基于KPCA-Bagging的高斯过程回归建模方法及应用
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摘要
工业污水处理过程具有高度非线性的特点,对水质指标中的生物需氧量的实时监测提出了挑战,提出一种基于核主元分析和Bagging算法的高斯过程回归建模方法。首先,采用核主元分析方法将采集到的污水数据投影到高维空间进行降维处理,提取非线性主元作为模型输入;然后采用Bagging集成学习算法得到若干样本子集,建立相应的高斯过程回归模型;最后根据贝叶斯后验概率计算得到各子模型的权重,对各子模型的输出进行融合,得到全局预测值。对实际污水处理过程数据的仿真结果表明,所提方法具有良好的预测精度与泛化能力。
Industrial sewage treatment processes are often characterized by strong nonlinearity,which poses a great challenge for real-time monitoring and prediction of water quality index-biochemical oxygen demand value.Therefore,a Gaussian process regression modeling method is proposed based on KPCA-Bagging algorithm.Firstly,the kernel principal component analysis is employed to project the low dimensional sewage dataset to the higher space for dimension reduction,and nonlinear principle components can be extracted as the new input dataset of the soft sensor model.Then,a bagging based ensemble learning algorithm is utilized to obtain several sample subsets from the original dataset.For each sub dataset a Gaussian process regression model can be constructed accordingly.Finally,the global model prediction output can be obtained by combining Bayesian posterior probabilities with prediction values of all sub-models.Simulation results for the real sewage treatment process dataset have indicated that the proposed algorithm has a good prediction accuracy as well as the generalization performance.
Industrial sewage treatment processes are often characterized by strong nonlinearity,which poses a great challenge for real-time monitoring and prediction of water quality index-biochemical oxygen demand value.Therefore,a Gaussian process regression modeling method is proposed based on KPCA-Bagging algorithm.Firstly,the kernel principal component analysis is employed to project the low dimensional sewage dataset to the higher space for dimension reduction,and nonlinear principle components can be extracted as the new input dataset of the soft sensor model.Then,a bagging based ensemble learning algorithm is utilized to obtain several sample subsets from the original dataset.For each sub dataset a Gaussian process regression model can be constructed accordingly.Finally,the global model prediction output can be obtained by combining Bayesian posterior probabilities with prediction values of all sub-models.Simulation results for the real sewage treatment process dataset have indicated that the proposed algorithm has a good prediction accuracy as well as the generalization performance.
引文
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[15]夏陆岳,王海宁,朱鹏飞,等.KPCA-bagging集成神经网络软测量建模方法[J].信息与控制,2015,44(5):519-524.Xia L Y,Wang H N,Zhu P F,et al.Soft Sensor Modeling Method Using Kernel Principal Component Analysis Bagging Ensemble Neural Network[J].Information and Control,2015,44(5):519-524.
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[18]嵇小辅,张翔.基于FCM与集成高斯过程回归的赖氨酸发酵软测量[J].智能系统学报,2015,10(1):156-162.Ji X F,Zhang X.Soft Measurement of Lysine Fermentation Based on FCM and Intergrated Gaussian Process Regression[J].CAAITransactions on Intelligent Systems,2015,10(1):156-162.
[19]张伟,熊伟丽,徐保国.基于实时学习的高斯过程回归多模型融合建模[J].信息与控制,2015,44(4):487-492,498.Zhang W,Xiong W L,Xu B G.Multi-model Combination Modeling Based on Just-in-time Learning Using Gaussian Process Regression[J].Information and Control,2015,44(4):487-492,498.
[20]Liu Y,Chen J.Integrated Soft Sensor Using Just-in-time Support Vector Regression and Probabilistic Analysis for Quality Prediction of Multi-grade Processes[J].Journal of Process Control,2013,23(6):793-804.
[21]程起才,王洪元,吴小俊,等.一种基于ISOMAP的分类算法[J].控制与决策,2011,26(6):826-830.Cheng Q C,Wang H Y,Wu X J,et al.An Algorithm for Classification Based on ISOMAP[J].Control and Decision,2011,26(6):826-830.
[2]张昭昭.污水处理过程出水水质多模型在线软测量方法[J].控制工程,2014,21(1):88-93.Zhang Z Z.An Online Multi-Mode Softsening Method of Water Quality in Wastewater Treatment Process[J].Control Engineering of China,2014,21(1):88-93.
[3]Aguado D,Ferrer A,Seco A,et al.Comparison of Different Predictive Models for Nutrient Estimation in a Sequencing Batch Reactor for Wastewater Treatment[J].Chemometrics and Intelligent Laboratory Systems,2006,84(1):75-81.
