An evolving fuzzy neural predictor for multi-dimensional system state forecasting

Highlights

• An evolving fuzzy neural network (eFNN) predictor is proposed to conduct system state forecasting with multi-dimensional data sets.

• In eFNN, VARMA filter is used to capture linear correlations; nonlinear correlations are modeled by a fuzzy network scheme.

• A novel cumulative clustering algorithm is proposed to evolve fuzzy reasoning rules for nonlinear modeling.

• The developed eFNN is implemented for real world applications such as currency exchange rate and induction motor system state prognosis.

Abstract

In many applications of system state forecasting, the prediction is performed using multi-dimensional data sets. The traditional methods for dealing with multi-dimensional data sets have some shortcomings, such as a lack of nonlinear correlation modeling capability (e.g., for vector autoregressive moving average (VARMA) models), and an inefficient linear correlation modeling mechanism (e.g., for generic neural fuzzy systems). To tackle these problems, an evolving fuzzy neural network (eFNN) predictor is proposed in this paper to extract representative information from multi-dimensional data sets for more accurate system state forecasting. In the proposed eFNN predictor, linear correlations among multi-dimensional data sets are captured by a VARMA filter, while nonlinear correlations of the data sets are modeled by a fuzzy network scheme, whose fuzzy rules are generated adaptively using a novel evolving algorithm. The proposed predictor possesses online learning capability and can address non-stationary properties of data sets. The effectiveness of the proposed eFNN predictor is verified by simulation tests. It is also implemented for induction motor system state prognosis. Test results show that the proposed eFNN predictor can capture the dynamic properties involved in the multi-dimensional data sets effectively, and track system characteristics accurately.

Introduction

Multi-dimensional system state forecasting is a complex and important research and development area, which aims to predict future states of a dynamic system based on past observations from multiple sources (e.g., sensors). The classical approaches for multi-dimensional data sets forecasting are mainly based on analytical modeling, such as vector autoregressive (VAR) models, and vector autoregressive moving average (VARMA) models [1]. These classical analytical models can describe the underlying relationships among multi-dimensional data sets to extrapolate future states of a dynamic system, and have been used in some forecasting applications, such as the electricity load demand [2], [3], and some economic indicators [4], [5]. The VAR/VARMA models, however, can only predict the linear correlations among multi-dimensional data sets; they are unable to efficiently characterize nonlinear correlations (e.g., those related to impulses and transients) among multi-dimensional data sets. Comparing the VAR with the VARMA, the former estimates future states of a system based on its past multi-dimensional observations, while the latter deploys both past multi-dimensional observations and past multi-dimensional innovations for system state prediction. Thus VARMA could provide more comprehensive linear modeling than VAR. Since a long autoregressive (AR) process can be represented by a compact moving average (MA) process, the dimension of the parameter space may be further reduced by VARMA, especially for data sets involving long AR characteristics [6]. Accordingly, VARMA will be used in this work to filter out linear correlations among multi-dimensional data sets.

The alternative approach for multi-dimensional data set modeling is the use of soft-computing tools, such as neural networks (NNs) [7], [8], [17], [18], [26], [27], [28], [29] and neural fuzzy (NF) systems [9], [10]. An NF scheme is usually superior to NNs in mimicking human reasoning processes and extracting knowledge as interpretable IF–THEN rules. Although an NF scheme can track the nonlinear correlations among multi-dimensional data sets, the performance of NF in catching linear correlations may not be efficient, because of its complex modeling nature. Moreover, the performance of an NF predictor with a fixed network architecture cannot be guaranteed when system properties vary significantly in applications (e.g., equipment just after repair and maintenance), and/or when new information is provided (e.g., from a new sensor) [11], [12]. In recent years, more work has been focused on the use of evolving NF paradigms that can adaptively adjust their network structures in response to new system conditions (i.e., data sets). Kasabov et al. successfully proposed evolving fuzzy NN models (EFuNN) [13], [14], [15] and dynamic evolving NF inference system (DENFIS) techniques [16] for different applications such as learning, knowledge acquisition, and time-series forecasting. These evolving paradigms employ clustering algorithms to adaptively tune model structure and parameters. Although they treat both linear correlations and nonlinear correlations in a data set with the fuzzy NN (nonlinear modeling), they may increase the computational burden, especially when they use nonlinear models to capture linear correlations from the data with large size and dimensions.

Another solution to model both linear and nonlinear characteristics of data sets for system state forecasting is the use of hybrid modeling. For example, Medeiros et al. proposed a neural coefficient smooth transition autoregressive model for time series forecasting [24]. Khashei et al. integrated the NNs and ARMA models to conduct time series prediction [25]. One remarkable merit of using the hybrid modeling strategy is its capacity for dealing with non-stationary data sets. The linear, non-stationary, components could be captured by a linear modeling method, and nonlinear components characterized by some nonlinear modeling technique [19]. However, these hybrid methods lack the ability to characterize multi-dimensional data sets; moreover, they cannot adapt their reasoning structures to new system conditions in real time (online), and consequently the model structure may be suboptimal.

To tackle the aforementioned challenges, the objective of this work is to develop a new evolving fuzzy neural network (eFNN) technique for the prognosis of complex dynamic systems with multi-dimensional data sets. Compared with EFuNN and DENFIS, the proposed eFNN applies a different approach in processing linear correlation and nonlinear correlation in a data set: a compact VARMA filter to model linear property and an evolving fuzzy network to model nonlinear correlation. Based on this approach, the system structures can become more transparent, which can facilitate system training for optimization and error tracking. The method׳s novelty lies in the following aspects: (1) the developed eFNN predictor applies both linear and nonlinear modeling strategies to characterize properties of multi-dimensional data sets; (2) a novel cumulative clustering algorithm is proposed to evolve fuzzy reasoning rules for nonlinear modeling; and (3) the developed eFNN predictor is implemented for real-world applications such as the forecasting of currency exchange rates, as well as induction motor (IM) system state prognosis.

The remainder of this paper is organized as follows: The proposed eFNN predictor and the proposed adaptive clustering algorithm are discussed in Section 2. In Section 3, the effectiveness of the proposed eFNN predictor is examined by simulation tests; the new predictor is also implemented for IM system state prognosis. Some concluding remarks are summarized in Section 4.