A fuzzy C‐regression model algorithm using a new PSO algorithm

Abstract

SummaryIn this paper, a new methodology is introduced for the identification of the parameters of the multiple-input-multiple-output local linear Takagi-Sugeno fuzzy models using the weighted recursive least squares (WRLS). The WRLS is sensitive to initialization, which leads to no convergence. In order to overcome this problem, adaptive chaos particle swarm optimization is proposed to optimize the initial states of WRLS. This new algorithm is improved versions of the original particle swarm optimization algorithm. Finally, comparative experiments are designed to verify the validity of the proposed clustering algorithm and the Takagi-Sugeno fuzzy model identification method, and the results show that the new method is effective in describing a complicated nonlinear system with significantly high accuracies compared with approaches in the literature. KEYWORDSchaos adaptive particle swarm optimization, fuzzy C-regression model clustering algorithm, identification, multiple-input multiple-output, Takagi-Sugeno fuzzy models

Training High-Order Takagi-Sugeno Fuzzy Systems Using Batch Least Squares and Particle Swarm Optimization

“…The parameters c 1 , c 2 are positive constants equal to 2.05 and v is equal to 0.7298. In (24), three components can be distinguished-inertia, cognitive, and social. The first component models the particle's tendency to continue moving in the same direction.…”

“…The parameter estimation is related with determining the parameters of fuzzy sets and the coefficients of regression functions in the consequence part. These tasks can be achieved by various optimization techniques such as least squares [24,26,32], evolutionary algorithms [5,8,32] or particle swarm optimization. Particle swarm optimization (PSO) is a stochastic optimization method that was developed by Kennedy and Eberhart [9,12].…”

“…In the second step, the consequent parameters are calculated using a kernel ridge regression. The adaptive chaos PSO algorithm (ACPSO) for identification of the T-S fuzzy model parameters using weighted recursive least squares was proposed in [24]. This approach is a compromise between the chaos and adaptive PSO algorithms.…”

“…In addition to Gaussian sets, triangular sets will also be used that do not require determining the value of the exponential function but use simple linear functions. It is also worth noting that in the mentioned papers, the number of rules is fixed [6,7,14,15,17,19], which raises the question of its selection, either selected by means of clustering [11,16,20,21,26,30,31] or a PSO method [4,18,24,29,33]. These methods require an additional mechanism in the learning algorithm to enable their selection.…”

“…Hence, we suggest choosing the number of rules using a cross-validation method that is simple in implementation. Moreover, in papers in which regressions are used to determine system parameters, regularized regressions are not applied [21,24,26,29,30] (except for the work [4]). We propose here the use of ridge regression that allows us to consider ill-defined problems, e.g.…”