Extracting compact fuzzy rules for nonlinear system modeling using subtractive clustering, GA and unscented filter

Abstract

This paper presents a two stage procedure for building optimal fuzzy model from data for nonlinear dynamical systems. Both stages are embedded into Genetic Algorithm (GA) and in the first stage emphasis is placed on structural optimization by assigning a suitable fitness to each individual member of population in a canonical GA. These individuals represent coded information about the structure of the model (number of antecedents and rules). This information is consequently utilized by subtractive clustering to partition the input space and construct a compact fuzzy rule base. In the second stage, Unscented Filter (UF) is employed for optimization of model parameters, that is, parameters of the input-output Membership Functions (MFs).The proposed hybrid approach exploits the advantages and utilizes the desirable characteristics of all three algorithms for extracting accurate and compact fuzzy models.Case studies are given to illustrate the efficiency of the modeling procedure. Benchmark examples are analyzed and the results are compared with those obtained by Adaptive Nero-fuzzy Inference System (ANFIS). In all cases enhanced performance and superior results are obtained from the proposed procedure.

A network-based fuzzy inference system for sonodisruption process of re-assembled casein micelles

“…Table 2 details that the ANFIS obtained by grid partition had a better trainability as well, a better recognition capability of process. This model however, suffered from the drawback of requiring a longer time for training and especially from the explosion of rule base (Eftekhari and Katebi, 2008). On the other hand, the ANFIS obtained by subtractive clustering although possessed an acceptable error for training but expunged by a very large error of testing.…”

“…3 demonstrates the membership functions before and after developing the ANFIS model by grid partitioning. In subtractive clustering method the membership functions are obtained automatically after generation of clusters (Eftekhari and Katebi, 2008) and thus possessed completely different shapes and characteristics from those obtained by grid partitioning. In subtractive clustering all data points are inside a hypercube (Chen et al, 2008).…”

“…In subtractive clustering all data points are inside a hypercube (Chen et al, 2008). The centers and widths of membership functions are therefore obtained on the basis of identified clusters in the cube as the widths are obtained on the basis of clusters' radii (Eftekhari and Katebi, 2008).…”

Filter modeling using gravitational search algorithm

“…Genetic algorithm (GA; Goldberg, 1989), simulated annealing (SA; Kirkpatrick et al, 1983), ant colony optimization (ACO; Dorigo et al, 1996), and particle swarm optimization (PSO; Kennedy and Eberhart, 1995) are four well-known classes of such global optimization methods. The heuristic algorithms are widely used in solving system identification and filter modeling problems (Valarmathi et al, 2009;Chang, 2007;Eftekhari and Katebi, 2008;Chen and Luk, 1999;Howell and Gordon, 2001;Karaboga et al, 2004;Kalinli and Karaboga, 2005;Das and Konar, 2007;Lin et al, 2008).…”

Designing simulated annealing and subtractive clustering based fuzzy classifier

“…Zhao et al [27], used particle swarm optimization algorithm to find the optimal membership functions (MFs), which are initially found by the SC, and consequent parameters of the rule base. In the work of Efektari and Katebi [28], Genetic Algorithm (GA) is used to construct compact fuzzy model by selecting more efficient inputs and to determine the optimum number of rules by finding the optimum SC radius. The discussions on the effects of parameters of the SC such as squash factor, cluster radius, accept and reject ratio on fuzzy model performance are given in [29].…”