Separable multi-innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems

This article is concerned with the parameter identification problem of nonlinear dynamic responses for the linear time-invariant system by means of an impulse excitation signal and discrete observation data. Using the impulse signal as the input, the impulse response experiment is carried out and the dynamical moving sampling is designed to generate the measured data for deriving new identification algorithms. By applying the moving window data that contain the dynamical information of the system to be identified, an objective function with respect to the parameters of the systems is constructed according to the impulse response. In accordance with different functional relations between the system parameters and the system output response, the unknown parameter vector of the system is separated into a linear parameter vector and a nonlinear parameter vector. Based on the separated parameter vectors, two subidentification models are constructed and a separable identification algorithm is presented through the gradient search to improve the accuracy. Moreover, for the purpose of enhancing the estimation accuracy and capturing the dynamical feature of the systems, the moving window data are employed to develop the separable identification algorithm. The performance of the proposed separable identification method is illustrated via a numerical example.