Multimodal process monitoring based on transition-constrained Gaussian mixture model

Reliable process monitoring is important for ensuring process safety and product quality. A production process is generally characterized by multiple operation modes, and monitoring these multimodal processes is challenging. Most multimodal monitoring methods rely on the assumption that the modes are independent of each other, which may not be appropriate for practical application. This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring. This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data. This process enables the identified modes to reflect the stability of actual working conditions, improve mode identification accuracy, and enhance monitoring reliability in cases of mode overlap. Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach in multimodal process monitoring with mode overlap.     

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。     

Adaptive soft sensor for online prediction and process monitoring based on a mixture of Gaussian process models

Linear models can be inappropriate when dealing with nonlinear and multimode processes, leading to a soft sensor with poor performance. Due to time-varying process behaviour it is necessary to derive and implement some kind of adaptation mechanism in order to keep the soft sensor performance at a desired level. Therefore, an adaptation mechanism for a soft sensor based on a mixture of Gaussian process regression models is proposed in this paper. A procedure for input variable selection based on mutual information is also presented. This procedure selects the most important input variables for output variable prediction, thus simplifying model development and adaptation. Apart from online prediction of the difficult-to-measure variable, this soft sensor can be used for adaptive process monitoring. The efficiency of the proposed method is benchmarked with the commonly applied recursive PLS and recursive PCA method on the Tennessee Eastman process and two real industrial examples.     

基于高斯混合模型与主元分析的多模型切换方法

针对多模型预测控制的模型切换问题,提出了一种基于工况判断的多模型切换方法,利用工业过程中的可测变量综合反映系统的动态特性,根据动态特性的变化进行多模型切换。首先利用高斯混合模型(GMM)将历史数据划分为若干个工况,然后利用不同工况下的历史数据建立负荷向量矩阵和预测模型,最后根据主元模型的平方预报误差(SPE)选择预测模型。以乙烯裂解炉的反应管出口温度(COT)的控制为例进行仿真,仿真结果表明:提出的方法实现了多个反应管出口温度的稳定均衡控制,当系统的工况发生改变时,通过不同主元模型的SPE统计量的比较,可以很容易地找到匹配的工况,并切换为相应的预测模型,解决了当系统动态特性发生改变时,预测模型切换滞后的问题。     

Data‐based linear Gaussian state‐space model for dynamic process monitoring

This article develops a data‐based linear Gaussian state‐space model for monitoring of dynamic processes under noisy environment. The Kalman filter is introduced for construction of the linear Gaussian state‐space model, and an iterative expectation‐maximization algorithm is used for model parameters learning. With the incorporation of the dynamic data information, a new fault detection and identification approach is proposed. The feasibility and effectiveness of the two monitoring statistics in the new method are theoretically evaluated and further confirmed through two case studies. Furthermore, detailed fault smearing effect analysis of the proposed method is provided and compared with other identification methods. Based on the simulation results of two case studies, the superiority of the proposed method is explored. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes

A nonlinear kernel Gaussian mixture model (NKGMM) based inferential monitoring method is proposed in this article for chemical process fault detection and diagnosis. Aimed at the multimode non-Gaussian process with within-mode nonlinearity, the developed NKGMM approach projects the operating data from the raw measurement space into the high-dimensional kernel feature space. Thus the Gaussian mixture model can be estimated in the feature space with each component satisfying multivariate Gaussianity. As a comparison, the conventional independent component analysis (ICA) searches for the non-Gaussian subspace with maximized negentropy, which is not equivalent to the multi-Gaussianity in multimode process. The regular Gaussian mixture model (GMM) method, on the other hand, assumes the Gaussianity of each cluster in the original data space and thus cannot effectively handle the within-mode nonlinearity. With the extracted kernel Gaussian components, the geometric distance driven inferential index is further derived to monitor the process operation and detect the faulty events. Moreover, the kernel Gaussian mixture based inferential index is decomposed into variable contributions for fault diagnosis. For the simulated multimode wastewater treatment process, the proposed NKGMM approach outperforms the ICA and GMM methods in early detection of process faults, minimization of false alarms, and isolation of faulty variables of nonlinear and non-Gaussian multimode processes.     

基于高斯过程和贝叶斯决策的组合模型软测量

为了提高化工生产过程中软测量建模的估计精度,提出了一种基于高斯过程和贝叶斯决策的组合模型建模方法。该方法在对原始数据进行分类的基础上,利用高斯过程对每个子类建立软测量子模型,通过贝叶斯决策方法实现模型的联合估计输出。将该建模方法应用于某双酚A装置的软测量建模中,仿真结果表明,相比于传统的开关切换或加权组合多模型,该组合模型能在实际生产中充分利用样本信息,使得具有更高的估计精度和更强的泛化性能。     

