Symbolic deep learning-based method for modeling complex rate-independent hysteresis

Many hysteresis models have been proposed and applied in engineering practices to describe and predict complex hysteretic behaviors observed in various engineering systems. However, selection of suitable hysteresis model usually costs extra time. In this paper, a symbolic deep learning (SDL) based method is proposed to fully describe the complex hysteresis behavior of structural systems and generate hysteretic model that fit experimental or simulated data. An explicit expression for nonlinear analysis can be obtained through symbolic deep learning without extra steps of model selection or parameter identification. The proposed method can be utilized in the modeling of complex hysteresis behavior including asymmetry, pinching, and degradation. Data from three classical hysteresis models including Bouc-Wen, generalized Bouc-Wen and Bouc-Wen-Baber-Noori, as well as the experimental data from pseudo-static testing are utilized to validate the performance of the proposed SDL model. The error accumulation and the influence of input noise is discussed.