基于LM算法的相关模糊神经网络及其应用

针对输入变量相关性较高的非线性建模模型,经典模糊神经网络算法存在收敛速度缓慢、模糊规则数大、陷入局部最小值的问题。提出一种基于LM算法的相关模糊神经网络模型;该模型基于聚类思想,构建多变量高斯模糊隶属度函数,将其表示为不可分离的模糊关系来处理相关变量模型;再采用LM优化算法,通过Hessian矩阵和一阶梯度向量同时调整网络参数;并引入Cholesky定理缩减网络参数个数。应用LM算法的模糊神经网络模型实验结果表明,可以加快收敛速度、减少模糊规则数,比经典的模糊神经网络有更好的预测精度。

LM Algorithm Based Relevance Fuzzy Neural Network and Its Application

In this paper, a novel LM-based relevance fuzzy neural network was proposed to resolve the problems of classical fuzzy neural network, such as low convergence rate, large fuzzy rule numbers and easily failing into local minimum, in the high input variable relevance nonlinearity modeling model. Based on the cluster theory, the proposed model structures multivariable Gaussian fuzzy membership function, and expresses it as indivisible fuzzy relation to process relevant variable model. Then the LM optimization algorithm is adapted to adjust the network parameters by using Hessian matrix and first-order gradient vector simultaneously, in addition, the Cholesky theorem is introduced to reduce the number of network parameters. The experiment results on LM-based fuzzy neural network model indicated that the propose method can accelerate the convergence rate, reduce the fuzzy rule numbers and achieve higher prediction accuracy compared with classical fuzzy neural network.