Optimal nonlinear dynamic sparse model selection and Bayesian parameter estimation for nonlinear systems

Abstract

This work develops algorithms for the estimation of sparse interpretable data-driven models. Linear combination of linear and nonlinear basis functions is considered for candidate models, where the optimal basis functions are selected by using the branch and bound algorithm. Model parameters are optimally estimated by employing Bayesian inferencing to seek the maximum a posteriori estimates conditioned on the available data. This is implemented in a two-step expectation-maximization algorithm enabling simultaneous estimation of noise characteristics along with the model parameters. A priori analysis is undertaken based on the ranking of the basis functions in the library. In presence of correlated noise, special properties of the Jacobian matrix are exploited for efficient pruning. Model selection is done by using modified Akaike information criterion that rewards model fitness while penalizing model size and complexity. The algorithm, called Bayesian identification of Dynamic Sparse Algebraic Models (BIDSAM), is tested for three case studies.