基于KPLS的工业过程监测方法研究
|
摘要
随着现代工业朝着大规模、复杂化的方向发展,工业生产的过程监控和故障检测成为了工业系统关注的主要问题之一。通过对复杂生产过程的运行状态进行监测,及时发现过程干扰、故障以及其它异常工况,诊断出故障发生的原因,从而可以保证生产过程安全运行,提高产品质量和经济效益。近年来,随着计算机技术的发展和分布式控制系统(DCS)在工业过程中的广泛应用,大量的过程数据被采集并存储下来。因此,如何从海量数据中挖掘出隐藏的有用信息,使其服务于生产安全和产品质量控制,已经成为迫切需要解决的问题。在这种工程背景下,基于数据的多元统计方法受到了广泛关注,并被成功应用于过程建模、监控和控制领域。
传统的多元统计监控方法以主成分分析(PCA)和偏最小二乘(PLS)为主,这些方法通过降维的策略提取高维、变量相关的过程数据的主要信息,从而对过程的运行状况进行分析。然而在实际应用中,传统的基于多元统计的方法存在一定的局限性,表现之一在于这些方法要求过程变量之间是线性相关的,然而流程工业中过程变量之间、过程变量与质量变量之间往往存在着非线性关系,用线性的方法对数据的非线性特性进行建模将难以得到精确的模型。本文主要将针对过程数据存在的非线性问题,将一种非线性的PLS方法一核PLS (Kernel PLS, KPLS)方法应用于工业过程的在线监控,并考虑到实际应用中存在的各种问题,对基本的KPLS方法进行改进,使其能在过程监控、故障诊断和质量预测中得到更好的应用。本文的主要研究工作包括以下几个方面：
(1)针对过程监控数据的非线性特点,提出了一种基于核偏最小二乘(KPLS)的过程监控方法。该方法首先通过核函数将输入数据映射到高维特征空间,再在高维特征空间进行PLS运算。与线性PLS算法相比,KPLS算法在处理非线性问题时能够很好地建立起输入变量与输出变量之间的非线性关系,充分提取非线性系统的特征。通过构造相应的监控统计量,将KPLS方法应用于过程的在线监控,取得了比普通的PLS方法更好的监控效果。
(2)针对非线性过程采集的数据存在离群值的问题,提出了一种基于球形化KPLS (Spherical KPLS, SKPLS)的鲁棒在线监控策略。该鲁棒策略通过将高维特征空间的特征向量投影到一个单位球球面得到新的特征向量,再对新的特征向量进行KPLS算法。通过球形化的处理,减少甚至消除了离群点对建模精度的影响。与普通的KPLS方法相比,提出的SKPLS方法具有鲁棒特性,能够处理含有离群点的建模数据。此外,SKPLS方法的性能要优越于其它线性的鲁棒算法,因为它能有效地捕捉变量之间的非线性关系。通过将具有鲁棒性的方法与基于核的非线性方法相结合,提出的新方法同时具有鲁棒特性和非线性特性,在应用于过程监控时能获得更精确的过程模型。
(3)针对间歇过程的数据特点,将KPLS方法应用于间歇过程的数据处理,提出了一种基于多向KPLS (Multiway KPLS, MKPLS)的间歇过程监控方法。在提出的监控策略中,首先将正常间歇过程的三维数据按批次方向展开成两维的数据,再用KPLS方法建立起输入输出之间的非线性关系,最后构建相应的统计量对新的操作批次进行监控。由于KPLS方法具有很强的非线性特征提取能力,所以将提出的MKPLS方法应用于间歇过程中能获得比多向PLS (Multiway PLS, MPLS)方法更好的监控性能。
(4)针对间歇过程存在的时变问题、多阶段问题以及阶段不等长问题,将“即时学习(Just-in-time-learning, JITL)"策略引入到KPLS方法中,提出了一种新的基于JITL-KPLS方法的间歇过程在线监控策略。在该策略中,用JITL方法来选取用于建模的最相似样本,然后基于相似样本建立KPLS模型用于对过程进行监控。基于局部邻域信息的JITL模型可以很好地捕捉过程的变化特性,因此适合于解决间歇过程的时变和多阶段问题。同时,KPLS方法还可以有效地处理复杂的非线性数据。此外,本文提出的监控策略应用于在线监控时不需要对未来的未知测量值进行预估。因此,提出的基于JITL-KPLS方法的监控策略在很大程度上改进了间歇过程监控性能。(5)针对KPLS方法在实际应用中存在的核矩阵计算复杂的问题和故障变量辨识的问题,提出了一种有效的非线性过程监控和故障辨识策略。从大量历史数据库中挑选出
一定数量的特征样本,再基于该特征样本集建立KPLS模型,由于样本数量的减少,核矩阵的计算变得较为简单,从而缩短了KPLS方法的建模时间。同时,由于特征样本包含有足够的过程信息,所以建立的模型具有较高的精度,能获得很好的过程监控性能。为了对故障变量进行辨识,还提出了一种基于回归重构的方法,通过构造故障辨识指标可以有效地找出引发故障的重要变量,该方法提供了一种可供选择的非线性故障辨识方法。
在对上述方法进行分析的同时,通过不同方法之间的比较,利用Tennessee Eastman过程和青霉素发酵过程等仿真应用进行验证,结果充分证明了本文所提出的新方法的有效性。最后,在对本文主要工作进行总结的基础上对未来的研究工作进行了展望。
The modern industrial processes have become more and more large-scale and complex, so the process safety and product quality are two important issues in industries. Also, process monitoring and fault detection have attracted more attention. In the past several years, because of the development of computer technique and the wide utilization of the distributed control system (DCS), large amounts of data have been collected and stored. Therefore, it is necessary and desirable to solve the problems about how to extract useful information from the large amounts of data and how to utilize the obtained information for process safety and product quality control. In this context, data-based multivariate statistical methods have become more popular and have been successfully applied in process modeling, monitoring and control.
Traditional multivariate statistical process monitoring (MSPM) methods mainly contain principal component analysis (PCA) and partial least squares (PLS). However, the traditional multivariate statistical-based method has several limitations. One of these limitations is that they require the process variables to be linearly correlated, but nonlinear relationships among different process variables are very common in the process industry, as well as between the process variables and the quality variables. This paper will focus on the nonlinear problem in the process monitoring and employ a nonlinear PLS method, called kernel PLS (KPLS), for online monitoring of industrial processes. The main contributions of this dissertation are summarized as follows:
(1) To handle the nonlinear problem for process monitoring, a new technique based on kernel partial least squares (KPLS) is developed. KPLS is to first map the input space into a high-dimensional feature space via a nonlinear kernel function and then to use the standard PLS in that feature space. Compared to linear PLS, KPLS can effectively capture the nonlinear relationship between the input variables and output variables. For process monitoring, two statistics of KPLS method are constructed. KPLS can obtain precise process model and show superior process monitoring performance compared to linear PLS.
(2) In order to eliminate the effect of outliers in the modeling data, a robust online monitoring approach is developed and presented for nonlinear process monitoring, which is based on spherical kernel partial least squares (SKPLS). Through projecting the feature vectors onto a unit sphere, we get new feature vectors, and then an ordinary KPLS is applied onto these new feature vectors. Due to the sphering, the influence of outliers is reduced heavily. Compared with ordinary KPLS, the proposed method incorporates a robustness feature for coping with the contaminated modeling data. By integrating a robust method into a kernel based method, the proposed method has both robust and nonlinear characteristic and can be applied to obtain more accurate models for process monitoring purposes.
(3) For the batch process, a process monitoring method is developed based on multiway kernel partial least squares (MKPLS). Three-way batch data of normal batch process is unfolded batch-wise, and then kernel partial least squares (KPLS) is applied to capture the nonlinear relationship between the latent structures and predictive variables. Because of its good ability to descript the nonlinear characteristic, MKPLS can detect faults or disturbance more accurately and rapidly than multiway PLS (MPLS), especially for batch process having nonlinear characteristics.
(4) An integrated framework consisting of just-in-time-learning (JITL) method and kernel partial least squares (KPLS) is described for the monitoring of the performance of batch processes. The training data set for modeling is defined by using JITL, and KPLS is employed to build the model for process monitoring purpose. The JITL model based on local neighborhoods of similar samples is very accurate and sensitive because it can well track the change of the process. Meanwhile, KPLS is a very efficient technique for tacking complex nonlinear data sets. Furthermore, the proposed monitoring strategy does not require the estimation of future values of the process variables during online application. As a result, the proposed scheme greatly improves the monitoring performance of batch processes.
(5) An efficient KPLS-based fault diagnosis framework is proposed to address the problems of the complex kernel matrix calculation and the kernel method based fault identification. A small subset of feature samples is chosen from the large dataset and the KPLS model is built base on the selected feature samples. Since the small subset contains enough information of the process data, the precise model can be obtain and the calculation burden can be reduced significantly. Besides, the proposed fault identification approach can identify the fault source efficiently.
Several monitoring methods are compared with the proposed methods, and the TE process and fed-batch penicillin fermentation process are applied to illustrate the efficient of the proposed methods. Finally, some conclusions and future research directions are discussed.
