Identification of time-varying nonlinear systems using differential evolution algorithm

Online monitoring of modal and physical parameters which change due to damage progression and aging of mechanical and structural systems is important for the condition and health monitoring of these systems. Usually, only the limited number of imperfect, noisy system state measurements is available, thus identification of time-varying systems with nonlinearities can be a very challenging task. In order to avoid conventional least squares and gradient identification methods which require uni-modal and double differentiable objective functions, this work proposes a modified differential evolution (DE) algorithm for the identification of time-varying systems. DE is an evolutionary optimisation method developed to perform direct search in a continuous space without requiring any derivative estimation. DE is modified so that the objective function changes with time to account for the continuing inclusion of new data within an error metric. This paper presents results of identification of a time-varying SDOF system with Coulomb friction using simulated noise-free and noisy data for the case of time-varying friction coefficient, stiffness and damping. The obtained results are promising and the focus of the further work will be on the convergence study with respect to parameters of DE and on applying the method to experimental data.