PCA和PPCA在化工分离过程监控中的应用比较

在利用主元分析(PCA)作统计监控时,没有主元与变量之间的生成模型,出现了检测指标量度不一致且只能离线故障识别等缺陷.而概率主元分析(PPCA)则在确定主元和误差的概率函数后,利用期望最大化(EM)算法建立了过程的生成模型,克服了PCA的不足.最后通过PCA和PPCA在化工分离过程监控中的应用比较,证明PPCA监控法方便、有效.     

基于稀疏核主元分析的在线非线性过程监控

核主元分析(KPCA)适合非线性过程的监控,但存在计算量大、实时性差等缺点。提出一种基于稀疏KPCA(SKPCA)的过程监控方法,先使用SKPCA对正常建模数据进行加权,少数权值大的数据基本能代表全部正常数据的信息,因此稀化了建模数据,然后根据稀化后的正常数据建立过程的KPCA模型,并提出监控指标,大大减少了计算量,提高了监控的实时性,最后以化工分离过程为对象,就KPCA与SKPCA的监控效果和实时性进行了详细的对比研究,结果表明了基于SKPCA监控方法的优越性。     

因子分析及其在过程监控中的应用

概率主元分析（PPCA）模型是因子分析（FA）模型的一种特殊形式，而主元分析（PCA）模型是PPCA模型的一种特例。PPCA和PCA已经在过程监控中得到了成功的应用，但是这两种方法的约束条件较多，而FA约束条件少，因此更能反映数据的本质特征。本文将FA引入工业过程监控，通过期望最大化（EM）算法建立FA模型，然后提出基于FA的监控指标，并讨论了因子个数的选择方案。在田纳西-伊斯曼（TE）过程中的应用结果以及与PCA、PPCA监控结果的对比表明了该方法的优越性。     

基于互信息的PCA方法及其在过程监测中的应用

主元分析(PCA)是一种经典的特征提取方法,已被广泛用于多变量统计过程监测,其算法的本质在于提取过程数据各变量之间的相关性。然而,传统PCA算法中定义的相关性矩阵局限于计算变量间的线性关系,无法衡量两个变量间相互依赖的强弱程度。为此,提出一种新的基于互信息的PCA方法(MIPCA)并将之应用于过程监测。与传统PCA所不同的是,MIPCA通过计算两两变量间的互信息来定义相关性,将原始相关性矩阵取而代之为互信息矩阵,并利用该互信息矩阵的特征向量实现对过程数据的特征提取。在此基础上,可以建立相应的统计监测模型。最后,通过实例验证MIPCA用于过程监测的可行性和有效性。     

步进MPCA及其在间歇过程监控中的应用

针对多向主元分析法(MPCA)在间歇过程监控过程中需要预测过程未来输出的困难,提出了一种新的步进多向主元分析方法。该方法通过建立一系列的PCA模型,避免了对预估过程变量未来输出的需要,通过引入遗忘因子能够自然地处理多阶段间歇过程的情况。对于多阶段链霉素发酵过程的监控表明,相对于普通MPCA,步进MPCA能够更精确地对过程故障行为进行描述。     

改进PCA及其在过程监测与故障诊断中的应用

提出一种改进的主元分析 (PCA)方法 ,采用主元相关变量残差 (PVR)统计量代替通常的平方预测误差Q统计量 ,用于工业过程的监测与故障诊断。改进PCA避免了Q统计量的保守性 ,能够提供更详细的过程变化信息 ,从而有效识别正常工况改变与过程故障引起的T² 图变化。通过对双效蒸发过程的仿真监测 ,与普通PCA方法进行了比较 ,表明了改进PCA方法的有效性     

基于奇异值识别的模式切换过程递归PCA监控

常规的PCA方法难于对发生模式变化的过程参数进行监控,为此,本文提出了一种基于奇异值识别递归PCA技术,用于解决多模式切换过程的监控问题。首先建立了在线奇异值识别算法,通过识别奇异值的变化可以准确判断过程发生模式切换的时间,然后采用递归PCA对过程的模式切换过渡阶段进行监控。将TE过程用于实例研究,验证了所提出方法的有效性。     

基于核PLS方法的非线性过程在线监控

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）的监控方法。KPLS方法是将原始输入数据通过核函数映射到高维特征空间,然后在高维特征空间再进行偏最小二乘（PLS）运算。与线性PLS相比,KPLS方法能充分利用样本空间信息,建立起输入输出变量之间的非线性关系。与其他非线性PLS方法不同,KPLS方法只需要进行线性运算,从而避免非线性优化问题。在对过程进行监控时,首先采用KPLS方法建立模型,得到得分向量,然后计算出T²和SPE统计量及其相应的控制限。Tennessee Eastman(TE)模型上的仿真研究结果表明,所提方法比线性PLS相似文献   

基于PCA混合模型的多工况过程监控

针对传统多元统计故障检测方法大多假设测量数据服从单一高斯分布的不足,提出了一种基于PCA(principal component analysis)混合模型的多工况过程监测方法。首先通过直接对混合模型的各高斯成分的协方差进行PCA降维变换,使得协方差阵对角化,既减少了运算量又避免了变量相关而导致的奇异性问题;同时采用BYY增量EM算法自动获取混合模型的最佳混合分量数目,避免了常规EM算法的不足。所得的混合模型,除包括均值、协方差和先验概率等参数外,还包括了PCA载荷阵,即对每个混合元建立了PCA模型。然后给出了统计量定义,实现对多工况过程的故障检测。数值例子和TE过程的应用表明,本文提出的方法无需过程先验知识,能自动获取工况数目、精确估计各个工况的统计特性,并更准确及时地检测出多工况过程的各种故障。     

基于Jarque-Bera检验的非线性多分布过程故障检测

针对现代工业过程的非线性和多分布问题,提出一种基于Jarque-Bera test的故障检测方法.首先,对标准化后的原始数据进行Jarque-Bera test,将变量划分为两个部分;其次,对所有的JB统计量做-ln处理,并采用正态置信概率权值进一步划分,从而使原始变量空间划分为正态和非正态分布的两个子空间;再次,在两...     