传统的多元统计监控方法以主成分分析(PCA)和偏最小二乘(PLS)为主,这些方法通过降维的策略提取高维、变量相关的过程数据的主要信息,从而对过程的运行状况进行分析。然而在实际应用中,传统的基于多元统计的方法存在一定的局限性,表现之一在于这些方法要求过程变量之间是线性相关的,然而流程工业中过程变量之间、过程变量与质量变量之间往往存在着非线性关系,用线性的方法对数据的非线性特性进行建模将难以得到精确的模型。本文主要将针对过程数据存在的非线性问题,将一种非线性的PLS方法一核PLS (Kernel PLS, KPLS)方法应用于工业过程的在线监控,并考虑到实际应用中存在的各种问题,对基本的KPLS方法进行改进,使其能在过程监控、故障诊断和质量预测中得到更好的应用。本文的主要研究工作包括以下几个方面：
(1)针对过程监控数据的非线性特点,提出了一种基于核偏最小二乘(KPLS)的过程监控方法。该方法首先通过核函数将输入数据映射到高维特征空间,再在高维特征空间进行PLS运算。与线性PLS算法相比,KPLS算法在处理非线性问题时能够很好地建立起输入变量与输出变量之间的非线性关系,充分提取非线性系统的特征。通过构造相应的监控统计量,将KPLS方法应用于过程的在线监控,取得了比普通的PLS方法更好的监控效果。
(2)针对非线性过程采集的数据存在离群值的问题,提出了一种基于球形化KPLS (Spherical KPLS, SKPLS)的鲁棒在线监控策略。该鲁棒策略通过将高维特征空间的特征向量投影到一个单位球球面得到新的特征向量,再对新的特征向量进行KPLS算法。通过球形化的处理,减少甚至消除了离群点对建模精度的影响。与普通的KPLS方法相比,提出的SKPLS方法具有鲁棒特性,能够处理含有离群点的建模数据。此外,SKPLS方法的性能要优越于其它线性的鲁棒算法,因为它能有效地捕捉变量之间的非线性关系。通过将具有鲁棒性的方法与基于核的非线性方法相结合,提出的新方法同时具有鲁棒特性和非线性特性,在应用于过程监控时能获得更精确的过程模型。
(3)针对间歇过程的数据特点,将KPLS方法应用于间歇过程的数据处理,提出了一种基于多向KPLS (Multiway KPLS, MKPLS)的间歇过程监控方法。在提出的监控策略中,首先将正常间歇过程的三维数据按批次方向展开成两维的数据,再用KPLS方法建立起输入输出之间的非线性关系,最后构建相应的统计量对新的操作批次进行监控。由于KPLS方法具有很强的非线性特征提取能力,所以将提出的MKPLS方法应用于间歇过程中能获得比多向PLS (Multiway PLS, MPLS)方法更好的监控性能。
(4)针对间歇过程存在的时变问题、多阶段问题以及阶段不等长问题,将“即时学习(Just-in-time-learning, JITL)"策略引入到KPLS方法中,提出了一种新的基于JITL-KPLS方法的间歇过程在线监控策略。在该策略中,用JITL方法来选取用于建模的最相似样本,然后基于相似样本建立KPLS模型用于对过程进行监控。基于局部邻域信息的JITL模型可以很好地捕捉过程的变化特性,因此适合于解决间歇过程的时变和多阶段问题。同时,KPLS方法还可以有效地处理复杂的非线性数据。此外,本文提出的监控策略应用于在线监控时不需要对未来的未知测量值进行预估。因此,提出的基于JITL-KPLS方法的监控策略在很大程度上改进了间歇过程监控性能。(5)针对KPLS方法在实际应用中存在的核矩阵计算复杂的问题和故障变量辨识的问题,提出了一种有效的非线性过程监控和故障辨识策略。从大量历史数据库中挑选出
一定数量的特征样本,再基于该特征样本集建立KPLS模型,由于样本数量的减少,核矩阵的计算变得较为简单,从而缩短了KPLS方法的建模时间。同时,由于特征样本包含有足够的过程信息,所以建立的模型具有较高的精度,能获得很好的过程监控性能。为了对故障变量进行辨识,还提出了一种基于回归重构的方法,通过构造故障辨识指标可以有效地找出引发故障的重要变量,该方法提供了一种可供选择的非线性故障辨识方法。
在对上述方法进行分析的同时,通过不同方法之间的比较,利用Tennessee Eastman过程和青霉素发酵过程等仿真应用进行验证,结果充分证明了本文所提出的新方法的有效性。最后,在对本文主要工作进行总结的基础上对未来的研究工作进行了展望。
The modern industrial processes have become more and more large-scale and complex, so the process safety and product quality are two important issues in industries. Also, process monitoring and fault detection have attracted more attention. In the past several years, because of the development of computer technique and the wide utilization of the distributed control system (DCS), large amounts of data have been collected and stored. Therefore, it is necessary and desirable to solve the problems about how to extract useful information from the large amounts of data and how to utilize the obtained information for process safety and product quality control. In this context, data-based multivariate statistical methods have become more popular and have been successfully applied in process modeling, monitoring and control.
Traditional multivariate statistical process monitoring (MSPM) methods mainly contain principal component analysis (PCA) and partial least squares (PLS). However, the traditional multivariate statistical-based method has several limitations. One of these limitations is that they require the process variables to be linearly correlated, but nonlinear relationships among different process variables are very common in the process industry, as well as between the process variables and the quality variables. This paper will focus on the nonlinear problem in the process monitoring and employ a nonlinear PLS method, called kernel PLS (KPLS), for online monitoring of industrial processes. The main contributions of this dissertation are summarized as follows:
(1) To handle the nonlinear problem for process monitoring, a new technique based on kernel partial least squares (KPLS) is developed. KPLS is to first map the input space into a high-dimensional feature space via a nonlinear kernel function and then to use the standard PLS in that feature space. Compared to linear PLS, KPLS can effectively capture the nonlinear relationship between the input variables and output variables. For process monitoring, two statistics of KPLS method are constructed. KPLS can obtain precise process model and show superior process monitoring performance compared to linear PLS.
(2) In order to eliminate the effect of outliers in the modeling data, a robust online monitoring approach is developed and presented for nonlinear process monitoring, which is based on spherical kernel partial least squares (SKPLS). Through projecting the feature vectors onto a unit sphere, we get new feature vectors, and then an ordinary KPLS is applied onto these new feature vectors. Due to the sphering, the influence of outliers is reduced heavily. Compared with ordinary KPLS, the proposed method incorporates a robustness feature for coping with the contaminated modeling data. By integrating a robust method into a kernel based method, the proposed method has both robust and nonlinear characteristic and can be applied to obtain more accurate models for process monitoring purposes.
(3) For the batch process, a process monitoring method is developed based on multiway kernel partial least squares (MKPLS). Three-way batch data of normal batch process is unfolded batch-wise, and then kernel partial least squares (KPLS) is applied to capture the nonlinear relationship between the latent structures and predictive variables. Because of its good ability to descript the nonlinear characteristic, MKPLS can detect faults or disturbance more accurately and rapidly than multiway PLS (MPLS), especially for batch process having nonlinear characteristics.
(4) An integrated framework consisting of just-in-time-learning (JITL) method and kernel partial least squares (KPLS) is described for the monitoring of the performance of batch processes. The training data set for modeling is defined by using JITL, and KPLS is employed to build the model for process monitoring purpose. The JITL model based on local neighborhoods of similar samples is very accurate and sensitive because it can well track the change of the process. Meanwhile, KPLS is a very efficient technique for tacking complex nonlinear data sets. Furthermore, the proposed monitoring strategy does not require the estimation of future values of the process variables during online application. As a result, the proposed scheme greatly improves the monitoring performance of batch processes.
(5) An efficient KPLS-based fault diagnosis framework is proposed to address the problems of the complex kernel matrix calculation and the kernel method based fault identification. A small subset of feature samples is chosen from the large dataset and the KPLS model is built base on the selected feature samples. Since the small subset contains enough information of the process data, the precise model can be obtain and the calculation burden can be reduced significantly. Besides, the proposed fault identification approach can identify the fault source efficiently.
Several monitoring methods are compared with the proposed methods, and the TE process and fed-batch penicillin fermentation process are applied to illustrate the efficient of the proposed methods. Finally, some conclusions and future research directions are discussed.
引文
[1]Martin, E., Morris, J., Lane, S. Monitoring process manufacturing performance. IEEE Control Systems Magazine.2002,22(5):26-39.
[2]Downs, J.J., Vogel, E.F. A plant-wide industrial process control problem. Computers & Chemical Engineering.1993,17(3):245-255.
[3]Kourti, T. Process analysis and abnormal situation detection:From theory to practice. IEEE Control Systems Magazine.2002,22(5):10-25.
[4]Qin, S.J. Statistical process monitoring:basics and beyond. Journal of Chemometrics. 2003,17(8-9):480-502.
[5]张曦.基于统计理论的工业过程综合性能监控、诊断及质量预测方法研究.2008,上海交通大学：上海.
[6]Chiang, L.H., Russell, E.L., Braatz, R.D. Fault Detection and Diagnosis in Industrial Systems.2001, London:Springer-Verlag.
[7]Frank, P.M. Fault diagnosis in dynamics systems using analytical and knowledge-based redundancy:a survey and some new results. Automatica.1990,26(3):459-474.
[8]Venkatasubramanian, V., Rengaswamy, R., Yin, K., et. al. A review of process fault detection and diagnosis:Part I:Quantitative model-based methods. Computers & Chemical Engineering.2003,27(3):293-311.
[9]Venkatasubramanian, V., Rengaswamy, R., Kavuri, S.N. A review of process fault detection and diagnosis:Part Ⅱ:Qualitative models and search strategies. Computers & Chemical Engineering.2003,27(3):313-326.
[10]Venkatasubramanian, V., Rengaswamy, R., Kavuri, S.N., et. al. A review of process fault detection and diagnosis:Part Ⅲ:Process history based methods. Computers & Chemical Engineering.2003,27(3):327-346.
[11]李晗,萧德云.基于数据驱动的故障诊断方法综述.控制与决策.2011,26(1)：1-9.
[12]周东华,胡艳艳.动态系统的故障诊断技术.自动化学报.2009,35(6)：748-758.
[13]周东华,李钢,李元.数据驱动的工业过程故障诊断技术.2011,北京：科学出版社.
[14]侯忠生,许建新.数据驱动控制理论及方法的回顾和展望.自动化学报.2009,35(6)：650—667.
[15]Bakshi, B.R. Multiscale PC A with application to multivariate statistical process monitoring. AIChE Journal.1998,44(7):1596-1610.
[16]Yu, J. Multiway discrete hidden Markov model-based approach for dynamic batch process monitoring and fault classification. AIChE Journal.2012,58(9):2714-2725.
[17]Choi, S.W., Martin, E.B., Morris, A.J., et. al. Fault detection based on a maximum-likelihood principal component analysis (PCA) mixture. Industrial & Engineering Chemistry Research.2005,44(7):2316-2327.
[18]Facco, P., Tomba, E., Bezzo, F., et. al. Transfer of process monitoring models between different plants using latent variable techniques. Industrial & Engineering Chemistry Research.2012,51(21):7327-7339.
[19]文成林,胡静,王天真,陈志国.相对主元分析及其在数据压缩和故障诊断中的应用研究.自动化学报.2008,34(9)：1128-1139.
