A Comparison of Neural Networks and Fuzzy Logic Methods for Process Modeling

The goal of this work was to analyze the potential of neural networks and fuzzy logic methods to develop approximate response surfaces as process modeling, that is for mapping of input into output. Structural response was chosen as an example. Each of the many methods surveyed are explained and the results are presented. Future research directions are also discussed. Introduction Neural networks and fuzzy logic methods have been enjoying vigorous developments. They are well suited for development of computable models for complex processes given sufficient data for the correspondence between input and output variables of the process at hand. The principal goal of this investigation was to compare the accuracy of approximation of these two methods on the same set of data. Fuzzy logic models are limited to only about a half dozen variables because of computational explosion. The value of these approaches is in cases where no computable analytic model exists, only experimental data. For this investigation, in order to generate well controllable data sets, a conveniently computable set was chosen in the form of the response of a small plane truss with well known behavior characteristics. The methods are applicable for physical phenomena for which only experiments can provide reliable data sets. In those cases fast executing computable models are often still desirable, for example for optimization. It should be noted that the two methods, neural networks and fuzzy logic are fundamentally different. The neural networks produce the trained model as a 'l_lack box" of weights associated with the network topology. The fuzzy logic methods, on the other hand produce expert rules captioning the behavior of the system. These rules, in general, can be examined by the experts, modified if needed, and validated on new data. Another case studied was a model from output to input to simulate inverse behavior for reverse engineering for which the inverse of the computable models are not available. The chosen simple structural example is the well known ten bar truss used intensively in optimization research and literature. Despite the small number of variables the behavior characteristics of statically indeterminate structures, the nonlinear dependence of internal load distribution on relative member size, is sufficiently represented. The ten-bar truss is depicted in Figure 1. The data for neural networks (NN) and fuzzy logic (FL) methods were supplied in the form of numerical inputoutput pairs generated by the finite element method. E=107 [ psi ] A1=4.51 A2=2.16 A3=0.1 A4=0.1 A5=4.38 A6=0.1 A7=3.05 As=3.23 Ag=0.1 A,o=3.05 [ in 2 ] 5 4