基于动态多核相关向量机的软测量建模研究
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摘要
针对污水处理过程中存在的多变量耦合、强非线性以及参数时变等问题,提出基于多核学习相关向量机的软测量建模方法,并采用粒子群算法对多核权重以及核参数进行优化。同时,引入时间差分(time difference)方法改进多核相关向量机的动态特性。为了验证所提模型的有效性,通过一仿真案例与单核相关向量机、多层前馈神经网络和基于遗传算法的支持向量机进行对比研究。结果表明,所提模型具有更好的预测效果。最后,对模型的鲁棒性在数据漂移和异常的场景下进行了讨论。
Considering the characteristics of strong multivariable coupling, significant non-linearity and parameter time-varying in the wastewater treatment processes, a multi-kernel relevance vector machine(MRVM) is proposed for soft-sensor modeling. Particle swarm optimization algorithm is further used to optimize multi-kernel weights and kernel parameters. Meanwhile, the time difference(TD) method is introduced to improve the dynamic characteristics of MRVM. The proposed model was demonstrated through a WWTP simulated case study by comparison with relevance vector machine(RVM) with a single kernel, back propagation(BP) neural network and the genetic algorithm-based support vector machine(GA-SVM). Results showed that the proposed model achieved better prediction accuracy. Finally, the robustness of the models is discussed in the context of data drift and anomalies.
Considering the characteristics of strong multivariable coupling, significant non-linearity and parameter time-varying in the wastewater treatment processes, a multi-kernel relevance vector machine(MRVM) is proposed for soft-sensor modeling. Particle swarm optimization algorithm is further used to optimize multi-kernel weights and kernel parameters. Meanwhile, the time difference(TD) method is introduced to improve the dynamic characteristics of MRVM. The proposed model was demonstrated through a WWTP simulated case study by comparison with relevance vector machine(RVM) with a single kernel, back propagation(BP) neural network and the genetic algorithm-based support vector machine(GA-SVM). Results showed that the proposed model achieved better prediction accuracy. Finally, the robustness of the models is discussed in the context of data drift and anomalies.
引文
[1]肖红军,刘乙奇,黄道平.面向污水处理的动态变分贝叶斯混合因子故障诊断[J].控制理论与应用, 2016, 33(11):1519-1526.Xiao H J, Liu Y Q, Huang D P. Dynamic fault diagnosis via variational Bayesian mixture factor analysis with application to wastewater treatment[J]. Control Theory&Applications, 2016, 33(11):1519-1526.
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[3]曹鹏飞,罗雄麟.化工过程软测量建模方法研究进展[J].化工学报, 2013, 64(3):788-800.Cao P F, Luo X L. Modeling of soft sensor for chemical process[J].CIESC Journal, 2013, 64(3):788-800.
[4] Haimi H, Mulas M, Corona F, et al. Data-derived soft-sensors for biological wastewater treatment plants:an overview[J].Environmental Modelling&Software, 2013, 47:88-107.
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[6] Huang Y R, Zhang S D. Dissolved oxygen intelligent optimization control system in the aeration tank of wastewater treatment[J].Information and Control, 2011, 40(3):393-400.
[7]曹巍,赵英凯,高世伟.基于模糊核聚类的多类支持向量机[J].化工学报, 2010, 61(2):420-424.Cao W, Zhao Y K, Gao S W. Multi-class support vector machines based on fuzzy kernel cluster[J]. CIESC Journal, 2010, 61(2):420-424.
[8]刘瑞兰,徐艳,戎舟.基于稀疏最小二乘支持向量机的软测量建模[J].化工学报, 2015, 66(4):1402-1406.Liu R L, Xu Y, Rong Z. Modeling soft sensor based on sparse least square support vector machine[J]. CIESC Journal, 2015, 66(4):1402-1406.
[9]马建,邓晓刚,王磊.基于深度集成支持向量机的工业过程软测量方法[J].化工学报, 2018, 69(3):1121-1128.Ma J, Deng X G, Wang L. Industrial process soft sensor method based on deep learning ensemble support vector machine[J].CIESC Journal, 2018, 69(3):1121-1128.