基于分布式ICA-PCA模型的工业过程故障监测

提出基于分布式ICA-PCA( independent component analysis-principal component analysis)模型的工业过程故障监测方法,适合于复杂工业过程难以自动划分子块及过程数据存在非高斯信息的情况。首先,对过程数据进行PCA分解,并在PCA主成分不同的方向上构建不同的子块,把原始特征空间自动划分为不同子空间。然后,对各个子块采用ICA-PCA两步信息提取的策略,提取出高斯信息和非高斯信息,并构建新的统计量和统计限。最后,通过Tennessee Eastman(TE)过程的仿真实验,验证所提出故障监测模型的有效性和可行性。     

Dynamic soft sensor development based on Gaussian mixture regression for fermentation processes

The dynamic soft sensor based on a single Gaussian process regression (GPR) model has been developed in fermentation processes.However,limitations of single regression models,for multiphase/multimode fermentation processes,may result in large prediction errors and complexity of the soft sensor.Therefore,a dynamic soft sensor based on Gaussian mixture regression (GMR) was proposed to overcome the problems.Two structure parameters,the number of Gaussian components and the order of the model,are crucial to the soft sensor model.To achieve a simple and effective soft sensor,an iterative strategy was proposed to optimize the two structure parameters synchronously.For the aim of comparisons,the proposed dynamic GMR soft sensor and the existing dynamic GPR soft sensor were both investigated to estimate biomass concentration in a Penicillin simulation process and an industrial Erythromycin fermentation process.Results show that the proposed dynamic GMR soft sensor has higher prediction accuracy and is more suitable for dynamic multiphase/multimode fermentation processes.     

Statistical process monitoring based on dissimilarity of process data

Multivariate statistical process control (MSPC) has been widely used for monitoring chemical processes with highly correlated variables. In this work, a novel statistical process monitoring method is proposed based on the idea that a change of operating condition can be detected by monitoring a distribution of process data, which reflects the corresponding operating conditions. To quantitatively evaluate the difference between two data sets, a dissimilarity index is introduced. The monitoring performance of the proposed method, referred to as DISSIM, and that of the conventional MSPC method are compared with their applications to simulated data collected from a simple 2 × 2 process and the Tennessee Eastman process. The results clearly show that the monitoring performance of DISSIM, especially dynamic DISSIM, is considerably better than that of the conventional MSPC method when a time-window size is appropriately selected.     

基于流程拓扑信息的统计过程监测方法

传统数据驱动的过程监测方法主要基于历史数据和统计学知识建立,往往忽视了对过程机理的考虑。基于预测残差的过程监测方法则通过数据驱动的回归模型实现对局部过程机理的近似,在预测残差的基础上建立监测模型实现了对过程偏离更好的识别。但其建立回归模型实现对局部过程机理的近似时主要基于数据,很少考虑具体流程信息。作为流程信息的一种表现形式,流程拓扑结构常被用来提取变量间的进程与因果关系,如果在建立回归模型时结合流程的拓扑结构,则可使得所建立的回归模型中包含一定的流程信息,使其对局部机理的近似更为准确。基于此,本文提出一种基于流程拓扑信息的统计过程监测方法。该方法利用流程的拓扑结构,提取变量间的进程与因果关系,建立回归模型实现对局部过程机理的近似。在此基础上建立基于预测残差的过程监测模型,实现对过程偏离的监测。该方法被应用于某连续重整装置的过程监测中,结果表明其监测效果要优于基于主元分析和基于预测残差的过程监测方法。     

Local component based principal component analysis model for multimode process monitoring

For plant-wide processes with multiple operating conditions,the multimode feature imposes some chal-lenges to conventional monitoring techniques.Hence,to solve this problem,this paper provides a novel local component based principal component analysis(LCPCA)approach for monitoring the status of a multimode process.In LCPCA,the process prior knowledge of mode division is not required and it purely based on the process data.Firstly,LCPCA divides the processes data into multiple local components using finite Gaussian mixture model mixture(FGMM).Then,calculating the posterior probability is applied to determine each sample belonging to which local component.After that,the local component information(such as mean and standard deviation)is used to standardize each sample of local component.Finally,the standardized samples of each local component are combined to train PCA monitoring model.Based on the PCA monitoring model,two monitoring statistics T2 and SPE are used for monitoring multimode pro-cesses.Through a numerical example and the Tennessee Eastman(TE)process,the monitoring result demonstrates that LCPCA outperformed conventional PCA and LNS-PCA in the fault detection rate.     

