 Shear in the piping system without damping

43


Fig. 5.9 Moment in the piping system with Rayleigh damping (0.5%)

Fig. 5.10 Shear in the piping system with Rayleigh damping (0.5%)

Maximum values of shear and moment and stresses due to bending moments are reported in Table 5.2 to Table 5.4. Table 5.2 Maximum moment, M max and stress,

Components Elbow2 Straight pipe

 max without damping

M max (kN)

 max (Mpa)

69.15 81.56

503.56 296.03

Table 5.3 Maximum moment, M max and stress,

Components Elbow2 Straight pipe

Stress level Above yield strength Below yield strength

 max with damping

M max (kN)

 max (Mpa)

43.63 45.62

317.74 288.12

Stress level Below yield strength Below yield strength

Table 5.4 Maximum shear,  max in the straight pipe

 max in the straight pipe without damping  max in the straight pipe with damping

95.48kN 48.50kN

It can be observed that although the maximum bending moment is in the straight pipe, the maximum stress is found in Elbow #2. From the above tables, it can also be found that Rayleigh damping reduces moments and shears in the piping system.

5.3.3 Substructuring of the piping system One of the unique features and advantages of hybrid tests is dynamic substructuring. In order to divide the piping system under exam into two substructures, i.e., PS and NS, we need to find proper coupling nodes and ensure the compatibility and equilibrium conditions at these nodes. Since it is much easier to impose a displacement by an actuator, we plan to do this in our coupling nodes. We, therefore, look for two points in the piping system where there are 44

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development minimum bending moments close to zero under an earthquake loading. From Fig. 5.7 andFig. 5.8, we can find minimum bending points in the piping system. Hence, we divided the piping system into two substructures as presented in Fig. 5.11. The PS and its dimensions are presented in Fig. 5.12. The actual setup of the PS is shown in Fig. 5.13.

(a) The physical and numerical substructures

(b) Coupling nodes and forces in the piping system

Fig. 5.11 The physical and numerical substructures of the piping system

Fig. 5.12 Dimensions and actuator position

Fig. 5.13 Actual test set-ups for hybrid tests

The two substructures are now defined for hybrid tests. We have made some approximations in order to establish these two substructures. We modify our original piping model by restraining the displacements of the two coupling DoFs in y and z directions thereby reproducing our approximations in the model. We called this model as the “Continuous model”. During the hybrid tests, we will apply displacement commands to the two coupling nodes of the NS in the x direction; these displacements will be the same in the coupling nodes. To better reflect this situation, we consider a model where the two coupling nodes are constrained to move together in the x direction thus satisfying the compatibility condition. The other movements are kept free retaining the two restraints of the Continuous model. We refer to this model as the “Reference model” of. A comparison of modal properties between the Continuous model and the Reference model is carried out and it shows a good agreement. Also the MAC matrix shows a good agreement in the first 8 modes; also time history analyses were carried out with an earthquake having a PGA of 1.0g. The comparison between time history responses of the two coupling nodes are shown in Fig. 5.14 and Fig. 5.15. 45


Fig. 5.14 Displacement history of coupling node 1 in direction x

Fig. 5.15 Displacement history of coupling node 2 in direction x

The good agreement between the Continuous model and the Reference model ensures that by satisfying the compatibility condition, we will potentially be able to reproduce the seismic response of the piping system by means of experimental tests.

5.3.4 Model reduction of the PS A model reduction technique can be defined as follow: a technique that is used to reduce the numbers of degrees of freedom of a model to a few interested degrees of freedom while potentially retaining the original characteristics of the model. The technique we used here in order to reduce the physical substructure to the two coupling degrees of freedom is called the Craig Bampton method. The Craig-Bampton (CB) reduction technique, originally developed by Craig and Bampton (Craig and Bampton, 1968), is a particularly useful technique for the reduction of a substructure. The equation of motion of the PS without considering damping reads:

M nP unP  K nP unP  FenP

(3.1)

In the CB reduction, the coordinate vector of the PS, u P is divided into two parts: one containing the coupling DoFs, uC , and the other containing the internal DoFs (rest of DoFs), u L . The CB reduction is then defined as, uC   I 0  uC  (3.2) unP        uL  R L  q  where, I 0     CB  CB , the Transformation matrix L  R

uC , the Coupling DoF u L , the Internal DoF R , Rigid body vector L , Fixed based mode shapes q , modal coordinates 46


5.3.5 Results from experimental tests The Implementation of the reduction technique on the treatment of the PS of the piping system allowed for a pseudodynamic test program to be carried out. This program is reported in Table 5.5. The piping system and all of its components showed a favourable performance under all limit state earthquake levels reported in Table 5.5. Table 5.5 Hybrid test program

Test Case Identifica-tion tests Elastic Tests Service-ability limit state tests Ultimate limit state tests

PGA g

PGA m/s2

Identification test of the PS, IDT

Hammer Test

-

-

Elastic test, ET1 Elastic test, ET2 Operational limit state test, SLOT1 Operational limit state test, SLOT2 Damage limit state test, SLDT Safe life limit state test, SLVT Collapse limit state test, SLCT

PDDS RTDS

0.042 0.042

0.413 0.413

PDDS

0.079

0.772

RTDS

0.079

0.772

PDDS PDDS PDDS

0.112 0.421 0.599

1.098 4.128 5.878

Even under the Collapse Limit State (SLCT) earthquake event, the piping system was found to remain below its yield limit. Small levels of rotations were found in elbows. A maximum rotation of about 7 millirad during the SLCT was found in Elbow #1, as illustrated in Fig. 5.16. Acceleration levels in the piping system during experiments showed significant amplification from the input earthquake PGAs. Displacements and accelerations of Coupling Node #1 are presented in Fig. 5.17 and Fig. 5.18.

Fig. 5.16 Rotations of the two end nodes of Elbow #1 at SLTC

47


Fig. 5.17 Horizontal accelerations of Coupling Node #1 at SLTC

Fig. 5.18 Horizontal displacements of Coupling Node #1 at SLTC

In all tests, a favourable agreement between numerical and experimental responses of the piping system was found. From Fig. 5.18, it can be observed that the maximum acceleration in the Coupling Node #1 is about twice the PGA, i.e., of the input earthquake. All experimental tests confirmed a quite good seismic performance of the piping system and of its components under earthquake levels suggested by Standards.

48


6

Integration of Testing Equipment and Specimen Model in order to Build a Virtual Model

6.1

INTRODUCTION

The hybrid testing technique has been introduced in the early 90s, with interesting applications in different fields. It has been used in different engineering branches, not only in civil engineering. In hybrid test, physical and numerical models are needed. Structural identification can be used to update or calibrate structural models in order to improve the prediction of the structural response. In this chapter, an advanced method for updating structural computational models is introduced. Moreover, an integration of testing equipment and specimen model for shaking tables is depicted in which the hardware and software is described; a novel method for delay assessment is introduced and the results of implementation of this method are shown.

