Structural dynamic nonlinear model and parameter identification based on the stiffness and damping marginal curves

Abstract

This paper presents a novel structural dynamic nonlinear model and parameter identification method based on the stiffness and damping marginal curves. The stiffness and damping marginal curves are first extracted from the structural dynamic responses. Then, nine nonlinear feature indices (NFIs) are defined based on the marginal curves to describe the characteristics of various nonlinear models. To reduce the dimension of NFIs and facilitate the subsequent calculation of the support vector machine (SVM), the principal component analysis (PCA) is implemented. Afterwards, the NFIs processed by PCA are employed as the training samples to SVM classifier, which is used to identify the structural nonlinear model. According to the identified nonlinear model corresponding to the type of nonlinearity, the parameters of the nonlinear model are further identified by the nonlinear least square method. The numerical results of a single degree of freedom (SDOF) system and a cantilever beam structure demonstrate that the proposed method can effectively identify both nonlinear model and corresponding parameters under various excitations even considering the noise effect. Subsequently, the proposed method is also verified by a benchmark system subjected to a semisinusoidal pulse load and a beam bridge structure subjected to an earthquake load. The proposed method is also applied to the experimental test of a bolted joint cantilever beam subjected to a random excitation in the laboratory. Both numerical and test results demonstrate that the proposed method can identify both nonlinear model and corresponding parameters within good accuracy and robustness.