基于EKF与TLS动态模糊神经网络算法
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摘要
提出了一种动态模糊神经网络(D-FNN)算法。在实际应用中,可以用卡尔曼滤波(KF)方法来调节D-FNN结果参数,同时,EKF (扩展卡尔曼滤波)方法用于更新前提参数的中心和宽度,从而使得所有参数都被修正。该算法可用于平滑、滤波或者预测非线性动态系统的状态,同其他基于梯度的在线算法相比,EKF可以加快D-FNN收敛速度。采用总体最小二乘(TLS)方法作为修剪技术来选择D-FNN重要的模糊规则。如果在学习进行时,检测到不活跃的模糊规则并加以剔除,则可获得更为紧凑的D-FNN结构,TLS方法是用来补偿线性参数估计问题中数据误差的一种技术。最后针对实际案例进行了仿真分析,验证了该算法的有效性和高效性。
A dynamic fuzzy neural network algorithm(D-FNN) is proposed.In practical application,Kalman filter(KF) is used to adjust the result parameters of D-FNN.Meanwhile,extended Kalman filter(EKF) is used to update the center and width of the premise parameters,so that all parameters can be modified.This algorithm is used to smooth,filter or predict the state of a nonlinear dynamic system.Comparing to other online algorithms which are based on gradient,EKF can accelerate the convergence speed of D-FNN.The total least squares(TLS) is a pruning technique to select the important fuzzy rules of D-FNN,which also is a technique to compensate data error in linear parameter estimation problem.If the inactive fuzzy rules are detected and removed during the learning process,a more compact D-FNN structure can be obtained.Finally,a simulation analysis for actual case verify the effectiveness and efficiency of the algorithm.
A dynamic fuzzy neural network algorithm(D-FNN) is proposed.In practical application,Kalman filter(KF) is used to adjust the result parameters of D-FNN.Meanwhile,extended Kalman filter(EKF) is used to update the center and width of the premise parameters,so that all parameters can be modified.This algorithm is used to smooth,filter or predict the state of a nonlinear dynamic system.Comparing to other online algorithms which are based on gradient,EKF can accelerate the convergence speed of D-FNN.The total least squares(TLS) is a pruning technique to select the important fuzzy rules of D-FNN,which also is a technique to compensate data error in linear parameter estimation problem.If the inactive fuzzy rules are detected and removed during the learning process,a more compact D-FNN structure can be obtained.Finally,a simulation analysis for actual case verify the effectiveness and efficiency of the algorithm.
引文
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[2]LEONTARITIS I J,BILLINGS S A.Input-output parametric models for nonlinear systems,Part 1:deterministic nonlinear systems[J].Int J Contr,1985,41(2):303-328.
[3]van HUFFEL S,VANDEWALLE J.The total least squares problem:computational aspects and analysis[M].Philadelphia,PA:SIAM,2015.
[4]van HUFFEL S,VANDEWALLE J.Subset selection using the least squares approach in collinearity problems with errors in the variables[J].Linear Algeb Applicat,2014,88/89:695-714.
[5]CHAO C T,CHEN Y J,TENG C C.Simplification of fuzzy-neural systems using similarity analysis[J].IEEETrans Syst Man Cybern B Cybern,1996,26(2):344-354.
[6]张雨浓,肖争利,丁思彤,等.带后续迭代的双极S函数激励的WASD神经网络[J].中山大学学报(自然科学版),2016,55(4):1-10.ZHANG Y N,XIAO Z L,DING S T,et al.WASD neural network activated by bipolar sigmoid functions together with subsequent iterations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2016,55(4):1-10.
[7]LU Y,SUNDARARAJAN N,SARATCHANDRAN P.Asequential learning scheme for function approximation by using minimal radial basis function networks[J].Neural Computation,1997,9(2):461-478.
[8]杨文光,钟云香,李强丽,等.双输入样条神经网络权值与结构确定算法[J].中山大学学报(自然科学版),2014,53(3):61-66.YANG W G,ZHONG Y X,LI Q L,et al.Weights and structure determination of dual-input spline neural network[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(3):61-66.
[9]TURK M A,PENTLAND A P.Eigenfaces for recognition[J].J Cognitive Neuroscience,1991,3(1):71-86.
[10]JANG J-S R.ANFIS:adaptive-network-based fuzzy inference system[J].IEEE Trans Syst Man Cybern,1993,23(3):665-685.
[11]PLATT J.A resource-allocating network for function interpolation[J].Neural Computation,1991,3(2):213-225.
[12]KADIRKAMANATHAN V,NIRANJAN M.A function estimation approach to sequential learning with neural networks[J].Neural Computation,1993,5(6):954-975.
[13]吴志攀,赵跃龙,罗中良,等.基于PSO-BP神经网络的车牌号码识别技术[J].中山大学学报(自然科学版),2017,56(1):46-52WU Z P,ZHAO Y L,LUO Z L,et al.License plate recognition technology based on PSO-BP neural network[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2017,56(1):46-52.
[14]CHEN S,COWAN C F N,GRANT P M.Orthogonal least squares learning algorithm for radial basis function networks[J].IEEE Trans Neural Networks,1991,2(2):302-309.
[15]WU S Q,ER M J.Dynamic fuzzy neural networks:a novel approach to function approximation[J].IEEETrans Syst Man Cybern Part B:Cybern,2000,30(2):358-364.