6.2

ADVANCED METHODS APPLIED IN UPDATING STRUCTURAL COMPUTATIONAL MODELS

Structural identification can be used to update or calibrate structural models in order to improve the prediction of the structural response and to achieve most cost-effective design. More than that, by tracking changes of key parameters, structural identification can be used for nondestructive assessment including updating of structural models for CE structures exposed to extreme event such as earthquakes and also for process monitoring of damage due to the ageing of structures overtime.

6.2.1 The advanced method When system identification is treated as an optimization problem in terms of minimizing the errors between the measured and predicted signals, it can be typically classified as classic and non-classic methods. The purpose of these methods is to find a set of parameters within a reasonable search range in parameters space to minimize the objective function through numerical iterations. One of the classic (deterministic) minimizing algorithms to find the elements of mass, damping and stiffness matrices of structure based on the time domain method used here is Nelder-Mead downhill simplex algorithm which does not require the calculation of derivatives. Moreover the non-classic (stochastic) algorithm and genetic algorithm (GA) are adopted in order to solve the problems of structural identification. 49


6.2.2 Implementation of the methods The presented methods are implemented with a computational model made of 3-DoFs, is a twodimensional shear building. The structure consists of rigid beams and flexible columns, reducing the motion to a single translational degree of freedom at each floor level. The mass of structure is lumped at each floor level and the response is a vector representing the motion at the respective floor levels which is shown in Fig. 6.1. . The input force, applied to the third level, is of the form: F3 (t )  1000* (sin 6 t  sin15 t ) * N

(6.1)

The physical parameters of the structure are listed in Table 6.1. Table 6.1 Initial model’s characterization

Level 1 2 3

Mass [Kg] 350 103 263 103 175 103

Stiffness [kN/m] 31521.26 21014.17 10507.09

m3

F3 k3

c3

k2

c2

m2 m1

k1

c1

Fig. 6.1 2D shear type model

Case І Structural system identification a. Deterministic optimization approach For many civil engineering structures, such as bridges or offshore platforms, it is a reasonable assumption to consider that the mass of system is known, as the mass may be estimated with reasonable accuracy. On the other hand, in some cases accurate calculation of mass is not possible, particularly when the mass has to be modelled as lumped values. In these cases, identification of mass can help to obtain more realistic estimates of stiffness. Results of model’s characteristics based on the application of the deterministic method are shown in Table 6.2; and the process of iterative optimization for model updating based on deterministic method is shown in Fig. 6.2. If the optimization algorithm is correctly initialized, then one can obtains the global

50

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development minimum of an objective function, i.e. the values of system parameters that predict adequately the responses of the actual system. Table 6.2 Results of model’s characteristics

Level 1 2 3

Actual 350 103 263 103 175 103

Mass [Kg] Estimates/Updated 349.35 103 262.73 103 174.93 103

Stiffness [kN/m] Actual Estimated/Updated 31521.26 31465.35 21014.17 21015.01 10507.09 10508.91

Fig. 6.2 Process of iterative optimization for model updating

b. Stochastic optimization approach Fig. 6.3 shows the results of model’s characteristic based on the application of the stochastic method application; and the values of estimated parameters over the process of iterative optimization are presented in Fig. 6.3. Table 6.3 Results of model’s characteristics

Level 1 2 3

Mass [Kg] Actual 350 103 263 103 175 103

Estimates 395.17 103 283.13 103 176.69 103

Stiffness [kN/m] Actual Estimated 31521.26 35065.01 21014.17 23367.03 10507.09 11043.17

Fig. 6.3 Process of iterative optimization for model updating

51

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development On the bases of the results, one can concluded that a correct selection of the GA operators and parameters is crucial as they affect the solution and the algorithm runtime. However, there is no general rule to select them; the right decision depends on the number of genes, the objective function and the nature of the problem. Thus, one must study the problem of selecting the GA operators and parameters during the implementation of a structural identification algorithm. This can result in guidelines for a GA operator and parameter selections in similar structural identification problems.

Case II Output-only structural system identification In reality, the measurement of input forces in situations outside the laboratory may not always be feasible. So, the presented method must be adapted to identify structural stiffnesses for problems where the input force is not measured. A simultaneous evaluation of structural parameters and input force is presented in what followed. a. Deterministic optimization approach The model updating results of output only based on the deterministic optimization approach are shown in Table 6.4; in addition, Fig. 6.4 shows the process of iterative optimization for model updating based on this method. Table 6.4 Model updating results of output only – deterministic method

Level 1 2 3


Fig. 6.4 Process of iterative optimization for model updating based on output only-deterministic method

b. Stochastic optimization approach The model updating results of output only – stochastic optimization approach are shown in Table 6.5. Fig. 6.5 shows the process of iterative optimization for model updating based on this method. Table 6.5 Model updating results of output only-stochastic method

Level 1 2 3


52


Fig. 6.5 Process of iterative optimization for model updating based on output-stochastic method

Conventional optimization techniques used in damage detection or model updating employ sensitivity-based on searching mechanisms which do not assure the achievement of a unique optimum solution because their high sensitivity to the initial conditions. Therefore, further investigations are needed to implement a robust optimization approach to solve these problems. Finally, one could apply genetic algorithms to solve a variety of optimization problems that are not well suited for standard optimization algorithms, including problems in which the objective function is discontinuous, non-differentiable, stochastic or highly nonlinear.

6.3

INTEGRATION OF TESTING EQUIPMENT AND SPECIMEN MODEL FOR SHAKING TABLES

The combined use of Physical Substructures and Numerical Substructures, dynamically interacting with each other in real-time fashion, defines a hybrid environment with several interesting capabilities. The main capabilities of such hybrid system can be grouped in three categories: - Real-Time Dynamic Hybrid Testing (RTDHT); - Hardware or, in general, physical components identification; - Tuning of the hybrid testing system. The Real-Time Hybrid Testing technique has been introduced in the early 90s, with interesting applications in different fields. As reported in Williams (2007), RTDHT found application not only in civil engineering, but in different engineering branches. It is currently used in automotive for components testing; Applications are also found in aerospace field as reported in Footdale (2008). A further possibility related to the hybrid environment is the identification of physical components of a given system. In this way it is possible to investigate and characterize the response of the physical component in its real conditions, without the need of realizing the whole structural system. This allows one to reduce the associated costs and to focus on the sub-structure of interest. Particular emphasis is given here to the possibility of tuning a hybrid testing system in an efficient way, as described in the following subsections.

