Response prediction of nonlinear hysteretic systems by deep neural networks.

Nonlinear hysteretic systems are common in many engineering problems. The maximum response estimation of a nonlinear hysteretic system under stochastic excitations is an important task for designing and maintaining such systems. Although a nonlinear time history analysis is the most rigorous method to accurately estimate the responses in many situations, high computational costs and modelingtime hamper adoption of the approach in a routine engineering practice. Thus, various simplified regression equations are often introduced to replace a nonlinear time history analysis in engineering practices, but the accuracy of the estimated responses is limited. This paper proposes a deep neural network trained by the results of the nonlinear time history analyses as an alternative of such simplified regression equations. To this end, a convolutional neural network (CNN) which is usually applied to abstract features from visual imagery is introduced to analyze the information of the hysteretic behavior of the system, then, merged with neural networks representing the stochastic random excitation to predict the responses of a nonlinear hysteretic system. For verification, the proposed deep neural network is applied to the earthquake engineering area to predict the structural responses under earthquake excitations. The results confirm that the proposed deep neural network provides a superior performance compared to the simplified regression equations which are developed based on a limited dataset. Moreover, to give an insight of the proposed deep neural network, the extracted features from the deep neural network are investigated with various numerical examples. The method is expected to enable engineers to effectively predict the response of the hysteretic system without performing nonlinear time history analyses, and provide a new prospect in the relevant engineering fields. The supporting source code and data are available for download at https://github.com/TyongKim/ERD2.