Nonlinear dynamic process monitoring based on dynamic kernel PCA

Nonlinear dynamic process monitoring based on dynamic kernel principal component analysis (DKPCA) is proposed. The kernel functions used in kernel PCA (KPCA) are profitable for capturing nonlinear property of processes and the time-lagged data extension is suitable for describing dynamic characteristic of processes. DKPCA enables us to monitor an arbitrary process with severe nonlinearity and (or) dynamics. In this respect, it is a generalized concept of multivariate statistical monitoring approaches. A unified monitoring index combined T² with SPE is also suggested. The proposed monitoring method based on DKPCA is applied to a simulated nonlinear process and a wastewater treatment process. A comparison study of PCA, dynamic PCA, KPCA, and DKPCA is investigated in terms of type I error rate, type II error rate, and detection delay. The monitoring results confirm that the proposed methodology results in the best monitoring performance, i.e., low missing alarms and small detection delay, for all the faults.     

Block adaptive kernel principal component analysis for nonlinear process monitoring

On‐line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing with the existing work, the proposed algorithm (1) does not rely on iterative computation in the calculating process, (2) combines the up‐ and downdating operations to become a single one (3) and describes the adaptation of the Gram matrix as a series of rank‐1 modification. In addition, (4) the updation of the eigenvalues and eigenvectors is of and high‐precision. The computational complexity analysis and the numerical study show that the derived strategy possesses better ability to model the time‐varying nonlinear variable interrelationships in process monitoring. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4334–4345, 2016     

Learning a data-dependent kernel function for KPCA-based nonlinear process monitoring

Kernel principal component analysis (KPCA)-based process monitoring methods have recently shown to be very effective for monitoring nonlinear processes. However, their performances largely depend on the kernel function and currently there is no general rule for kernel selection. Existing methods simply choose the kernel function empirically or experimentally from a given set of candidates. This paper proposes a kernel function learning method for KPCA to learn a kernel function tailored to specific data and explores its potential for KPCA-based process monitoring. Motivated by the manifold learning method maximum variance unfolding (MVU), we obtain the kernel function by optimizing over a family of data-dependent kernels such that the nonlinear structure in input data is unfolded in the kernel feature space and gets more likely to be linear there. Using the optimized kernel, the nonlinear principal components of KPCA which are linear principal components in the kernel feature space can effectively capture the variation in data, and thus the data under normal operating conditions can be more precisely modeled by KPCA for process monitoring. Simulation results on an simple nonlinear system and the benchmark Tennessee Eastman (TE) demonstrate that the optimized kernel functions lead to significant improvement in the performance over the popular Gaussian kernels when used in the KPCA-based process monitoring.     

Improved dynamic kernel PCA based on local preserving projections and its application for electric submersible pump fault diagnosis

Dynamic kernel principal component analysis (DKPCA) has been frequently implemented for nonlinear and dynamic process monitoring of complex industrial processes. However, traditional DKPCA focuses only on the global structural analysis of data sets and strongly neglects the local information, which is equally essential for process detection and identification. In this paper, an improved DKPCA, referred to as the local DKPCA (LDKPCA), is proposed based on local preserving projections (LPP) for nonlinear dynamic process fault diagnosis. The method combines the advantages of LPP and DKPCA by utilizing the local structure feature to maintain the geometric structure of the data in a unified framework. To achieve a highly comprehensive feature extraction, the local characteristics are fused in DKPCA to produce an optimization objective. The neighbouring points of the new objective function projection in the feature space are still maintained in proximity, and the variance information is retained simultaneously. For the purpose of fault detection, two statistics, known as the T² and squared prediction error (SPE) statistics, are constructed, based on the LDKPCA model, and used to monitor the latent variable space and the residual space, respectively. In addition, the sensitivity analysis is brought in for fault identification of the two statistics. Based on the experimental analysis using the shaft breakage data of an offshore oilfield electric submersible pump (ESP), the proposed method outperforms the conventional DKPCA in terms of fault monitoring performance. The experimental results demonstrate the potential of the method in nonlinear dynamic process fault diagnosis.     

基于贝叶斯推理的PKPCAM的非线性多模态过程故障检测与诊断方法

针对一类非线性多模态的化工过程,提出一种基于概率核主元的混合模型(PKPCAM),并利用贝叶斯推理策略进行过程监控与故障诊断.在提出的模型中, 每个操作模态由一个局部化的概率核主元分量描述,从而构建的一系列分量对应了不同的操作模态.首先,将过程数据从原始的度量空间投影到高维特征空间;其次,在该特征空间建立概率主元混合模型,从概率角度刻画数据集的多个局部分量特征;最后,在提取的核主元分量内获得测试样本的后验概率,结合模态内的马氏距离贡献度,提出基于贝叶斯推理的全局概率指标进行故障检测,同时利用模态内变量的相对贡献度,基于全局贡献度指标进行故障诊断.利用TEP仿真平台,与基于k均值聚类的次级主元分析和核主元分析的方法进行了对比分析,验证了提出的贝叶斯推理的PKPCAM方法对非线性多模态过程进行故障检测与诊断的可行性和有效性.     

基于主元分析和核密度估计的多变量统计过程监控及在工厂聚丙烯催化剂反应器的应用

Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.