۱- Introduction

۲- Response prediction of a nonlinear hysteretic system under stochastic excitations

۳- Proposed deep neural network and its application to the earthquake engineering field

۴- Validation of trained deep neural network

۵- Conclusions and future research

References

Abstract

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.

Introduction

Assessment of nonlinear hysteretic systems under stochastic excitations is one of the essential topics in many engineering fields such as mechanical, robotics and civil. In such systems, the output values depend not only on the instantaneous input at the given time but also on its past history between an input and an output (i.e. path-dependent system). A shape memory alloy (SMA) is a typical example of a smart material having hysteretic behaviors, which is widely used in industrial fields vibration attenuation (Aizawa et al., 1998) and SMA-based microactuators(Ma et al., 2000; Shin and Garman, 2001). A wire cable vibration isolator which has found many applications in industrial machinery due to its dry friction damping performance is another example of a nonlinear hysteretic system. As the inherent interfacial damping is exerted by sliding or rubbing, the deformation and the force relationship of the wire cable isolator is a nonlinear hysteretic (Chungui et al., 2009). In civil engi neering, the structural member is a typical element that shows a nonlinear hysteretic behavior under stochastic excitations. It is, therefore, important for predicting the responses of the system in order to improve the design of the system and make the system reliable during the operation. When a nonlinear hysteretic system is subjected to a relatively low-intensity stochastic excita tion and thus the maximum normalized force is smaller than the yield force, the system exhibits vibration in the linear elastic range. The response estimation of the system under such small external forces is simple and obvious so that a time history analysis is not required. On the other hand, a relatively large-intensity stochastic excitation tends to make a hysteretic system behave nonlinearly during an excitation, which makes it difficult to accurately predict the responses. A time history analysis using both refined numerical models and recorded stochastic excitations is considered as the most accurate way to estimate the responses of the system. This approach solves the dynamic equilibrium equation at every time step using a numerical integration scheme, then the correspond ing responses of the nonlinear hysteretic system can be numerically estimated. It is, however, noted that the nonlinear time history analysis involves exceedingly high computational efforts, which makes the approach impractical in most routine engineering processes. In addition, due to the ran domness of external vibrations and the uncertainties in the hysteretic behavior of a system, adopting a highly precise yet computationally inefficient method cannot be fully justified.