Integration of locating baseline-free nonlinear elements and identifying model-free nonlinear restoring forces in structures

Abstract

Structural local nonlinearity often occurs when a structure is subject to strong excitation. Therefore, the identification of structural nonlinearity localizations and the characteristics of nonlinear restoring forces is of great significance in ensuring structural safety and reliability. Among the existing nonlinearity identification methods, locating structural nonlinear elements under seismic excitations is still a challenging problem and identifying model-free nonlinear restoring forces requires prior knowledge of nonlinearity position. To overcome these limitations, a novel two-step nonlinearity localization and identification algorithm is proposed in this paper. First, by considering the wavelet energy distribution in the nonlinear element become different from those of other linear elements, relative wavelet entropy which is able to quantify the difference or similarity between two wavelet energy distributions is employed to localize structural nonlinear elements based on the sparsity of structural nonlinearity. In the localization process, structural response data of the baseline linear structure are not required. Then, nonlinear restoring forces from nonlinear elements are regarded as ‘unknown virtual forces’ to the underlying linear structure. The generalized Kalman filter with unknown input, which was recently proposed by the authors, is used to identify the ‘unknown virtual forces’ and reconstruct the characteristics of nonlinear restoring forces without the models of nonlinear restoring forces. The proposed method is verified by numerical simulations of different types of nonlinear elements in different structures. Furthermore, it is tested by locating the MR damper and identifying its model-free nonlinear restoring forces in a laboratory four-story shear-type frame.