Hammerstein Modeling with Structure Identification for Multi-input Multi-output Nonlinear Industrial Processes

Hammerstein modeling with structure identification for multi-input multi-output (MIMO) nonlinear industrial processes is investigated in this study. The structure identification of the Hammerstein model is very challenging because the model terms are vectors, and some model terms are inputs of other model terms (i.e., model term coupling). An efficient model structure selection algorithm for the Hammerstein model is proposed with the multi-output locally regularized orthogonal least-squares (LROLS), A-optimality design, and a vector model term selection. To enhance the well-posedness of the regressors, estimation robustness, and model adequacy, the A-optimality criterion is integrated into the model error reduction criterion in the multi-output LROLS. To handle the vector model term coupling problem, a vector model term selection rule is synthesized into the multi-output LROLS. Alter the model structure is determined, to improve the robustness of the parameter estimation, the regularized least-squares method with the singular value decomposition (RLS-SVD) is used. The simple or sparse Hammerstein model structure can be determined from the noisy process data. The structure identification algorithm only includes a few user-designed parameters which are easy to select. Therefore, the ability of automatic construction of the Hammerstein model is enhanced. Three application examples are used to illustrate the effectiveness of the proposed modeling approach, including the simple model structure, the satisfactory modeling accuracy, the robustness of the algorithm to the noise, and the easy selection of user-designed parameters.