[20]常玉清,王姝,谭帅,王福利,杨洁.基于多时段MPCA模型的间歇过程监测方法研究.自动化学报.2010,36(9)：1312-1320.
[21]陈国金,梁军,钱积新.独立元分析方法(ICA)及其在化工过程监控和故障诊断中的应用.化工学报.2003,54(10)：1474-1477.
[22]解翔,侍洪波.多模态化工过程的全局监控策略.化工学报.2012,63(7)：2156-2162.
[23]Wold, S., Martens, H., Wold, H. The multivariate calibration method in chemistry solved by the PLS method, in Proceedings of a Conference on Matrix Pencils, Lecture Notes in Mathematics.1983:Heidelberg.
[24]Geladi, P., Kowalski, B.R. Partial least-squares regression:a tutorial. Analytica Chimica Acta.1986,185(3):1-17.
[25]Doymaz, F., Palazoglu, A., Romagnoli, J.A. Orthogonal nonlinear partial least-squares regression. Industrial & Engineering Chemistry Research.2003,42(23):5836-5849.
[26]王惠文.偏最小二乘回归方法及其应用.1999,北京：国防工业出版社.
[27]王惠文,吴载斌,孟洁.偏最小二乘回归的线性与非线性方法.2006,北京：国防工业出版社.
[28]Dayal, B.S., MacGregor, J.F. Improved PLS algorithms. Journal of Chemometrics. 1997,11(1):73-85.
[29]De Jong, S. SIMPLS:An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems.1993,18(3):251-263.
[30]Saeys, Y., Inza, I., Larraniaga, P. A review of feature selection techniques in bioinformatics. Bioinformatics.2007,23(19):2507-2517.
[31]Mehmood, T., Liland, K.H., Snipen, L., et. al. A review of variable selection methods in partial least squares regression. Chemometrics and Intelligent Laboratory Systems.2012, 118(3):62-69.
[32]Frank, I.E. Intermediate least squares regression method. Chemometrics and Intelligent Laboratory Systems.1987,1(3):233-242.
[33]Frenich, A.G., Jouan-Rimbaud, D., Massart, D.L., et. al. Wavelength selection method for multicomponent spectrophotometric determinations using partial least squares. Analyst.1995,120(12):2787-2792.
[34]Chong, I.G., Jun, C.H. Performance of some variable selection methods when multicollinearity is present. Chemometrics and Intelligent Laboratory Systems.2005, 78(1):103-112.
[35]Cai, W., Li, Y., Shao, X. A variable selection method based on uninformative variable elimination for multivariate calibration of near-infrared spectra. Chemometrics and Intelligent Laboratory Systems.2008,90(2):188-194.
[36]Li, H.D., Zeng, M.M., Tan, B.B., et. al. Recipe for revealing informative metabolites based on model population analysis. Metabolomics.2010,6(3):353-361.
[37]Lindgren, F., Geladi, P., Berglund, A., et. al. Interactive variable selection (IVS) for PLS. Part II:Chemical applications. Journal of Chemometrics.1995,9(5):331-342.
[38]Shao, J. Linear model selection by cross-validation. Journal of the American Statistical Association.1993,88(422):486-494.
[39]Wold, S. Cross-validation estimation of the number of components in factor and principal component analysis. Technometrics.1978,20(4):397-405.
[40]Qin, S.J., Dunia, R. Determining the number of principal components for best reconstruction. Journal of Process Control.2000,10(2):245-250.
[41]Messick, N.J., Kalivas, J.H., Lang, P.M. Selecting factors for partial least squares. Microchemical Journal.1997,55(2):200-207.
[42]Kaspar, M.H., Harmon Ray, W. Dynamic PLS modelling for process control. Chemical Engineering Science.1993,48(20):3447-3461.
[43]Chen, J., Liu, K. On-line batch process monitoring using dynamic PC A and dynamic PLS models. Chemical Engineering Science.2002,57(1):63-75.
[44]Lee, G., Han, C., Yoon, E.S. Multiple-fault diagnosis of the Tennessee Eastman process based on system decomposition and dynamic PLS. Industrial & Engineering Chemistry Research.2004,43(25):8037-8048.
[45]Lee, G., Song, S.O., Yoon, E.S. Multiple-fault diagnosis based on system decomposition and dynamic PLS. Industrial & Engineering Chemistry Research.2003, 42(24):6145-6154.
[46]Li, Y., Wang, Z., Yuan, J. On-line fault detection using SVM-based dynamic MPLS for batch processes. Chinese Journal of Chemical Engineering.2006,14(6):754-758.
[47]Adebiyi, O.A., Corripio, A.B. Dynamic neural networks partial least squares (DNNPLS) identification of multivariable processes. Computers & Chemical Engineering.2003, 27(2):143-155.
[48]Baffi, G., Martin, E.B., Morris, A.J. Non-linear dynamic projection to latent structures modelling. Chemometrics and Intelligent Laboratory Systems.2000,52(1):5-22.
[49]Lee, D.S., Lee, M.W., Woo, S.H., et. al. Nonlinear dynamic partial least squares modeling of a full-scale biological wastewater treatment plant. Process Biochemistry. 2006,41(9):2050-2057.
[50]Martens, K.H.H.E. Recursive algorithm for partial least squares regression. Chemometrics and Intelligent Laboratory Systems.1992,14(1):129-137.
[51]Qin, S.J. Recursive PLS algorithms for adaptive data modeling. Computers & Chemical Engineering.1998,22(4):503-514.
[52]Wang, X., Kruger, U., Lennox, B. Recursive partial least squares algorithms for monitoring complex industrial processes. Control Engineering Practice.2003,11(6): 613-632.
[53]Li, C., Ye, H., Wang, G., et. al. A recursive nonlinear PLS algorithm for adaptive nonlinear process modeling. Chemical Engineering & Technology.2005,28(2): 141-152.
[54]Lee, H.W., Lee, M.W., Park, J.M. Robust adaptive partial least squares modeling of a full-scale industrial wastewater treatment process. Industrial & Engineering Chemistry Research.2007,46(3):955-964.
[55]Bakshi, B.R. Multiscale PCA with application to multivariate statistical process monitoring. AIChE Journal.1998,44(7):1596-1610.
[56]Teppola, P., Minkkinen, P. Wavelet-PLS regression models for both exploratory data analysis and process monitoring. Journal of Chemometrics.2000,14(5-6):383-399.
[57]Lee, H.W., Lee, M.W., Park, J.M. Multi-scale extension of PLS algorithm for advanced on-line process monitoring. Chemometrics and Intelligent Laboratory Systems.2009, 98(2):201-212.
[58]Mohammad, S.E.R., Mehdi, S. Multi-scale PLS modeling for industrial process monitoring. International Journal of Computer Applications.2011,26(6):26-33.
[59]Westerhuis, J.A., Kourti, T., MacGregor, J.F. Analysis of multiblock and hierarchical PCA and PLS models. Journal of Chemometrics.1998,12(5):301-321.
[60]Westerhuis, J.A., Smilde, A.K. Deflation in multiblock PLS. Journal of Chemometrics. 2001,15(5):485-493.
[61]MacGregor, J.F., Jaeckle, C., Kiparissides, C., et. al. Process monitoring and diagnosis by multiblock PLS methods. AIChE Journal.1994,40(5):826-838.
[62]Kourti, T., Nomikos, P., MacGregor, J.F. Analysis, monitoring and fault diagnosis of batch processes using multiblock and multiway PLS. Journal of Process Control.1995, 5(4):277-284.
[63]Qin, S.J., Valle, S., Piovoso, M.J. On unifying multiblock analysis with application to decentralized process monitoring. Journal of Chemometrics.2001,15(9):715-742.
[64]Choi, S.W., Lee, I. Multiblock PLS-based localized process diagnosis. Journal of Process Control.2005,15(3):295-306.
[65]Nomikos, P., MacGregor, J.F. Multi-way partial least squares in monitoring batch processes. Chemometrics and Intelligent Laboratory Systems.1995,30(1):97-108.
[66]Wold, S., Kettaneh, N., FridIn, H., et. al. Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemometrics and Intelligent Laboratory Systems. 1998,44(1):331-340.
[67]Rannar, S., MacGregor, J.F., Wold, S. Adaptive batch monitoring using hierarchical PC A. Chemometrics and Intelligent Laboratory Systems.1998,41(1):73-81.
[68]Lu, N., Gao, F., Wang, F. Sub-PCA modeling and on-line monitoring strategy for batch processes. AIChE Journal.2004,50(1):255-259.
[69]Lee, J., Yoo, C.K., Lee, I. Enhanced process monitoring of fed-batch penicillin cultivation using time-varying and multivariate statistical analysis. Journal of Biotechnology.2004,110(2):119-136.
[70]Lee, J., Yoo, C., Lee, I. On-line batch process monitoring using different unfolding method and independent component analysis. Journal Chemical Engineering of Japan. 2003,36(11):1384-1396.
[71]Wakelinc, I.N., Macfie, H. A robust PLS procedure. Journal of Chemometrics.1992, 6(4):189-198.
[72]Griep, M.I., Wakeling, I.N., Vankeerberghen, P., et. al. Comparison of semirobust and robust partial least squares procedures. Chemometrics and Intelligent Laboratory Systems.1995,29(1):37-50.
[73]Cummins, D.J., Andrews, C.W. Iteratively reweighted partial least squares:a performance analysis by Monte Carlo simulation. Journal of Chemometrics.1995,9(6): 489-507.
[74]Gil, J.A., Romera, R. On robust partial least squares (PLS) methods. Journal of Chemometrics.1998,12(6):365-378.
[75]Pell, R.J. Multiple outlier detection for multivariate calibration using robust statistical techniques. Chemometrics and Intelligent Laboratory Systems.2000,52(1):87-104.
[76]Forma, M., Casolino, C., Almansa, E.M. The refinement of PLS models by iterative weighting of predictor variables and objects. Chemometrics and Intelligent Laboratory Systems.2003,68(1):29-40.
[77]Serneels, S., Croux, C., Filzmoser, P., et. al. Partial robust M-regression. Chemometrics and Intelligent Laboratory Systems.2005,79(1-2):55-64.
[78]Chen, D., Shao, X., Hu, B., et. al. Simultaneous wavelength selection and outlier detection in multivariate regression of near-infrared spectra. Analytical Sciences.2005, 21(2):161-166.
