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Abstract
This paper proposes the design and a comparative study of two nonlinear systems modeling techniques. These two approaches are developed to address a class of nonlinear systems with time-varying parameter. The first is a Radial Basis Function (RBF) neural networks and the second is a Multi Layer Perceptron (MLP). The MLP model consists of an input layer, an output layer and usually one or more hidden layers. However, training MLP network based on back propagation learning is computationally expensive. In this paper, an RBF network is called. The parameters of the RBF model are optimized by two methods: the Gradient Descent (GD) method and Genetic Algorithms (GA). However, the MLP model is optimized by the Gradient Descent method. The performance of both models are evaluated first by using a numerical simulation and second by handling a chemical process known as the Continuous Stirred Tank Reactor CSTR. It has been shown that in both validation operations the results were successful. The optimized RBF model by Genetic Algorithms gave the best results.
Highlights
Neural networks are widely used in the characterization of nonlinear systems [1,2,3,4,5,6,7], time-varying time-delay nonlinear systems [8] and they are applied in various applications [9,10,11,12].The system may be with invariant parameters or timevarying parameters
This paper focuses on the optimization of radial basis functions architecture, and compares it to the Multi Layer Perceptron (MLP) architecture
To test the effectiveness of the MLP and Radial Basis Function (RBF) models we test them on a Continuous Stirred Tank Reactor, CSTR, which is a type of slowly time-varying nonlinear system used for the conduct of the chemical reactions [39,40,41]
Summary
Neural networks are widely used in the characterization of nonlinear systems [1,2,3,4,5,6,7], time-varying time-delay nonlinear systems [8] and they are applied in various applications [9,10,11,12]. We investigate the possibility of extending the well conventional methods to model a nonlinear system in presence of time-varying parameters. Several methods such as iterative methods [28,29,30,31,32] with the gradient descent method and evolutionary algorithms [32] that genetic algorithms are used in this paper to optimize the structure and determine the parameters of the RBF model. A comparative study between the MLP and RBF model, applied to two examples of nonlinear systems is presented in the forth section.
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