Abstract
This article introduces a robust hybrid computational method for the data-driven model-free identification of nonlinear systems that exhibit hysteretic behavior. The proposed approach combines Genetic Programming, which incorporates discontinuous basis functions, for discovering the structure of the governing differential equations, Genetic Algorithms for optimizing the parameters of the differential equations, and Computer Algebra for simplifying mathematical expressions symbolically, and consequently, controlling bloat through condensing dependent terms. A similar technique has been previously proposed by the authors for the identification of nonhysteretic Single Degree of Freedom (SDOF) systems. That technique is extended in this article and is utilized to provide parsimonious differential equations that represent the Bouc-Wen model and the bilinear hysteretic oscillatorboth exhibit abrupt change in their memory-dependent response. The representative models are subjected to validation excitations that are substantially different from the probing signals to confirm the generalizability of the models for different dynamical phenomena. The results verify the effectiveness of the approach and the accuracy of the subsequent differential operators that characterize the behavior of the studied hysteretic systems even under new dynamical conditions. Beside the presented application of this approach, the introduced methodology is more general and can be employed across different disciplines, specifically in data analytics for mathematical modeling of various complex systems.