[79]Hubert, M., Branden, K.V. Robust methods for partial least squares regression. Journal of Chemometrics.2003,17(10):537-549.
[80]Vanden Branden, K., Hubert, M. Robustness properties of a robust partial least squares regression method. Analytica Chimica Acta.2004,515(1):229-241.
[81]Kruger, U., Zhou, Y., Wang, X., et. al. Robust partial least squares regression:Part II, new algorithm and benchmark studies. Journal of Chemometrics.2008,22(1):14-22.
[82]Gonzalez, J., Pe a, D., Romera, R. A robust partial least squares regression method with applications. Journal of Chemometrics.2009,23(2):78-90.
[83]董胜利,王树青,谢磊.鲁棒PLS在间歇生产过程监控中的应用.控制与决策.2005,20(7)：823-826.
[84]Wang, D. Robust data-driven modeling approach for real-time final product quality prediction in batch process operation. IEEE Transactions on Industrial Informatics. 2011,7(2):371-377.
[85]Frank, I.E. A nonlinear PLS model. Chemometrics and Intelligent Laboratory Systems. 1990,8(2):109-119.
[86]Wold, S. Nonlinear partial least squares modelling Ⅱ. Spline inner relation. Chemometrics and Intelligent Laboratory Systems.1992,14(1):71-84.
[87]Baffi, G., Martin, E.B., Morris, A.J. Non-linear projection to latent structures revisited: the quadratic PLS algorithm. Computers & Chemical Engineering.1999,23(3): 395-411.
[88]Qin, S.J., McAvoy, T.J. Nonlinear PLS modeling using neural networks. Computers & Chemical Engineering.1992,16(4):379-391.
[89]Malthouse, E.C., Tamhane, A.C., Mah, R.S.H. Nonlinear partial least squares. Computers & Chemical Engineering.1997,21(8):875-890.
[90]Baffi, G., Martin, E.B., Morris, A.J. Non-linear projection to latent structures revisited (the neural network PLS algorithm). Computers & Chemical Engineering.1999,23(9): 1293-1307.
[91]Lee, J., Yoo, C., Choi, S.W., et. al. Nonlinear process monitoring using kernel principal component analysis. Chemical Engineering Science.2004,59(1):223-234.
[92]Choi, S.W., Lee, I. Nonlinear dynamic process monitoring based on dynamic kernel PCA. Chemical Engineering Science.2004,59(24):5897-5908.
[93]Lee, J., Yoo, C., Lee, I. Fault detection of batch processes using multiway kernel principal component analysis. Computers and Chemical Engineering.2004,28(9): 1837-1847.
[94]Cho, H.W. Nonlinear feature extraction and classification of multivariate data in kernel feature space. Expert Systems with Applications.2007,32(2):534-542.
[95]Xi, Z., Weiwu, Y., Xu, Z., et. al. Nonlinear biological batch process monitoring and fault identification based on kernel fisher discriminant analysis. Process Biochemistry. 2007,42(8):1200-1210.
[96]Zhang, Y., Qin, S.J. Fault detection of nonlinear processes using multiway kernel independent component analysis. Industrial & Engineering Chemistry Research.2007, 46(23):7780-7787.
[97]Lee, J., Qin, S.J., Lee, I. Fault detection of non-linear processes using kernel independent component analysis. Canadian Journal of Chemical Engineering.2007, 85(5):526-536.
[98]Zhang, Y. Fault detection and diagnosis of nonlinear processes using improved kernel independent component analysis (KICA) and support vector machine (SVM). Industrial & Engineering Chemistry Research.2008,47(18):6961-6971.
[99]Ge, Z., Yang, C., Song, Z. Improved kernel PCA-based monitoring approach for nonlinear processes. Chemical Engineering Science.2009,64(9):2245-2255.
[100]Yu, J. Nonlinear bioprocess monitoring using multiway kernel localized Fisher discriminant analysis. Industrial & Engineering Chemistry Research.2011,50(6): 3390-3402.
[101]Zhang, Y., Li, S., Teng, Y. Dynamic processes monitoring using recursive kernel principal component analysis. Chemical Engineering Science.2012,72(3):78-86.
[102]Rosipal, R., Trejo, L.J. Kernel partial least squares regression in reproducing kernel Hilbert space. Journal of Machine Learning Research.2001,2(3):97-123.
[103]Rosipal, R., Trejo, L.J., Matthews, B. Kernel PLS-SVC for Linear and Nonlinear Classification. in Proceedings of the Twentieth International Conference on Machine Learning.2003. Washington DC.
[104]Rosipal, R. Kernel partial least squares for nonlinear regression and discrimination. Neural Network World.2003,13(3):291-300.
[105]Kim, K., Lee, J., Lee, I. A novel multivariate regression approach based on kernel partial least squares with orthogonal signal correction. Chemometrics and Intelligent Laboratory Systems.2005,79(1):22-30.
[106]Lee, D.S., Lee, M.W., Woo, S.H., et. al. Multivariate online monitoring of a full-scale biological anaerobic filter process using kernel-based algorithms. Industrial & engineering chemistry research.2006,45(12):4335-4344.
[107]Zhang, X., Yan, W., Shao, H. Nonlinear multivariate quality estimation and prediction based on kernel partial least squares. Industrial & Engineering Chemistry Research. 2008,47(4):1120-1131.
[108]Zhang, Y., Zhang, Y. Complex process monitoring using modified partial least squares method of independent component regression. Chemometrics and Intelligent Laboratory Systems.2009,98(2):143-148.
[109]Zhang, Y., Fan, Y., Zhang, P. Combining kernel partial least-squares modeling and iterative learning control for the batch-to-batch optimization of constrained nonlinear processes. Industrial & Engineering Chemistry Research.2010,49(16):7470-7477.
[110]Zhang, Y., Teng, Y. Process data modeling using modified kernel partial least squares. Chemical Engineering Science.2010,65(4):6353-6361.
[111]Zhang, Y., Teng, Y., Zhang, Y. Complex process quality prediction using modified kernel partial least squares. Chemical Engineering Science.2010,65(6):2153-2158.
[112]Zhang, Y., Hu, Z. On-line batch process monitoring using hierarchical kernel partial least squares. Chemical Engineering Research and Design.2011,89(10):2078-2084.
[113]Jia, R.D., Mao, Z.Z., Chang, Y.Q., et. al. Kernel partial robust M-regression as a flexible robust nonlinear modeling technique. Chemometrics and Intelligent Laboratory Systems.2010,100(2):91-98.
[114]Zhang, Y., Ma, C. Fault diagnosis of nonlinear processes using multiscale KPCA and multiscale KPLS. Chemical Engineering Science.2011,66(1):64-72.
[115]Zhang, Y., Hu, Z. Multivariate process monitoring and analysis based on multi-scale KPLS. Chemical Engineering Research and Design.2011,89(12):2667-2678.
[116]Zhang, Y., Hong, Z., Qin, S.J., et. al. Decentralized fault diagnosis of large-scale processes using multiblock kernel partial least squares. IEEE Transactions on Industrial Informatics.2010,6(1):3-10.
[117]Zhang, Y., Li, S., Hu, Z., et. al. Dynamical process monitoring using dynamical hierarchical kernel partial least squares. Chemometrics and Intelligent Laboratory Systems.2012,118(3):150-158.
[118]Li, G., Qin, S.J., Zhou, D. Geometric properties of partial least squares for process monitoring. Automatica.2010,46(1):204-210.
[119]Genton, M.G. Classes of kernels for machine learning:a statistical perspective. Journal of Machine Learning Research.2001,2(3):299-312.
[120]Zhao, S.J., Zhang, J., Xu, Y.M., et. al. Nonlinear projection to latent structures method and its applications. Industrial & Engineering Chemistry Research.2006,45(11): 3843-3852.
[121]Scholkopf, B., Smola, A., Muller, K. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation.1998,10(5):1299-1319.
[122]Bach, F.R., Jordan, M.I. Kernel independent component analysis. Journal of Machine Learning Research.2002,3(3):1-48.
[123]胡益,王丽,马贺贺,侍洪波.基于核PLS方法的非线性过程在线监控.化工学报.2011,62(9)：2555-2561.
[124]Rantalainen, M., Bylesjo, M., Cloarec, O., et. al. Kernel-based orthogonal projections to latent structures (K-OPLS). Journal of Chemometrics.2007,21(7-9):376-385.
[125]Chen, J., Bandoni, A., Romagnoli, J.A. Robust statistical process monitoring. Computers & Chemical Engineering.1996,20(3):497-502.
[126]Doymaz, F., Chen, J., Romagnoli, J.A., et. al. A robust strategy for real-time process monitoring. Journal of Process Control.2001,11(4):343-359.
[127]Wang, D., Romagnoli, J.A. Robust multi-scale principal components analysis with applications to process monitoring. Journal of Process Control.2005,15(8):869-882.
[128]Ge, Z., Yang, C., Song, Z., et. al. Robust online monitoring for multimode processes based on nonlinear external analysis. Industrial & Engineering Chemistry Research. 2008,47(14):4775-4783.
[129]Locantore, N., Marron, J.S., Simpson, D.G., et. al. Robust principal component analysis for functional data. Test.1999,8(1):1-73.
[130]Debruyne, M., Hubert, M., Van Horebeek, J. Detecting influential observations in kernel PCA. Computational Statistics & Data Analysis.2010,54(12):3007-3019.
[131]Huber, P.J. Robust Statistics.1981, New York:Wiley.
[132]Rousseeuw, P.J., Croux, C. Alternatives to the median absolute deviation. Journal of the American Statistical Association.1993,88(424):1273-1283.
[133]Rousseeuw, P.J., Van Driessen, K. A fast algorithm for the minimum covariance determinant estimator. Technometrics.1999,41(3):212-223.
[134]Nomikos, P., MacGregor, J.F. Monitoring batch processes using multiway principal component analysis. AIChE J.1994,40(8):1361-1375.
[135]蒋丽英,王树青.基于MPCA-MDPLS的间歇过程的故障诊断.化工学报.2005,56(3)：482-486.
[136]Chen, J., Song, C., Hsu, T. Online monitoring of batch processes using IOHMM based MPLS. Industrial & Engineering Chemistry Research.2010,49(6):2800-2811.