[4]Huang M,Wan J,Ma Y,et al.A Fast Predicting Neural Fuzzy Model for On-line Estimation of Nutrient Dynamics in an Anoxic/Oxic Process[J].Bioresource Technology,2010,101(6):1642-1651.
[5]Yan W,Shao H,Wang X.Soft Sensing Modeling Based on Support Vector Machine and Bayesian Model Selection[J].Computers&Chemical Engineering,2004,28(8):1489-1498.
[6]Lee D S,Jeon C O,Park J M,et al.Hybrid Neural Network Modeling of a Full-scale Industrial Wastewater Treatment Process[J].Biotechnology and bioengineering,2002,78(6):670-682.
[7]Aguado D,Ribes J,Montoya T,et al.A Methodology for Sequencing Batch Reactor Identification with Artificial Neural Networks:A Case Study[J].Computers&Chemical Engineering,2009,33(2):465-472.
[8]沈学华,周志华.Boosting和Bagging综述[J].计算机工程与应用,2000,36(12):31-32.Shen X H,Zhou Z H.Survey of Boosting and Bagging[J].Computer Engineering and Applications,2000,36(12):31-32.
[9]Chen T,Ren J.Bagging for Gaussian Process Regression[J].Neurocomputing,2009,72(7):1605-1610.
[10]唐伟,周志华.基于Bagging的选择性聚类集成[J].软件学报,2005,16(4):496-502.Tang W,Zhou Z H.Bagging-Based Selective Clusterer Ensemble[J].Journal of Software,2005,16(4):496-502.
[11]Borra S,Di Ciaccio A.Improving Nonparametric Regression Methods by Bagging and Boosting[J].Computational Statistics&Data Analysis,2002,38(4):407-420.
[12]黄永红,孙丽娜,程浩.燃料乙醇发酵过程中生物参量的软测量建模[J].控制工程,2014,21(2):263-267.Huang Y H,Sun L N,Cheng H.Soft Sensing Modeling of Biological Parameters in the Fuel Ethanol Fermentation Process[J].Control Engineering of China,2014,2(21):263-267.
[13]Li Z,Tian X.Study of Soft Sensor Modeling Method Based on KPCA-SVM[C].Intelligent Control and Automation,2006.WCICA2006.The Sixth World Congress on.IEEE,2006,1:4876-4880.
[14]Yang H,Huang M.A Soft Sensor Based on Kernel PCA and Composite Kernel Support Vector Regression for a Flotation Circuit[C].Advanced Computer Control(ICACC),2010 2nd International Conference on.IEEE,2010,5:375-378.
[15]夏陆岳,王海宁,朱鹏飞,等.KPCA-bagging集成神经网络软测量建模方法[J].信息与控制,2015,44(5):519-524.Xia L Y,Wang H N,Zhu P F,et al.Soft Sensor Modeling Method Using Kernel Principal Component Analysis Bagging Ensemble Neural Network[J].Information and Control,2015,44(5):519-524.
[16]Rasmussen C E.Gaussian Processes for Machine Learning[M].Cambridge,Massachusetts,MIT Press,2006.
[17]何志昆,刘光斌,赵曦晶,等.高斯过程回归方法综述[J].控制与决策,2013,28(8):1121-1129.He Z K,Liu G B,Zhao X J,et al.Overview of Gaussian Process Regression[J].Control and Decision,2013,28(8):1121-1129.
[18]嵇小辅,张翔.基于FCM与集成高斯过程回归的赖氨酸发酵软测量[J].智能系统学报,2015,10(1):156-162.Ji X F,Zhang X.Soft Measurement of Lysine Fermentation Based on FCM and Intergrated Gaussian Process Regression[J].CAAITransactions on Intelligent Systems,2015,10(1):156-162.
[19]张伟,熊伟丽,徐保国.基于实时学习的高斯过程回归多模型融合建模[J].信息与控制,2015,44(4):487-492,498.Zhang W,Xiong W L,Xu B G.Multi-model Combination Modeling Based on Just-in-time Learning Using Gaussian Process Regression[J].Information and Control,2015,44(4):487-492,498.
[20]Liu Y,Chen J.Integrated Soft Sensor Using Just-in-time Support Vector Regression and Probabilistic Analysis for Quality Prediction of Multi-grade Processes[J].Journal of Process Control,2013,23(6):793-804.
[21]程起才,王洪元,吴小俊,等.一种基于ISOMAP的分类算法[J].控制与决策,2011,26(6):826-830.Cheng Q C,Wang H Y,Wu X J,et al.An Algorithm for Classification Based on ISOMAP[J].Control and Decision,2011,26(6):826-830.