PARAMETRIC IDENTIFICATION OF PIECEWISE LINEAR SYSTEMS WITH PARTIAL RESPONSE MEASUREMENTS: APPROACH AND VALIDATION

When structural damage occurs, nonlinearity usually exists in damaged structures. Piecewise linear is a simple and typical nonlinear model. In recent years, some progresses have been made in the identification of piecewise linear systems. The least square estimation is adopted to identify the physical parameters of the piecewise linear structural systems with full observations of structural responses. However, it is difficult to install so many sensors to measure all the response outputs in practice. In this paper, extended Kalman filter (EKF) is adopted for such purpose. First, the locations of structural bi-linear parts are detected based on the identification of the equivalent linear stiffness of the nonlinear system by the EKF using partial structural response measurements. Then, the piecewise linear restoring force of the bi-linear parts are approximated by Legendre series with unknown coefficients and these Legendre coefficients are identified by EKF. At last, the physical parameters of the piecewise linear restoring force, i.e., the primary and the secondary stiffness and the knots, are extracted from the identified values of Legendre coefficients. To validate the effectiveness of the proposed approach, numerical simulation examples of identifying the parameters of piecewise linear structural systems are investigated.