[137]Zhao, C., Gao, F., Wang, F. Nonlinear batch process monitoring using phase-based kernel-independent component analysis-principal component analysis (KICAHPCA). Industrial & Engineering Chemistry Research.2009,48(20):9163-9174.
[138]Birol, G., Undey, C., Cinar, A. A modular simulation package for fed-batch fermentation:penicillin production. Computers and Chemical Engineering.2002, 26(11):1553-1565.
[139]Yoo, C.K., Lee, J., Vanrolleghem, P.A., et. al. On-line monitoring of batch processes using multiway independent component analysis. Chemometrics and Intelligent Laboratory Systems.2004,71(2):151-163.
[140]Albazzaz, H., Wang, X.Z. Introduction of dynamics to an approach for batch process monitoring using independent component analysis. Chemical Engineering Communications.2007,194(2):218-233.
[141]Zhao, C., Gao, F., Wang, F. Spectra data analysis and calibration modeling method using spectra subspace separation and multiblock independent component regression strategy. AIChE Journal.2011,57(5):1202-1215.
[142]Hu, K., Yuan, J. Statistical monitoring of fed-batch process using dynamic multiway neighborhood preserving embedding. Chemometrics and Intelligent Laboratory Systems. 2008,90(2):195-203.
[143]Hu, K., Yuan, J. Multivariate statistical process control based on multiway locality preserving projections. Journal of Process Control.2008,18(7):797-807.
[144]Yu, J., Qin, S.J. Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models. AIChE Journal.2008,54(7):1811-1829.
[145]Xie, X., Shi, H. Dynamic multimode process modeling and monitoring using adaptive Gaussian mixture models. Industrial & Engineering Chemistry Research.2012,51(15): 5497-5505.
[146]Yu, J., Qin, S.J. Multiway Gaussian mixture model based multiphase batch process monitoring. Industrial & Engineering Chemistry Research.2009,48(18):8585-8594.
[147]Jia, M., Chu, F., Wang, F., et. al. On-line batch process monitoring using batch dynamic kernel principal component analysis. Chemometrics and Intelligent Laboratory Systems. 2010,101(2):110-122.
[148]Lee, D.S., Park, J.M., Vanrolleghem, P.A. Adaptive multiscale principal component analysis for on-line monitoring of a sequencing batch reactor. Journal of Biotechnology. 2005,116(2):195-210.
[149]Zhao, C., Wang, F., Jia, M. Dissimilarity analysis based batch process monitoring using moving windows. AIChE Journal.2007,53(5):1267-1277.
[150]Zhao, C., Wang, F., Mao, Z., et. al. Adaptive monitoring based on independent component analysis for multiphase batch processes with limited modeling data. Industrial & Engineering Chemistry Research.2008,47(9):3104-3113.
[151]Undey, C., Cinar, A. Statistical monitoring of multistage, multiphase batch processes. IEEE Control Systems Magazine.2002,22(2):40-52.
[152]Ge, Z., Zhao, L., Yao, Y., et. al. Utilizing transition information in online quality prediction of multiphase batch processes. Journal of Process Control.2012,22(3): 599-611.
[153]Camacho, J., PicS, J. Multi-phase principal component analysis for batch processes modelling. Chemometrics and Intelligent Laboratory Systems.2006,81(2):127-136.
[154]Zhao, C., Gao, F., Niu, D., et. al. Enhanced process comprehension and quality analysis based on subspace separation for multiphase batch processes. AIChE Journal.2011, 57(2):388-403.
[155]Lu, N., Gao, F., Yang, Y., et. al. PCA-based modeling and on-line monitoring strategy for uneven-length batch processes. Industrial & Engineering Chemistry Research.2004, 43(13):3343-3352.
[156]Yao, Y., Dong, W., Zhao, L., et. al. Multivariate statistical monitoring of multiphase batch processes with between-phase transitions and uneven operation durations. The Canadian Journal of Chemical Engineering.2012,90(6):1383-1392.
[157]Bontempi, G., Birattari, M., Bersini, H. Lazy learning for local modelling and control design. International Journal of Control.1999,72(7-8):643-658.
[158]Atkeson, C.G., Moore, A.W., Schaal, S. Locally weighted learning. Artificial intelligence review.1997,11(1):11-73.
[159]Cleveland, W.S., Devlin, S.J. Locally weighted regression:an approach to regression analysis by local fitting. Journal of the American Statistical Association.1988,83(403): 596-610.
[160]Cheng, C., Chiu, M.S. A new data-based methodology for nonlinear process modeling. Chemical Engineering Science.2004,59(13):2801-2810.
[161]Cheng, C., Chiu, M. Nonlinear process monitoring using JITL-PCA. Chemometrics and Intelligent Laboratory Systems.2005,76(1):1-13.
[162]Fujiwara, K., Kano, M., Hasebe, S., et. al. Soft-sensor development using correlation-based just-in-time modeling. AIChE Journal.2009,55(7):1754-1765.
[163]Ge, Z., Song, Z. Online monitoring of nonlinear multiple mode processes based on adaptive local model approach. Control Engineering Practice.2008,16(12):1427-1437.
[164]Ge, Z., Song, Z. A comparative study of just-in-time-learning based methods for online soft sensor modeling. Chemometrics and Intelligent Laboratory Systems.2010,104(2): 306-317.
[165]葛志强,刘毅,宋执环,王海清.一种基于局部模型的非线性多工况过程监测方法.自动化学报.2008,34(7)：792-797.
[166]Liu, Y., Gao, Z., Li, P., et. al. Just-in-time kernel learning with adaptive parameter selection for soft sensor modeling of batch processes. Industrial & Engineering Chemistry Research.2012,51(11):4313-4327.
[167]刘毅,王海清,李平.局部最小二乘支持向量机回归在线建模方法及其在间歇过程的应用.化工学报.2007,58(11)：2846-2851.
[168]Nomikos, P., MacGregor, J.F. Multivariate SPC charts for monitoring batch processes. Technometrics.1995,37(1):41-59.
[169]Chen, J., Chen, H. On-line batch process monitoring using MHMT-based MPCA. Chemical Engineering Science.2006,61(10):3223-3239.
[170]Ge, Z., Song, Z. Batch process monitoring based on multilevel ICA-PCA. Journal of Zhejiang University-Science A.2008,9(8):1061-1069.
[171]Xu, Q.S., Liang, Y.Z. Monte Carlo cross validation. Chemometrics and Intelligent Laboratory Systems.2001,56(1):1-11.
[172]Russell, E.L., Chiang, L.H., Braatz, R.D. Fault detection in industrial processes using canonical variate analysis and dynamic principal component analysis. Chemometrics and Intelligent Laboratory Systems.2000,51(1):81-93.
[173]Yoo, C.K., Choi, S.W., Lee, I. Dynamic monitoring method for multiscale fault detection and diagnosis in MSPC. Industrial & Engineering Chemistry Research.2002, 41(17):4303-4317.
[174]付克昌,吴铁军.基于特征子空间的KPCA及其在故障检测与诊断中的应用.化工学报.2006,57(11)：2664-2669.
[175]Tian, X., Zhang, X., Deng, X., et. al. Multiway kernel independent component analysis based on feature samples for batch process monitoring. Neurocomputing.2009,72(7): 1584-1596.
[176]范玉刚,李平,宋执环.基于特征样本的KPCA在故障诊断中的应用.控制与决策.2005,20(12)：1415-1418.
[177]薄翠梅,张湜,张广明,王执铨.基于特征样本核主元分析的TE过程快速故障辨识方法.化工学报.2008,59(7)：1783-1789.
[178]Cui, P., Li, J., Wang, G. Improved kernel principal component analysis for fault detection. Expert Systems with Applications.2008,34(2):1210-1219.
[179]Li, J., Cui, P. Kernel scatter-difference-based discriminant analysis for nonlinear fault diagnosis. Chemometrics and Intelligent Laboratory Systems.2008,94(1):80-86.
[180]Cho, J., Lee, J., Choi, S.W., et. al. Fault identification for process monitoring using kernel principal component analysis. Chemical Engineering Science.2005,60(1): 279-288.
[181]Choi, S.W., Lee, C., Lee, J., et. al. Fault detection and identification of nonlinear processes based on kernel PCA. Chemometrics and Intelligent Laboratory Systems. 2005,75(1):55-67.
[182]He, X.B., Yang, Y.P., Yang, Y.H. Fault diagnosis based on variable-weighted kernel Fisher discriminant analysis. Chemometrics and Intelligent Laboratory Systems.2008, 93(1):27-33.
[183]Suykens, J.A.K., Van Gestel, T., De Brabanter, J., et. al. Least squares support vector machines. Tutorial IJCNN.2003,
[184]Arteaga, F., Ferrer, A. Dealing with missing data in MSPC:several methods, different interpretations, some examples. Journal of Chemometrics.2002,16(8-10):408-418.
[2]Downs, J.J., Vogel, E.F. A plant-wide industrial process control problem. Computers & Chemical Engineering.1993,17(3):245-255.
[3]Kourti, T. Process analysis and abnormal situation detection:From theory to practice. IEEE Control Systems Magazine.2002,22(5):10-25.
[4]Qin, S.J. Statistical process monitoring:basics and beyond. Journal of Chemometrics. 2003,17(8-9):480-502.
[5]张曦.基于统计理论的工业过程综合性能监控、诊断及质量预测方法研究.2008,上海交通大学：上海.
[6]Chiang, L.H., Russell, E.L., Braatz, R.D. Fault Detection and Diagnosis in Industrial Systems.2001, London:Springer-Verlag.
[7]Frank, P.M. Fault diagnosis in dynamics systems using analytical and knowledge-based redundancy:a survey and some new results. Automatica.1990,26(3):459-474.
[8]Venkatasubramanian, V., Rengaswamy, R., Yin, K., et. al. A review of process fault detection and diagnosis:Part I:Quantitative model-based methods. Computers & Chemical Engineering.2003,27(3):293-311.
[9]Venkatasubramanian, V., Rengaswamy, R., Kavuri, S.N. A review of process fault detection and diagnosis:Part Ⅱ:Qualitative models and search strategies. Computers & Chemical Engineering.2003,27(3):313-326.
[10]Venkatasubramanian, V., Rengaswamy, R., Kavuri, S.N., et. al. A review of process fault detection and diagnosis:Part Ⅲ:Process history based methods. Computers & Chemical Engineering.2003,27(3):327-346.
