A two-step method to identify parameters of piecewise linear systems

Based on the direct parameter estimation method and the Legendre series approximation, a two-step method is presented to estimate by measured data the physical parameters, i.e., mass, damping, stiffness and knot, of nonlinear systems with symmetrical piecewise linear restoring force. At first, the piecewise linear restoring force of the system is approximated by Legendre series. A least squares direct parameter estimation method is adopted to identify the mass and damping parameters of the system and the corresponding coefficients of the Legendre series. Secondly, the physical parameters of the piecewise linear restoring force, i.e., the primary and the secondary stiffness and the knots, are extracted from the estimated Legendre coefficients. Neither iteration nor search process is needed in this method. The validity of the method is demonstrated by numerical simulation on a single-degree-of-freedom and a three-degree-of-freedom system with both noise-free data and noise-polluted data.