[10] Tipping M E. Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 2001,(1):211-244.
[11] Ge Z Q, Song Z H. Nonlinear soft sensor development based on relevance vector machine[J]. Industrial&Engineering Chemistry Research, 2010, 49(18):8685-8693.
[12] Motai Y. Kernel association for classification and prediction:a survey[J]. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(2):208-223.
[13] Liu Y, Chen J, Sun Z, et al. A probabilistic self-validating softsensor with application to wastewater treatment[J]. Computers&Chemical Engineering, 2014, 71(71):263-280.
[14] Liu Y. Adaptive just-in-time and relevant vector machine based soft-sensors with adaptive differential evolution algorithms for parameter optimization[J]. Chemical Engineering Science, 2017,172:571-584.
[15]许玉格,曹涛,罗飞.基于相关向量机的污水处理出水水质预测模型[J].华南理工大学学报(自然科学版), 2014, 42(5):103-108.Xu Y G, Cao T, Luo F. Wastewater effluent quality prediction model base on relevance vector machine[J]. Journal of South China University of Technology(Natural Science Edition), 2014, 42(5):103-108.
[16]汪洪桥,孙富春,蔡艳宁,等.多核学习方法[J].自动化学报,2010, 36(8):1037-1050.Wang H Q, Sun F C, Cai Y N, et al. On multiple kernel learning methods[J]. Acta Automatica Sinica, 2010, 36(8):1037-1050.
[17]杨柳,张磊,张少勋,等.单核和多核相关向量机的比较研究[J].计算机工程, 2010, 36(12):195-197.Yang L, Zhang L, Zhang S X, et al. Comparison research of single kernel and multi-kernel relevance vector machine[J]. Computer Engineering, 2010, 36(12):195-197.
[18] Lee W J, Verzakov S, Duin R P W. Kernel combination versus classifier combination[C]//International Workshop on Multiple Classifier Systems. Heidelberg, Berlin:Springer, 2007:22-31.
[19] G?nen M, Alpayd?n E. Localized multiple kernel learning[C]//Proceedings of the 25th International Conference on Machine Learning. Helsinki, Finland:ACM, 2008:352-359
[20] Kloft M, Brefeld U, Laskov P, et al. Non-sparse multiple kernel learning[C]//Proceedings of the Workshop on Kernel Learning:Automatic Selection of Optimal Kernels. Whistler, Canada:The MIT Press, 2008:1-4
[21]曹涛.基于相关向量机的污水软测量建模研究[D].广州:华南理工大学, 2015.Cao T. Study of soft sensor modeling for wastewater treatment process base on relevance vector machine[D]. Guangzhou:South China University of Technology, 2015.
[22] Lin Y, Xia K, Jiang X, et al. Landslide susceptibility mapping based on particle swarm optimization of multiple kernel relevance vector machines:case of a low Hill Area in Sichuan Province,China[J]. ISPRS International Journal of Geo-Information, 2016, 5(10):191.
[23]赵朋程,刘彬,高伟,等.用于水泥熟料fCaO预测的多核最小二乘支持向量机模型[J].化工学报, 2016, 67(6):2480-2487.Zhao P C, Liu B, Gao W, et al. Multiple kernel least square support vector machine model for prediction of cement clinker lime content[J]. CIESC Journal, 2016, 67(6):2480-2487.
[24] Kaltwang S, Todorovic S, Pantic M. Doubly sparse relevance vector machine for continuous facial behavior estimation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016,38(9):1748-1761.
[25] Souza F A A, Araujo R, Mendes J. Review of soft sensor methods for regression applications[J]. Chemometrics and Intelligent Laboratory Systems, 2016, 152:69-79.
[26] Kaneko H, Funatsu K. Moving window and just-in-time soft sensor model based on time differences considering a small number of measurements[J]. Industrial&Engineering Chemistry Research, 2015, 54(2):700-704.
[27] Qin S J. Recursive PLS algorithms for adaptive data modeling[J].Computers&Chemical Engineering, 1998, 22(4/5):503-514.
