A novel function approximation based on robust fuzzy regression algorithm model and particle swarm optimization

Approximation of two-variable functions using high-order Takagi–Sugeno fuzzy systems, sparse regressions, and metaheuristic optimization

This paper proposes a new hybrid method for training high-order Takagi–Sugeno fuzzy systems using sparse regressions and metaheuristic optimization. The fuzzy system is considered with Gaussian fuzzy sets in the antecedents and high-order polynomials in the consequents of fuzzy rules. The fuzzy sets can be chosen manually or determined by a metaheuristic optimization method (particle swarm optimization, genetic algorithm or simulated annealing), while the polynomials are obtained using ordinary least squares, ridge regression or sparse regressions (forward selection, least angle regression, least absolute shrinkage and selection operator, and elastic net regression). A quality criterion is proposed that expresses a compromise between the prediction ability of the fuzzy model and its sparsity. The conducted experiments showed that: (a) the use of sparse regressions and/or metaheuristic optimization can reduce the validation error compared with the reference method, and (b) the use of sparse regressions may simplify the fuzzy model by zeroing some of the coefficients.

Sparse regressions and particle swarm optimization in training high-order Takagi–Sugeno fuzzy systems

This paper proposes a method for training Takagi–Sugeno fuzzy systems using sparse regressions and particle swarm optimization. The fuzzy system is considered with Gaussian fuzzy sets in the antecedents and high-order polynomials in the consequents of the inference rules. The proposed method can be applied in two variants: without or with particle swarm optimization. In the first variant, ordinary least squares, ridge regression, or sparse regressions (forward selection, least angle regression, least absolute shrinkage and selection operator, and elastic net regression) determine the polynomials in the fuzzy system in which the fuzzy sets are known. In the second variant, we have a hybrid method in which particle swarm optimization determines the fuzzy sets, while ordinary least squares, ridge regression, or sparse regressions determine the polynomials. The first variant is simpler to implement but less accurate, the second variant is more complex, but gives better results. A new quality criterion is proposed in which the goal is to make the validation error and the model density as small as possible. Experiments showed that: (a) the use of sparse regression and/or particle swarm optimization can reduce the validation error and (b) the use of sparse regression may simplify the model by zeroing some of the coefficients.

A PSO-Based Fuzzy c-Regression Model Applied to Nonlinear Data Modeling

This paper presents a new method for fuzzy c-regression models clustering algorithm. The main motivation for this work is to develop an identification procedure for nonlinear systems using weighted recursive least squares and particle swarm optimization. The fuzzy c-regression models algorithm is sensitive to initialization which leads to the convergence to a local minimum of the objective function. In order to overcome this problem, particle swarm optimization is employed to achieve global optimization of FCRM and to finally tune parameters of obtained fuzzy model. The weighted recursive least squares is used to identify the unknown parameters of the local linear model. Finally, validation results involving simulation of two examples have demonstrated the effectiveness and practicality of the proposed algorithm.

Nonlinear System Identification Using Clustering Algorithm Based on Kernel Method and Particle Swarm Optimization

Many clustering algorithms have been proposed in literature to identify the parameters involved in the Takagi–Sugeno fuzzy model, we can quote as an example the Fuzzy C-Means algorithm (FCM), the Possibilistic C-Means algorithm (PCM), the Allied Fuzzy C-Means algorithm (AFCM), the NEPCM algorithm and the KNEPCM algorithm. The main drawback of these algorithms is the sensitivity to initialization and the convergence to a local optimum of the objective function. In order to overcome these problems, the particle swarm optimization is proposed. Indeed, the particle swarm optimization is a global optimization technique. Thus, the incorporation of local research capacity of the KNEPCM algorithm and the global optimization ability of the PSO algorithm can solve these problems. In this paper, a new clustering algorithm called KNEPCM-PSO is proposed. This algorithm is a combination between Kernel New Extended Possibilistic C-Means algorithm (KNEPCM) and Particle Swarm Optimization (PSO). The effectiveness of this algorithm is tested on nonlinear systems and on an electro-hydraulic system.