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Non-Gaussian noises always exist in the nonlinear system, which usually lead to inconsistency and divergence of the regression and identification applications. The conventional evolving fuzzy systems (EFSs) in common sense have succeeded to conquer the uncertainties and external disturbance employing the specific variable structure characteristic. However, non-Gaussian noises would trigger the frequent changes of structure under the transient criteria, which severely degrades performance. Statistical criterion provides an informed choice of the strategies of the structure evolution, utilizing the approximation uncertainty as the observation of model sufficiency. The approximation uncertainty can be always decomposed into model uncertainty term and noise term, and is suitable for the non-Gaussian noise condition, especially relaxing the traditional Gaussian assumption. In this article, a novel incremental statistical evolving fuzzy inference system (SEFIS) is proposed, which has the capacity of updating the system parameters, and evolving the structure components to integrate new knowledge in the new process characteristic, system behavior, and operating conditions with non-Gaussian noises. The system generates a new rule based on the statistical model sufficiency which gives so insight into whether models are reliable and their approximations can be trusted. The nearest rule presents the inactive rule under the current data stream and further would be deleted without losing any information and accuracy of the subsequent trained models when the model sufficiency is satisfied. In our article, an adaptive maximum correntropy extend Kalman filter is derived to update the parameters of the evolving rules to cope with the non-Gaussian noises problems to further improve the robustness of parameter updating process. The parameter updating process shares an estimate of the uncertainty with the criteria of the structure evolving process to make the computation less of a burden dramatically. The simulation studies show that the proposed SEFIS has faster learning speed and is more accurate than the existing evolving fuzzy systems (EFSs) in the case of noise free and noisy conditions. [ABSTRACT FROM AUTHOR]

In this article, a novel recursive maximum correntropy-based evolving fuzzy system (RMCEFS) is proposed. The proposed system has the capability of reorganizing the structure and adapting itself in a dynamically changing environment with non-Gaussian noises. The system generates a new rule based on the correntropy criterion which represents a robust nonlinear similarity measure between two random variables and avoids recruiting the noises as the rules. Maximizing the cross-correntropy between the system output and the desired response leads to the maximum correntropy criterion for system self-adaptation. In our article, a recursive solution of the maximum correntropy criterion is derived to update the parameters of the evolving rules. This avoids the convergence problem produced by the learning size in the gradient-based learning. Also, the steady-state convergence performance of the proposed RMCEFS is studied, where the analytical solutions of the steady-state excess mean square error for the Gaussian noise and non-Gaussian noises are derived. The simulation studies show that the proposed RMCEFS using the recursive maximum correntropy converges much faster and is more accurate than the existing evolving fuzzy systems in the case of noise-free and noisy conditions. [ABSTRACT FROM AUTHOR]

Evolving fuzzy systems (EFSs) are now well developed and widely used, thanks to their ability to self-adapt both their structures and parameters online. Since the concept was first introduced two decades ago, many different types of EFSs have been successfully implemented. However, there are only very few works considering the stability of the EFSs, and these studies were limited to certain types of membership functions with specifically predefined parameters, which largely increases the complexity of the learning process. At the same time, stability analysis is of paramount importance for control applications and provides the theoretical guarantees for the convergence of the learning algorithms. In this paper, we introduce the stability proof of a class of EFSs based on data clouds, which are grounded at the AnYa type fuzzy systems and the recently introduced empirical data analytics (EDA) methodological framework. By employing data clouds, the class of EFSs of AnYa type considered in this paper avoids the traditional way of defining membership functions for each input variable in an explicit manner and its learning process is entirely data driven. The stability of the considered EFS of AnYa type is proven through the Lyapunov theory, and the proof of stability shows that the average identification error converges to a small neighborhood of zero. Although, the stability proof presented in this paper is specially elaborated for the considered EFS, it is also applicable to general EFSs. The proposed method is illustrated with Box–Jenkins gas furnace problem, one nonlinear system identification problem, Mackey–Glass time series prediction problem, eight real-world benchmark regression problems as well as a high-frequency trading prediction problem. Compared with other EFSs, the numerical examples show that the considered EFS in this paper provides guaranteed stability as well as a better approximation accuracy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a Sequential Adaptive Fuzzy Inference System called SAFIS is developed based on the functional equivalence between a radial basis function network and a fuzzy inference system (FIS). In SAFIS, the concept of “Influence” of a fuzzy rule is introduced and using this the fuzzy rules are added or removed based on the input data received so far. If the input data do not warrant adding of fuzzy rules, then only the parameters of the “closest” (in a Euclidean sense) rule are updated using an extended kalman filter (EKF) scheme. The performance of SAFIS is compared with several existing algorithms on two nonlinear system identification benchmark problems and a chaotic time series prediction problem. Results indicate that SAFIS produces similar or better accuracies with less number of rules compared to other algorithms. [Copyright &y& Elsevier]