Structural Health Monitoring of Four-Story Benchmark

Structural Health Monitoring of Four-Story Benchmark Structure by Wireless Smart Sensor Network Considering Time Synchronization Touraj Taghikhany1, Mohsen Tehranizadeh2 , Nastaran Dabiran3 and Abouzar Dolati4 1

Assistant Professor, Civil Engineering, Amirkabir University of Technology, Tehran, Iran, [email protected] 2

Professor, Civil Engineering, Amirkabir University of Technology, Tehran, Iran, [email protected]

3

MSc student, Civil Engineering, Amirkabir University of Technology, Tehran, Iran, [email protected] 4

PhD student, Civil Engineering, Sharif University of Technology, Tehran, Iran, [email protected]

Abstract Structural health monitoring (SHM) is an emerging field in civil engineering, offering the potential for continuous and periodic assessment of the safety of civil structures; and therefore industrialized nations have an intense exertion in this field, on which our lives rely. SHM of civil engineering structures faces with many impediments on installation and maintenance of wired systems. However, wireless smart sensor network (WSSN) can effectively remove the disadvantages associated with current wire-based sensing systems. WSSN recorded data sets may have relative time-delays due to interference in radio transmission or inherent internal sensor clock errors. For structural system identification and damage detection purposes, sensor data require that they are time synchronized. In this study, the application of auto-regressive moving average vector (ARMAV) for measurement data synchronization is investigated. As the structure is excited by ambient excitation, where the excitation cannot be measured, ARMAV models constructed from output signals and the time-delay between them is evaluated. Results from the identification of structural modal parameters show that frequencies and damping ratios are not influenced by the asynchronous data; however, the error in identifying structural mode shapes can be significant. The introduced method also allows the estimation of modal parameter uncertainties. Based on these uncertainties, a statistically based damage detection scheme is performed and it becomes possible to assess whether changes of modal parameters are caused by, e.g. some damage or simply by estimation inaccuracies. Keywords: System Identification; Structural Health Monitoring; Synchronization; Wireless smart sensor network (WSSN); ARMAV. 1

2nd International Conference on Acoustics & Vibration (ISAV2012), Tehran, Iran, 26-27 Dec. 2012

1. Introduction Civil engineering structures such as bridges and high-rise building sustains a crucial role in human’s life. The failure of any one of these structures can significantly affect the economy of a region or a country. Currently the prevailing method for structural evaluation is simple visual inspection. However, these conventional techniques are not able to achieve a high level of reliability or efficiency. Moreover, drawbacks such as inspector workload, visual acuity, light intensity, perceptions of maintenance, and complexity resulted in significant variability in these routine visual inspections. Therefore, there exists a clear need to monitor the performance of civil structures over their operational lives. Structural Health Monitoring (SHM) system is fulfilled this requirement. Current wirebased sensing systems suffer from high installation and upkeep costs, which limit widespread adoption. In response to the technological and economic limitations of present commercial monitoring systems, a novel wireless module monitoring system was proposed for the health monitoring of civil structures. It provides a high-performance yet low-cost data acquisition technique for structural health monitoring. When wireless sensing units record measurements independently, recorded data sets may exist with relative time-delays due to blockage of sensors or inherent internal clock errors or radio transmission. Thus, it is necessary to perform time synchronization among these recordings for the purpose of accurate structural identification and damage detection. Time synchronization of signals has been developed for other applications by Kozek and Cusani, but not for wireless structural health monitoring purposes. In this paper, an algorithm is developed that can be used for synchronizing data in wireless sensor networks. To provide an accurate estimate of structural damage, the reliable identification of modal properties is a prerequisite. Although forced vibrations provide accurate quantitative modal information, the use of ambient loading constitutes an attractive alternative in terms of cost and simplicity. The autoregressive moving average vector (ARMAV) technique is one of the most promising techniques to make use of ambient vibration data [1]. By means of ARMAV technique, modal analysis can be conducted for structures under unknown excitation forces, presumed to be random, such as wind gusts and traffic loads, which allow the fully automated real-time monitoring of the structure under in-service damage assessment [2]. The purpose of this paper is to present introductory results regarding the modal identification of the Four-Story Benchmark Structure considering time synchronization, which instrumented by Wireless Smart Sensor Network and excited by ambient excitation. This benchmark proposed by the ASCE Task Group on structural health monitoring as shown in Figure 1. The implementation of the ARMAV approach is considered by examining the accuracy of the results using various orders of models. The results demonstrate that this approach is promising for automated modal identification of this structure.

