基于统计学方法的自适应过程监控与故障诊断
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摘要
随着工业过程规模的不断扩大和复杂性的日益提高,有效的过程监控和故障诊断是保证生产安全、提高产品质量和经济效益的关键。对复杂的工业过程来说,准确详细的数学模型往往很难得到。即使能够得到,这些理论上的等式也只能描述系统中一部分能量及物料平衡关系。这就限制了基于模型的过程监控方法的应用。另外,随着计算机集散控制系统的应用和发展,大量的测量数据被及时采集和存储。如何从这些海量数据中挖掘出隐藏的有用信息,提高过程监控和故障诊断能力,已经成为越来越迫切需要解决的问题。统计过程监控就是在这种背景下发展起来的,并且受到了广泛关注。
统计过程监控是一种基于多元统计理论的方法。它通过对测量数据进行分析和解释,建立统计监控模型,判断过程所处的运行状态,在线检测和识别过程中出现的异常工况,从而减小由过程故障所造成的损失,提高生产效率。
本文在介绍统计过程监控的研究内容、方法和发展现状的基础上,首先关注了连续生产过程自适应监控方法。基于主元分析(PCA)模型的传统过程监控假设工业过程是静止的,PCA模型一旦建立就不需要发生变化。而实际的工业过程大部分都是时变的,当用一个固定的PCA模型去监控一个时变系统必然引起高的错误率。其次,对于广泛应用于过程故障诊断的Fisher判别分析(FDA),尽管比PCA或偏最小二乘(PLS)具有更好的故障诊断性能,但是当故障数据存在相互重叠时,它的故障诊断能力显著下降。与其它模式分类问题不同,过程故障诊断具有一个特殊类:正常数据类。改进的FDA充分利用这个特殊类,有效提高了FDA的故障诊断能力。最后,通过核方法将上述自适应监控方法和改进的FDA推广到非线性情况。具体来说,本文的主要工作和贡献体现在以下几个方面:
1、针对工业过程时变特性,提出了一种新的基于可变移动窗PCA(VMWPCA)的自适应监控方法。在递归更新协方差矩阵的基础上,VMWPCA首先将移动窗技术与经典的秩r奇异值分解算法(R-SVD)结合起来,实现了PCA监控模型的递归更新。另一方面,移动窗的长度应该是一个取决于过程变化快慢的重要调节参数,而不能简单凭经验选择一个固定长度。为此,提出了一种可变移动窗策略,并详细讨论了各参数的选择方法。它的最大特点是最优移动窗长度直接由反映过程变化的均值和协方差矩阵的变化来决定。
2、针对非线性时变工业过程,结合核主元分析(KPCA)处理非线性数据的优点,提出了基于可变移动窗核主元分析(VMWKPCA)的非线性自适应监控方法。通过核方法将VMWPCA推广到VMWKPCA,需要解决两个主要问题:一是通过核化R-SVD实现KPCA监控模型的递归更新;二是实现特征空间上的可变移动窗策略。
3、结合过程故障诊断的特点,提出了基于变量加权FDA(VW-FDA)的故障诊断方法。VW-FDA将变量加权与传统FDA结合起来。通过变量加权获得每一个故障的加权向量后,对所有故障数据类分别进行加权。VW-FDA能够从这些加权数据中获得更多判别信息,从而提过FDA的故障诊断能力。准确的变量加权是VW-FDA的重要一环。为此,提出了基于偏F值和累计变化百分比(CPV)的变量加权方法。CPV从全部测量变量中挑选候选变量后,只计算候选变量的偏F值,而不是全部测量变量的偏F值。这样,不仅提高了偏F值的计算效率,而且也有效消除了无关变量的影响,改善了偏F值的加权性能。
4、将非线性变量加权与核FDA(KFDA)结合起来,提出了基于变量加权KFDA(VW-KFDA)的非线性故障诊断方法。这里非线性变量加权通过最大化变量加权准则:核目标对齐(Kernel Target Alignment)来获得每一个故障的加权变量。与KFDA中的瑞利商(Reyleigh Quotient)准则不同,核目标对齐只与核矩阵有关,而不需要在优化过程中反复计算判别向量。通过对加权故障数据集执行KFDA,VW-KFDA能够从相互重叠数据中获得更多判别信息,从而提高KFDA的故障诊断能力。
With the progress of industrial processes in scale and complexity, e?ectivelyprocess monitoring is the key to ensure safety, enhance product quality and economybenefit. It is di?cult to construct the accurate mathematical model for a complexindustrial process. Even if it could be achieved, the predigested equations can onlydescribe partial relationships of energy and mass. These limit the application ofmethods based on the rigorous mathematical model. On the other hand, with therapid development of computer technology, a large amount of process data havebeen collected. How to transform these data into valuable information to improvethe monitoring performance becomes a challenge issue. It is one of the most activeresearch areas in the field of process control.