53

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development 6.3.1 Hardware and software architecture A newly designed real-time dynamic hybrid testing system has been implemented at the experimental laboratory Eucentre TREES Lab (Laboratory for Training and Research in Earthquake Engineering and Seismology) of Pavia (Italy). The testing system integrates a MDOF shake table coupled with a vertical reaction structure, specifically designed for conventional and sub-structure testing of seismic isolation devices. The main components of the designed and implemented RTDHT system and their connections are sketched in Fig. 6.6.

Fig. 6.6 Implemented RTDHT system

The Eucentre TREES Lab’s Bearing Testing System (BTS) is one of the few large bearing testing machines in the world and the unique in Europe with dynamic capabilities. The customized design of the actuation system and the control software allows for forming biaxial tests on real scale bearings and seismic isolation devices both in static and dynamic conditions. The BTS is shows in Fig. 6.7. The Eucentre BTS is composed by two main devices: a multi-axial shake table system and a vertical reaction structure. The horizontal control is performed by means of two inclined dynamic servo-hydraulic actuators, which are showed in Fig. 6.7. The table slides on 5 vertical thrust bearings, see Fig. 6.8, which allows for the vertical, pitch and roll DoF control and provide a thin oil film suitable to create a low-friction sliding interface.

Fig. 6.7 Eucentre Bearing Testing System (Left) and BTS horizontal actuator (Right)

54


Fig. 6.8 Vertical and lateral thrust bearings of BTS table

6.3.2 The implemented real‐time algorithm The RTDHT system is coordinated by the implemented real-time code running on the xPC Target; within this code, different specific sub-routines are running with precise triggering and coordination. The numerical sub-structure and the integration scheme, as well as procedures for delay estimation and compensation, reliability monitoring, etc. are implemented. The real-time code has been developed on the Host PC within the Simulink (Mathworks) environment and it is referred to as Real-Time (RT) Algorithm in this description. The main window of the RT algorithm is shown in Fig. 6.9, from this window, all sub-routines can be easily accessed to tune parameters, to change the xPC Target scopes, the channels to record, etc. The main window is also used as the GUI for the xPC Target; however, the algorithm has been programmed in such a way that the code is able to run and to end in a suitable manner in a “stand-alone” mode, without the need of external actions from the Host PC. [rec 5] LA

dm dd

E nergy

T arget Scope Id: 6

Energy

forc e des ired_dis p

S cope (xPC) 4

Hys teres is_meas

[rec 4] W

ref des ired_dis p dly (s)

dly_as s

fbk Res t_forc e

[Fr] From

u1

Comp Di sp

In1 c omp_di sp

Out1

acc 2 eq_load

interlock -K-

DLY _COMP_A i

CCA

DLY _A S S_ai_down

DLY

RTalg+NUM_Subs tr

[dly]

Dly2us e

DLY _grad_limit

fbk_dis p

CMD Dis p des ired_dis p

E xt_load E q_load I

Manual Swi tch

Dly_as s

1/z 1Dly

fbk_dis p

Forc e fbk

Interlocks _v4

[dly]

-1 0

[Fr] Goto

BT S

GNO 5 Chirp S ignal

Gain1

-KMvec

0.060 Manual Swi tch1 Constant rec1

MANUAL INTERLOCK ON

From4

DATA ACQUISITION

rec2 From2

1 rec3 man_i nt 0 OFF

Goto2 MANUAL INT ERLOCK

From3

File Sc ope Id: 8 REC

rec4 From5 rec5 From6

Fig. 6.9 Simulink experimental model: main window

6.3.3 Tuning of the hybrid testing system The implemented algorithm is based on the Newmark time domain solution of the equation of motion; it uses sub-stepping, instead of iteration, to reach the equilibrium within each time-step. This procedure employs a stable implicit time integration scheme, which is independent of the 55

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development specimen behaviour and of the type of loading (Bayer et al., 2005).The force error at the end of each step typical of non-iterative integration schemes is compensated with a sort of PID (Proportional-Integral-Derivative) control that reads: t D (6.2) f (et )  P[et  t  I   k 0 e k  (et  et t )] t where the equilibrium error force et is defined as the sum of all dynamic internal and external forces, at the end of each step. P, I and D are the proportional, integral and derivative gains of the controller. The effect of the delay in hybrid testing has been recently observed by several researchers (Agrawal et al., 1993, Horiuchi et al., 1999, etc.). Since the actuation delay cannot be completely eliminated, an effective compensation procedure must be implemented. The first logical operation to carry out is the physical reduction of the phase-lag; since perfect delay compensation cannot be achieved, its reduction to the lowest possible level becomes of a primary importance. Once a satisfactory performance is obtained, prior to compensate, an accurate delay estimation must be provided. A novel simple and effective delay estimation procedure has been proposed in Lanese (2012) and is briefly described herein. Delay Assessment Reliable delay estimation is a fundamental requirement in order to perform an effective compensation. In some previous works, a constant value of delay has been assumed, e.g. Carrion and Spencer (2006). This can be a good approximation in some cases, leading to a simplification of the assessment/compensation procedure. However, it has several disadvantages. Hence, new delay estimation techniques are deemed to be necessary. In the research work suggested by Lanese (2012), both off line and on line delay assessment procedures, in frequency and time domain, are analysed. Advantages and drawbacks of the implemented procedures are presented, and a novel simple and effective procedure is proposed and briefly described here. The proposed online estimation procedure considers increasing length signal portions which are shown in Fig. 6.10. The initial increasing length allows for taking advantage of all available information, while the maximum imposed length ( N samp ,max ) is a tunable parameter that limits the number of operations to carry out. At a given instant of time t , a pre-defined length of command and feedback signal is considered; the length of the feedback is exactly equal to the considered window, while the length of the command is the length of the window plus a number of samples N dly ,max multiplied by the time step dts , i.e. a conservative estimation of the maximum expected delay. For instance, the main window of the Simulink implemented routine is shown in Fig. 6.11.

