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Procedia Computer Science 9 (2012) 1149 – 1158

Procedia Computer Science 00 (2009) 000–000

Science

www.elsevier.com/locate/procedia

International Conference on Computational Science, ICCS 2012

Toward a Computational Steering Framework for Large-Scale Composite Structures Based on Continually and Dynamically Injected Sensor Data Y. Bazilevs* a

,a

b

a

, A.L. Marsden , F. Lanza di Scalea , A. Maj

c

c

umdar , and M. Tatineni

b

Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA Department of Mechanical c and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA San Diego Supecomputing Center, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA

Abstract Recent advances in simulation, optimization, structural health monitoring, and high-performance computing create a unique opportunity to combine the developments in these fields to formulate a Dynamics Data Driven Application System (DDDAS) framework. In this paper we propose such a framework, which consists of the following items and features: a structural health monitoring (SHM) system, an advanced fluid—structure interaction (FSI) simulation module, and a sensitivity analysis, optimization and control software module. High-performance computing (HPC) is employed for the various parts of the framework and is viewed as its essential element. The intended application of the developed framework is the analysis of medium-to-large-scale composite structures. These include aerospace structures, such as military aircraft fuselage and wings, helicopter blades, and unmanned aerial vehicles, and civil structures, such as wind turbine blades and towers. The proposed framework will continuously and dynamically integrate the SHM data into the FSI analysis of these structures. This capability allows one to: 1. Shelter the structures from excessive stress levels during operation; 2. Make informed decisions to perform structural maintenance and repair; and 3. Predict the remaining fatigue life of the structure.

Keywords: DDDAS; fluid—structure interaction; composite structures; optimization and control; high-performance computing

1. Introduction

Recent developments in computational mechanics, optimization, structural health monitoring (SHM), and highperformance computing (HPC) create a unique opportunity to formulate a Dynamics Data Driven Application System (DDDAS) framework (see Figure 1 for an illustration). Within this framework computational steering can be used for the class of medium to large-scale structural applications. These include aerospace structures such as military aircraft fuselage and wings, helicopter blades, unmanned aerial vehicles, and civil structures such as wind turbine blades and towers. Computational steering enables real-time monitoring and control of structures of

* Corresponding author. Tel.: +1-858-534-3663; fax: +1-858-822-2260. E-mail address: [email protected].

1877-0509 © 2012 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.procs.2012.04.124

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Y. Bazilevs / Procedia Computer Science 9 (2012) 1149 – 1158

Fig. 1. Illustration of the proposed DDDAS framework. A composite helicopter blade structure is used as an example.

structures to minimize fatigue loads, and thereby lengthen structural life, prevent premature failure, and predict the onset of failure. There are several well-known damage scenarios that occur in composite structures primarily resulting from manufacturing. The ability to shelter these structures from excessive fatigue loading, in real time and under fully operational status, results in fewer hours spent on structural maintenance and repair, and could ultimately lead to significant cost savings. The computationally intensive components of this DDDAS framework necessitate utilization of HPC. In this paper we provide an overview of such a framework, which consists of the following items and features: 1.

2.

3.

Simulation of composite structures, aerodynamics, and fluid-structure interaction (FSI). The simulation methods incorporate time-dependence, complex geometry, and nonlinear material behavior and produce highfidelity outputs (e.g., stress distributions). The structural mechanics simulation makes use of Isogeometric Analysis (IGA), while the fluid mechanics simulation is based on standard FEM. This combination yields and accurate, robust, and efficient FSI. The fluid and structure are strongly coupled, and the FSI coupling assumes non-matching interface discretizations. Sensitivity analysis, optimization and control software module. Inputs to the structural model coming from the SHM damage diagnosis step have error bounds, requiring sensitivity analysis using efficient uncertainty quantification methods and tools. Optimization and control of the structure operating conditions is preformed to systematically explore and evaluate potential modes in which the structure gives the desired response. These are performed using the surrogate management framework (SMF). SHM system. The SHM system is comprised of ultrasonic sensor arrays and infrared thermographic imaging, which collect the time-dependent data, such as strains. The data is used to assess the extent of local structural damage and to quantify it for the purposes of updating the inputs to the advanced simulation model. The SHM system is designed to detect damage that is typical of composite materials and structures. The ability to dynamically update the simulation model with such damage data will result in the prediction of a more realistic structural response and, ultimately, enable the prediction of the onset of failure or the remaining fatigue life of the structure.

