A subspace parameter identification method for nonlinear structures under oversampling conditions

Abstract

In engineering practice, sampling frequencies much higher than the Nyquist frequency are often used to obtain accurate measurements of the dynamic characteristics of nonlinear systems. However, it may lead to oversampling when using the nonlinear subspace identification method (NSIM). This study proposes a subspace parameter identification method to address the identification of nonlinear structures under oversampling conditions. The proposed method first employs the prediction error method (PEM) to estimate the linear part of the state space model. In noisy environments, the PEM can achieve more accurate results than the NSIM by minimizing an error criterion function. The initial values fed into the PEM are obtained by the stochastic subspace identification method. The nonlinear part of the state space model is estimated by solving a linear regression equation. The proposed method effectively reduces the impact of high sampling frequencies on identification accuracy by combining data with different sampling frequencies to construct the linear regression equation. Among them, the low sampling frequency data is obtained by downsampling the high sampling frequency measurement data. The proposed method effectively reduces the effect of high sampling frequencies and environmental noise on identification accuracy by accurately estimating both the linear and nonlinear parts of the state space model. The identification accuracy of the proposed method is numerically verified by a chain-type structure with five degrees of freedom and a cantilever beam structure. Additionally, experimental verification is carried out on a two degrees of freedom floor structure with local nonlinearities. The results show that the proposed method achieves high identification accuracy in oversampling conditions and noisy environments.