Fig. 6.10 Proposed assessment procedure; step # 56


lim 1 ref

assessment frequency (samples)

Buffer2

2 fbk ref

Buffer

dts

fbk

-Cmaxdly

1 dly (s)

Gain1

dly (samp)

maxdly

Routine

Fig. 6.11 Simulink experimental model: delay estimation

In order to illustrated in the proposed algorithm of delay estimation, a pseudo-random displacement signal has been considered as Fig. 6.12. This test represents the real testing conditions, where random noise is added to the acquired feedback. Since the delay is in general not constant, both fixed and variable imposed delay conditions have been investigated. As reported in Fig. 6.13, the algorithm prediction is very close to the actual delay, and delay variations can be effectively followed. Delay assessment test

Delay assessment test 0.15 0.055

CMD FBK

0.1

0.045 Displacement (m)

Displacement (m)

0.05

0

-0.05

0.04

0.035

-0.1

0.03

-0.15

0.025

-0.2

CMD FBK

0.05

0.02 0

5

10

15

20 25 Time (s)

30

35

40

45

12.2

12.4

12.6

12.8

13 13.2 Time (s)

13.4

13.6

13.8

Fig. 6.12 Pseudo-random displacement signal and simulated constant delay feedback with noise Delay assessment test

Delay assessment test

0.1

0.1 imposed dly est dly

0.08

0.08

0.07

0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01 0

imposed dly est dly

0.09

Delay (s)

Delay (s)

0.09

0.01

0

5

10

15

20 25 Time (s)

30

35

40

45

0

0

5

10

15

20 25 Time (s)

30

35

40

45

Fig. 6.13 Imposed and estimated delay (noisy feedback)

Validation tests show that short windows are likely to provide the updated estimation; this results to be appropriate for systems where the delay is expected to rapidly change during the timehistory.

57

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Since few samples are used for the assessment, the effect of noise and actuator tracking errors can significantly reduce its effectiveness. Longer windows guarantee more stable results, so minimizing the effect of feedback distortions. If rapid delay evolution is expected, it can worsen its effectiveness since the real-time prediction actually results in an average value of the considered signals length. A good point of the proposed algorithm is that no information about the testing system or of the expected delay is needed; the initial range of possible delay can be quite large, while further refinements can be performed afterwards, thus reducing the required computational load. If the effect of noise importantly affects the procedure effectiveness, in the experimental testing phase, an alternative strategy can be adopted: in particular, the feedback displacement can be pre-processed with a low-pass real-time filter before being sent to the procedure. In order to maintain the synchronization, the same real-time filter can be applied to the command signal too; nonetheless, this has to be done separately, without affecting the timing of the xPC Target-BTS controller communication. In sum, the multiple possibilities of a hybrid environment integrating a testing equipment with a specimen model have been described; particular emphasis has been given to the possibility of effectively tune a hybrid testing system with optimized costs. The effectiveness of the procedure has been shown through a case study relative to a Real-Time Dynamic Hybrid Testing system mainly oriented to seismic isolated structures which has been recently implemented.

58


7

Summary

This report covered the research activities of Task JRA2.4. Several parts of Deliverable D13.3 edited by EUCENTRE and reviewed by UNITN were issued. With regard to the state of the art, initially UNITN issued the parts relevant to System Identification and Model Updating. Relevant applications of System Identification were performed by ITU with a vision system, and by UNITN that identified both single -a Magneto Rheological damper- and multiple -two and four storey frame structures- degrees of freedom hysteretic systems. With reference to modelling of Physical Substructures in view of real-time pseudo-dynamic tests, UNITN applied component mode synthesis to a full scale piping system specimen subjected to earthquake loading. Finally, TUIASI and EUCENTRE developed and implemented virtual models of specimens to be used for shaking table tests.

59


References Agrawal A.K., Fujino Y., Bhartia B.K.. Instability due to Time-delay and its Compensation in Active Control of Structures. Earthquake Engineering & Structural Dynamics, 1993; 22(3): p. 211-224. Allemang R.J., Brown D.L., 1998. A unified matrix polynomial approach to modal identification. Journal of Sound and Vibration 211, 301–322, Section 1. Allemang R.J., 2002. The Modal Assurance Criterion MAC: twenty years of use and abuse. IMAC. Allemang R.J., Phillips A.W., 2004. The unified matrix polynomial approach to understanding modal parameter estimation: an update, in Proceedings of the International Seminar on Modal Analysis ISMA, Leuven. Auweraer H., Van Der, 2002. Testing in the Age of Virtual Prototyping. Proceedings of International Conference on Structural Dynamics Modelling, Funchal, 2002, Section 1. Baruch M., Bar-Itzhack I.Y., 1978. Optimal weighted orthogonalization of measured modes. AIAA Journal, 16, 4: 346-351. Bayer V., Dorka U.E., Fulekrug U., Gschwilm J., 2005. On real-time pseudo-dynamic substructure testing: algorithm, numerical and experimental results. Aerospace science an Technology, 9:223-232. Bellizzi S., Defilippi M., 2003. Non-linear mechanical systems identification using linear systems with random parameters. Mechanical Systems and Signal Processing, 17: 203– 210. Benhafsi Y., Penny J.E., Friswell M.I., 1992. A parameter identification method for discrete nonlinear systems incorporating cubic stiffness elements. International Journal of Analytical and Experimental Modal Analysis, 7: 179–195. Benedettini F., Capecchi D., Vestroni F., 1995. Identification of hysteretic oscillators under earthquake loading by nonparametric models. J. Engrg. Mech., 121: 606-612. Berg J.S., Zhang Q., Ljung L., Beneviste A., Delyon B., Glorennec P.Y., Hjalmarsson H., Juditsky A., 1995. Nonlinear black-box modelling in system identification: a unified 60

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development overview. Automatica, 31: 1691–1724. Berman A., Nagy E.J., 1983. Improvement of large analytical model using test data. AIAA Journal, 21, 8: 1168-1173. Billings S.A., Jamaluddin H.B., Chen S., 1991. Properties of neural networks with applications to modelling non-linear dynamical systems. International Journal of Control, 55: 193–224. Blakeborough A., et al. 2001. The development of real-time substructure testing. Philosophical Transactions of the Royal Society of London A 359:1869-1891. Bonato P., Ceravolo R., Stefano A. De, 1997. Time-Frequency and Ambiguity Function Approaches in Structural Identification. Journal of Engineering Mechanics ASCE, Vol. 123, No. 12, pp.1260-1267. Bonato P., Ceravolo R., Stefano A.De, Knaflitz M., 1997. Bilinear time-Frequency transformations in the analysis of damaged structures. Mechanical Systems and Signal Processing, 11: 509-527. Bonelli A., Bursi O.S., 2004. Generalized-  methods for seismic structural testing. Earthquake Engng Struct. Dyn, 33: 1067-1102. Bouc R., 1971. Modele mathematique d’hysteresis. Acustica 1971, 24: 16-25. Brincker R., Moller N. eds 2007. Proceedings of the 2nd International Operational Modal Analysis Conference. IOMAC, Copenhagen. Brownjohn J.M.W., Lee J., Cheong B., 1999. Dynamic performance of a curved cable-stayed bridge. Engineering structures, n. 21: 1015-1027. Bursi O.S. Ceravolo, R. Demarie, G.V. Erlicher, S., 2009. Molinari, M. Zanotti Fragonara, L. 2009. Identification of the Damage Evolution in a Benchmark SteelConcrete Composite Structure during Pseudo-dynamic Testing. Proc. of Compdyn 2009, Rhodes, 22-24 June, CD-ROM paper n.324, Rhodes, Greece. Bursi O.S., Ceravolo R., Erlicher S., Fragonara L.Z., 2012. Identification of the Hysteretic Behaviour of a Partial-strength Steel-concrete Moment-resisting Frame Structure Subject to Pseudodynamic tests. Earthquake Engng Struct. Dyn, DOI 10.1002/eqe. 2163. Caesar B., 1986. Update and identification of dynamic mathematical models. IMAC IV, 394-401. Casciati, F., 1989. Stochastic dynamics of hysteretic media. Struct. Safety, 6: 259-269. Caughey T.K., 1959. Equivalent linearisation techniques. Journal of the Acoustical Society of America, 35, 1963, 1706–1711. Ceravolo R., 2004. Use of instantaneous estimators for the evaluation of structural damping. J. Sound Vib., 2741-2, 385-401. 61


