Metamodeling through Deep Learning of High-Dimensional Dynamic Nonlinear Systems Driven by General Stochastic Excitation

Abstract

Modern performance evaluation and design procedures for structural systems against severe natural hazards generally require the propagation of uncertainty through the repeated evaluation of high-dimensional nonlinear dynamic systems. This often leads to intractable computational problems. A potential remedy to this situation is to accelerate the evaluation of the dynamic system through leveraging metamodeling techniques. In this work, deep learning is combined with a data-driven model order reduction technique for defining a highly efficient and nonintrusive metamodeling approach for nonlinear dynamic systems subject to general stochastic excitation. Potentially high-dimensional building structures are reduced first through Galerkin projection by leveraging a set of proper orthogonal decomposition bases via singular value decomposition. A long-short term memory deep learning network is subsequently trained to mimic the mapping from the space of the excitation to the responses of the reduced model. In addition, to accelerate the efficiency of the network, wavelet approximations of the reduced excitation and responses are incorporated. The potential of the metamodeling framework is illustrated through the application to both a multi-degree-of-freedom Bouc–Wen system as well as a multi-degree-of-freedom fiber-discretized nonlinear steel moment resisting frame. The calibrated metamodels are shown to be over three orders of magnitude faster than state-of-the-art high-fidelity nonlinear dynamic solvers while preserving remarkable accuracy in reproducing both global and local dynamic response.