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。     

基于MPCA-MDPLS的间歇过程的故障诊断

针对间歇过程的故障诊断问题,提出了一种新的混合模型方法——MPCA-MDPLS.这种方法包括两个模型：多向主元分析(MPCA)模型和多向判别部分最小二乘(MDPLS)模型.这两个模型的建模数据不仅包括正常工况的数据,而且还包含了各种已知故障数据.因此,MPCA模型具有检测未知故障的能力.给出了MDPLS模型故障诊断限,对经MPCA模型检测不是未知故障的故障做进一步诊断.如果故障是未知的,可以采取其他的方法来分析新的故障,并按不同类别存入到数据库中.当多次出现这种故障之后（一般≥5次）,把新的故障数据加入到建模数据中,并重新建立MPCA-MDPLS模型.通过对实际工业链霉素发酵过程数据的分析,表明了提出的算法是可行的、有效的,并具有识别未知新故障的能力.     

Raman spectra of high‐density,low‐density,and linear low‐density polyethylene pellets and prediction of their physical properties by multivariate data analysis

Raman spectra have been measured for pellets of five samples of high‐density polyethylene (HDPE), seven samples of low‐density polyethylene (LDPE), and six samples of linear low‐density polyethylene (LLDPE). The obtained Raman spectra have been compared to find out characteristic Raman bands of HDPE, LDPE, and LLDPE. Principal component analysis (PCA) was applied to the Raman spectra in the 1600–650 cm^?1 region after multiplicative scatter correction (MSC) to discriminate the Raman spectra of the three different PE species. They are classified into three groups by a score plot of PCA factor 1 vs. 2. HDPE with high density and high crystallinity gives high scores on the factor 1 axis, while LDPE with low density and low crystallinity yields negative scores on the same axis. It seems that factor 1 reflects the density or crystallinity. A PC weight loadings plot for factor 1 shows six upward peaks corresponding to the bands arising from the crystalline parts or all‐trans ? (CH₂)_n? groups and seven downward peaks ascribed to the bands of the amorphous or anisotropic regions and those arising from the short branches. Partial least‐squares (PLS‐1) regression was applied to the Raman spectra after MSC to propose calibration models that predict the density, crystallinity, and melting points of the polyethylenes. The correlation coefficient was calculated to be 0.9941, 0.9800, and 0.9709 for the density, crystallinity, and melting point, respectively, and their root‐mean‐square error of cross validation (RMSECV) was found to be 0.0015, 3.3707, and 2.3745, respectively. The loadings plot of factor 2 for the prediction of melting point is largely different from those for the prediction of density and crystallinity. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 443–448, 2002     

An in silico evaluation of data‐driven optimization of biopharmaceutical processes

Two methodological improvements of the design of dynamic experiments (C. Georgakis, Ind Eng Chem Res. 2013) for the modeling and optimization of (semi‐) batch processes are proposed. Their effectiveness is evaluated in two representative classes of biopharmaceutical processes. First, we incorporate prior process knowledge in the design of the experiments. Many batch processes and, in particular, biopharmaceutical processes are usually not understood completely to enable the development of an accurate knowledge‐driven model. However, partial process knowledge is often available and should not be ignored. We demonstrate here how to incorporate such knowledge. Second, we introduce an evolutionary modeling and optimization approach to minimize the initial number of experiments in the face of budgetary and time constraints. The proposed approach starts with the estimation of only a linear Response Surface Model, which requires the minimum number of experiments. Accounting for the model's uncertainty, the proposed approach calculates a process optimum that meets a maximum uncertainty constraint. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2796–2805, 2017     

Subspace identification for data‐driven modeling and quality control of batch processes

In this work, we present a novel, data‐driven, quality modeling, and control approach for batch processes. Specifically, we adapt subspace identification methods for use with batch data to identify a state‐space model from available process measurements and input moves. We demonstrate that the resulting linear time‐invariant (LTI), dynamic, state‐space model is able to describe the transient behavior of finite duration batch processes. Next, we relate the terminal quality to the terminal value of the identified states. Finally, we apply the resulting model in a shrinking‐horizon, model predictive control scheme to directly control terminal product quality. The theoretical properties of the proposed approach are studied and compared to state‐of‐the‐art latent variable control approaches. The efficacy of the proposed approach is demonstrated through a simulation study of a batch polymethyl methacrylate polymerization reactor. Results for both disturbance rejection and set‐point changes (i.e., new quality grades) are demonstrated. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1581–1601, 2016     

Two‐step principal component analysis for dynamic processes monitoring

In this study, a two‐step principal component analysis (TS‐PCA) is proposed to handle the dynamic characteristics of chemical industrial processes in both steady state and unsteady state. Differently from the traditional dynamic PCA (DPCA) dealing with the static cross‐correlation structure and dynamic auto‐correlation structure in process data simultaneously, TS‐PCA handles them in two steps: it first identifies the dynamic structure by using the least squares algorithm, and then monitors the innovation component by using PCA. The innovation component is time uncorrelated and independent of the initial state of the process. As a result, TS‐PCA can monitor the process in both steady state and unsteady state, whereas all other reported dynamic approaches are limited to only processes in steady state. Even tested in steady state, TS‐PCA still can achieve better performance than the existing dynamic approaches.     