Ceravolo R., Demarie G.V., Erlicher S., 2007. Instantaneous Identification of Bouc-Wen-type Hysteretic Systems from Seismic Response Data. Key Eng. Mater., 347: 331-338. Ceravolo, R., 2009. Time-frequency analysis. In: Boller, C., Chang, F.-K. and Fujino, Y. (eds), Encyclopedia of Structural Health Monitoring, pp. 503–524, Chichester, UK: John Wiley & Sons Ceravolo R., Demarie G.V., Erlicher S., 2010. Instantaneous identification of degrading hysteretic oscillators under earthquake excitation. Struct. Health Monitor, 9(5):447 –464. Ceravolo R., Fragonara L.Z., Erlicher S., Bursi O.S., 2011. Parametric Identification of Damaged Dynamic Systems with Hysteresis and Slip. 9th International Conference on Damage Assessment of Structures. Chassiakos A.G., Masri S.F., 1996. Modelling unknown structural systems through the use of neural networks. Earthquake Engineering and Structural Dynamics, 25: 117–128. Cheng C.C., Chen C.Y., 1999. A PID Approachto Suppressing Stick-slip in the Positioning of Transmission Mechanisms. Control Engineering Practice, vol. 6, no. 2, 471-479. Christodoulou K., Ntotsios E., Papdimitriou C., Panetsos P., 2008. Structural model updating and prediction variability using Pareto optimal models. Computer Methods in Applied Mechanics and Engineering, 198: 138-149. Craig R.R., Bampton M.C.C., 1968. Coupling of Substructures for Dynamic Analysis, AIAA Journal, Vo1.6, (7). Cunha A., Caetano E., eds 2007. Proc. of the experimental vibration analysis for civil engineering structures. EVACES07 conference, FEUP, Porto. Dack T.B., Hoffmeistert F., Schwefel H.P., 1991. A survey of evolutionary strategies. Proceeding of the international conference of Genetic Algorithms, San Diego. Deblauwe F., Allemang R.J., 1985. The polyreference time domain technique. Proceedings of the 10th International Seminar on Modal Analysis, Part IV, Katholieke Universiteit Leuven Belgium. DeGrassi G., Nie J., Hofmayer C., 2008. Seismic Analysis of Large-Scale Piping Systems for the JNES-NUPEC Ultimate Strength Piping Test Program U.S. NRC. NUREG/CR-6983, BNL-NUREG-81548-2008. Demarie G.V., Ceravolo R., De Stefano A., 2005. Instantaneous identification of polynomial nonlinearity based on Volterra series representation. Key Engineering Materials, 293-294, 703-710. Du X., Wang F., 2009. New modal identification method under the non-stationary Gaussian ambient excitation. Appl. Math. Mech. 3010, 1295–1304.

62

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Dyke S.J., Spencer B.F., Sain Jr.M.K., Carlson J.D., 1996. Modeling and Control of Magnetorheological dampers for Seismic Response Reduction. Smart Mater. Struct., 5-565. Er M.J., Lee S.C., Tan L.L., 1996. Digital-signal-processor Based Multirate PID Control of a Two-link Flexible-Joint Robot. Proc. Of the IEEE TENCON. Digital Signal Processing Application, vol. 2, 900-905. Erlicher S., Argoul P., 2007. Modal identification of linear non-proportionally damped systems by wavelet transform. Mechanical Systems and Signal Processing 21:1386–1421. Erlicher S., Bursi O.S., 2008. Bouc-Wen-type Models with Stiffness Degradation: Thermodynamic Analysis and Applications. J. Engrg. Mech., 13410: 843-855. Erlicher S., Point N., 2008. Pseudopotentials and Loading Surfaces for an Endochronic Plasticity Theory with Isotropic Damage. J. Eng. Mech., 134(10): 832-842. Ewins D.J., 2000. Modal testing. Research Studies Press LTD. Fan Y., Li C.J., 2002. Non-linear system identification using lumped parameter models with embedded feedforward neural networks. Mechanical Systems and Signal Processing 16: 357–372. Fassois S.D., Lee J.E., 1993. On the problem of stochastic experimental modal analysis based on multiple-response data, Part II: the modal analysis approach. J. Sound Vib., 1611: 57-87. Felber A.J., Ventura C.E., 1996. Frequency Domain Analysis of the Ambient Vibration Data of the Queensborough Bridge Main Span. 14th International Modal Analysis Conference, Dearborn, Michigan, February 12-15. Feldman M., 1994. Nonlinear system vibration analysis using the Hilbert transform-I. Free vibration analysis method ‘FREEVIB’. Mechanical Systems and Signal Processing 8: 119-127. Feldman M., 1994. Nonlinear system vibration analysis using the Hilbert transform-I. Forced vibration analysis method ‘FORCEVIB’. Mechanical Systems and Signal Processing 8: 309-318. Feldman M., Braun S., 1995. Identification of non-linear system parameters via the instantaneous frequency: application of the Hilbert transform and Wigner-Ville technique. Proceedings of the 13th International Modal Analysis Conference, Nashville, 637–642. Foliente G.C., 1995. Hysteresis modeling of wood joints and structural systems. J. Struct. Engrg., 1216: 1013-1022. Footdale J.N., 2008. Multi-Axis Real-Time Hybrid Testing for Precision Aerospace Structures. PhD Dissertation, University Of Colorado At Boulder, USA. Friswell M.I., Mottershead J.E., 1995. Finite Element Model Updating in Structural Dynamics. 63

