基于加速梯度求法的置信规则库参数训练方法
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摘要
置信规则库(belief rule base,BRB)的参数训练问题实质上是一个带有约束条件的非线性优化问题,目前在求解该问题上主要使用FMINCON函数及群智能算法,但在算法的应用中存在移植性差,难实现,计算时间长等局限性。通过对这些问题的研究,结合现有的参数训练方法提出了基于加速梯度求法的置信规则库参数训练方法,并将其应用在多峰函数、输油管道泄漏检测的置信规则库的参数训练上。以收敛误差、收敛时间和皮尔森相关系数作为衡量指标,对新方法与其他传统方法进行了对比,实验结果表明,新算法在收敛精度和收敛速度上具有更理想的综合效益。
The problem of training parameters for belief rule base(BRB) is essentially a nonlinear optimization problem with constraints, which is mainly solved by the FMINCON function or the swarm intelligence algorithms. However, these approaches have many shortages, such as poor portability, difficult to be implemented and requiring a large amount of calculation. To solve these problems, this paper proposes a new parameter training approach for BRB using the accelerating of gradient algorithm, which is improved from the existing parameter training methods,and is applied to the parameter training of multimodal function and pipeline leak detection. The proposed approach is compared with other traditional approaches in terms of convergence error, convergence precision and Pearson correlation coefficient in experiment analysis. The results show the better comprehensive benefits of the proposed approach, including convergence accuracy and convergence speed.
The problem of training parameters for belief rule base(BRB) is essentially a nonlinear optimization problem with constraints, which is mainly solved by the FMINCON function or the swarm intelligence algorithms. However, these approaches have many shortages, such as poor portability, difficult to be implemented and requiring a large amount of calculation. To solve these problems, this paper proposes a new parameter training approach for BRB using the accelerating of gradient algorithm, which is improved from the existing parameter training methods,and is applied to the parameter training of multimodal function and pipeline leak detection. The proposed approach is compared with other traditional approaches in terms of convergence error, convergence precision and Pearson correlation coefficient in experiment analysis. The results show the better comprehensive benefits of the proposed approach, including convergence accuracy and convergence speed.
引文
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[10]常瑞,张速.基于优化步长和梯度法的置信规则库参数学习方法[J].华北水利水电学院学报,2011,32(1):154-157.
[13]马昌凤.最优化方法及其Matlab程序设计[M].北京:科学出版社,2010.
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[20]王沫然.MATLAB与科学计算[M].北京:电子工业出版社,2003.
[23]郝黎仁.SPSS实用统计分析[M].北京:中国水利水电出版社,2003.
[2]Yang Jianbo,Liu Jun,Wang Jin,et al.Belief rule-base inference methodology using the evidential reasoning approach—RIMER[J].IEEE Transactions on Systems,Man,and Cybernetics:Part A Systems and Humans,2006,36(2):266-285.
[3]Dempster A P.A generalization of Bayesian inference[J].Journal of the Royal Statistical Society:Series B Methodological,1968,30(2):205-247.
[4]Shafer G.A mathematical theory of evidence[M].Princeton,USA:Princeton University Press,1976.
[5]Hwang C,Yoon K.Methods for multiple attribute decision making[J].Multiple Attribute Decision Making Lecture Nodes in Economics and Mathematical Systems,1981,186:58-191.
[6]Zadeh L Z.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[7]Jiang Jiang,Li Xuan,Zhou Zhijie,et al.Weapon system capability assessment under uncertainty based on the evidential reasoning approach[J].Expert Systems with Applications,2011,38(11):13773-13784.
[8]Zhou Zhijie,Hu Changhua,Yang Jianbo,et al.Online updating belief-rule-based system for pipeline leak detection under expert intervention[J].Expert Systems with Applications,2009,36(4):7700-7709.
[9]Yang Jianbo,Liu Jun,Xu Dongling,et al.Optimization model for training belief-rule-based systems[J].IEEE Transactions on Systems,Man,and Cybernetics:Part A Systems and Humans,2007,37(4):569-585.
[10]Chang Rui,Zhang Su.An algorithm for training parameters in belief rule-bases based on gradient methods with optimization step size[J].North China Institute of Water Conservancy and Hydroelectric Power,2011,32(1):154-157.
[11]Lee B H,Kim S,Seok J W,et al.Nonlinear system identification based on support vector machine using particle swarm optimization[C]//Proceedings of the International Joint Conference on SICE-ICASE.Piscataway,NJ,USA:IEEE,2006:5614-5618.
[12]Chang Leilei,Li Mengjun,Jiang Jiang,et al.Parameter learning for the belief rule base system in the residual life probability prediction of metalized film capacitor[J].European Journal of Operational Research,submitted.
[13]Ma Changfeng.Optimization method and Matlab programming[M].Beijing:Science Press,2010.
[14]Wang Yingming,Yang Jianbo,Xu Dongling.Environmental impact assessment using the evidential reasoning approach[J].European Journal of Operational Research,2006,174(3):1885-1913.
[15]Duan Xinsheng.Evidence theory,decision&artificial intelligence[M].Beijing:Renmin University of China Press,1993.
[16]Wang Yingming,Yang Jianbo,Xu Dongling,et al.The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees[J].European Journal of Operational Research,2006,175(1):35-66.
[17]Chen Yuwang,Yang Jianbo,Xu Dongling,et al.Inference analysis and adaptive training for belief rule based systems[J].Expert Systems with Applications,2011,38(10):12845-12860.
[18]Jia Dongli.Modified differential evolution algorithm and its application in communications signal processing[D].Shanghai:Shanghai University,2011.
[19]Department of Mathematics,Tongji University.Advanced mathematics/Volume 1[M].Beijing:Higher Education Press,2007.
[20]Wang Moran.MATLAB and scientific computing[M].Beijing:Electronic Industry Press,2003.
[21]Shi Zhenjun.A new super-memory gradient method for unconstrained optimization[J].Advances in Mathematics,2006,3(35):265-274.
[22]Chen Yuwang,Yang Jianbo,Xu Dongling,et al.On the inference and approximation properties of belief rule based systems[J].Information Sciences,2013,234:121-135.
[23]Hao Liren.SPSS practical statistics[M].Beijing:China Water & Power Press,2003.
[10]常瑞,张速.基于优化步长和梯度法的置信规则库参数学习方法[J].华北水利水电学院学报,2011,32(1):154-157.
[13]马昌凤.最优化方法及其Matlab程序设计[M].北京:科学出版社,2010.
[15]段新生.证据理论与决策、人工智能[M].北京:中国人民大学出版社,1993.
[18]贾东立.改进的差分进化算法及其在通信信号处理中的应用研究[D].上海:上海大学,2011.
[19]同济大学数学系.高等数学/上册[M].北京:高等教育出版社,2007.
[20]王沫然.MATLAB与科学计算[M].北京:电子工业出版社,2003.
[23]郝黎仁.SPSS实用统计分析[M].北京:中国水利水电出版社,2003.