A self-organizing recurrent fuzzy neural network based on multivariate time series analysis
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ORIGINAL ARTICLE
A self‑organizing recurrent fuzzy neural network based on multivariate time series analysis Haixu Ding1,2 · Wenjing Li1,2 · Junfei Qiao1,2 Received: 12 February 2020 / Accepted: 1 August 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Fuzzy neural networks (FNNs) have attracted considerable interest for modeling nonlinear dynamic systems in recent years. However, the recurrent design and the self-organizing design of FNNs generally lack adaptability, and their analyses on the change rule of networks in continuous time are insufficient. To solve these problems, a self-organizing recurrent fuzzy neural network based on multivariate time series analysis (SORFNN-MTSA) is proposed in this paper. First, a recurrent mechanism, based on wavelet transform fuzzy Markov chain algorithm, is introduced to obtain adaptive recurrent values and accelerate convergence speed of the network. Second, a self-organization mechanism, based on weighted dynamic time warping algorithm and sensitivity analysis algorithm, is presented to optimize the network structure. Third, the convergence of SORFNN-MTSA is theoretically analyzed to show the efficiency in both fixed structure and self-organizing structure cases. Finally, several benchmark nonlinear systems and a real application of wastewater treatment are used to verify the effectiveness of SORFNN-MTSA. Compared with other existing methods, the proposed SORFNN-MTSA performs better in terms of both high accuracy and compact structure. Keywords Self-organizing recurrent fuzzy neural network · Multivariate time series analysis · Prediction · Wastewater
1 Introduction Fuzzy neural networks (FNNs) are the combination product of fuzzy theory and neural network, which have the fuzzy reasoning ability of fuzzy systems [1, 2]. The model can not only update automatically, but also correct the membership functions of the fuzzy subset continuously [3]. However, as a kind of feedforward network, FNNs have the limited ability to model nonlinear systems and cannot adapt to more complex dynamic environments [4, 5]. To solve this problem, some scholars built recurrent fuzzy neural networks (RFNNs) based on FNNs by constructing recurrent * Junfei Qiao [email protected] Haixu Ding [email protected] Wenjing Li [email protected] 1
Faculty of Information Technology, Beijing University of Technology, Beijing, China
Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing, China
2
channels [6–11]. RFNNs have the ability of fuzzy reasoning and state feedback, which can solve large time-varying and over-fitting problems, thus enhancing the networks’ ability to describe nonlinear dynamic systems [12–16]. However, the structures of RFNNs usually depend on the experience of experts, which leads to a decrease in applicability, and fixed network structures are also difficult to apply to system modeling in different states [17–19]. To solve this problem, some scholars have established self-organizing mechanisms [20–26]
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