2. Description of the Benchmark and Instrumentation A 4-story two-bay by two-bay shear building under ambient excitation is considered to demonstrate the application of the proposed algorithm. The Benchmark designed by ASCE Task Group at the University of British Columbia, Canada (UBC). The structure has dimension of 2.5X2.5 m in plan and height of 3.6 m. The sections are designed for a scale model, with properties as given in Table.1[3].The excitation is wind which loading at each floor in the y-direction as shown in Fig. 1. Wireless Smart Sensor Network (WSSN), has four wireless sensors in each floor that recorded output data [3].The MATLAB program was provided by the ASCE Task Group [3] generates the input and output sampling data with time interval equal to 0.001s. It is assumed that the measured acceleration from the wireless sensing unit at the first, second and third floor have time delay relative to acceleration response of the fourth floor.

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3. Modal Identification Technique 3.1. The auto-regressive moving average vector model Although several algorithms, such as ARX, ARMAX, ARMAV and … have been proposed to implement modal identification, in current studies ARMAV model has become a modulus apparatus in both system description and control design. Table 1. Properties of Structural Members Property Section type Cross-sectional area A (m2) Moment of inertia (strong direction) Iy (m4) Moment of inertia (weak direction) Iz (m4) St. Venant torsion constant J (m4) Young’s modulus E (Pa) Shear modulus G (Pa) Mass per unit volume (kg/m3)

Columns

Floor Beam

Braces

Fig. 1- Diagram of model (The wi are excitations and the ̈ are accelerometer measurements) [3]

After extensive evaluation, Auto-regressive moving average vector (ARMAV) model was applied for analysis of ambient excitation of multi-DOF’s systems. This model only uses time series obtained from output signals of the system. It can be shown that the ARMAV model allows us to describe dynamic of structure subjected to filtered white noise. The parametric ARMAV(p,q) model is described by the matrix equation (3-1) for a m-dimensional time series output y[n] and the time sampling interval of t [4]. [ ]

∑

[

]

[ ]

∑

[

]

(3-1)

3

2nd International Conference on Acoustics & Vibration (ISAV2012), Tehran, Iran, 26-27 Dec. 2012 Where, u[n] is a stationary zero-mean Gaussian white noise process, ak and bk are matrices of AR (auto-regressive) and MA (moving-average) coefficients, respectively. The AR part of order, p, describes the system dynamics while the MA part of order, q, is related to the external noise as well as to the white noise excitation. In this linear parametric model, the system output y[n] is supposed to be produced by a stationary Gaussian white noise input u[n]. In the state space, the ARMAV model can be demonstrated through equations (3-2) and (3-3). Where C is the observation matrix, A is a matrix containing the different coefficients of the auto-regressive part while [ ] includes the moving-average terms of the ARMAV model [4]. [ ]

[ [ ]

]

[ ]

(3-2)

[ ]

(3-3)

Parameters of the model are estimated by the prediction error method. The vector θ is defined as equation (3-4) [

]

(3-4)

As the systems are stochastic the output y[n] at time tn cannot be determined exactly from data available at time tn−1. Therefore ̂ [ ] is defined, the one-step ahead predicted system response at time tn based on parameter θ and on the available data for tn−1 [5] ̂[

]

[

∑

]

∑

[

]

(3-5)

The variable ε[n|θ] is the prediction error and is defined as [

]

[ ]

]

̂[

(3-6)

