On-line batch process monitoring using dynamic PCA and dynamic PLS models

Producing value-added products of high-quality is the common objective in industries. This objective is more difficult to achieve in batch processes whose key quality measurements are not available on-line. In order to reduce the variations of the product quality, an on-line batch monitoring scheme is developed based on the multivariate statistical process control. It suggests using the past measured process variables without real-time quality measurement at the end of the batch run. The method, referred to as BDPCA and BDPLS, integrates the time-lagged windows of process dynamic behavior with the principal component analysis and partial least square respectively for on-line batch monitoring. Like traditional MPCA and MPLS approaches, the only information needed to set up the control chart is the historical data collected from the past successful batches. This leads to simple monitoring charts, easy tracking of the progress in each batch run and monitoring the occurrence of the observable upsets. BDPCA and BDPLS models only collect the previous data during the batch run without expensive computations to anticipate the future measurements. Three examples are used to investigate the potential application of the proposed method and make a comparison with some traditional on-line MPCA and MPLS algorithms.     

基于支持向量机MPLS的间歇过程故障诊断方法

1 INTRODUCTION In batch or fed-batch processes, raw materials are converted to products within a finite duration. In prac- tical production, the process commonly exhibits large variations from batch to batch due to such influencing factors as the quality fluctuation of raw materials, de- fect of equipments, contaminations, and other unpre- dicted disturbances. These variations may have an adverse effect on the final product quantity and quality. But it is generally difficult to discern th…     

基于高阶偏最小二乘的间歇过程建模

间歇过程的产品与现代人的生活息息相关,而建立可靠的模型是保障间歇过程安全运行的基础。针对间歇过程的数据特点,引入一种新的广义线性回归模型--高阶偏最小二乘（higher order partial least squares,HOPLS）。它与传统的间歇过程建模方法具有本质的不同,三维数据（批次×变量×时间）不需要展开成二维矩阵,而是直接被分解成一组正交的Tucker矩阵之和。通过高阶奇异值分解（high order singular value decomposition,HOSVD）,张量变换和高阶正交迭代（higher order orthogonal iteration,HOOI）找到能同时包含自变量和因变量最大信息的潜向量,与此同时得到对应的负载向量。对于新观测值,通过模型就可以实现对因变量的预测。最后利用PenSim2.0,对青霉素发酵过程进行仿真研究,验证了该间歇过程建模方法的有效性。     

On-line batch process monitoring using MHMT-based MPCA

A novel technique of on-line batch process monitoring based on the wavelet-based multi-hidden Markov model tree (MHMT) is developed. Unlike most of the existing batch process monitoring methods for only time scale, MHMT cannot only analyze the measurements at multiple scales in time and frequency but also capture the clustering and persistence of the statistical characteristics for practical measured data. This approach provides less signal distortion and better understanding of the principal source of the system variability affecting the process. In order to conduct the on-line batch monitoring, a simple modification of the unfolded structure that trains MHMT to set up the batch-monitoring model is derived. Also, the tying structure of MHMT for increasing the number of training data is developed. The proposed method is developed in this paper to improve the conventional MPCA-based method by extending the time-domain analysis into the time-frequency using the stochastic model analysis. After extracting the essential features of the past operating information, subsequently, two simple monitoring charts are presented to track the progress of each batch run and monitor the occurrence of observable upsets. The applications are discussed through two sets of benchmark data, a DuPont industrial batch polymerization reactor and a fed-batch penicillin production, those of which are characterized by some fault sources to illustrate the advantages of the proposed method in comparison to some conventional methods.     

On-line batch process monitoring using hierarchical kernel partial least squares

In this paper, new monitoring approach, hierarchical kernel partial least squares (HKPLS), is proposed for the batch processes. The advantages of HKPLS are: (1) HKPLS gives more nonlinear information compared to hierarchical partial least squares (HPLS) and multi-way PLS (MPLS) and (2) a new batch process monitoring using HKPLS does not need to estimate or fill in the unknown part of the process variable trajectory deviation from the current time until the end. The proposed method is applied to the penicillin process and continuous annealing process and is compared with MPLS and HPLS monitoring results. Applications of the proposed approach indicate that HKPLS effectively capture the nonlinearities in the process variables and show superior fault detectability.     