[28]刘乙奇.自确认软测量模型研究及其在污水处理中的应用[D].广州:华南理工大学, 2013.Liu Y Q. Research on self-validating soft sensor modeling and its application in wastewater treatment process[D]. Guangzhou:South China University of Technology, 2013.
[29] Kaneko H, Funatsu K. Maintenance-free soft sensor models with time difference of process variables[J]. Chemometrics and Intelligent Laboratory Systems, 2011, 107(2):312-317.
[30] Kaneko H, Funatsu K. Classification of the degradation of soft sensor models and discussion on adaptive models[J]. AIChE Journal, 2013, 59(7):2339-2347.
[31] Xiong W, Li Y, Zhao Y, et al. Adaptive soft sensor based on time difference Gaussian process regression with local time-delay reconstruction[J]. Chemical Engineering Research and Design,2017, 117:670-680.
[32] Duvenaud D. Automatic model construction with Gaussian processes[D]. Cambridge:University of Cambridge, 2014.
[2]黄道平,刘乙奇,李艳.软测量在污水处理过程中的研究与应用[J].化工学报, 2011, 62(1):1-9.Huang D P, Liu Y Q, Li Y. Soft sensor research and its application in wastewater treatment[J]. CIESC Journal, 2011, 62(1):1-9.
[3]曹鹏飞,罗雄麟.化工过程软测量建模方法研究进展[J].化工学报, 2013, 64(3):788-800.Cao P F, Luo X L. Modeling of soft sensor for chemical process[J].CIESC Journal, 2013, 64(3):788-800.
[4] Haimi H, Mulas M, Corona F, et al. Data-derived soft-sensors for biological wastewater treatment plants:an overview[J].Environmental Modelling&Software, 2013, 47:88-107.
[5] Vapnik V N, Vapnik V. Statistical Learning Theory[M]. New York:Wiley, 1998.
[6] Huang Y R, Zhang S D. Dissolved oxygen intelligent optimization control system in the aeration tank of wastewater treatment[J].Information and Control, 2011, 40(3):393-400.
[7]曹巍,赵英凯,高世伟.基于模糊核聚类的多类支持向量机[J].化工学报, 2010, 61(2):420-424.Cao W, Zhao Y K, Gao S W. Multi-class support vector machines based on fuzzy kernel cluster[J]. CIESC Journal, 2010, 61(2):420-424.
[8]刘瑞兰,徐艳,戎舟.基于稀疏最小二乘支持向量机的软测量建模[J].化工学报, 2015, 66(4):1402-1406.Liu R L, Xu Y, Rong Z. Modeling soft sensor based on sparse least square support vector machine[J]. CIESC Journal, 2015, 66(4):1402-1406.
[9]马建,邓晓刚,王磊.基于深度集成支持向量机的工业过程软测量方法[J].化工学报, 2018, 69(3):1121-1128.Ma J, Deng X G, Wang L. Industrial process soft sensor method based on deep learning ensemble support vector machine[J].CIESC Journal, 2018, 69(3):1121-1128.
[10] Tipping M E. Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 2001,(1):211-244.
[11] Ge Z Q, Song Z H. Nonlinear soft sensor development based on relevance vector machine[J]. Industrial&Engineering Chemistry Research, 2010, 49(18):8685-8693.
[12] Motai Y. Kernel association for classification and prediction:a survey[J]. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(2):208-223.
[13] Liu Y, Chen J, Sun Z, et al. A probabilistic self-validating softsensor with application to wastewater treatment[J]. Computers&Chemical Engineering, 2014, 71(71):263-280.
[14] Liu Y. Adaptive just-in-time and relevant vector machine based soft-sensors with adaptive differential evolution algorithms for parameter optimization[J]. Chemical Engineering Science, 2017,172:571-584.
[15]许玉格,曹涛,罗飞.基于相关向量机的污水处理出水水质预测模型[J].华南理工大学学报(自然科学版), 2014, 42(5):103-108.Xu Y G, Cao T, Luo F. Wastewater effluent quality prediction model base on relevance vector machine[J]. Journal of South China University of Technology(Natural Science Edition), 2014, 42(5):103-108.
