本文主要研究基于神经网络和模糊系统的分层混合模糊—神经网络模型(HHFNN)的训练算法设计,分别提出了基于三角波隶属函数, 梯形隶属函数,Gauss型隶属函数以及基于Takagi-Sugeno型模糊系统的四种训练算法.与HHFNN已有的训练算法和经典BP算法相比,这四种新的训练算法在训练精度和参数数量上更有优势.按照在模糊子系统部分所调整参数位置的不同,本文所提出的训练算法可以分为以下的两种类型.第一种类型包括基于三角波, 梯形和Gauss型隶属函数的三个训练算法.调整的参数主要是模糊子系统规则前件中的隶属函数(三角波和梯形)的中心(Gauss型隶属函数的参数包括中心和宽度),在上层神经网络部分采用梯度下降法调整权重和偏置值.其中,在2.3节中本文重点研究了基于三角波隶属函数的训练算法,该训练算法具有如下良好的性质:(1).所需要调整的参数个数一定少于HHFNN已有的训练算法所需调整的参数个数;(2).当隐层神经元个数大于2时(该条件在实际应用中一般都能被满足),该训练算法需要调整的参数个数就少于经典BP算法所需要调整的参数个数;(3).在相同条件下通过仿真实验对比,基于三角波隶属函数的训练算法的精度(训练精度和测试精度)都要比模型原有训练算法和经典BP算法高.2.4节和2.5节分别给出了基于梯形和Gauss型隶属函数的训练算法及其仿真实验对比结果,并分析了基于不同隶属函数的训练算法的性能.第二种类型是基于Takagi-Sugeno型模糊系统的训练算法,2.6节详细讨论了该训练算法.这个训练算法在模糊子系统部分使用的是Takagi-Sugeno模型,模糊规则后件采用输入变量的齐次线性函数.调整的参数包括规则后件中齐次线性函数的系数和上层神经网络的权重以及偏置值,仍然采用了梯度下降法实现这些参数的更新.该训练算法的参数个数与HHFNN原有的训练算法相同,但是在训练误差和学习速度方面都要大大优于原有训练算法和经典BP算法.

This thesis concentrates on the researches of training algorithms for hierarchical hybrid fuzzy-neural networks (HHFNN) based on neural network and fuzzy system. Four training algorithms are proposed in the thesis based on triangular membership function,trapezoid membership function, Gaussian membership function and Takagi-Sugeno fuzzy system respectively, which outperform the existing training algorithm for HHFNN and standard BP algorithm in terms of accuracy and number of parameters.The four training algorithms can be divided into two categories according to the parameters in different parts of fuzzy rules in fuzzy sub-systems. The first category includes the three training algorithms based on triangular, trapezoid and Gaussian membership functions. The parameters adjusted in the algorithms are centers of triangular and trapezoid membership functions, and widths and centers of Gaussian membership functions of the IF parts of fuzzy rules in the lower fuzzy sub-systems; meanwhile, gradient-descent method is employed toupdate the weights and bias terms of the upper neural network. The triangular membership function based training algorithm is discussed in detail in Subsection 2.3, which is demonstrated to have thefollowing advantages: (1) The parameters updated in this training algorithm are usually fewer than those of the existing training algorithm for HHFNN. (2) The number of parameters updated in this training algorithm is fewer in comparison with standard BPalgorithm, when the number of hidden neurons is more than 2 (which is frequently valid in applications). (3) According to the simulation results, triangular membership function based trainingalgorithm outperforms the existing training algorithm for HHFNN and standard BP algorithm in terms of training accuracy and testing accuracy.The trapezoid and Gaussian membership functions based training algorithms are proposed and illustrated by simulation comparisons in Subsection 2.4 and 2.5 repectively. And the performance of the threetraining algorithms above are also analyzed and compared.The other category described specifically in Subsection 2.6 is the Takagi-Sugeno fuzzy system based training algorithm that appliesTakagi-Sugeno model to fuzzy sub-systems. Homogeneous linear function of input variables is adopted in the THEN parts of fuzzy rules. The parameters consist of coefficients of homogeneous linear function in the THEN parts of fuzzy rules and the weights and biasterms of upper neural network, which are updated by gradient-descent method simultaneously. The number of parameters of this algorithm isequal to that of the existing training algorithm for HHFNN, however, the training algorithm based on Takagi-Sugeno fuzzy system performs much better than the existing training algorithm and standard BPalgorithm in terms of accuracy and time consumed in learning.