Both the FSI and SMF modules are implemented in the HPC environment. The integration of the above items into a single DDDAS framework is illustrated on a conceptual diagram in Figure 2.


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Fig. 2. Conceptual diagram of the proposed DDDAS framework. The use of both sensors and actuators is illustrated in the diagram.

2. Supporting computational, sensing, and HPC technology for the proposed DDDAS framework In this Section we present the computational, sensing, and HPC methods employed, which are the supporting technology of the proposed DDDAS framework.

2.1. Computational modeling of composite structures, aerodynamics, and FSI The structural mechanics is modeled using Isogeometric Analysis (IGA). IGA is a recently introduced FEM-like simulation methodology that relies on the basis function technology of Computer-Aided design (CAD), Computer Graphics (CG), and Animation [1-3]. In IGA the geometry and computational solution fields are represented using the same functional description. The most widely used discretization in IGA makes use of nonUniform Rational B-Splines (NURBS) [4], but other alternatives, such as T-splines [5,6] and Subdivision surfaces [7,8] and solids [9] are possible. As a result of this choice, integration of structural design and computational analysis is greatly simplified. This single representation of the geometry and solution fields allows for a simple integration of different software components needed for different stages of modeling and simulation. Isogeometric analysis is an inherently higher-order accurate technique. In addition, isogeometric functions are of higher continuity than standard finite elements. This additional continuity is a distinguishing feature of IGA and it is beneficial in many applications of computational mechanics (see [2] for a summary of applications of IGA in computational engineering and sciences). Composite structures of interest in this work (e.g., military aircraft fuselage sections, helicopter blades, wings of the UAV, etc.), due to their nature, are curved thin shells reinforced with structural stiffeners. As a result, to simulate such structures, discretization of thin shell theories are employed for computational efficiency and are key to structural modeling of composites. Low-order, bi-linear quadrilateral finite elements, which are widely used and are considered standard shell element technology, exhibit several shortcomings: These elements require the use of displacement and rotation degrees of freedom to describe shell kinematics; One needs a fine mesh to represent shell geometries with high local curvature and to simultaneously achieve the desired solution accuracy; Ad-hoc element technology (e.g., hourglass stabilization) is necessary to overcome locking; In the case of explicit time stepping, the rotational inertias must be artificially increased to alleviate severe time step size stability restrictions; In the case implicit time stepping is employed, the presence of rotational degrees of freedom doubles the size of the solution and right-hand-side residual

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(a)

(b)

(c) Fig. 3. The non-matching FSI discretization applied used in the simulation of a 5MW wind turbine rotor. The data is taken from [21]. (a) The three-bladed rotor modeled as a Kirchhoff—Love shell. (b) Snapshots the air speed and structural deflection. Zoom on the blade tip at different time instances in the simulation. (c) Aerodynamic torque generated by a single blade FSI simulation coupling NURBS for the fluid and T-splines for the structure, and a full three-blade simulation coupling linear FEM for the fluid and T-splines for the structure.