Subspace based model identification for missing data

This article addresses the problem of missing process data in data-driven dynamic modeling approaches. The key motivation is to avoid using imputation methods or deletion of key process information when identifying the model, and utilizing the rest of the information appropriately at the model building stage. To this end, a novel approach is developed that adapts nonlinear iterative partial least squares (NIPALS) algorithms from both partial least squares (PLS) and principle component analysis (PCA) for use in subspace identification. Note that the existing subspace identification approaches often utilize singular value decomposition (SVD) as part of the identification algorithm which is generally not robust to missing data. In contrast, the NIPALS algorithms used in this work leverage the inherent correlation structure of the identification matrices to minimize the impact of missing data values while generating an accurate system model. Furthermore, in computing the system matrices, the calculated scores from the latent variable methods are utilized as the states of the system. The efficacy of the proposed approach is shown via simulation of a nonlinear batch process example.     

Local dynamic partial least squares approaches for the modelling of batch processes

The application of multivariate statistical projection based techniques has been recognized as one approach to contributing to an increased understanding of process behaviour. The key methodologies have included multi‐way principal component analysis (PCA), multi‐way partial least squares (PLS) and batch observation level analysis. Batch processes typically exhibit nonlinear, time variant behaviour and these characteristics challenge the aforementioned techniques. To address these challenges, dynamic PLS has been proposed to capture the process dynamics. Likewise approaches to removing the process nonlinearities have included the removal of the mean trajectory and the application of nonlinear PLS. An alternative approach is described whereby the batch trajectories are sub‐divided into operating regions with a linear/linear dynamic model being fitted to each region. These individual models are spliced together to provide an overall nonlinear global model. Such a structure provides the potential for an alternative approach to batch process performance monitoring. In the paper a number of techniques are considered for developing the local model, including multi‐way PLS and dynamic multi‐way PLS. Utilising the most promising set of results from a simulation study of a batch process, the local model comprising individual linear dynamic PLS models was benchmarked against global nonlinear dynamic PLS using data from an industrial batch fermentation process. In conclusion the results for the local operating region techniques were comparable to the global model in terms of the residual sum of squares but for the global model structure was evident in the residuals. Consequently, the local modelling approach is statistically more robust.     

Development of a batch manager for dynamic scheduling and process management in multiproduct batch processes

A batch manager is developed for the dynamic scheduling and on-line management of process operations. The developed system consists of a process monitoring module and a dynamic scheduling module. When a deviation from the initial schedule is detected in a process monitoring module, dynamic scheduling is performed in the dynamic scheduling module and the initial schedule is adjusted to the proper schedule by using rescheduling algorithms presented in this paper. The adjusted schedule is shown in the process monitoring module. The dynamic scheduler in the batch manager copes with several unexpected process events of batch process operations by adjusting the EST (Earliest Start Time) of equipment, redetermining the batch path and reassigning tasks to equipment. This study focuses on the implementation of a batch manager with on-line dynamic scheduling for batch process management. Examples of fodder production batch processes illustrate the efficiency of the algorithms. This paper was supported by nondirected research fund, Korea Research Foundation, 1997.     

多变量统计过程监控:进展及其在化学工业的应用

Multivariate statistical process monitoring and control (MSPM&C) methods for chemical process monitoring with statistical projection techniques such as principal component analysis (PCA) and partial least squares (PLS) are surveyed in this paper. The four-step procedure of performing MSPM&C for chemical process, modeling of processes, detecting abnormal events or faults, identifying the variable(s) responsible for the faults and diagnosing the source cause for the abnormal behavior, is analyzed. Several main research directions of MSPM&C reported in the literature are discussed, such as multi-way principal component analysis (MPCA) for batch process, statistical monitoring and control for nonlinear process, dynamic PCA and dynamic PLS, and on-line quality control by inferential models. Industrial applications of MSPM&C to several typical chemical processes, such as chemical reactor, distillation column, polymerization process, petroleum refinery units, are summarized. Finally, some concluding remarks an     

Development of hidden semi-Markov models for diagnosis of multiphase batch operation

This paper deals with automatic on-line detection and diagnosis of fault patterns in multiphase batch processes. A novel and flexible approach based on the combination of hidden segmental semi-Markov models (HSMM) and multiway principal component analysis (MPCA) is proposed. In all batch operations, process variables may have correlations with each other, and MPCA is used to handle cross-correlation among process variables. In multiphase batch processes, the effect of external factors on process variables is phase-specific and the duration of each phase varies from batch to batch. HSMM is used to model the multiphase batch operation by representing each phase with a macro-state whose duration is determined by a phase-specific probability distribution of a number of micro-states. The output of each micro-state corresponds to the values of the monitored variables at a specific point in time. Given this structure, MPCA-HSMM parameters are trained by the batch operation data and recursive Viterbi algorithm is used to find out the optimum state sequence from each batch. Probability values of the optimum state sequence are collected to construct the probabilistic model which is used to compute the corresponding control limit for the specified operating condition. One MPCA-HSMM model is to be built for each type of previously known operating condition—normal and fault events. The power and advantages of the proposed method are successfully demonstrated in a simulated fed-batch penicillin cultivation process. MPCA-HSMM correctly identifies the type of fault from the batch operation data.     

