A neuro-fuzzy modular system for modeling nonlinear systems

The real world is nonlinear and in the control application field, this aspect needs to be resolved to build models so we need to refer to nonlinear system modeling techniques. Neuro-fuzzy systems and modular neural networks (NNs) are among the best modeling approaches for nonlinear systems. The combined features of both approaches provide better models. Thus, we propose in this paper a neuro-fuzzy modular architecture for modeling nonlinear systems. The modular architecture consists of dividing a nonlinear problem into several simpler subproblems. We assigned to each subproblem an NN. Each NN provides individual solutions that will be combined to provide a general solution to the original problem. In this respect, the decomposition of the original problem is based on a fuzzy decision mechanism. This mechanism consists of a set of fuzzy rules for processing nonlinear problems using two different strategies. The first involves training only the network weights, and the second adds the fuzzy set parameters to the training step. A comparative study of both strategies reveals the competence of the second strategy in providing better accuracy and simplicity. Using the neuro-fuzzy combination among the modular NNs reduces the complexity of the original problem and achieves much better performance. The proposed architecture is evaluated by two second-order nonlinear systems, a numerical system and a real system called "the chemical reactor," which is used to carry out a chemical reaction not only in chemical and biochemical engineering, but also in the petrochemical industry. For both systems, the proposed approach provides better performance in terms of the learning time, learning error, and number of neurons.