[11]李晗,萧德云.基于数据驱动的故障诊断方法综述.控制与决策.2011,26(1)：1-9.
[12]周东华,胡艳艳.动态系统的故障诊断技术.自动化学报.2009,35(6)：748-758.
[13]周东华,李钢,李元.数据驱动的工业过程故障诊断技术.2011,北京：科学出版社.
[14]侯忠生,许建新.数据驱动控制理论及方法的回顾和展望.自动化学报.2009,35(6)：650—667.
[15]Bakshi, B.R. Multiscale PC A with application to multivariate statistical process monitoring. AIChE Journal.1998,44(7):1596-1610.
[16]Yu, J. Multiway discrete hidden Markov model-based approach for dynamic batch process monitoring and fault classification. AIChE Journal.2012,58(9):2714-2725.
[17]Choi, S.W., Martin, E.B., Morris, A.J., et. al. Fault detection based on a maximum-likelihood principal component analysis (PCA) mixture. Industrial & Engineering Chemistry Research.2005,44(7):2316-2327.
[18]Facco, P., Tomba, E., Bezzo, F., et. al. Transfer of process monitoring models between different plants using latent variable techniques. Industrial & Engineering Chemistry Research.2012,51(21):7327-7339.
[19]文成林,胡静,王天真,陈志国.相对主元分析及其在数据压缩和故障诊断中的应用研究.自动化学报.2008,34(9)：1128-1139.
[20]常玉清,王姝,谭帅,王福利,杨洁.基于多时段MPCA模型的间歇过程监测方法研究.自动化学报.2010,36(9)：1312-1320.
[21]陈国金,梁军,钱积新.独立元分析方法(ICA)及其在化工过程监控和故障诊断中的应用.化工学报.2003,54(10)：1474-1477.
[22]解翔,侍洪波.多模态化工过程的全局监控策略.化工学报.2012,63(7)：2156-2162.
[23]Wold, S., Martens, H., Wold, H. The multivariate calibration method in chemistry solved by the PLS method, in Proceedings of a Conference on Matrix Pencils, Lecture Notes in Mathematics.1983:Heidelberg.
[24]Geladi, P., Kowalski, B.R. Partial least-squares regression:a tutorial. Analytica Chimica Acta.1986,185(3):1-17.
[25]Doymaz, F., Palazoglu, A., Romagnoli, J.A. Orthogonal nonlinear partial least-squares regression. Industrial & Engineering Chemistry Research.2003,42(23):5836-5849.
[26]王惠文.偏最小二乘回归方法及其应用.1999,北京：国防工业出版社.
[27]王惠文,吴载斌,孟洁.偏最小二乘回归的线性与非线性方法.2006,北京：国防工业出版社.
[28]Dayal, B.S., MacGregor, J.F. Improved PLS algorithms. Journal of Chemometrics. 1997,11(1):73-85.
[29]De Jong, S. SIMPLS:An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems.1993,18(3):251-263.
[30]Saeys, Y., Inza, I., Larraniaga, P. A review of feature selection techniques in bioinformatics. Bioinformatics.2007,23(19):2507-2517.
[31]Mehmood, T., Liland, K.H., Snipen, L., et. al. A review of variable selection methods in partial least squares regression. Chemometrics and Intelligent Laboratory Systems.2012, 118(3):62-69.
[32]Frank, I.E. Intermediate least squares regression method. Chemometrics and Intelligent Laboratory Systems.1987,1(3):233-242.
[33]Frenich, A.G., Jouan-Rimbaud, D., Massart, D.L., et. al. Wavelength selection method for multicomponent spectrophotometric determinations using partial least squares. Analyst.1995,120(12):2787-2792.
[34]Chong, I.G., Jun, C.H. Performance of some variable selection methods when multicollinearity is present. Chemometrics and Intelligent Laboratory Systems.2005, 78(1):103-112.
[35]Cai, W., Li, Y., Shao, X. A variable selection method based on uninformative variable elimination for multivariate calibration of near-infrared spectra. Chemometrics and Intelligent Laboratory Systems.2008,90(2):188-194.
[36]Li, H.D., Zeng, M.M., Tan, B.B., et. al. Recipe for revealing informative metabolites based on model population analysis. Metabolomics.2010,6(3):353-361.
[37]Lindgren, F., Geladi, P., Berglund, A., et. al. Interactive variable selection (IVS) for PLS. Part II:Chemical applications. Journal of Chemometrics.1995,9(5):331-342.
[38]Shao, J. Linear model selection by cross-validation. Journal of the American Statistical Association.1993,88(422):486-494.
[39]Wold, S. Cross-validation estimation of the number of components in factor and principal component analysis. Technometrics.1978,20(4):397-405.
[40]Qin, S.J., Dunia, R. Determining the number of principal components for best reconstruction. Journal of Process Control.2000,10(2):245-250.
[41]Messick, N.J., Kalivas, J.H., Lang, P.M. Selecting factors for partial least squares. Microchemical Journal.1997,55(2):200-207.
[42]Kaspar, M.H., Harmon Ray, W. Dynamic PLS modelling for process control. Chemical Engineering Science.1993,48(20):3447-3461.
[43]Chen, J., Liu, K. On-line batch process monitoring using dynamic PC A and dynamic PLS models. Chemical Engineering Science.2002,57(1):63-75.
[44]Lee, G., Han, C., Yoon, E.S. Multiple-fault diagnosis of the Tennessee Eastman process based on system decomposition and dynamic PLS. Industrial & Engineering Chemistry Research.2004,43(25):8037-8048.
[45]Lee, G., Song, S.O., Yoon, E.S. Multiple-fault diagnosis based on system decomposition and dynamic PLS. Industrial & Engineering Chemistry Research.2003, 42(24):6145-6154.
[46]Li, Y., Wang, Z., Yuan, J. On-line fault detection using SVM-based dynamic MPLS for batch processes. Chinese Journal of Chemical Engineering.2006,14(6):754-758.
[47]Adebiyi, O.A., Corripio, A.B. Dynamic neural networks partial least squares (DNNPLS) identification of multivariable processes. Computers & Chemical Engineering.2003, 27(2):143-155.
[48]Baffi, G., Martin, E.B., Morris, A.J. Non-linear dynamic projection to latent structures modelling. Chemometrics and Intelligent Laboratory Systems.2000,52(1):5-22.
[49]Lee, D.S., Lee, M.W., Woo, S.H., et. al. Nonlinear dynamic partial least squares modeling of a full-scale biological wastewater treatment plant. Process Biochemistry. 2006,41(9):2050-2057.
[50]Martens, K.H.H.E. Recursive algorithm for partial least squares regression. Chemometrics and Intelligent Laboratory Systems.1992,14(1):129-137.
[51]Qin, S.J. Recursive PLS algorithms for adaptive data modeling. Computers & Chemical Engineering.1998,22(4):503-514.
[52]Wang, X., Kruger, U., Lennox, B. Recursive partial least squares algorithms for monitoring complex industrial processes. Control Engineering Practice.2003,11(6): 613-632.
[53]Li, C., Ye, H., Wang, G., et. al. A recursive nonlinear PLS algorithm for adaptive nonlinear process modeling. Chemical Engineering & Technology.2005,28(2): 141-152.
[54]Lee, H.W., Lee, M.W., Park, J.M. Robust adaptive partial least squares modeling of a full-scale industrial wastewater treatment process. Industrial & Engineering Chemistry Research.2007,46(3):955-964.
[55]Bakshi, B.R. Multiscale PCA with application to multivariate statistical process monitoring. AIChE Journal.1998,44(7):1596-1610.
[56]Teppola, P., Minkkinen, P. Wavelet-PLS regression models for both exploratory data analysis and process monitoring. Journal of Chemometrics.2000,14(5-6):383-399.
[57]Lee, H.W., Lee, M.W., Park, J.M. Multi-scale extension of PLS algorithm for advanced on-line process monitoring. Chemometrics and Intelligent Laboratory Systems.2009, 98(2):201-212.
[58]Mohammad, S.E.R., Mehdi, S. Multi-scale PLS modeling for industrial process monitoring. International Journal of Computer Applications.2011,26(6):26-33.
[59]Westerhuis, J.A., Kourti, T., MacGregor, J.F. Analysis of multiblock and hierarchical PCA and PLS models. Journal of Chemometrics.1998,12(5):301-321.
[60]Westerhuis, J.A., Smilde, A.K. Deflation in multiblock PLS. Journal of Chemometrics. 2001,15(5):485-493.
[61]MacGregor, J.F., Jaeckle, C., Kiparissides, C., et. al. Process monitoring and diagnosis by multiblock PLS methods. AIChE Journal.1994,40(5):826-838.
[62]Kourti, T., Nomikos, P., MacGregor, J.F. Analysis, monitoring and fault diagnosis of batch processes using multiblock and multiway PLS. Journal of Process Control.1995, 5(4):277-284.
[63]Qin, S.J., Valle, S., Piovoso, M.J. On unifying multiblock analysis with application to decentralized process monitoring. Journal of Chemometrics.2001,15(9):715-742.
[64]Choi, S.W., Lee, I. Multiblock PLS-based localized process diagnosis. Journal of Process Control.2005,15(3):295-306.
[65]Nomikos, P., MacGregor, J.F. Multi-way partial least squares in monitoring batch processes. Chemometrics and Intelligent Laboratory Systems.1995,30(1):97-108.
[66]Wold, S., Kettaneh, N., FridIn, H., et. al. Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemometrics and Intelligent Laboratory Systems. 1998,44(1):331-340.
[67]Rannar, S., MacGregor, J.F., Wold, S. Adaptive batch monitoring using hierarchical PC A. Chemometrics and Intelligent Laboratory Systems.1998,41(1):73-81.
[68]Lu, N., Gao, F., Wang, F. Sub-PCA modeling and on-line monitoring strategy for batch processes. AIChE Journal.2004,50(1):255-259.
[69]Lee, J., Yoo, C.K., Lee, I. Enhanced process monitoring of fed-batch penicillin cultivation using time-varying and multivariate statistical analysis. Journal of Biotechnology.2004,110(2):119-136.
[70]Lee, J., Yoo, C., Lee, I. On-line batch process monitoring using different unfolding method and independent component analysis. Journal Chemical Engineering of Japan. 2003,36(11):1384-1396.