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Kluwer Academic Publishers. Gladwell G.M.L., 1986. Inverse Problems in Vibration. Dordrecht: Springer. Ghanem R., Shinozuka M., 1995. Structural-System Identification: Theory. Journal of Engineering Mechanics, ASCE, 121, 255-264. Giraldo D.F., Song W., Dyke S.J., Caicedo J.M., 2009. Modal Identification through Ambient Vibration: Comparative Study. Journal of Engineering Mechanics 135: 759-770. ISSN: 0733-9399. American Society of Civil Engineers. Goller B., Padlwarter H.J., G.I. 2009. Schueller. Robust model updating with insufficient data. Computer methods in applied Mechanics and Engineering 198: 3096-3104. Govers Y., Link M., 2009. Stochastic model updating Covariance matrix adjustment from uncertain experimental modal data. Mechanical Systems and Signal Processing. Gresnigt A.M., Varelis G.E., Karamanos S. A., 2012. Pipe Elbows under Strong Cyclic Loading. Proceedings of the ASME 2012 Pressure Vessels & Piping Division Conference PVP2012, July 15-19, 2012, Toronto, Ontario, CANADA. Guyan R., 1965. Reduction of Stiffness and Mass Matrices. AIAA Journal 3, n. 2: 380. Hammond J.K., White P.R., 1996. The analysis of non-stationary signals using time–frequency methods. Journal of Sound and Vibration 190: 419–447. Hammond J.K, Waters T.P., 2001. Signal processing for experimental modal analysis. Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 359:41–59. Hasselman T.K., Anderson M.C., Gan W.G., 1988. Principal component analysis for nonlinear model correlation. Proceedings of the 16th International Modal Analysis Conference, Santa Barbara, pp. 644–651. Hagedorn P., Wallaschek J., 1987. On equivalent harmonic and stochastic linearization. Proceedings of the IUTAM Symposium on Nonlinear Stochastic Dynamic Engineering Systems, Berlin, pp. 23–32. Hemez F.M., Doebling S.W., 2001. Review and assessment of model updating for non-linear, transient dynamics. Mechanical Systems and Signal Processing, 15: 45–74. Heylen W., Lammens S., Sas P., 1997. Modal Analysis Theory and Testing. KUL Press, Leuven, Sections 1, 3.4. Hibbit, H.D., Karlsson, B.I., Sorensen, 2003. Theory Manual, ABAQUS, version 6.3, Providence, RI. USA. Horiuchi T., Inoue M., Konno T., Namita Y.. Real-time Hybrid Experimental System with Actuator Delay Compensation and its Application to a Piping System with Energy 64

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Absorber. Earthquake Engineering & Structural Dynamics, 1999; 28(10): p. 1121-1141. Huang N.E., Shen Z., Long S.R., Wu M.C., Shih H.H., Zheng Q., Yen N.C., Tung C.C., Liu H.H., 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London Series A-Mathematical, Physical and Engineering Sciences 454: 903–995. Hunag L., Ge S.S., Lee T.H., 2006. Position/force of Uncertain Constrained Flexible joint Robots. Mechatronics, vol. 16, 111-120. Ider S.K., 1999. Inverse Dynamics Control of Constrained Robots in the Presence of Joint Flexibility. Journal of Sound and Vibraion, vol. 224, no. 5, 879-895. Ibrahim S.R., Mikulcik E.C., 1977. A Method for the direct identification of vibration parameters from the free response. The Shock and Vibration Bulletin, 474, 183-198. Ikhouane F., Mañosa V., Rodellar J., 2007. Dynamic properties of the hysteretic Bouc-Wen model. Systems & Control Letters, 563: 197-205. James G.H., Carne G.T., Lauffer J.P., 1995. The natural excitation tecnique NexT for modal parameter extraction from operating structures. Modal Analysis, 10, 260-277. Johnson D.S., Aragon C.R., Schevon L.A., 1989. Optimization by Simulated Annealing: an Experimental evaluation. Graph Partitioning, 365-392. Juang J.N., Pappa R.S., 1984. An eigensystem realisation algorithm ERA for modal parameter identification and modal reduction. NASA/JPL Workshop on Identification and Control of Flexible Space Structures. Juditsky A., Hjalmarsson H., Beneviste A., Delyon B., Ljung L., Berg J.S., Zhang Q., 2005. Nonlinear black-box models in system identification: mathematical foundations. Automatica, 31, 1725–1750. Karamanos S. A., Varelis G. E. and Pappa P.. 2011. Finite Element Analysis of Industrial Steel Elbows Under Strong Cyclic Loading. Pressure Vessel and Piping Conference, ASME, PVP2011, Baltimore, Maryland, July 2011 Kim S.B., Powers E.J., 1993. Frequency-domain Volterra kernel estimation via higher-order statistical signal processing. IEEE Transactions on Signal Processing, 446-450. Kirkpatrick S., Gelatt C.D., Vecchi M.P., 1983. Optimization by Simulated Annealing. Science 1, n. 220: 671-680. Kosmatopoulos E.B., Smyth A.W., Masri S.F., Chassiakos A.G., 2001. Robust adaptive neural estimation of restoring forces in nonlinear structures. Journal of Applied Mechanics 68, 880–893. Koukoulas P., Kalouptsidis N., 2000. Second-Order Volterra system identification. IEEE Trans. 65

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development on Signal Processing, 48: 3574-3577. Kovotovic P.V., Khalil H.K., O’Reolly J.., 1986. Singular Perturbation Method in Control: Analysis and Design. Academic Press, New York. Kyprianou A., Worden K., Panet M., 2001. Identification of hysteretic systems using differential evolution algorithm. J Sound Vib, 2482: 289-314. Lanese, I., 2012. Development and Implementation of an Integrated Architecture for Real-Time Dynamic Hybrid Testing in the Simulation of Seismic Isolated Structures. PhD thesis, ROSE Programme, UME School, IUSS Pavia, Italy, 2012. Leontaritis I.J., Billings S.A., 1985. Input-output parametric models for nonlinear systems, part I: deterministic nonlinear systems. International Journal of Control 41:303–328. Leontaritis I.J., Billings S.A., 1985. Input-output parametric models for nonlinear systems, part II: stochastic nonlinear systems. International Journal of Control 41:329–344. Lew, J.S., Juang, J.N., Longman R.W., 1993. Comparison of several system identification methods for flexible structures. J. Sound Vib., 1673, 461-480. Li S.J., Suzuki Y., Noori M., 2004. Identification of Non-linear Hysteretic Systems with Slip Using bootstrap Filter. Mechanical Systems and Signal Processing, vol. 18: 781-795. Liang Y.C., Feng D.P., 2001. Cooper J.E., Identification of restoring forces in non-linear vibration systems using fuzzy adaptive neural networks. Journal of Sound and Vibration 242: 47–58. Ljung L., 1999. System identification theory. Prentice Hall. Loh C.H., Lin C.Y., Huang C.C., 2000. Time domain identification of frames under earthquake loadings. J. Eng. Mech. ASCE, 1267, 693-703. Maia N.M.M., Silva J.M.M., 1997. Theoretical and Experimental Modal Analysis, Research Studies Press LTD, Taunton, Sections 1, 3, 4. Maia, N.M.M., and Silva, J.M.M. 1998. Theoretical and Experimental Modal Analysis. Research Studies Press LTD. Mares C., Mottershead J.E., Friswell M.I., 2006. Stochastic model updating: Part 1 theory and simulated example. Mechanical Systems and Signal Processing, 1074-1095. Masri S.F., Sassi H., Caughey T.K., 1982. Nonparametric identification of early arbitrary nonlinear system. J.Appl. Mech. ASME, 49: 619-628. Masri S.F., Caffrey J.P., Caughey T.K., Smyth A.W., Chassiakos A.G., 2004. Identification of the state equation in complex non-linear systems. Int. J. Nonlin. Mech., 39: 1111-1127

