A Merged Fuzzy Neural Network and Its Applications in Battery State-of-Charge Estimation

To solve learning problems with vast number of inputs, this paper proposes a novel learning structure merging a number of small fuzzy neural networks (FNNs) into a hierarchical learning structure called a merged-FNN. In this paper, the merged-FNN is proved to be a universal approximator. This computing approach uses a fusion of FNNs using B-spline membership functions (BMFs) with a reduced-form genetic algorithm (RGA). RGA is employed to tune all free parameters of the merged-FNN, including both the control points of the BMFs and the weights of the small FNNs. The merged-FNN can approximate a continuous nonlinear function to any desired degree of accuracy. For a practical application, a battery state-of-charge (BSOC) estimator, which is a twelve input, one output system, in a lithium-ion battery string is proposed to verify the effectiveness of the merged-FNN. From experimental results, the learning ability of the newly proposed merged-FNN with RGA is superior to that of the traditional neural networks with back-propagation learning.

I. Introduction

Since neural networks and fuzzy logic systems are universal approximators [1], [2], nonlinear functions approximated by these systems have been widely developed for many practical applications [3], [4]. Moreover, many studies [4], [5] combining fuzzy logic with neural networks have been done to improve the efficiency of function approximation. Fuzzy neural networks (FNNs) have been used in many applications, especially in identification of unknown systems. In nonlinear system identification, FNNs can effectively fit the nonlinear system by calculating the optimized coefficients of the learning mechanism [6]–[9]. But the traditional multiple-input–multiple-output fuzzy neural network (MIMOFNN) cannot directly be used when there are a large number of input variables. The main reason is that if many inputs are required, there will be too many free parameters in the MIMOFNN to be trained. For example, a MIMOFNN system with 12 inputs and 3 membership functions for each input will have adjustable weights for each output. Hence, we propose a novel structure called merged-FNN, which uses a number of small FNNs to solve this problem. The basic idea of the merged-FNN is that a system with high dimensionality and complexity can be modeled by a family of subsystems with fewer dimensions [16], [26]. In [24], [25], although the merged-FNN was used in the battery state-of-charge (BSOC) problem, the properties of convergence and universal approximation of the merged-FNN were not discussed.