[71]Wakelinc, I.N., Macfie, H. A robust PLS procedure. Journal of Chemometrics.1992, 6(4):189-198.
[72]Griep, M.I., Wakeling, I.N., Vankeerberghen, P., et. al. Comparison of semirobust and robust partial least squares procedures. Chemometrics and Intelligent Laboratory Systems.1995,29(1):37-50.
[73]Cummins, D.J., Andrews, C.W. Iteratively reweighted partial least squares:a performance analysis by Monte Carlo simulation. Journal of Chemometrics.1995,9(6): 489-507.
[74]Gil, J.A., Romera, R. On robust partial least squares (PLS) methods. Journal of Chemometrics.1998,12(6):365-378.
[75]Pell, R.J. Multiple outlier detection for multivariate calibration using robust statistical techniques. Chemometrics and Intelligent Laboratory Systems.2000,52(1):87-104.
[76]Forma, M., Casolino, C., Almansa, E.M. The refinement of PLS models by iterative weighting of predictor variables and objects. Chemometrics and Intelligent Laboratory Systems.2003,68(1):29-40.
[77]Serneels, S., Croux, C., Filzmoser, P., et. al. Partial robust M-regression. Chemometrics and Intelligent Laboratory Systems.2005,79(1-2):55-64.
[78]Chen, D., Shao, X., Hu, B., et. al. Simultaneous wavelength selection and outlier detection in multivariate regression of near-infrared spectra. Analytical Sciences.2005, 21(2):161-166.
[79]Hubert, M., Branden, K.V. Robust methods for partial least squares regression. Journal of Chemometrics.2003,17(10):537-549.
[80]Vanden Branden, K., Hubert, M. Robustness properties of a robust partial least squares regression method. Analytica Chimica Acta.2004,515(1):229-241.
[81]Kruger, U., Zhou, Y., Wang, X., et. al. Robust partial least squares regression:Part II, new algorithm and benchmark studies. Journal of Chemometrics.2008,22(1):14-22.
[82]Gonzalez, J., Pe a, D., Romera, R. A robust partial least squares regression method with applications. Journal of Chemometrics.2009,23(2):78-90.
[83]董胜利,王树青,谢磊.鲁棒PLS在间歇生产过程监控中的应用.控制与决策.2005,20(7)：823-826.
[84]Wang, D. Robust data-driven modeling approach for real-time final product quality prediction in batch process operation. IEEE Transactions on Industrial Informatics. 2011,7(2):371-377.
[85]Frank, I.E. A nonlinear PLS model. Chemometrics and Intelligent Laboratory Systems. 1990,8(2):109-119.
[86]Wold, S. Nonlinear partial least squares modelling Ⅱ. Spline inner relation. Chemometrics and Intelligent Laboratory Systems.1992,14(1):71-84.
[87]Baffi, G., Martin, E.B., Morris, A.J. Non-linear projection to latent structures revisited: the quadratic PLS algorithm. Computers & Chemical Engineering.1999,23(3): 395-411.
[88]Qin, S.J., McAvoy, T.J. Nonlinear PLS modeling using neural networks. Computers & Chemical Engineering.1992,16(4):379-391.
[89]Malthouse, E.C., Tamhane, A.C., Mah, R.S.H. Nonlinear partial least squares. Computers & Chemical Engineering.1997,21(8):875-890.
[90]Baffi, G., Martin, E.B., Morris, A.J. Non-linear projection to latent structures revisited (the neural network PLS algorithm). Computers & Chemical Engineering.1999,23(9): 1293-1307.
[91]Lee, J., Yoo, C., Choi, S.W., et. al. Nonlinear process monitoring using kernel principal component analysis. Chemical Engineering Science.2004,59(1):223-234.
[92]Choi, S.W., Lee, I. Nonlinear dynamic process monitoring based on dynamic kernel PCA. Chemical Engineering Science.2004,59(24):5897-5908.
[93]Lee, J., Yoo, C., Lee, I. Fault detection of batch processes using multiway kernel principal component analysis. Computers and Chemical Engineering.2004,28(9): 1837-1847.
[94]Cho, H.W. Nonlinear feature extraction and classification of multivariate data in kernel feature space. Expert Systems with Applications.2007,32(2):534-542.
[95]Xi, Z., Weiwu, Y., Xu, Z., et. al. Nonlinear biological batch process monitoring and fault identification based on kernel fisher discriminant analysis. Process Biochemistry. 2007,42(8):1200-1210.
[96]Zhang, Y., Qin, S.J. Fault detection of nonlinear processes using multiway kernel independent component analysis. Industrial & Engineering Chemistry Research.2007, 46(23):7780-7787.
[97]Lee, J., Qin, S.J., Lee, I. Fault detection of non-linear processes using kernel independent component analysis. Canadian Journal of Chemical Engineering.2007, 85(5):526-536.
[98]Zhang, Y. Fault detection and diagnosis of nonlinear processes using improved kernel independent component analysis (KICA) and support vector machine (SVM). Industrial & Engineering Chemistry Research.2008,47(18):6961-6971.
[99]Ge, Z., Yang, C., Song, Z. Improved kernel PCA-based monitoring approach for nonlinear processes. Chemical Engineering Science.2009,64(9):2245-2255.
[100]Yu, J. Nonlinear bioprocess monitoring using multiway kernel localized Fisher discriminant analysis. Industrial & Engineering Chemistry Research.2011,50(6): 3390-3402.
[101]Zhang, Y., Li, S., Teng, Y. Dynamic processes monitoring using recursive kernel principal component analysis. Chemical Engineering Science.2012,72(3):78-86.
[102]Rosipal, R., Trejo, L.J. Kernel partial least squares regression in reproducing kernel Hilbert space. Journal of Machine Learning Research.2001,2(3):97-123.
[103]Rosipal, R., Trejo, L.J., Matthews, B. Kernel PLS-SVC for Linear and Nonlinear Classification. in Proceedings of the Twentieth International Conference on Machine Learning.2003. Washington DC.
[104]Rosipal, R. Kernel partial least squares for nonlinear regression and discrimination. Neural Network World.2003,13(3):291-300.
[105]Kim, K., Lee, J., Lee, I. A novel multivariate regression approach based on kernel partial least squares with orthogonal signal correction. Chemometrics and Intelligent Laboratory Systems.2005,79(1):22-30.
[106]Lee, D.S., Lee, M.W., Woo, S.H., et. al. Multivariate online monitoring of a full-scale biological anaerobic filter process using kernel-based algorithms. Industrial & engineering chemistry research.2006,45(12):4335-4344.
[107]Zhang, X., Yan, W., Shao, H. Nonlinear multivariate quality estimation and prediction based on kernel partial least squares. Industrial & Engineering Chemistry Research. 2008,47(4):1120-1131.
[108]Zhang, Y., Zhang, Y. Complex process monitoring using modified partial least squares method of independent component regression. Chemometrics and Intelligent Laboratory Systems.2009,98(2):143-148.
[109]Zhang, Y., Fan, Y., Zhang, P. Combining kernel partial least-squares modeling and iterative learning control for the batch-to-batch optimization of constrained nonlinear processes. Industrial & Engineering Chemistry Research.2010,49(16):7470-7477.
[110]Zhang, Y., Teng, Y. Process data modeling using modified kernel partial least squares. Chemical Engineering Science.2010,65(4):6353-6361.
[111]Zhang, Y., Teng, Y., Zhang, Y. Complex process quality prediction using modified kernel partial least squares. Chemical Engineering Science.2010,65(6):2153-2158.
[112]Zhang, Y., Hu, Z. On-line batch process monitoring using hierarchical kernel partial least squares. Chemical Engineering Research and Design.2011,89(10):2078-2084.
[113]Jia, R.D., Mao, Z.Z., Chang, Y.Q., et. al. Kernel partial robust M-regression as a flexible robust nonlinear modeling technique. Chemometrics and Intelligent Laboratory Systems.2010,100(2):91-98.
[114]Zhang, Y., Ma, C. Fault diagnosis of nonlinear processes using multiscale KPCA and multiscale KPLS. Chemical Engineering Science.2011,66(1):64-72.
[115]Zhang, Y., Hu, Z. Multivariate process monitoring and analysis based on multi-scale KPLS. Chemical Engineering Research and Design.2011,89(12):2667-2678.
[116]Zhang, Y., Hong, Z., Qin, S.J., et. al. Decentralized fault diagnosis of large-scale processes using multiblock kernel partial least squares. IEEE Transactions on Industrial Informatics.2010,6(1):3-10.
[117]Zhang, Y., Li, S., Hu, Z., et. al. Dynamical process monitoring using dynamical hierarchical kernel partial least squares. Chemometrics and Intelligent Laboratory Systems.2012,118(3):150-158.
[118]Li, G., Qin, S.J., Zhou, D. Geometric properties of partial least squares for process monitoring. Automatica.2010,46(1):204-210.
[119]Genton, M.G. Classes of kernels for machine learning:a statistical perspective. Journal of Machine Learning Research.2001,2(3):299-312.
[120]Zhao, S.J., Zhang, J., Xu, Y.M., et. al. Nonlinear projection to latent structures method and its applications. Industrial & Engineering Chemistry Research.2006,45(11): 3843-3852.
[121]Scholkopf, B., Smola, A., Muller, K. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation.1998,10(5):1299-1319.
[122]Bach, F.R., Jordan, M.I. Kernel independent component analysis. Journal of Machine Learning Research.2002,3(3):1-48.
[123]胡益,王丽,马贺贺,侍洪波.基于核PLS方法的非线性过程在线监控.化工学报.2011,62(9)：2555-2561.
[124]Rantalainen, M., Bylesjo, M., Cloarec, O., et. al. Kernel-based orthogonal projections to latent structures (K-OPLS). Journal of Chemometrics.2007,21(7-9):376-385.
[125]Chen, J., Bandoni, A., Romagnoli, J.A. Robust statistical process monitoring. Computers & Chemical Engineering.1996,20(3):497-502.
[126]Doymaz, F., Chen, J., Romagnoli, J.A., et. al. A robust strategy for real-time process monitoring. Journal of Process Control.2001,11(4):343-359.
[127]Wang, D., Romagnoli, J.A. Robust multi-scale principal components analysis with applications to process monitoring. Journal of Process Control.2005,15(8):869-882.