The variable ε[n|θ] thus represents the part of the output y[n] that cannot be predicted from the past data. [

[

]

(3-7)

]

(3-8)

Let us define L, the matrix formed with the eigenvectors of A positioned as columns. The complex mode shapes stocked in matrix Φ are extracted from the matrix L as (3-9)

4. Time Synchronization Algorithm for Output Recordings of the Benchmark When a structure is subject to ambient excitation, the inputs to the structures cannot be measured; therefore ARMAV models have been applied for system identification of these structures that use a time series of output signals and the excitation is assumed to be stationary Gaussian white noise. Typically, the recorded data set by wireless sensing units instrumented at different locations of the structure have relative time-delays due to interference in radio transmission or inherent internal sensor clock errors. For structural system identification and damage detection purposes, sensor data 4

2nd International Conference on Acoustics & Vibration (ISAV2012), Tehran, Iran, 26-27 Dec. 2012 require that they are time synchronized. A time synchronization algorithm for output signals based on the ARMAV models is performed. For this purpose one of the measured output signals yr is chosen as the reference signal. The remaining measured acceleration responses have time-delays in recording data relative to the reference signal. Thus, the following asynchronous output data are recorded [6]. ̈(

) ̈( ̈(

) ̈( ) ̈(

)

) ̈(

)

̈(

̈(

)

) (4-1)

̈ (

)

̈ (

)

̈ (

)

̈ (

)

Where is the unknown time-delay of the recorded output ̈ relative to the reference signal ̈ . The values of the reference signal at shifted time instants are also evaluated by spline interpolation to yield the following data ̈(

) ̈(

) ̈(

)

̈(

)

(4-2)

Where is the value of the time shift. With different values of , a set of shifted reference signals is obtained. An ARMAV model can be constructed from a shifted reference signal and another output ̈ by [6] ̈[ ]

∑

̈[

]

[ ]

∑

[

]

(4-3)

As mentioned above the ARMAV models written in state space and parameters of the ARMAV models are estimated by the prediction error method. The vector is defined in (4-1). The prediction error vector ε[n|θ] of the ARMAV model under a given value of can be expressed as [6] [

̈[ ]

]

̂̈ [

]

(4-4)

With a given value of , ̂ can be obtained as the minimum point of a criterion function ( The criterion function ( ) is given as [7,4] (

)

{ ∑ [

] [

] }

The minimum value of the criterion function under a given value of ( )

(

)

).

(4-5) ,

is defined as [6] (4-6)

The variation of ( ) for a range of values is observed. The value of , which gives the minimum value of ( ), is taken as the estimated value of the time-delay in recording the selected output ̈ relative to the reference signal ̈ . Moreover for ARMAV model, the best model order is in general not known, and several criteria have been proposed to evaluate the best model order. Two of the most widely used techniques for selecting the order of a parametric model are Akaike’s final prediction error criterion (FPE) and Akaike’s information theoretic

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2nd International Conference on Acoustics & Vibration (ISAV2012), Tehran, Iran, 26-27 Dec. 2012 criterion (AIC) [8]. These criteria are based on monitoring the decrease in the criterion function V N(θ) as the order increases. The definition of VN(θ) is mentioned in (4-5).

5. Modal Identification of the Benchmark The identified modal parameters of the Benchmark discussed in this section. The first step of the identification procedure is the selection of the ARMAV model order. In order to validate the model order ARMAV(2,2) ,ARMAV(4,3) ,ARMAV(4,4), ARMAV(5,4) and ARMAV(6,6) were selected. As the results show, in compare with reported true mode shape in benchmark, the obtained results from model order ARMAV(6,6) gave the most accurate mode shapes. The four first mode shapes have been compared as follow.