Multivariate statistical monitoring of process operating performance

Process computers routinely collect hundreds to thousands of pieces of data from a multitude of plant sensors every few seconds. This has caused a “data overload” and due to the lack of appropriate analyses very little is currently being done to utilize this wealth of information. Operating personnel typically use only a few variables to monitor the plant's performance. However, multivariate statistical methods such as PLS (Partial Least Squares or Projection to Latent Structures) and PCA (Principal Component Analysis) are capable of compressing the information down into low dimensional spaces which retain most of the information. Using this method of statistical data compression a multivariate monitoring procedure analogous to the univariate Shewart Chart has been developed to efficiently monitor the performance of large processes, and to rapidly detect and identify important process changes. This procedure is demonstrated using simulations of two processes, a fluidized bed reactor and an extractive distillation column.     

Multivariate Modeling of a Chemical Toner Manufacturing Process

Modeling, optimization, process monitoring, and product development in a toner process using multiway principal component analysis and multiway partial least square method is described. Process measurements and product quality values of past successful batches were collected in a data matrix and preprocessed through time alignment, centering, and scaling. Following the identification of latent variables, an empirical model was built through a fourfold cross validation that can represent the operation of a successful batch. The prepared model provided a realistic prediction of process behavior, realistically represented the operation of the industrial unit, and is mathematically simple enough to be used in online optimization and for automatic control strategies of selected abnormal batches.     

一种鲁棒半监督建模方法及其在化工过程故障检测中的应用

复杂化工过程的观测样本往往包含着测量噪声与少量的离群点数据,而这些受污染的数据会影响数据驱动的过程建模与故障检测方法的准确性。本文考虑了化工过程测量样本的这一实际情况,提出了一种鲁棒半监督PLVR模型（RSSPLVR）,并利用核方法将其扩展为非线性的形式（K-RSSPLVR）。此类算法利用基于样本相似度的加权系数作为概率模型的先验参数,能有效消除离群点对建模的影响。利用加权后的建模样本,本文通过EM算法训练了RSSPLVR和K-RSSPLVR的模型参数,并提出了相应的故障检测算法。最后,通过TE过程仿真实验验证了所提出方法的有效性。     

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.     

Analyzing the occurrence of foaming in batch fermentation processes using multiway partial least square approaches

This article presents an application of multiway partial least squares (MPLS) methods to develop interpretative correlation models to monitor the foaming occurrence and improve batch fermentation. We choose the exhaust differential pressure as a quality variable to quantify the foaming occurrence and consider three-dimensional datasets of different batches, process variables, and measurements. We integrate batch-wise unfolding (BWU) and observation-wise unfolding (OWU) of plant datasets with standard, dynamic, and kernel PLS methods. We find that dynamic PLS (DPLS) with OWU and time-lagged quality variables to be the most efficient, accurate, and easy to implement. The BWU approach is useful for analyzing the differences between batches and identifying abnormalities and outliers, while the OWU quantifies the variation within a given batch. With OWU, the DPLS method with one unit of time lag in the quality variable is the most effective, accurate, and easy to implement. With both BWU and OWU, we identify the quantitative effects of process variables on the quality variable and providence guidance to improve fermentation performance.     

A quality relevant non‐Gaussian latent subspace projection method for chemical process monitoring and fault detection

Partial least‐squares (PLS) method has been widely used in multivariate statistical process monitoring field. The goal of traditional PLS is to find the multidimensional directions in the measurement‐variable and quality‐variable spaces that have the maximum covariances. Therefore, PLS method relies on the second‐order statistics of covariance only but does not takes into account the higher‐order statistics that may involve certain key features of non‐Gaussian processes. Moreover, the derivations of control limits for T² and squared prediction error (SPE) indices in PLS‐based monitoring method are based on the assumption that the process data follow a multivariate Gaussian distribution approximately. Meanwhile, independent component analysis (ICA) approach has recently been developed for process monitoring, where the goal is to find the independent components (ICs) that are assumed to be non‐Gaussian and mutually independent by means of maximizing the high‐order statistics such as negentropy instead of the second‐order statistics including variance and covariance. Nevertheless, the IC directions do not take into account the contributions from quality variables and, thus, ICA may not work well for process monitoring in the situations when the quality variables have strong influence on process operations. To capture the non‐Gaussian relationships between process measurement and quality variables, a novel projection‐based monitoring method termed as quality relevant non‐Gaussian latent subspace projection (QNGLSP) approach is proposed in this article. This new technique searches for the feature directions within the measurement‐variable and quality‐variable spaces concurrently so that the two sets of feature directions or subspaces have the maximized multidimensional mutual information. Further, the new monitoring indices including I² and SPE statistics are developed for quality relevant fault detection of non‐Gaussian processes. The proposed QNGLSP approach is applied to the Tennessee Eastman Chemical process and the process monitoring results of the present method are demonstrated to be superior to those of the PLS‐based monitoring method. © 2013 American Institute of Chemical Engineers AIChE J 60: 485–499, 2014     

