Multi-region System Modelling by using Genetic Programming to Extract Rule Consequent Functions in a TSK Fuzzy System

Abstract

This paper aims to build a fuzzy system by means of genetic programming, which is used to extract the relevant function for each rule consequent through symbolic regression. The employed TSK fuzzy system is complemented with a variational Bayesian Gaussian mixture clustering method, which identifies the domain partition -simultaneously specifying the number of rules and the parameters of the fuzzy sets. The genetic programming approach is accompanied with an orthogonal least square algorithm to extract robust rule consequent functions for the fuzzy system. The proposed method provides a flexible grey-box modelling strategy, which brings three main advantages: 1) it is suitable for estimating a system with varying behavior across the elements of a partition of its domain; 2) it can automatically determine the necessary number of rules, without searching for redundant rule information; and 3) it only requires small data sets, in contrast with other machine learning approaches such as deep learning. The proposed model is validated with a synthetic surface, and then with real data from a gas turbine compressor map case, which is compared with an adaptive neuro fuzzy inference system model. The results have shown the adequateness of the proposed method for modelling systems with bifurcating dynamics, and where the analytical equations are not available, such as those in a typical industrial setting.

Estimation of Performance Parameters of Turbine Engine Components Using Experimental Data in Parametric Uncertainty Conditions

“…The framework that supported the formalization of the regularization problem used fuzzy sets theory [33,37]. Similarly to the solution of Tanaka et al [38], membership functions were introduced directly into the minimized functional, which contained a priori information about an acceptable range of estimated parameters.…”

“…This problem is overcome by adapting genetic optimization algorithm to the specifics of the engine model matching [35]. Genetic algorithms are increasingly used in gas turbines to solve complex optimization problems [4,10,36,37].…”

Design of a New 1D Halbach Magnet Array with Good Sinusoidal Magnetic Field by Analyzing the Curved Surface

“…Therefore, the heights of the small pieces are optimized by SQP. The shape of the curved surface is obtained by optimization results and is fitted by a least squares method [ 21 , 22 ]. Consequently, a new 1D Halbach magnet array with a curved surface is proposed.…”