66

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development McAskill B., Dunford W.G., 1988. Self-tuning Pole Placement control of a Manipulator with flexible Jiont. Proc. Of the 19th Annual IEEE Power Electronics Specialists Conference, vol. 1, 445-451. Meyer S., Weiland M., Link M., 2003. Modelling and updating of local non-linearities using frequency response residuals. Mechanical Systems and Signal Processing 17: 219–226. Minas C., Inman D., 1988. Correcting finite element models with measured modal results using eigenstructure assignment methods. International Modal Analysis Conference, Kissimmee, 583-587. Molina F.J., Pegon P., Verzeletti G.. Time-Domain Identification from Seismic Pseudodynamic Test Results on Civil Engineering Specimens, Proceedings of the Second International Conference on Identification of Engineering Systems, Swansea, March 1999. Natke H.G., Yao J.T.P., 1986. Research topics in structural identification. Proc., 3rd Conf. On Dyn. Response of Struct., American Society of Civil Engineers ASCE, New York, 542550. Natke, H.G., Tomlinson, G.R., Yao, J.T., 1993. Safety Evaluation Based on Identification Approaches. Vieweg & Sohn, Braunschweig/Wiesbaden. Nayfeh A.H., 1981. Introduction to Perturbation Techniques, Wiley-Interscience, New York. Nayyar M.L., 2007. Piping Handbook. McGraw Hill, New York. Newland D.E., 1999. Ridge and phase identification in the frequency analysis of transient signals by harmonic wavelets. Journal of Vibration and Acoustics, 121:149–155. O'Callahan J., 1989. A new procedure for and Improved Reduced System IRS. IMAC VII. Las Vegas. O'Callahan J., Avitabile P., Riemer R., 1989. System Equivalent Reduction Expansion Process SEREP. IMAC VII. Las Vegas. Ortega R., Spong M.W., 1989. Adaptive Motion Control of Rigid Robots. A tutorial, Automatica, vol.25, 877-888. Ortize G.A., Alvarez D.A., Bedoya-Ruiz D., 2013. Identification of Bouc-Wen Type Models Using Multi-objective Optimization Algorithms. Computers and Structures, 121-132. Ozer M.E., Ven H.N., Ozgu¨ T.J., Royston, 2005. Identification of structural non-linearities using describing functions and Sherman–Morrison method. Proceedings of the 23rd International Modal Analysis Conference, Orlando. Ozcelik O., Conte J.P., Luco J.E., 2006. Virtual Model of the UCSD_NEES High Performance Outdoor Shake Table. 4th World Conference on Structural Control and Monitoring, 4WCSCM-285. 67


Ozcelik O., Luco J.E., Conte1 J.P., Trombetti T.L., Restrepo J.I., 2007. Experimental characterization, modeling and identification of the NEES-UCSD shake table mechanical system, Earthquake Engng Struct. Dyn., 37:243–264. Ozcelik O., Luco J.E., Conte J.P., 2008. Identification of the Mechanical Subsystem of the NEES-UCSD Shake Table by a Least-Squares Approach. Journal of Engineering Mechanics, Vol. 134, No. 1. Ozcelik O., Luco J.E., Conte J.P., 2008. Identification of the Mechanical Subsystem of the NEES-UCSD Shake Table by a Least-Squares Approach. Journal of Engineering Mechanics, Vol. 134, No. 1, 23-34. Peeters B., DeRoeck G., 1999. Reference-based stochastic subspace identification for outputonly modal analysis. Mech. Sys. Sig. Proc. 13, 855-878. Pei J.S., Smyth A.W., Kosmatopoulos E., 2004. Analysis and modification of Volterra/Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems. J. Sound Vib., 275: 693-718. Poulimenos A.G., Fassois S.D., 2008. Output-only stochastic identification of a time-varying experimental structure via functional series TARMA models. Mechanical Systems and Signal Processing, 234: 1180–1204. Priestley M.B., 1967. Power spectral analysis of nonstationary processes, Journal of Sound and Vibration 6: 86–97. Ravn Ole, 2000. On-line system identification and adaptive control using the adaptive blockset. Proceeding of the 12th IFAC Symposium on System Identification SYSID, Santa Barbara, CA, USA. Reynders E., Pintelon R., De Roeck G., 2008. Uncertainty bounds on modal parameters obtained from stochastic subspace identification. Mechanical Systems and Signal Processing 22:948-969. ISSN: 0888-3270. Elsevier. Riche R.L., Gualandris D., 2001. Thomas J.J., Hemez F.M., 2001. Neural identification of nonlinear dynamic structures. Journal of Sound and Vibration 248, 247–265. Roberts J.B., Spanos P.D., 1990. Random Vibrations and Statistical Linearization. Wiley, New York. Rosenberg R.M., On nonlinear vibrations of systems with many degrees of freedom, Advances in Applied Mechanics 9 1966 155–242. Saadat S., Buckner G.D., Furukawa T., Noori M.N., 2004. An intelligent parameter varying IPV approach for non-linear system identification of base excited structures. Int. J. Nonlin. Mech., 39: 993-1004.

68

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Safak E, Celebi M., 1991. Seismic response of Transamerica building. II: System-identification, Journal of Structural Engineering, ASCE., 1178, 2405-2425. SAP2000, 2004. Linear and Nonlinear Static and Dynamic Analysis and Design of ThreeDimensional Structures, v9, Computers and Structures, Inc. Berkeley, California, USA. Saravanakumar G., WahidhaBanu R.S.D., 2006. An adaptive controller based on system identification for plants with uncertainties using well known tuning formulas. ACSE Journal, Volume (6), Issue (3), Oct. Sarkka

S., 2011. EKF/UKF toolbox http://becs.aalto.fi/en/research/bayes/ekfukf/

for

Matlab.