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。     

一种基于混合建模技术的MIMO软测量建模方法

针对复合肥产品中几种养分含量需要同时预报的一类多输入/多输出(MIMO)软测量建模问题,提出一种基于混合建模方法的复合肥养分含量MIMO软测量模型。该混合模型首先对几个不能实时测量的关键辅助变量采用基于限定记忆部分最小二乘算法的数据驱动建模方法建立自适应软测量模型,然后采用简化机理模型实时计算三种养分含量。基于实际工业过程数据的仿真结果表明,所建模型运算速度快、预测精度高,可以满足复合肥养分含量在线预报的要求。     

Dynamic model-based batch process monitoring

An integrated framework consisting of a multivariate autoregressive (AR) model and multi-way principal component analysis (MPCA) is described for the monitoring of the performance of a batch process. After pre-processing the data, i.e., batch data unfolding, mean-centring and scaling, the data are then filtered using an AR model to remove the auto- and cross-correlation inherent within the pre-processed batch data. Model order is determined using Akaike information criterion and the model parameters are estimated through the application of partial least squares to attain a stable solution. MPCA is then applied to the residuals from the AR model. Three monitoring statistics are considered for the detection of the onset of process abnormalities in the batch process. The main advantage of the proposed approach is that it can monitor batch dynamics along the mean trajectory without the requirement to estimate future observed values. The proposed AR model-based approach is illustrated through its application to two polymerization processes. The case studies indicate that it gives better monitoring results in terms of sensitivity and time to fault detection than the approaches proposed by Nomikos and MacGregor [1994. Monitoring batch processes using multi-way principal components. A.I.Ch.E. Journal 40(8), 1361-1375] and Wold et al. [1998. Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemometrics and Intelligent Laboratory Systems 44, 331-340].     

基于KPLS模型的间歇过程产品质量控制

针对间歇过程所具有的非线性特性,提出了一种基于核偏最小二乘(KPLS)模型的最终产品质量控制策略。利用初始条件、批次展开后的过程数据以及最终产品质量建立了间歇过程的KPLS模型;采用基于主成分分析(PCA)映射的预估方法对未知的过程数据进行补充,实现了最终产品质量的在线预测。为了解决最终产品质量的控制,利用T2统计量确定KPLS模型的适用范围,并作为约束引入产品质量控制问题,提高控制策略的可行性;采用粒子群优化(PSO)算法实现了优化问题的高效求解。仿真结果表明,与基于偏最小二乘(PLS)模型的控制策略相比,所提出的方法具有更高的预测精度,且能有效解决产品质量控制中出现的各种问题。     

Batch-to-batch iterative learning control and within-batch on-line control for end-point qualities using MPLS-based dEWMA

A new feedback batch control strategy based on multiway partial least squares (MPLS) model and dEWMA (double exponentially weighted moving average) control for the end-point product quality system is proposed in this paper. It combines batch-to-batch (BtB) control with on-line tracking control within a batch. In the BtB operation, MPLS-based dEWMA control is done by applying feedback from the final output quality of the batch process. It utilizes the information from the current batch to improve quality for the next batch. The advantage of MPLS is to extract the strongest relationship between the input and the output variables in the reduced space of the latent variables model rather than in the real space of the highly dimensional manipulated variable trajectories. It is particularly useful for inherent noise suppression. Then the optimal manipulated variable trajectories in the score space without decoupler design can be directly and individually applied to each control loop under the MPLS modeling structure. Then the dEWMA controller can be applied to each SISO control loop respectively to address the model errors gradually reduced from model-plant mismatches and unmeasured disturbances. In on-line tracking control within a batch, the MPLS-based dEWMA control strategy is developed to explore the possible adjustments of the future input trajectories. It fixes up the disturbances just in time instead of until the next batch run and maintains the product specification when this batch is finished. To demonstrate the potential applications of the proposed design method, a typical batch reactor with processes of different dynamics is applied. Comparisons between MPLS-based dEWMA BtB control and MPLS-based dEWMA within-batch control are also made.     

