RBF 神经网络的结构动态优化设计

第36卷第6期自动化学报Vol.36,No.62010年6月ACTAAUTOMATICASINICAJune,2010RBF神经网络的结构动态优化设计乔俊飞1韩红桂1摘要针对径向基函数(Radialbasisfunction,RBF)神经网络的结构设计问题,提出一种结构动态优化设计方法.利用敏感度法(Sensitivityanalysis,SA)分析隐含层神经元的输出加权值对神经网络输出的影响,以此判断增加或删除RBF神经网络隐含层中的神经元,解决了RBF神经网络结构过大或过小的问题,并给出了神经网络结构动态变化过程中收敛性证明;利用梯度下降的参数修正算法保证了最终RBF网络的精度,实现了神经网络的结构和参数自校正.通过对非线性函数的逼近与污水处理过程中关键参数的建模结果,证明了该动态RBF具有良好的自适应能力和逼近能力,尤其是在泛化能力、最终网络结构等方面较之最小资源神经网络(Minimalresourceallocationnetworks,MRAN)与增长和修剪RBF神经网络(Generalizedgrowingandpruningradialbasisfunction,GGAP-RBF)有较大提高.关键词径向基函数神经网络,动态设计,动态结构RBF,化学需氧量建模DOI10.3724/SP.J.1004.2010.00865OptimalStructureDesignforRBFNNStructureQIAOJun-Fei1HANHong-Gui1AbstractDuetothefactthattheconventionalradialbasisfunction(RBF)neuralnetworkcannotchangethestructureon-line,anewdynamicstructureRBF(D-RBF)neuralnetworkisdesignedinthispaper.D-RBFisbasedonthesensitivityanalysis(SA)methodtoanalyzetheoutputvaluesofthehiddennodesforthenetworkoutput,thenthehiddennodesintheRBFneuralnetworkcanbeinsertedorpruned.ThefinalstructureofD-RBFisnottoolargeorsmallfortheobjectives,andtheconvergenceofthedynamicprocessisinvestigatedinthispaper.Thegrad-descendmethodfortheparameteradjustingensurestheconvergenceofD-RBFneuralnetwork.ThestructureoftheRBFneuralnetworkisself-organizing,andtheparametersareself-adaptive.Intheend,D-RBFisusedforthenon-linearfunctionsapproximationandthenon-linearsystemsmodelling.TheresultsshowthatthisproposedD-RBFobtainsfavorableself-adaptiveandapproximatingability.Especially,comparisonswiththeminimalresourceallocationnetworks(MRAN)andthegeneralizedgrowingandpruningRBF(GGAP-RBF)revealthattheproposedalgorithmismoreeffectiveingeneralizationandfinallyneuralnetworkstructure.KeywordsRadialbasisfunction(RBF)neuralnetwork,dynamicdesign,dynamicstructureRBF(D-RBF),chemicaloxygendemand(COD)modelling径向基函数(Radialbasisfunction,RBF)神经网络由于其简单的拓扑结构和全局逼近能力,在模式识别[1]、信号处理[2]、非线性系统的建模和控制等方面[3−4]得到了广泛的应用.目前,高斯径向基神经网络最为常见.RBF神经网络应用的关键问题是其结构设计问题.近年来,相继提出一些RBF神经网络结构优收稿日期2009-08-27录用日期2009-10-23ManuscriptreceivedAugust27,2009;ac