Parameter Estimation of Nonlinear Structural Systems Using Bayesian Filtering Methods

This paper examines the performance of Bayesian filtering system identification in the context of nonlinear structural and mechanical systems. The objective is to assess the accuracy and limitations of the four most well-established filtering-based parameter estimation methods: the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and the particle filter. The four methods are applied to estimate the parameters and the response of benchmark dynamical systems used in structural mechanics, including a Duffing oscillator, a hysteretic Bouc–Wen oscillator, and a hysteretic Bouc–Wen chain system. Based on the performance, accuracy, and computational efficiency of the methods under different operating conditions, it is concluded that the unscented Kalman filter is the most effective filtering system identification method for the systems considered, with the other filters showing large estimation errors or divergence, high computational cost, and/or curse of dimensionality as the dimension of the system and the number of uncertain parameters increased.