基于混合建模技术的复合肥养分含量MIMO软测量模型

In compound fertilizer production, several quality variables need to be monitored and controlled simultaneously. It is very difficult to measure these variables on-line by existing instruments and sensors. So, soft-sensor technique becomes an indispensable method to implement real-time quality control. In this article, a new model of multi-inputs multi-outputs (MIMO) soft-sensor, which is constructed based on hybrid modeling technique, is proposed for these interactional variables. Data-driven modeling method and simplified first principle modeling method are combined in this model. Data-driven modeling method based on limited memory partial least squares (LM-PLS) algorithm is used to build soft-senor models for some secondary variables; then, the simplified first principle model is used to compute three primary variables on line. The proposed model has been used in practical process; the results indicate that the proposed model is precise and efficient, and it is possible to realize on line quality control for compound fertilizer process.     

在线自适应批次过程监视的双滑动窗口MPCA方法

Online monitoring of chemical process performance is extremely important to ensure the safety of a chemical plant and consistently high quality of products. Multivariate statistical process control has found wide applications in process performance analysis, monitoring and fault diagnosis using existing rich historical database. In this paper, we propose a simple and straight forward multivariate statistical modeling based on a moving window MPCA （multiway principal component analysis） model along the time and batch axis for adaptive monitoring the progress of batch processes in real-time. It is an extension to minimum window MPCA and traditional MPCA. The moving window MPCA along the batch axis can copy seamlessly with variable run length and does not need to estimate any deviations of the ongoing batch from the average trajectories. It replaces an invariant fixed-model monitoring approach with adaptive updating model data structure within batch-to-batch, which overcomes the changing operation condition and slows time-varying behaviors of industrial processes. The software based on moving window MPCA has been successfully applied to the industrial polymerization reactor of polyvinyl chloride （PVC） process in the Jinxi Chemical Company of China since 1999.     

基于混合建模技术的复合肥养分含量MIMO软测量模型

In compound fertilizer production, several quality variables need to be monitored and controlled simultaneously. It is very diifficult to measure these variables on-line by existing instruments and sensors. So, soft-sensor technique becomes an indispensable method to implement real-time quality control. In this article, a new model of multi-inputs multi-outputs （MIMO） soft-sensor, which is constructed based on hybrid modeling technique, is proposed for these interactional variables. Data-driven modeling method and simplified first principle modelingmethod are combined in this model. Data-driven modeling method based on limited memory partial least squares（LM-PLS） al.gorithm is used to build soft-senor models for some secondary variables.then, the simplified first principle model is used to compute three primary variables on line. The proposed model has been used in practicalprocess; the results indicate that the proposed model is precise and efficient, and it is possible to realize on line quality control for compound fertilizer process.     

基于泄漏积分型回声状态网络的软测量动态建模方法及应用

提出一种基于泄漏积分型回声状态网络（LiESN）的软测量动态建模方法,给出LiESN的岭回归离线学习算法与递推最小二乘（RLS）在线学习算法。通过引入正则化系数,岭回归离线学习算法可有效地控制输出权值的幅值,改善ESN的预测性能。RLS在线学习算法能适应大数据集的处理,满足过程建模实时性的需求。将基于LiESN的软测量方法分别用于预测脱丁烷塔底部丁烷组分的含量及计算硫回收装置中尾气的组成,实现对精炼厂相关产品质量的实时监控,并采用模型残差的四图分析对建模性能进行评价。在同等条件下,与基本的ESN网络以及支持向量机（SVM）等软测量建模方法进行了比较,结果表明,所提出的LiESN方法取得了很好的预测性能,计算精度满足工业生产的实际要求。     

Multiloop PID controller design using partial least squares decoupling structure

The goal of this paper is to identify and control multi-input multi-output (MIMO) processes by means of the dynamic partial least squares (PLS) model, which consists of a memoryless PLS model connected in series with linear dynamic models. Unlike the traditional decoupling MIMO process, the dynamic PLS model can decompose the MIMO process into a multiloop control system in a reduced subspace. Without the decoupler design, the optimal tuning multiloop PID controller based on the concept of general minimum variance and the constrained criteria can be directly and separately applied to each control loop under the proposed PLS modeling structure. Several potential applications using this technique are demonstrated.