Chapter 35 Applications of Reduced Order and Surrogate Modeling in Structural Dynamics Alexandros A. Taflanidis, Jize Zhang, and Dimitris Patsialis Abstract Despite recent advances in computational science, the adoption of computationally intensive, high-fidelity simulation models remains a challenge for many structural dynamics applications, especially those within the domain of uncertainty quantification (UQ), requiring repeated calls to a computationally intensive simulator. Reduced order and surrogate models offer an attractive alternative to circumvent this challenge. This contribution investigates how these modeling principles can be leveraged for different UQ applications. For both types of approximate models, the development of the corresponding (reduced order or surrogate) model is directly informed through simulations of the high-fidelity numerical model. The tuning of the approximate model aims to improve accuracy for the specific UQ task at hand, rather than targeting a globally accurate approximation. The specific applications discussed correspond to seismic loss estimation (for reduced order modeling) and posterior sampling for Bayesian inference (for surrogate modeling). Keywords Reduced order modeling · Surrogate modeling · Structural dynamics · Uncertainty quantification · Seismic loss estimation · Adaptive tuning · Posterior density approximation · Bayesian inference 35.1 Introduction Reduced order and surrogate models have emerged as powerful computational statistics tools for supporting UQ tasks in different structural dynamics applications [1–6]. Their objective is to replace the original, high-fidelity simulation model with an approximate one that has significantly smaller computational burden (therefore accelerating relevant computations), but can still provide adequate accuracy for the UQ task of interest. This accuracy can be enhanced through tuning, perhaps with adaptive characteristics, tailored to that specific task, instead of trying to accomplish a globally accurate approximation. Reduced order models simplify the physics-based description of the original system through some form of condensation of the initial degrees of freedom and equations of motion [7], sometimes coupled with an approximation of the nonlinear response characteristics [3]. In the latter case, which is the one emphasized in this contribution, the calibration of the nonlinear properties of the reduced order model can be performed using data from the original, high-fidelity simulation model, with ultimate objective that the reduced order approximate model matches closely the high-fidelity one [1] for excitation (and therefore operating conditions) similar to the ones entailed in the UQ task of interest. On the other hand, surrogate models (also frequently referenced as metamodels) offer an entirely data-driven mathematical approximation of the input/output relationships of the high-fidelity model. The characteristics of the metamodel are tuned using explicitly simulation data from the original model [8]. Among the different classes of surrogate models, Gaussian Process Metamodels (GPMs) have gained wide popularity for UQ applications. This can be attributed (1) to the fact that they correspond to a statistical emulator, providing also a local estimate for the metamodel prediction error, a feature that fits well within the broader UQ setting, and (2) to their computational efficiency in simultaneously providing, through vectorized algebraic manipulations, estimates for multiple input samples, a feature well aligned with stochastic simulation algorithms used frequently in UQ applications. For accurate UQ estimation, the selection of the database informing the metamodel development, what is formally known as Design of Experiments (DoE) [8], plays always a critical role. This contribution reviews some recent advances for the implementation of reduced order and surrogate modeling in structural dynamics applications. Discussion for each type of approximation model are couched within a specific application; seismic loss estimation for reduced order modeling and posterior sampling in Bayesian inference for surrogate modeling. A. A. Taflanidis ( ) · J. Zhang · D. Patsialis Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN, USA e-mail: a.taflanidis@nd.edu © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_35 297
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