A Comparative Study of Surrogate Modeling of Nonlinear Dynamic Systems

Abstract

Abstract Surrogate models play a vital role in overcoming the computational challenge in designing and analyzing nonlinear dynamic systems, especially in the presence of uncertainty. This paper presents a comparative study of different surrogate modeling techniques for nonlinear dynamic systems. Four surrogate modeling methods, namely Gaussian process (GP) regression, a long short-term memory (LSTM) network, a convolutional neural network (CNN) with LSTM (CNN-LSTM), and a CNN with bidirectional LSTM (CNN-BLSTM), are studied and compared. All these model types can predict future behavior of dynamic systems over long periods based on training data from relatively short periods. The multidimensional inputs of surrogate models are organized in a nonlinear autoregressive exogenous model (NARX) scheme to enable recursive prediction over long periods, where current predictions replace inputs from the previous time window. The Bouc-Wen nonlinear dynamic model, which can flexibly capture the behavior of many inelastic material models, is used to compare the performance of the four surrogate modeling techniques. The results show that the GP-NARX surrogate model tends to have more stable performance than the other three deep learning-based methods for this particular example. The tuning effort of GP-NARX is also much lower than its deep learning-based counterparts.