[16]汪洪桥,孙富春,蔡艳宁,等.多核学习方法[J].自动化学报,2010, 36(8):1037-1050.Wang H Q, Sun F C, Cai Y N, et al. On multiple kernel learning methods[J]. Acta Automatica Sinica, 2010, 36(8):1037-1050.
[17]杨柳,张磊,张少勋,等.单核和多核相关向量机的比较研究[J].计算机工程, 2010, 36(12):195-197.Yang L, Zhang L, Zhang S X, et al. Comparison research of single kernel and multi-kernel relevance vector machine[J]. Computer Engineering, 2010, 36(12):195-197.
[18] Lee W J, Verzakov S, Duin R P W. Kernel combination versus classifier combination[C]//International Workshop on Multiple Classifier Systems. Heidelberg, Berlin:Springer, 2007:22-31.
[19] G?nen M, Alpayd?n E. Localized multiple kernel learning[C]//Proceedings of the 25th International Conference on Machine Learning. Helsinki, Finland:ACM, 2008:352-359
[20] Kloft M, Brefeld U, Laskov P, et al. Non-sparse multiple kernel learning[C]//Proceedings of the Workshop on Kernel Learning:Automatic Selection of Optimal Kernels. Whistler, Canada:The MIT Press, 2008:1-4
[21]曹涛.基于相关向量机的污水软测量建模研究[D].广州:华南理工大学, 2015.Cao T. Study of soft sensor modeling for wastewater treatment process base on relevance vector machine[D]. Guangzhou:South China University of Technology, 2015.
[22] Lin Y, Xia K, Jiang X, et al. Landslide susceptibility mapping based on particle swarm optimization of multiple kernel relevance vector machines:case of a low Hill Area in Sichuan Province,China[J]. ISPRS International Journal of Geo-Information, 2016, 5(10):191.
[23]赵朋程,刘彬,高伟,等.用于水泥熟料fCaO预测的多核最小二乘支持向量机模型[J].化工学报, 2016, 67(6):2480-2487.Zhao P C, Liu B, Gao W, et al. Multiple kernel least square support vector machine model for prediction of cement clinker lime content[J]. CIESC Journal, 2016, 67(6):2480-2487.
[24] Kaltwang S, Todorovic S, Pantic M. Doubly sparse relevance vector machine for continuous facial behavior estimation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016,38(9):1748-1761.
[25] Souza F A A, Araujo R, Mendes J. Review of soft sensor methods for regression applications[J]. Chemometrics and Intelligent Laboratory Systems, 2016, 152:69-79.
[26] Kaneko H, Funatsu K. Moving window and just-in-time soft sensor model based on time differences considering a small number of measurements[J]. Industrial&Engineering Chemistry Research, 2015, 54(2):700-704.
[27] Qin S J. Recursive PLS algorithms for adaptive data modeling[J].Computers&Chemical Engineering, 1998, 22(4/5):503-514.
[28]刘乙奇.自确认软测量模型研究及其在污水处理中的应用[D].广州:华南理工大学, 2013.Liu Y Q. Research on self-validating soft sensor modeling and its application in wastewater treatment process[D]. Guangzhou:South China University of Technology, 2013.
[29] Kaneko H, Funatsu K. Maintenance-free soft sensor models with time difference of process variables[J]. Chemometrics and Intelligent Laboratory Systems, 2011, 107(2):312-317.
[30] Kaneko H, Funatsu K. Classification of the degradation of soft sensor models and discussion on adaptive models[J]. AIChE Journal, 2013, 59(7):2339-2347.
[31] Xiong W, Li Y, Zhao Y, et al. Adaptive soft sensor based on time difference Gaussian process regression with local time-delay reconstruction[J]. Chemical Engineering Research and Design,2017, 117:670-680.
[32] Duvenaud D. Automatic model construction with Gaussian processes[D]. Cambridge:University of Cambridge, 2014.
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