Hierarchical recursive Levenberg–Marquardt algorithm for radial basis function autoregressive models

The recursive Levenberg–Marquardt (L–M) algorithm has been generally implemented for the parameter identification of nonlinear models in online situations. However, owing to the intrinsic structural characteristics (i.e., the global nonlinear local linearity) of the radial basis function autoregressive (RBF-AR) model, the direct application of the recursive L–M (R-LM) algorithm significantly restricts its performance. To improve the comprehensive performance, a hierarchical recursive L–M (H-R-LM) algorithm is proposed in this paper. The concepts of parameter separation and model decomposition are integrated into the algorithm to reduce the model's complexity. Multi-innovation and forgetting factors leverage historical data more reasonably, thus accelerating the convergence. Hierarchical recognition and alternating optimization can improve identification accuracy. Two experiments on analog and actual data sets are used to compare the performance of the RBF-AR model using R-LM and H-R-LM algorithms. Compared with the R-LM algorithm, experiments verify that the new H-R-LM algorithm presents higher identification accuracy, faster convergence rate, improved predictive performance, and less computational effort.