Yilmaz Sevcan, Oysal Yusuf
Computer Engineering Department, Anadolu University, Eskisehir 26470, Turkey.
IEEE Trans Neural Netw. 2010 Oct;21(10):1599-609. doi: 10.1109/TNN.2010.2066285. Epub 2010 Sep 2.
This paper presents fuzzy wavelet neural network (FWNN) models for prediction and identification of nonlinear dynamical systems. The proposed FWNN models are obtained from the traditional Takagi-Sugeno-Kang fuzzy system by replacing the THEN part of fuzzy rules with wavelet basis functions that have the ability to localize both in time and frequency domains. The first and last model use summation and multiplication of dilated and translated versions of single-dimensional wavelet basis functions, respectively, and in the second model, THEN parts of the rules consist of radial function of wavelets. Gaussian type of activation functions are used in IF part of the fuzzy rules. A fast gradient-based training algorithm, i.e., the Broyden-Fletcher-Goldfarb-Shanno method, is used to find the optimal values for unknown parameters of the FWNN models. Simulation examples are also given to compare the effectiveness of the models with the other known methods in the literature. According to simulation results, we see that the proposed FWNN models have impressive generalization ability.
本文提出了用于非线性动力系统预测和识别的模糊小波神经网络（FWNN）模型。所提出的FWNN模型是从传统的高木-关野-康模糊系统获得的，通过用在时域和频域都具有局部化能力的小波基函数替换模糊规则的THEN部分。第一个和最后一个模型分别使用一维小波基函数的伸缩和平移版本的求和与乘积，在第二个模型中，规则的THEN部分由小波的径向函数组成。模糊规则的IF部分使用高斯型激活函数。一种基于快速梯度的训练算法，即布罗伊登-弗莱彻-戈德法布-沙诺方法，用于找到FWNN模型未知参数的最优值。还给出了仿真示例，以将这些模型的有效性与文献中的其他已知方法进行比较。根据仿真结果，我们发现所提出的FWNN模型具有令人印象深刻的泛化能力。
