基于互信息和自组织RBF神经网络的出水BOD软测量方法
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摘要
针对污水处理过程出水生化需氧量(biochemical oxygen demand,BOD)难以实时准确测量的问题,提出了一种基于互信息和自组织RBF神经网络的软测量方法对出水BOD进行预测。首先,使用基于互信息的方法提取相关特征参量作为软测量模型的输入变量;其次,设计一种基于误差校正-敏感度分析的自组织RBF神经网络,使用改进的Levenberg-Marquardt (LM)算法对网络进行训练以提高训练速度;最后将软测量模型应用于UCI公开数据集及实际的污水处理过程,实验结果表明该软测量模型结构紧凑,训练时间相对较短,预测精度有所提高,能够对出水BOD实现快速准确预测。
It is difficult to achieve real-time accurate measurement for effluent biochemical oxygen demand(BOD).To solve this problem, a soft-measurement method based on mutual information and a self-organizing RBF neuralnetwork is proposed for BOD prediction in this paper. First, a method based on mutual information is employed toextract feature variables, and these variables are used as inputs to the soft-measurement model. Second, a self-organizing radial basis function(RBF) neural network based on error-correction method and sensitivity analysis isdesigned, and the improved Levenberg-Marquardt(LM) algorithm is used to train parameters of the neural networkto shorten its training time. Finally, the soft-measurement model is applied to UCI public datasets and the realwastewater treatment process. The results show that the soft-measurement model has a more compact structure andrelatively short training time, and improves the prediction accuracy, which realizes a fast and accurate prediction for BOD.
It is difficult to achieve real-time accurate measurement for effluent biochemical oxygen demand(BOD).To solve this problem, a soft-measurement method based on mutual information and a self-organizing RBF neuralnetwork is proposed for BOD prediction in this paper. First, a method based on mutual information is employed toextract feature variables, and these variables are used as inputs to the soft-measurement model. Second, a self-organizing radial basis function(RBF) neural network based on error-correction method and sensitivity analysis isdesigned, and the improved Levenberg-Marquardt(LM) algorithm is used to train parameters of the neural networkto shorten its training time. Finally, the soft-measurement model is applied to UCI public datasets and the realwastewater treatment process. The results show that the soft-measurement model has a more compact structure andrelatively short training time, and improves the prediction accuracy, which realizes a fast and accurate prediction for BOD.
引文
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[11] Sharmin R, Sundararaj U, Shah S, et al. Inferential sensors for estimation of polymer quality parameters:industrial application of a PLS-based soft sensor for a LDPE plant[J]. Chemical Engineering Science, 2006, 61(19):6372-6384.
[12] Mirbagheri S A, Bagheri M, Boudaghpour S, et al. Performance evaluation and modeling of a submerged membrane bioreactor treating combined municipal and industrial wastewater using radial basis function artificial neural networks[J]. Journal of Environmental Health Science&Engineering, 2015, 13(1):1-15.
[13]王树东,葛珉昊,陈明明.基于混合递阶遗传算法优化RBF神经网络的BOD5软测量方法[J].给水排水, 2014, 40(3):149-153.Wang S D, Ge M H, Chen M M. A BOD5soft-sensing method based on a hybrid hierarchical genetic algorithm optimized RBF neural network[J]. Water&Wastewater Engineering, 2014, 40(3):149-153.
[14] Han H G, Chen Q L, Qiao J F. An efficient self-organizing RBF neural network for water quality prediction[J]. Neural Networks,2011, 24(7):717-725.
[15] Tyukin I Y, Prokhorov D V. Feasibility of random basis function approximators for modeling and control[C]//Alexander P.Proceedings of 2009 IEEE International Symposium on Intelligent Control(ISIC). St. Petersburg, Russia:IEEE, 2009:1391-1396.
[16] Li M, Wang D. Insights into randomized algorithms for neural networks:practical issues and common pitfalls[J]. Information Sciences, 2017, s382/383:170-178.
[17] Yu H, Reiner P D, Xie T, et al. An incremental design of radial basis function networks[J]. IEEE Transactions on Neural Network and Learning System, 2014, 25(10):1793-1803.
[18] Press W H, Teukolsky S A, Vetterling W T, et al. Numerical Recipes in C[M]. Cambridge:Cambridge University Press, 1988.