arrays, quadruples the size of the left-hand-side matrix, and results in an order-of-magnitude increase in linear solver time. Higher-order Lagrange finite elements present an alternative to the low-order approaches. However, their use in thin shell analysis is not common due to the observed lack of robustness relative to low-order elements. Furthermore, the fact that Lagrange elements are C0-continuous at the inter-element boundaries requires one to use rotational degrees of freedom. Isogeometric shell analysis was recently proposed in [10] to address the shortcomings of standard finite element technology for thin shells listed above. It was found that the higher-order continuity (C1 and above) of the IGA basis functions significantly improved per-degree-of-freedom accuracy and robustness of thin shell discretizations as compared to the FEM. Furthermore, the increased continuity of the IGA discretizations enabled the use of shell kinematics without rotational degrees of freedom [11,12], leading to further computational cost savings. In the lead author’s work on wind turbines, the rotor blade geometry was modeled as a thin shell (see Figure 3a). The isogeometric rotation-free Kirchhoff-Love shell formulation for structures composed of multiple


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structural patches, called the Bending-Strip method, was developed in [12] and applied to FSI of wind turbine rotors in [13-16]. Besides the significant computational savings, the rotation-free shell discretization makes FSI coupling simpler than for shells with rotational degrees of freedom. Further speed-up of the structural computations may be obtained by implementing the structural mechanics formulation on multicore processors and Graphics Processing Units (GPU), which provide dense and enormous compute power suitable for deployment in operational conditions. The aerodynamics modeling is performed using an in-house code that is a general-geometry FEM (and IGA), time-dependent, 3D, incompressible Navier--Stokes solver. The FEM for fluid mechanics methodology makes use of the Variational Multiscale (VMS) formulation [17,18], augmented with weakly enforced essential boundary conditions [19]. Weak boundary conditions improve the accuracy in the presence of marginally resolved or unresolved boundary layers and have similarities with wall-function technology. The fluid mechanics equations are posed on a moving domain using the Arbitrary Lagrangian—Eulerian (ALE) formulation [20]. As such, the method is called ALE-VMS. In this work, FEM is employed for aerodynamics simulations for reasons explained in what follows. The planned simulations incorporate FSI coupling. We assume strong coupling between the fluid and structure and employ Newton linearization. At the level of the Newton iteration, the implementation allows one to choose the degree of coupling between the fluid and structure in the left-hand-side matrix. This leads to a hierarchy of coupling techniques, which may be exploited for best efficiency for a given application. However, the right-handside vector of the coupled equation system is unchanged, which automatically guarantees convergence to a correctly coupled solution independent of the degree of coupling in the left-hand-side matrix. Given that the applications in this work involve relatively heavy structures and light fluids, we are likely to be able to remove the non-standard coupling terms from the left-hand-side matrix without degrading nonlinear convergence. This strategy was successfully employed in simulating wind turbine FSI in [13-16] (see also Figure 3b). The coupling framework will assume non-matching discretization from the outset (see Figures 3b and 3c). As a result, the mesh resolution of the structure and fluid will be tailored to the analysis requirements of the individual subsystems, leading to better computational efficiency. The increased complexity of structural geometry places heavy demands on the fluid mesh generation around the structure. Volumetric geometry modeling and mesh generation for IGA remains an active area of research [22,23], and no “automatic mesh generation” software for IGA exists today. As a result, in order to take advantage of the superior accuracy of IGA for structural mechanics applications, and to leverage the existing advanced volumetric mesh generation tools for the FEM, we choose to couple FEM for air flow and IGA for structural dynamics. Although IGA discretizations were shown to produce results that are of superior per-degree-of-freedom quality to standard FEM for fluid mechanics and turbulence applications, good-quality aerodynamics results for the proposed applications may also be achieved with standard low-order FEM, and with a manageable number of degrees of freedom (see [24,25]). To achieve the correct FSI coupling at the fluid-structure interface using FEM for the fluid and IGA for the structure, one needs a functional definition of kinematic quantities (velocity, displacement, etc.) and tractions at both interfaces, and the ability to “transfer” these quantities from one mesh to the other. These transfer operations, which we plan to implement using L2-projections, require the ability to find the locations of quadrature points of FEM fluid surface mesh on the isogeometric structural surface mesh, and vice versa. This non-standard approach requires appropriate formulation and implementation. Using L2-projections for the load transfer guarantees that the global forces and moments acting the on the structure are transferred exactly (see, e.g., [26]). We also feel this combination of FEM and IGA has the highest potential for adoption by (and, as a result, for broader impact on) industry and research labs.

