Stochastic Sparse Bayesian Identification for Nonlinear Systems From Large Dataset

This article addresses an identification problem of the sparse nonlinear system, which is described by a nonlinear autoregressive with exogenous input (NARX) model. The precision of using variational inference (VI) to identify the NARX model has been reported in recent works. However, the VI method tends to have high computational complexity in the presence of large datasets, especially for the NARX model structure determination. This article deals with this new challenge, and a stochastic VI identification method is proposed to estimate the model parameters. Different from the conventional VI, a stochastic natural gradient ascent method is used to update the posterior distributions of the latent variables, and the advantage is that only a small portion of a dataset is used to estimate the parameters. This will significantly reduce the computational complexity. To the best of the authors’ knowledge, it is the first time to use such a strategy for nonlinear system identification. A numerical example, simulation using a benchmark problem and a real-world experiment are conducted to show the performance of the proposed method, and the results clearly demonstrate that the precision of the proposed method is similar to the original VI, but the computational complexity is significantly reduced.