Multi-model decomposition of nonlinear dynamics using a fuzzy-CART approach

In this work, we propose an extension of the CART (Classification and Regression Tree) based methodology proposed earlier [Ind. Eng. Chem. Res. 31(8) (1992) 1989; Comp. Chem. Eng. 16(4) (1992) 413], for modelling and identification of complex nonlinear systems. The suggested scheme employs the ‘divide and rule’ based strategy which decomposes the overall complex nonlinear dynamics into a set of linear or simple nonlinear models. The CART analysis picks up only the most representative model at any time. This model strategy involves discontinuous boundaries in the overall model structure. Therefore this structure is further refined here using a fuzzification procedure. The traditional backpropagation algorithm is used to incorporate the fuzzification. The fuzzification imposed over the CART skeleton replaces the crisp boundaries of the CART models by smooth boundaries thus enabling better prediction during transitions. This approach can deal with both steady state and dynamic data. The models built using the proposed fuzzy-CART methodology has been shown to give significant improvement in performance over that built using the CART alone. Validation results involving simulations of a nonlinear fermenter of Henson and Seborg [Chem. Eng. Sci. 47 (1992) 821] have demonstrated the practicality of the approach.