[online]

Available:

Shinozuka M., Yum C.B., Imai H., 1982. Identification of linear structural dynamic systems. J. Engrg. Mech. Div., ASCE, 1086, 1371-1390. Sivaselvan M.V., Reinhorn A.M., 2000. Hysteretic Models for Deteriorating Inelastic Structures. Journal of Engineering Mechanics, June 2000: 633-640.20 Smyth A.W., Masri S.F., Kosmatopoulos E., Chassiakos, A.G., Caughey T.K., 2002. Development of adaptive modelling techniques for non-linear hysteretic systems. Int. J. Nonlin. Mech., 37: 1435-1451. Soderstrom T., Stoica P., 1989. System Identification, Prentice-Hall, Englewood Cliffs, Section 1. Song Y., Hartwigsen C.J., McFarland D.M., Vakakis A.F., Bergman L.A., 2004. Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements. Journal of Sound and Vibration 273: 249–276. Spencer B.F., Dyke Jr., Sain S., Carlson M., 2007. Phenomenological Model for MagnetoRheological Dampers. J. Eng. Mech., 123(3), 230-238. Spina D., Valente C., Tomlinson G.R., 1996. A new procedure for detecting nonlinearity from transient data using Gabor transform. Nonlinear Dynamics, 11: 235–254. Srinivas M., Patnaik L.M., 1994. Genetic algorithms: a survey. IEEE Computer Magazines: 1724. Staszewski W.J., 2000. Analysis of non-linear systems using wavelets, Proceedings of the Institution of Mechanical Engineers Part C—Journal of Mechanical Engineering Science 214: 1339-1353. Suzuki K., Abe H., 2005. Seismic Proving Test of Ultimate Piping Strength. PVP2005- 71005, ASME PVP Conference, Denver, CO. Tick L.J., 1961. The estimation of transfer functions of quadratic system. Technometrics, 3, 563567.

69

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Vakakis A.F., 1997. Non-linear normal modes and their applications in vibration theory: an overview. Mechanical Systems and Signal Processing, 11: 3–22. Van O.P., De M.B., 1996. Subspace identification for linear systems: theory implementation applications. Kluwer Academic Press Dordrecht The Netherlands. Vold H., Kundrat J., Rocklin G.T., Russell R., 1982. A multi-input modal estimation algorithm for mini-computers. SAE Paper Number 820194. Wang L., Zhang J., Wang C., Hu S., 2003. Time-frequency analysis of nonlinear systems: the skeleton linear model and the skeleton curves. Journal of Vibration and Acoustics 125: 170–177. Wei F.S., 1990. Structural dynamic model improvement using vibration test data. AIAA Journal 28, 175-177. Wen Y.K., 1976. Method for Random Vibration of Hysteretic Systems. Journal of the Engineering Mechanics Division, vol. 102, No. 2, 249-263. Williams M.S., 2007. Real-time Hybrid Testing in Structural Dynamics. Proceedings of the 5th Australasian Congress on Applied Mechanics, Brisbane, Australia, 2007. Wittrick W.H., 1962. Rates of change of eigenvalues with reference to buckling and vibration problems. Journal of the Royal Aeronautical Society, 66 : 590-591. Worden K., Tomlinson G.R., 2001. Nonlinearity in experimental modal analysis. Phil. Trans. R. Soc. Lond., 359 1778 113-130; 1471-2962. Wu M., Smyth A.W., 2008. Application of the unscented Kalman filter for real-time nonlinear structural system identification. Structural Control and Health Monitoring. Vol. 147: 971990. Xiong Y., Chen W., Tsui K.L., Apley D.W., 2009. A better understanding of model updating strategies in validating engineering models. Computer methods in applied mechanics and engineering, 1327-1337. Yao B., Almajed M., Tomizuka M., 1997. High Performance Robust Motion Control of Machine Tools: An Adaptive Robust Control Approach and Comparative Experiments. IEEE/ASME Trans. On Mechantronics, vol. 2, no. 2 62-67. Yang J.N., Lei Y., Pan S.W., Huang N., 2003. System identification of linear structures based on Hilbert–Huang spectral analysis; Part 1: Normal modes. Earthquake Engineering and Structural Dynamics 32: 1443–1467. Yang J.N., Lei Y., Pan S.W., Huang N., 2003. System identification of linear structures based on Hilbert–Huang spectral analysis; Part 2: Complex modes. Earthquake Engineering and Structural Dynamics 32 2003 1533–1554.

70

D13.3 ‒ Integration of modeling tools with test equipment and virtual model development Yang J.N., Lin S., 2004. Hilbert–Huang based approach for structural damage detection, Journal of Engineering Mechanics 13085–95. Yasuda K., Kawamura S., Watanabe K., 1988. Identification of nonlinear multi-degree-offreedom systems presentation of an identification technique. JSME International Journal Series III 31, 8–14. Yuen K.V., Beck J.L., Katafygiotis L.S., 2002. Probabilistic approach for modal identification using non-stationary noisy response measurements only. Earth. Eng. Struc. Dyn., 314, 1007-1023. Zeiger H.P., McEwen A.J., 1974. Approximate linear realisations of given dimension via Ho's algorithm. IEEE Transactions on Automatic Control, AC-19-2, 153. Zhang N., 1995. Dynamic condensation of mass and stiffness matrices. Journal of Sound and Vibration 188, n. 4: 601-615. Zhang Q.W., Chang T.Y.P., Chang C.C., 2001. Finite element model updating for the Kap Shui Mun cable-stayed bridge. Journal Bridge Engineering, n. 6: 285.

71

Report on integration of modelling tools with test ... - SERIES

Report on integration of modelling tools with test ... - SERIES

Suggest Documents

Internship Report Financial time series modelling with

Econometric Modelling with Time Series

Numerical modelling of dynamic spalling test on rock with an ...

Survey on Integration of Expetise Competency Test

Integration with Other Tools - Packt Publishing

Integration with Other Tools - Packt Publishing

Group-oriented Modelling Tools with Heterogeneous ... - CiteSeerX

Teaching Physics Modelling with Graphic Simulations Tools

Financial Time Series Modelling with Hybrid Model Based on ...

Econometric Modelling with Time Series

Econometric Modelling with Time Series

inflation targeting with dynamic time series modelling

On Diagnostic Checking Time Series Models with Portmanteau Test ...

Report on Europe - Archive of European Integration

Report on Europe - Archive of European Integration

Integration of EPC-related Tools with ProM - Institute of Information

Integration of heuristic knowledge with analytical tools ...

Report on the interactions with the Green-X modelling team ...

Integration of external tools with GLUE! in LAMS - 2011 International ...

ScopeMeter® Test Tools

Report of Earth Physical Parameters Test on

Modelling Opinion Formation with Physics Tools - Journal of Artificial ...

Modelling Opinion Formation with Physics Tools - Journal of Artificial

Security Report with FOOTNOTES - ICC Legal Tools