[19] Yu L, Liu H. Efficient feature selection via analysis of relevance and redundancy[J]. Journal of Machine Learning Research, 2004,5(12):1205-1224.
[20] Wilamowski B M, Yu H. Improved computation for LevenbergMarquardt training[J]. IEEE Transactions on Neural Networks,2010, 21(6):930-937.
[21] Xie T, Yu H, Hewlett J, et al. Fast and efficient second-order method for training radial basis function networks[J]. IEEE Transactions on Neural Networks&Learning Systems, 2012, 23(4):609-619.
[22] Hagan M T, Menhaj M B. Training feedforward networks with the Marquardt algorithm[J]. IEEE Transactions on Neural Networks,2002, 5(6):989-993.
[23] Yu W, Harris T J. Parameter uncertainty effects on variancebased sensitivity analysis[J]. Reliability Engineering&System Safety, 2009, 94(2):596-603.
[24] Saltelli A. Making best use of model evaluations to compute sensitivity indices[J]. Computer Physics Communications, 2002,145(2):280-297.
[25] Lauret P, Fock E, Mara T A. A node pruning algorithm based on a Fourier amplitude sensitivity test method[J]. IEEE Transactions on Neural Networks, 2006, 17(2):273-293.
[26] Qiao J, Li S, Han H, et al. An improved algorithm for building self-organizing feedforward neural networks[J]. Neurocomputing,2017, 262:28-40.
[27] Lu Y, Sundararajan N, Saratchandran P. A sequential learning scheme for function approximation using minimal radial basis function neural networks[J]. Neural Computation, 1997, 9(2):461-478.
[28] Huang G B, Saratchandran P, Sundararajan N. An efficient sequential learning algorithm for growing and pruning RBF(GAPRBF)networks[J]. IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics, 2004, 34(6):2284-2292.
[29] Huang G B, Saratchandran P, Sundararajan N. A generalized growing and pruning RBF(GGAP-RBF)neural network for function approximation[J]. IEEE Transactions on Neural Networks, 2005, 16(1):57-67.
[2]李一锦,夏善红. BOD微生物传感器关键技术及其发展[J].传感器与微系统, 2015, 34(7):5-11.Li Y J, Xia S H. Key techniques of BOD microbial sensor and its development[J]. Transducer and Microsystem Technologies, 2015,34(7):5-11.
[3]周平,柴天佑.典型赤铁矿磨矿过程智能运行反馈控制[J].控制理论与应用, 2014, 31(10):1352-1359.Zhou P, Chai T Y. Intelligent operational feedback control for typical hematite grinding processes[J]. Control Theory&Applications, 2014, 31(10):1352-1359.
[4]蒋朝辉,李晞月,桂卫华,等.分段线性回归和动态加权神经网络融合的高炉料位预测[J].控制理论与应用, 2015, 32(6):801-809.Jiang Z H, Li X Y, Gui W H, et al. Blast furnace stockline prediction by segmented linear-regression and dynamic weighting neural network[J]. Control Theory&Application, 2015, 32(6):801-809.
[5] Mustafa Y A, Jai G M, Alwared A I, et al. The use of artificial neural network(ANN)for the prediction and simulation of oil degradation in wastewater by AOP[J]. Environmental Science&Pollution Research, 2014, 21(12):1-8.
[6] Haimi H, Mulas M, Corrona F, et al. Data-derived soft-sensors for biological wastewater treatment plants:an overview[J].Environmental Modelling&Software, 2013, 47(3):88-107.
[7] Dürrenmatt D J, Gujer W. Data-driven modeling approaches to support wastewater treatment plant operation[J]. Environmental Modelling&Software, 2012, 30(5):47-56.
[8]冉维丽,乔俊飞.基于PCA-GABP神经网络的BOD软测量方法[J].控制工程, 2004, 11(3):212-215.Ran W L, Qiao J F. Soft-measuring technique to predict BOD based on PCA-GABP neural networks[J]. Control Engineering of China, 2004, 11(3):212-215.
[9] Tao E P, Shen W H, Liu T L, et al. Fault diagnosis based on PCA for sensors of laboratorial wastewater treatment process[J].Chemometrics&Intelligent Laboratory Systems, 2013, 128(15):49-55.