Statistical process monitoring is a method based on statistical theory. Moni-toring model is constructed by analysis and interpretation of the collected data foron-line fault detection and diagnosis so as to reduce the losses caused by faults andenhance product e?ciency.
After the content, method and development of statistical process monitoring aregeneralized, the dissertation firstly pays attention to adaptive process monitoring.Under the assumption that the industrial process is stationary or time-invariant,the static principal component analysis (PCA) model used for process monitoringis reasonable. However, the time-varying character of most industrial processesalways violates the assumption. When the PCA model for some particular processcondition is used to monitor these processes with normal changes, a number of falsealarms often arise. Secondly, as a classical linear technique for dimension reductionand pattern classification, Fisher discriminant analysis (FDA) has been approved tooutperform PCA-based or partial least squares-based diagnosis methods. However,the classification performance of FDA will degenerate as long as overlapping samplesexist. Unlike those classification problems in other fields, process fault diagnosis hasa common benchmark class: a normal data set. The improved FDA makes full useof the special class to improve the diagnosis performance of FDA. Finally,”kernel trick”has been used to develop the nonlinear versions of the adaptive monitoringapproach and the improved FDA.
Specifically, the main contributions of this dissertation are as follows:
1. In view of a time-invariant industrial process, an adaptive process monitoringapproach with variable moving window PCA (VMWPCA) is proposed. On the basisof recursively updating the correlation matrix, the approach combines the movingwindow technique with the classical rank-r singular value decomposition (R-SVD)to construct a new PCA model e?ciently and parsimoniously. Furthermore, thewindow size is an important tunable parameter that varies depending on how fast thenormal process can change. Instead of the fixed moving window selected empirically,a variable moving window strategy and the guidance to select its parameters arediscussed in detail. One merit is that the optimal moving window size is contingentupon the changes of the mean and covariance matrix that represent directly processchanges.
2. In view of the nonlinear time-variant industrial process and integrating themerit of kernel PCA (KPCA) to deal with nonlinear data, an nonlinear adaptiveprocess monitoring approach with variable moving window KPCA (VMWKPCA)is proposed. For the kernel version of VMWPCA: VMWKPCA, two key pointsare discussed: e?ciently updating the KPCA model though kernelizing the R-SVDalgorithm and the variable moving window strategy in the feature space.
3. An extension of FDA: variable-weighted FDA (VW-FDA) is proposed forprocess fault diagnosis. The approach incorporates the variable weighting into theconventional FDA. The variable weighting finds out each weight vector for all faults.The summed fault data weighted by the corresponding weight vectors involve morefault characteristic information than the original fault data. FDA is performed onthe summed fault data. It is helpful for VW-FDA to extract discriminative fea-tures from overlapping fault data so as to improve the fault diagnosis performanceof FDA. The exact variable weighting is a key procedure to VW-FDA. The vari-able weighting based on the partial F-values with the cumulative percent variation(CPV) is adopted. CPV based on each variable’s equivalent variation is proposedto determine candidate variables. Then, the partial F-values can be performed on these candidate variables rather than all variables. It not only reduces the com-putational complexity but also eliminates the redundant variables to improve thevariable weighting performance.
