Knowledge and data fusion-driven dynamical modeling approach for structures with hysteresis-affected uncertain boundaries

This paper introduces a novel approach for modeling the dynamics of structural systems, addressing challenges posed by uncertain boundary conditions and hysteresis forces. The methodology integrates low-dimensional dynamical modeling techniques with a blend of traditional knowledge-driven and contemporary data-driven methods. Applied to a flexible beam doubly constrained by uncertain forces containing hysteresis, this hybrid approach demonstrates the effectiveness of combining the knowledge-driven global mode method (GMM) with data-driven technologies. The GMM is employed to model the known components of the structure, while the transformer neural network (TNN) focuses on simulating the hysteresis-affected uncertain boundaries. The differential evolution algorithm is used to identify the parameters that influence the natural characteristics of the system. A comparative study is performed to demonstrate the validity of the developed model and its superior in computation time—99.2% less than that of employing the finite element models. This study establishes a robust theoretical basis for advancing dynamical modeling of systems with complex boundary conditions.