Structural nonlinear boundary condition identification using a hybrid physics data-driven approach

As civil infrastructures often exhibit nonlinearities, the identification of nonlinear behaviors is crucial to assess the structural safety state. However, existing physics-driven methods can only estimate the nonlinear parameters given a known nonlinear behavior pattern. By contrast, the data-driven methods can merely map the load-response relationship at the structural level, rather than identify an accurate nonlinear mapping relationship at the component level. To address these issues, a hybrid physics-data-driven strategy is developed in this study to identify the blind nonlinearity. The nonlinear structural components are surrogated by a data-driven multilayer perceptron, and the linear ones are simulated by using the finite element method. Subsequently, the global stiffness matrix and restoring force vector are assembled according to the elemental topology relationship to obtain the hybrid model. The discrepancy between the measured and hybrid model-predicted responses is formulated as the loss function, by minimizing which of the MLPs are indirectly trained and the nonlinearities can be identified without knowing the nonlinearity type. Three numerical cases are used to verify the proposed method in identifying the elastic, hysteretic, and multiple nonlinear boundary conditions. Results show that the proposed method is robust given different noise levels, sensor placements, and nonlinear types. Moreover, the trained hybrid model possesses a strong generalization ability to accurately predict full-field structural responses.