4. A new nonlinear fault diagnosis approach with variable-weighted kernel FDA(VW-KFDA) is proposed. The approach incorporates the nonlinear variable weight-ing into KFDA. The nonlinear variable weighting finds out the weighted vector ofeach fault by maximizing the variable weighting criteria: the kernel target alignment(KTA). Unlike the Rayleigh quotient in KFDA, KTA depends on only the kernel ma-trix and doesn’t time-consumingly calculate the optimal discriminant vector duringthe optimization procedure. KFDA is performed on the weighted fault data, whichis helpful for VW-KFDA to extract discriminative features from overlapping faultdata so as to improve the fault diagnosis performance of KFDA.
统计过程监控是一种基于多元统计理论的方法。它通过对测量数据进行分析和解释,建立统计监控模型,判断过程所处的运行状态,在线检测和识别过程中出现的异常工况,从而减小由过程故障所造成的损失,提高生产效率。
本文在介绍统计过程监控的研究内容、方法和发展现状的基础上,首先关注了连续生产过程自适应监控方法。基于主元分析(PCA)模型的传统过程监控假设工业过程是静止的,PCA模型一旦建立就不需要发生变化。而实际的工业过程大部分都是时变的,当用一个固定的PCA模型去监控一个时变系统必然引起高的错误率。其次,对于广泛应用于过程故障诊断的Fisher判别分析(FDA),尽管比PCA或偏最小二乘(PLS)具有更好的故障诊断性能,但是当故障数据存在相互重叠时,它的故障诊断能力显著下降。与其它模式分类问题不同,过程故障诊断具有一个特殊类:正常数据类。改进的FDA充分利用这个特殊类,有效提高了FDA的故障诊断能力。最后,通过核方法将上述自适应监控方法和改进的FDA推广到非线性情况。具体来说,本文的主要工作和贡献体现在以下几个方面:
1、针对工业过程时变特性,提出了一种新的基于可变移动窗PCA(VMWPCA)的自适应监控方法。在递归更新协方差矩阵的基础上,VMWPCA首先将移动窗技术与经典的秩r奇异值分解算法(R-SVD)结合起来,实现了PCA监控模型的递归更新。另一方面,移动窗的长度应该是一个取决于过程变化快慢的重要调节参数,而不能简单凭经验选择一个固定长度。为此,提出了一种可变移动窗策略,并详细讨论了各参数的选择方法。它的最大特点是最优移动窗长度直接由反映过程变化的均值和协方差矩阵的变化来决定。
2、针对非线性时变工业过程,结合核主元分析(KPCA)处理非线性数据的优点,提出了基于可变移动窗核主元分析(VMWKPCA)的非线性自适应监控方法。通过核方法将VMWPCA推广到VMWKPCA,需要解决两个主要问题:一是通过核化R-SVD实现KPCA监控模型的递归更新;二是实现特征空间上的可变移动窗策略。
3、结合过程故障诊断的特点,提出了基于变量加权FDA(VW-FDA)的故障诊断方法。VW-FDA将变量加权与传统FDA结合起来。通过变量加权获得每一个故障的加权向量后,对所有故障数据类分别进行加权。VW-FDA能够从这些加权数据中获得更多判别信息,从而提过FDA的故障诊断能力。准确的变量加权是VW-FDA的重要一环。为此,提出了基于偏F值和累计变化百分比(CPV)的变量加权方法。CPV从全部测量变量中挑选候选变量后,只计算候选变量的偏F值,而不是全部测量变量的偏F值。这样,不仅提高了偏F值的计算效率,而且也有效消除了无关变量的影响,改善了偏F值的加权性能。
4、将非线性变量加权与核FDA(KFDA)结合起来,提出了基于变量加权KFDA(VW-KFDA)的非线性故障诊断方法。这里非线性变量加权通过最大化变量加权准则:核目标对齐(Kernel Target Alignment)来获得每一个故障的加权变量。与KFDA中的瑞利商(Reyleigh Quotient)准则不同,核目标对齐只与核矩阵有关,而不需要在优化过程中反复计算判别向量。通过对加权故障数据集执行KFDA,VW-KFDA能够从相互重叠数据中获得更多判别信息,从而提高KFDA的故障诊断能力。
With the progress of industrial processes in scale and complexity, e?ectivelyprocess monitoring is the key to ensure safety, enhance product quality and economybenefit. It is di?cult to construct the accurate mathematical model for a complexindustrial process. Even if it could be achieved, the predigested equations can onlydescribe partial relationships of energy and mass. These limit the application ofmethods based on the rigorous mathematical model. On the other hand, with therapid development of computer technology, a large amount of process data havebeen collected. How to transform these data into valuable information to improvethe monitoring performance becomes a challenge issue. It is one of the most activeresearch areas in the field of process control.