2.2. Sensitivity analysis, optimization, and control module The data from embedded sensors is used to quantify internal damage of the structural system and provide input parameters to the structure modelled with IGA. The damage is quantified as the local reduction in material strength, separation of the composite layers, or disbonding of the joints and introduced into the structural model as a modification in the material model or geometric/topological parameters (see, e.g., Figure 4). These parameters will have error bounds, requiring sensitivity analysis using efficient uncertainty quantification tools to place confidence intervals on simulation outputs. Sensitivity analysis is performed using structural and FSI simulations to assess the impact of these parameter changes on the output quantities of interest (e.g., maximum blade deflection, vibration frequency, etc.).

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Fig. 4. Example of the interaction between the sensor network and the IGA model of a composite blade structure. In this case, in-plane fiber waviness is detected and incorporated into the IGA model by locally changing the constitutive matrix for the composite shell. The fact that in IGA one has complete parametric control of the geometric model, such changes require minimal implementation effort.

The analysis is performed using stochastic collocation methods developed in [27-29]. These methods have proven to be very efficient for both computational solid mechanics and cardiovascular simulation problems [30], offering significant savings over traditional Monte Carlo techniques, and are readily extendable to the present application. Each sensitivity analysis involves executing batches of independent simulations using systematically chosen input conditions determined via collocation with a sparse grid Smolyak algorithm [31]. Because the simulations may be launched independently, parallel scalability of the proposed steering framework is greatly enhanced. The results of such simulations are used to compute probability density functions (PDFs) of the output quantities of interest, from which confidence intervals and other relevant statistics are extracted. For example, given the error bounds on input parameters (such as damage model parameters and defect locations), it is possible, within the proposed DDDAS framework, to place confidence intervals (90%, 95%, etc) on output quantities of interest, such as maximum blade deflection or the ratio of the internal stress and material strength. This information may be used to assess the degree of importance of a given damage parameter versus the rest. This information will also provide guidance for nondestructive evaluation as to which damage parameters need to be estimated with higher accuracy. Optimization and control of the structural system operating conditions will be performed to systematically explore and evaluate potential modes in which the structural system gives the desired response. The surrogate management framework (SMF) [32-34] may be used for this purpose, and a recent extension of this method has been developed to incorporate stochastic collocation for robust design [27]. This method is an efficient derivativefree method that relies on the use of surrogate functions (or approximations) for improved efficiency of the optimization algorithm. The SMF method consists of two parts, a search step for efficiency and design space exploration, and a poll step to ensure mathematical convergence. Constraints may be introduced into the optimization and control algorithm in a straightforward fashion. See Figure 5 for a schematic the SMF algorithm.

2.3. The SHM system The biggest modeling challenge in this work is to use an output of a structural monitoring system and convert it into a quantifiable structural damage that is used to update the IGA simulation model. Another challenge is to enable the prediction of structural response of the updated model and to estimate the remaining fatigue life of the structure. This is known as the prognosis step of SHM. The types of damage often encountered in composite blade structures, which are of interest in this project, are local buckling of composite fibers (in-plane and/or out-of-plane fiber waviness (see Figure 4)), disbonding at the spar-panel adhesive, resin-starved areas, and delamination of the sandwich panel. These specific defects are being considered today as typical of aerospace and civil composite structures, and are the subject of current research by


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Fig. 5. Schematic of the surrogate management framework (SMF) used for optimization and control.