[128]Ge, Z., Yang, C., Song, Z., et. al. Robust online monitoring for multimode processes based on nonlinear external analysis. Industrial & Engineering Chemistry Research. 2008,47(14):4775-4783.
[129]Locantore, N., Marron, J.S., Simpson, D.G., et. al. Robust principal component analysis for functional data. Test.1999,8(1):1-73.
[130]Debruyne, M., Hubert, M., Van Horebeek, J. Detecting influential observations in kernel PCA. Computational Statistics & Data Analysis.2010,54(12):3007-3019.
[131]Huber, P.J. Robust Statistics.1981, New York:Wiley.
[132]Rousseeuw, P.J., Croux, C. Alternatives to the median absolute deviation. Journal of the American Statistical Association.1993,88(424):1273-1283.
[133]Rousseeuw, P.J., Van Driessen, K. A fast algorithm for the minimum covariance determinant estimator. Technometrics.1999,41(3):212-223.
[134]Nomikos, P., MacGregor, J.F. Monitoring batch processes using multiway principal component analysis. AIChE J.1994,40(8):1361-1375.
[135]蒋丽英,王树青.基于MPCA-MDPLS的间歇过程的故障诊断.化工学报.2005,56(3)：482-486.
[136]Chen, J., Song, C., Hsu, T. Online monitoring of batch processes using IOHMM based MPLS. Industrial & Engineering Chemistry Research.2010,49(6):2800-2811.
[137]Zhao, C., Gao, F., Wang, F. Nonlinear batch process monitoring using phase-based kernel-independent component analysis-principal component analysis (KICAHPCA). Industrial & Engineering Chemistry Research.2009,48(20):9163-9174.
[138]Birol, G., Undey, C., Cinar, A. A modular simulation package for fed-batch fermentation:penicillin production. Computers and Chemical Engineering.2002, 26(11):1553-1565.
[139]Yoo, C.K., Lee, J., Vanrolleghem, P.A., et. al. On-line monitoring of batch processes using multiway independent component analysis. Chemometrics and Intelligent Laboratory Systems.2004,71(2):151-163.
[140]Albazzaz, H., Wang, X.Z. Introduction of dynamics to an approach for batch process monitoring using independent component analysis. Chemical Engineering Communications.2007,194(2):218-233.
[141]Zhao, C., Gao, F., Wang, F. Spectra data analysis and calibration modeling method using spectra subspace separation and multiblock independent component regression strategy. AIChE Journal.2011,57(5):1202-1215.
[142]Hu, K., Yuan, J. Statistical monitoring of fed-batch process using dynamic multiway neighborhood preserving embedding. Chemometrics and Intelligent Laboratory Systems. 2008,90(2):195-203.
[143]Hu, K., Yuan, J. Multivariate statistical process control based on multiway locality preserving projections. Journal of Process Control.2008,18(7):797-807.
[144]Yu, J., Qin, S.J. Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models. AIChE Journal.2008,54(7):1811-1829.
[145]Xie, X., Shi, H. Dynamic multimode process modeling and monitoring using adaptive Gaussian mixture models. Industrial & Engineering Chemistry Research.2012,51(15): 5497-5505.
[146]Yu, J., Qin, S.J. Multiway Gaussian mixture model based multiphase batch process monitoring. Industrial & Engineering Chemistry Research.2009,48(18):8585-8594.
[147]Jia, M., Chu, F., Wang, F., et. al. On-line batch process monitoring using batch dynamic kernel principal component analysis. Chemometrics and Intelligent Laboratory Systems. 2010,101(2):110-122.
[148]Lee, D.S., Park, J.M., Vanrolleghem, P.A. Adaptive multiscale principal component analysis for on-line monitoring of a sequencing batch reactor. Journal of Biotechnology. 2005,116(2):195-210.
[149]Zhao, C., Wang, F., Jia, M. Dissimilarity analysis based batch process monitoring using moving windows. AIChE Journal.2007,53(5):1267-1277.
[150]Zhao, C., Wang, F., Mao, Z., et. al. Adaptive monitoring based on independent component analysis for multiphase batch processes with limited modeling data. Industrial & Engineering Chemistry Research.2008,47(9):3104-3113.
[151]Undey, C., Cinar, A. Statistical monitoring of multistage, multiphase batch processes. IEEE Control Systems Magazine.2002,22(2):40-52.
[152]Ge, Z., Zhao, L., Yao, Y., et. al. Utilizing transition information in online quality prediction of multiphase batch processes. Journal of Process Control.2012,22(3): 599-611.
[153]Camacho, J., PicS, J. Multi-phase principal component analysis for batch processes modelling. Chemometrics and Intelligent Laboratory Systems.2006,81(2):127-136.
[154]Zhao, C., Gao, F., Niu, D., et. al. Enhanced process comprehension and quality analysis based on subspace separation for multiphase batch processes. AIChE Journal.2011, 57(2):388-403.
[155]Lu, N., Gao, F., Yang, Y., et. al. PCA-based modeling and on-line monitoring strategy for uneven-length batch processes. Industrial & Engineering Chemistry Research.2004, 43(13):3343-3352.
[156]Yao, Y., Dong, W., Zhao, L., et. al. Multivariate statistical monitoring of multiphase batch processes with between-phase transitions and uneven operation durations. The Canadian Journal of Chemical Engineering.2012,90(6):1383-1392.
[157]Bontempi, G., Birattari, M., Bersini, H. Lazy learning for local modelling and control design. International Journal of Control.1999,72(7-8):643-658.
[158]Atkeson, C.G., Moore, A.W., Schaal, S. Locally weighted learning. Artificial intelligence review.1997,11(1):11-73.
[159]Cleveland, W.S., Devlin, S.J. Locally weighted regression:an approach to regression analysis by local fitting. Journal of the American Statistical Association.1988,83(403): 596-610.
[160]Cheng, C., Chiu, M.S. A new data-based methodology for nonlinear process modeling. Chemical Engineering Science.2004,59(13):2801-2810.
[161]Cheng, C., Chiu, M. Nonlinear process monitoring using JITL-PCA. Chemometrics and Intelligent Laboratory Systems.2005,76(1):1-13.
[162]Fujiwara, K., Kano, M., Hasebe, S., et. al. Soft-sensor development using correlation-based just-in-time modeling. AIChE Journal.2009,55(7):1754-1765.
[163]Ge, Z., Song, Z. Online monitoring of nonlinear multiple mode processes based on adaptive local model approach. Control Engineering Practice.2008,16(12):1427-1437.
[164]Ge, Z., Song, Z. A comparative study of just-in-time-learning based methods for online soft sensor modeling. Chemometrics and Intelligent Laboratory Systems.2010,104(2): 306-317.
[165]葛志强,刘毅,宋执环,王海清.一种基于局部模型的非线性多工况过程监测方法.自动化学报.2008,34(7)：792-797.
[166]Liu, Y., Gao, Z., Li, P., et. al. Just-in-time kernel learning with adaptive parameter selection for soft sensor modeling of batch processes. Industrial & Engineering Chemistry Research.2012,51(11):4313-4327.
[167]刘毅,王海清,李平.局部最小二乘支持向量机回归在线建模方法及其在间歇过程的应用.化工学报.2007,58(11)：2846-2851.
[168]Nomikos, P., MacGregor, J.F. Multivariate SPC charts for monitoring batch processes. Technometrics.1995,37(1):41-59.
[169]Chen, J., Chen, H. On-line batch process monitoring using MHMT-based MPCA. Chemical Engineering Science.2006,61(10):3223-3239.
[170]Ge, Z., Song, Z. Batch process monitoring based on multilevel ICA-PCA. Journal of Zhejiang University-Science A.2008,9(8):1061-1069.
[171]Xu, Q.S., Liang, Y.Z. Monte Carlo cross validation. Chemometrics and Intelligent Laboratory Systems.2001,56(1):1-11.
[172]Russell, E.L., Chiang, L.H., Braatz, R.D. Fault detection in industrial processes using canonical variate analysis and dynamic principal component analysis. Chemometrics and Intelligent Laboratory Systems.2000,51(1):81-93.
[173]Yoo, C.K., Choi, S.W., Lee, I. Dynamic monitoring method for multiscale fault detection and diagnosis in MSPC. Industrial & Engineering Chemistry Research.2002, 41(17):4303-4317.
[174]付克昌,吴铁军.基于特征子空间的KPCA及其在故障检测与诊断中的应用.化工学报.2006,57(11)：2664-2669.
[175]Tian, X., Zhang, X., Deng, X., et. al. Multiway kernel independent component analysis based on feature samples for batch process monitoring. Neurocomputing.2009,72(7): 1584-1596.
[176]范玉刚,李平,宋执环.基于特征样本的KPCA在故障诊断中的应用.控制与决策.2005,20(12)：1415-1418.
[177]薄翠梅,张湜,张广明,王执铨.基于特征样本核主元分析的TE过程快速故障辨识方法.化工学报.2008,59(7)：1783-1789.
[178]Cui, P., Li, J., Wang, G. Improved kernel principal component analysis for fault detection. Expert Systems with Applications.2008,34(2):1210-1219.
[179]Li, J., Cui, P. Kernel scatter-difference-based discriminant analysis for nonlinear fault diagnosis. Chemometrics and Intelligent Laboratory Systems.2008,94(1):80-86.
[180]Cho, J., Lee, J., Choi, S.W., et. al. Fault identification for process monitoring using kernel principal component analysis. Chemical Engineering Science.2005,60(1): 279-288.
[181]Choi, S.W., Lee, C., Lee, J., et. al. Fault detection and identification of nonlinear processes based on kernel PCA. Chemometrics and Intelligent Laboratory Systems. 2005,75(1):55-67.
[182]He, X.B., Yang, Y.P., Yang, Y.H. Fault diagnosis based on variable-weighted kernel Fisher discriminant analysis. Chemometrics and Intelligent Laboratory Systems.2008, 93(1):27-33.
[183]Suykens, J.A.K., Van Gestel, T., De Brabanter, J., et. al. Least squares support vector machines. Tutorial IJCNN.2003,
[184]Arteaga, F., Ferrer, A. Dealing with missing data in MSPC:several methods, different interpretations, some examples. Journal of Chemometrics.2002,16(8-10):408-418.