 ARMAV (6,6)

1 1 1   1  0.911 0.292 0.585 1.464    0.694 0.708 0.813 1.222     0.383 0.984 0.864 0.449 

true

1 1 1   1 0.907 0.313 0.573 1.425    0.690 0.689 0.825 1.215     0.379 0.998 0.825 0.463

Fig (2), Fig (3) and Fig (4) show the precision of ARMAV(6,6), ARMAV(4,4) and ARMAV(4,3) relative to the true mode shapes of the benchmark. Comparison of the true and identified values of mode shapes shows that the identified mode shapes using the data synchronized by the proposed algorithm are in a good compliance with true structural data. The accuracy can be also observed in all three modes of frequency.

Fig (2): Comparing the first three mode shapes obtained from ARMAV(6,6) and true mode shapes of the structure (ARMAV(6,6):_ _ _ , true mode shapes:____)


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By selecting the model order ARMAV(6,6), the synchronization algorithm is used to estimate the noisy asynchronous data with time delay. In accordance with equation (4-2), at the minimum value of ( ) shows the accurate amount of relative time-delays. This value has been obtained by a recursive MATLAB code and verified above by the true mode shapes and frequencies of the structure.

(a)

(b)

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(c) Fig(5): Variation of errors: (a) ( ); (b) ( ); and (c) for the benchmark problem

( ) with

( ) is shown in Fig (5) and the time-delays have been estimated in recording of all stories’ output relative to the reference signal at fourth floor. As it shown in As a result of this program, the variation

this figure, the acceleration response of first, second and third floor relatively have time delays equal to 2.6, 1.5, 0.9 respectively.

6. Conclusion For structural system identification and damage detection purposes, wireless smart sensor network (WSSN) recorded data sets have relative time-delays due to time synchronizing. In this paper, a time synchronization algorithm is investigated to synchronize asynchronous recorded data for the purpose of accurate structural parameter identification and damage detection. As the structure is excited by ambient excitation, where the excitation cannot be measured, autoregressive moving average vector (ARMAV) algorithm was selected to determine the time-delay, in this study. First of all, the ARMAV(6,6) was determined as a most accurate order to estimate the time-delay and mode shapes. In order to verifying this statement, the mode shapes obtained from different order of ARMAV were compared with true mode shapes. Then the algorithm is implemented to estimates the time-delay by minimizing the model error associated with ARMAV. As mentioned above, the acceleration response of first, second and third floor relatively have time delays equal to 2.6, 1.5, 0.9 respectively. The obtained time delay from asynchronous data could be employed to accurate-

ly estimate the modal parameters and damage detection of structures which are using WSSN.

References 1. Giraldo, D.Caicedo, J.M.Song, W.Mogan, B., & Dyke, S.J, “Modal identification through ambient vibration: a comparative study”. Process of the 24th Intl. Modal Analysis Conf.St. Louis, Missouri. 2. W. Song, D. Giraldo, E.H. Clayton, S.J. Dyke, “Application of ARMAV for Modal Identification of the Emerson Bridge” 3. E.A. Johnson, A.M.ASCE, H.F.Lam, L.S. Katafygiotis, A.M.ASCE, and J. L. Beck, M.ASCE, “Phase I IASC-ASCE Structural Health Monitoring Benchmark Problem Using Simulated Data” 4. Piombo B, Giorcelli E, Garibaldi L and Fasana A, “Structures identification using ARMAV models”,Proc. IMAC1, Orlando, Florida, USA. 5. Ljung L, “System identification—Theory for the User”, Englewood Cliffs, NJ: Prentice-Hall. 6. Ying Lei, Anne S. Kiremidjian, K. Krishnan Nair, Jerome P. Lynch and Kincho H. Law, “Algorithms for time synchronization of wireless structural monitoring sensors”,Alborg University,1998. 7. Giorcelli E, Fasana A, Garibaldi L, Riva A. “Modal Analysis and system identification using ARMAV models”. Proceedings of IMAC 12, pp. 676–680, Honolulu, HI, 1994. 8. Bodeux, J. B. & Golinval, J. C., “Application of ARMAV models to the identification and damage detection of mechanical and civil engineering structures”. Smart Mater. Struct. 10:479-489.

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