Statistical process monitoring is a method based on statistical theory. Moni-toring model is constructed by analysis and interpretation of the collected data foron-line fault detection and diagnosis so as to reduce the losses caused by faults andenhance product e?ciency.
After the content, method and development of statistical process monitoring aregeneralized, the dissertation firstly pays attention to adaptive process monitoring.Under the assumption that the industrial process is stationary or time-invariant,the static principal component analysis (PCA) model used for process monitoringis reasonable. However, the time-varying character of most industrial processesalways violates the assumption. When the PCA model for some particular processcondition is used to monitor these processes with normal changes, a number of falsealarms often arise. Secondly, as a classical linear technique for dimension reductionand pattern classification, Fisher discriminant analysis (FDA) has been approved tooutperform PCA-based or partial least squares-based diagnosis methods. However,the classification performance of FDA will degenerate as long as overlapping samplesexist. Unlike those classification problems in other fields, process fault diagnosis hasa common benchmark class: a normal data set. The improved FDA makes full useof the special class to improve the diagnosis performance of FDA. Finally,”kernel trick”has been used to develop the nonlinear versions of the adaptive monitoringapproach and the improved FDA.
Specifically, the main contributions of this dissertation are as follows:
1. In view of a time-invariant industrial process, an adaptive process monitoringapproach with variable moving window PCA (VMWPCA) is proposed. On the basisof recursively updating the correlation matrix, the approach combines the movingwindow technique with the classical rank-r singular value decomposition (R-SVD)to construct a new PCA model e?ciently and parsimoniously. Furthermore, thewindow size is an important tunable parameter that varies depending on how fast thenormal process can change. Instead of the fixed moving window selected empirically,a variable moving window strategy and the guidance to select its parameters arediscussed in detail. One merit is that the optimal moving window size is contingentupon the changes of the mean and covariance matrix that represent directly processchanges.
2. In view of the nonlinear time-variant industrial process and integrating themerit of kernel PCA (KPCA) to deal with nonlinear data, an nonlinear adaptiveprocess monitoring approach with variable moving window KPCA (VMWKPCA)is proposed. For the kernel version of VMWPCA: VMWKPCA, two key pointsare discussed: e?ciently updating the KPCA model though kernelizing the R-SVDalgorithm and the variable moving window strategy in the feature space.
3. An extension of FDA: variable-weighted FDA (VW-FDA) is proposed forprocess fault diagnosis. The approach incorporates the variable weighting into theconventional FDA. The variable weighting finds out each weight vector for all faults.The summed fault data weighted by the corresponding weight vectors involve morefault characteristic information than the original fault data. FDA is performed onthe summed fault data. It is helpful for VW-FDA to extract discriminative fea-tures from overlapping fault data so as to improve the fault diagnosis performanceof FDA. The exact variable weighting is a key procedure to VW-FDA. The vari-able weighting based on the partial F-values with the cumulative percent variation(CPV) is adopted. CPV based on each variable’s equivalent variation is proposedto determine candidate variables. Then, the partial F-values can be performed on these candidate variables rather than all variables. It not only reduces the com-putational complexity but also eliminates the redundant variables to improve thevariable weighting performance.
4. A new nonlinear fault diagnosis approach with variable-weighted kernel FDA(VW-KFDA) is proposed. The approach incorporates the nonlinear variable weight-ing into KFDA. The nonlinear variable weighting finds out the weighted vector ofeach fault by maximizing the variable weighting criteria: the kernel target alignment(KTA). Unlike the Rayleigh quotient in KFDA, KTA depends on only the kernel ma-trix and doesn’t time-consumingly calculate the optimal discriminant vector duringthe optimization procedure. KFDA is performed on the weighted fault data, whichis helpful for VW-KFDA to extract discriminative features from overlapping faultdata so as to improve the fault diagnosis performance of KFDA.
引文
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