基于k-近邻互信息的发酵过程高斯过程回归建模

发酵过程中基质浓度往往无法在线测量,采用高斯过程回归（GPR）建立基质浓度的估计模型,实现了其软测量。不同于传统软测量方法对基质浓度的估计,该方法不仅可以得到估计值,还能够得到其估计方差。考虑到发酵过程中各变量之间的非线性、相关性,为了提高模型的预测性能,在模型建立之前首先用k-近邻互信息（k-MI）辅助变量选择方法对模型的输入变量进行选择。从青霉素发酵过程的应用结果来看,采用kMI-GPR方法取得了较好的估计效果。     

基于改进Bagging算法的高斯过程集成软测量建模

为提高对工况复杂的工业过程进行软测量建模的模型精度和泛化能力,提出了一种基于改进Bagging算法的高斯过程集成软测量建模方法。该算法采用高斯过程回归算法建立集成学习模型的基学习器,并在Bagging算法对训练样本重采样生成基学习器训练子集的基础上,采用基于正则化互信息的特征排序指标进行基学习器的输入特征抽取,实现有监督的特征扰动,从而改善学习器的差异度。待测样本进行软测量估计时,根据各高斯过程基学习器输出的方差自适应地选择基学习器进行集成输出。采用工业双酚A生产装置反应器的现场数据建模仿真,结果表明该方法是有效的。     

适于混合气体基于k分布的灰气体加权和模型

工业燃烧环境的复杂性,使得传统的灰气体加权和（WSGG）模型很难满足气体辐射特性计算的精度要求。基于HITEMP2010数据库,利用等级相关原理将k分布法引入WSGG模型,并假设各参与性气体之间是统计非关联的,采用叠加法建立了适用于任意浓度、温度分布的混合气体WSGG模型。对四种不同燃烧条件下的非等温、非均匀混合气体的辐射换热进行了计算,将新模型计算的辐射热流和辐射源项与逐线法（LBL）及其他模型计算结果进行比较来验证新模型的有效性。结果显示新模型参数能很好地预测任意工况下混合气体的辐射特性。     

基于PICA的过程监控方法

工业过程中普遍存在噪声污染,本文在概率主元分析方法（PPCA）的基础上,把该方法推广到非高斯过程,提出一种新的基于概率独立成分分析（PICA）的过程监控方法.针对过程的非高斯和噪声信息,分别建立其对应的统计量I²和MR.通过对Tennessee Eastman（TE）过程的仿真研究,验证了该方法的可行性和有效性,较好地改善了过程的监控效果,从而更好地保证过程运行的安全、稳定性.     

层次变分高斯混合模型与主多项式分析的故障检测策略

针对多模态工业过程中模态数量难以确定问题,提出一种层次变分高斯混合模型（hierarchical variational Gaussian mixture model, HVGMM）。在此基础上,使用主多项式分析（principal polynomial analysis, PPA）用于多模态非线性过程故障检测。首先,变分贝叶斯高斯混合模型（variational Bayesian Gaussian mixture model, VBGMM）作为初始模型用于分解过程数据得到工作模态的初始数量,将过程按初始数量分解为多个子块;其次,应用包含多个局部模型的VBGMM将各子块分解为附属子块,并利用附属子块的均值、精度等信息对VBGMM进行重构;然后,将重构后的VBGMM作为初始模型再次用于分解原始过程数据,重复上述步骤直至重构VBGMM无法分解各子块时停止;最后,分别在各附属子块中建立局部PPA模型,并在每个局部模型中计算T²和SPE统计量进行故障检测。将该方法应用于数值例子和Tennessee Eastman（TE）化工过程,并将仿真结果与主元分析（principal component analysis, PCA）、PPA进行对比,验证了所提出方法的有效性。     

基于混合分块DMICA-PCA的全流程过程监控方法

分块策略被广泛运用于全流程过程监控领域,以解决全流程过程变量关系复杂性较高的问题,但传统的分块策略与子块建模方法都未考虑过程的动态性问题,并且传统的分块策略都片面依赖于过程知识或过程数据信息,影响了过程监控的效果,为此提出了一种基于混合分块DMICA-PCA的过程监控方法。在分析过程的动态性后,先利用已知的部分过程知识进行变量的初步分块,接着利用各分块变量之间改进的广义Dice's系数（MGDC）进行进一步的分块。然后采用DMICA-PCA方法对每个子块进行建模得到子块的统计量,并通过加权方法得到总的联合指标进行故障检测。同时对每个子块采用改进的故障诊断方法,提高了诊断效果。最后将该方法应用在TE过程的过程监控中,证明了该方法的有效性。     

基于循环自动编码器的间歇过程故障监测

针对间歇过程数据非线性、动态性特征,提出一种基于循环自动编码器(recurrent autoencoder,RAE)的过程故障监测方法。采用长短时记忆(long short-term memory,LSTM)循环神经网络构建自动编码器建立监控模型,相比传统自动编码器,其能有效挖掘时序样本间的动态关联信息。该方法首先利用批次展开与变量展开相结合的三步展开方法将间歇过程数据展开成二维,并通过滑动窗采样得到模型输入序列;然后使用LSTM构建自动编码器,重构输入序列。进一步,利用重构误差构造平方预测误差(squared prediction error, SPE)统计量实现在线监测。最后将所提方法应用于青霉素发酵仿真和重组大肠杆菌发酵过程监测,结果表明,该方法能及时监测到故障,具有较好的监测性能。