[10]郭民,张一弛,韩红桂.基于模糊神经网络的出水总磷软测量方法研究[J].计算机与应用化学, 2016, 33(2):223-227.Guo M, Zhang Y C, Han H G. Effluent total phosphorus detecting method and its application based on soft-sensor and FNN techniques[J]. Computers and Applied Chemistry, 2016, 33(2):223-227.
[11] Sharmin R, Sundararaj U, Shah S, et al. Inferential sensors for estimation of polymer quality parameters:industrial application of a PLS-based soft sensor for a LDPE plant[J]. Chemical Engineering Science, 2006, 61(19):6372-6384.
[12] Mirbagheri S A, Bagheri M, Boudaghpour S, et al. Performance evaluation and modeling of a submerged membrane bioreactor treating combined municipal and industrial wastewater using radial basis function artificial neural networks[J]. Journal of Environmental Health Science&Engineering, 2015, 13(1):1-15.
[13]王树东,葛珉昊,陈明明.基于混合递阶遗传算法优化RBF神经网络的BOD5软测量方法[J].给水排水, 2014, 40(3):149-153.Wang S D, Ge M H, Chen M M. A BOD5soft-sensing method based on a hybrid hierarchical genetic algorithm optimized RBF neural network[J]. Water&Wastewater Engineering, 2014, 40(3):149-153.
[14] Han H G, Chen Q L, Qiao J F. An efficient self-organizing RBF neural network for water quality prediction[J]. Neural Networks,2011, 24(7):717-725.
[15] Tyukin I Y, Prokhorov D V. Feasibility of random basis function approximators for modeling and control[C]//Alexander P.Proceedings of 2009 IEEE International Symposium on Intelligent Control(ISIC). St. Petersburg, Russia:IEEE, 2009:1391-1396.
[16] Li M, Wang D. Insights into randomized algorithms for neural networks:practical issues and common pitfalls[J]. Information Sciences, 2017, s382/383:170-178.
[17] Yu H, Reiner P D, Xie T, et al. An incremental design of radial basis function networks[J]. IEEE Transactions on Neural Network and Learning System, 2014, 25(10):1793-1803.
[18] Press W H, Teukolsky S A, Vetterling W T, et al. Numerical Recipes in C[M]. Cambridge:Cambridge University Press, 1988.
[19] Yu L, Liu H. Efficient feature selection via analysis of relevance and redundancy[J]. Journal of Machine Learning Research, 2004,5(12):1205-1224.
[20] Wilamowski B M, Yu H. Improved computation for LevenbergMarquardt training[J]. IEEE Transactions on Neural Networks,2010, 21(6):930-937.
[21] Xie T, Yu H, Hewlett J, et al. Fast and efficient second-order method for training radial basis function networks[J]. IEEE Transactions on Neural Networks&Learning Systems, 2012, 23(4):609-619.
[22] Hagan M T, Menhaj M B. Training feedforward networks with the Marquardt algorithm[J]. IEEE Transactions on Neural Networks,2002, 5(6):989-993.
[23] Yu W, Harris T J. Parameter uncertainty effects on variancebased sensitivity analysis[J]. Reliability Engineering&System Safety, 2009, 94(2):596-603.
[24] Saltelli A. Making best use of model evaluations to compute sensitivity indices[J]. Computer Physics Communications, 2002,145(2):280-297.
[25] Lauret P, Fock E, Mara T A. A node pruning algorithm based on a Fourier amplitude sensitivity test method[J]. IEEE Transactions on Neural Networks, 2006, 17(2):273-293.
[26] Qiao J, Li S, Han H, et al. An improved algorithm for building self-organizing feedforward neural networks[J]. Neurocomputing,2017, 262:28-40.
[27] Lu Y, Sundararajan N, Saratchandran P. A sequential learning scheme for function approximation using minimal radial basis function neural networks[J]. Neural Computation, 1997, 9(2):461-478.
[28] Huang G B, Saratchandran P, Sundararajan N. An efficient sequential learning algorithm for growing and pruning RBF(GAPRBF)networks[J]. IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics, 2004, 34(6):2284-2292.
[29] Huang G B, Saratchandran P, Sundararajan N. A generalized growing and pruning RBF(GGAP-RBF)neural network for function approximation[J]. IEEE Transactions on Neural Networks, 2005, 16(1):57-67.