Fig. 6. Pitch-catch guided wave monitoring of UAV wing skin-to-spar disbonds using flexible MFC transducers. Bond defects are detected by monitoring the strength of transmission of selected guided mode through the joint. Notice that the result is highly dependent on the ultrasonic frequency, with 200 kHz in this case yielding maximum sensitivity to bond state. (Adapted from [37].).

several groups. Experimental investigations of such phenomena are necessary to establish a reliable correspondence between the recorded sensor data and how to model the type and extent of the damage. The defect detection effort involves both ultrasonic sensor arrays and infrared thermographic imaging. The ultrasonic sensor arrays consist of either bulk piezoelectric transducers or the flexible Macro-Fiber Composite (MFC) transducers. Both devices have been used extensively in a variety of projects involving damage detection in composite structures in [35-37]. For damage detection and location, the sensors are used in an Acoustic Emission (AE) (passive) mode, as well as in an active mode of ultrasonic guided wave testing. In a passive mode, location of active damage may be performed using the traditional triangulation of time-of-flight information. In an active mode, several guided wave schemes may be employed, including traditional pitch-catch schemes and more elaborated diffraction-based schemes. Figure 6 shows an example of a pitch-catch guided wave monitoring of adhesive bond defects in a skin-to-spar joint of a scaled version of an unmanned aerial vehicle (UAV) composite wing [37]. In that application, a region of poorly cured adhesive and two adhesive disbonds were detected by monitoring the strength of transmission of specific guided wave modes through the joint. A similar approach is used for the detection of some of the defects in the proposed DDDAS framework. In addition to the ultrasonic sensor array, large-field inspections may be conducted by Infrared Thermographic methods aided by a statistical image processing approach, recently developed in [38]. The statistical approach, which is based on a Multivariate Outlier Analysis of the infrared thermographic images, was recently proven to enhance the defect contrast in aerospace-type composite panels.

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Figure 7. IGA computation of wind turbine rotor aerodynamics from [16]. The mesh is comprised of nearly 1.5 M quadratic NURBS elements. Left: Isosurfaces of air speed behind a spinning rotor. The rotor diameter is 63m and the air speed is 12.1 m/s. Right: Scalability study, on TACC’s Ranger machine [40], for wind turbine rotor simulation. The computational time is normalized by the result of 60-processor case.

2.4. Utilization of High Performance Computing As mentioned above, the computational modules of the DDDAS framework are implemented in traditional HPC environments. However, we plan to utilize multicore aspects of the current and evolving HPC environments, including GPUs, and other potential accelerator architectures, in an effort to reach near real-time DDDAS performance. The FSI code is already a parallel code using the Message Passing Interface (MPI) library, and the SMF framework allows for a straightforward parallel implementation due to the inherent independent nature of the simulations involved. The parallel FSI code uses the non-overlapping domain decomposition method for parallel implementation. The Generalized Minimum Residual (GMRES) iterative algorithm [39] is used for solving the underlying linear system of equations. The code has been thoroughly profiled, using the Integrated Performance Monitoring (IPM) tool, for parallel performance and load balance analysis, and shows good load balance and parallel scaling. The code scalability on a complex-geometry wind turbine simulation is shown in Figure 7.

3. Conclusions


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A DDDAS framework for large-scale composite structures based on continually and dynamically injected sensor data is proposed. The framework consists of several parts, which include FSI simulation, sensitivity analysis, optimization and control module, and an SHM system. The computational modules are implemented in the HPC environment, which is essential for deployment of the framework on real-life structures. The distinguishing features of the framework include: 1. IGA of composite structures, which provides efficiency and higher-order accuracy for thin shell analysis; 2. Stochastic collocation for uncertainty analysis and the SMF framework for optimization suitable for deployment on a very large numbers of compute cores; 3. An SHM system, with a variety of ultrasonic and thermographic imaging sensors, which is capable of accurately detecting typical failure modes of aerospace and civil composite structures. The ongoing research efforts are focused on the development of a workflow that allows the automatic management of the DDDAS framework, and its deployment on lab-scale and real-life aerospace and civil composite structures. Acknowledgements Support of the Air Force Office of Scientific Research Award FA9550-12-1-0005, Dr. Frederica Darema, award monitor, is gratefully acknowledged. References 1.

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