Network‐induced supervised learning: Network‐induced classification (NI‐C) and network‐induced regression (NI‐R)

Current supervised approaches, such as classification and regression methodologies, are strongly focused on optimizing estimation accuracy metrics, leaving the interpretation of the results produced as a secondary concern. However, in the analysis of complex systems, one of the main interests is precisely the induction of relevant associations, to understand or clarify the way the system operates. Two related frameworks for addressing supervised learning problems (classification and regression) are presented, that incorporate interpretational‐oriented analysis features right from the onset of the analysis. These features constrain the predictive space, in order to introduce interpretable elements in the final model. Interestingly, such constraints do not usually compromise the methods' performance, when compared to their unconstrained versions. The frameworks, called network‐induced classification (NI‐C), and network‐induced regression (NI‐R), share a common methodological backbone, and are described in detail, as well as applied to real‐world case studies. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1570–1587, 2013     

基于多元统计方法的过程单元缓变故障识别

在实际化工生产过程中存在一些缓变故障,在发生的初期过程偏离正常工况的程度较少,且受生产数据噪声的影响,不易被传统过程监测方法及时发现。本文针对缓变故障的特点,提出了一种基于偏最小二乘法-主元分析法(PLS-PCA)的过程监测方法。首先利用偏最小二乘法(PLS)回归提取出各变量之间的关系,通过获取变量实测值与回归预测值之间的误差,以放大装置运行状态与预设状态之间的偏差,在此基础上建立基于主元分析法(PCA)的过程监测模型,实现了对缓变故障的早期识别。该过程监测模型被应用在某制氢装置预转化反应器上,结果表明该方法对缓变故障具有较好的早期识别效果,能够比工程师提前13h,比基于传统PCA的过程监测模型提前8h。     

递归核PCA及其在非线性过程自适应监控中的应用

PCA、PLS作为常用的多变量统计监控算法,一般适用于线性、定常的过程。针对实际工业过程的时变、非线性特性,提出了一种递归核PCA（RKPCA）方法用于非线性过程的自适应监控。RKPCA算法通过将递归奇异值分解推广到核空间,给出了核形式描述的递归KPCA算法,运算复杂度比KPCA明显降低,保证非线性监控模型能够在线更新。在Alstom工业燃气发生装置上的自适应监控表明,所提出的RKPCA算法能够及时跟踪非线性过程的时变特征,保证了监控模型的有效性。     

乙醇发酵过程中酿酒酵母的磷脂组变化

磷脂分子是细胞膜的重要组成,在酵母发酵产乙醇过程中起重要作用。通过液质联用方法对两株酿酒酵母细胞（工业酵母O和实验室酵母S）的磷脂分子进行定性和定量分析,应用主成分分析（PCA）和正交偏最小二乘（OPLS）对O和S不同生长时期的磷脂图谱进行模式识别。结果发现,在乙醇发酵过程中,两株酵母共同的变化规律是：从延滞期进入指数期过程中,饱和短链磷脂分子增加,不饱和长链磷脂分子减少。而两株酵母的差异表现在延滞期时,具有较低生长速率的酵母PE分子含量更高。     

基于VPLS的TE过程统计产品质量与费用控制

Product quality and operation cost control obtain increasing emphases in modern chemical system engineering. To improve the fault detection power of the partial least square (PLS) method for quality control, a new QRPV statistic is proposed in terms of the VP (variable importance in projection) indices of monitored process variables, which is significantly advanced over and different from the conventional Q statistic. QRPV is calculated only by the residuals of the remarkable process variables (RPVs). Therefore, it is the dominant relation between quality and RPV not all process variables (as in the case of the conventional PLS) that is monitored by this new VP-PLS (VPLS) method. The combination of QRPV and T2 statistics is applied to the quality and cost control of the Tennessee Eastman (TE) process, and weak faults can be detected as quickly as possible. Consequently, the product quality of TE process is guaranteed and operation costs are reduced.     

Assessment of resin formulations and determination of the formaldehyde to urea molar ratio by near‐ and mid‐infrared spectroscopy and multivariate data analysis

The molar ratios of formaldehyde (F) to urea (U) of three resin formulations in the range from 0.90 to 1.49 have been analyzed by means of Attenuated Total Reflection‐Fourier Transform Infrared (ATR‐FTIR) spectroscopy and Fourier Transform‐Near‐Infrared (FT‐NIR) spectroscopy. Application of Principal Component Analysis (PCA) to the spectra (MIR and NIR) allowed to separate them according to the molar ratio and to distinguish between two groups of resins. Soft Independent Modeling of Class Analogy (SIMCA) allowed classification of new resin samples with high model distances between the classes. Partial Least Squares Regression (PLS‐R) models based on MIR (NIR) spectra resulted in high coefficients of determination (R²) values, low errors, and high residual prediction deviations (RPD). To confirm the reproducibility of the process and to carefully evaluate twice all multivariate analysis results obtained, different batches of resins have been prepared to have an additional independent sample set. The number of samples required for MIR and possible applications of MIR and NIR spectroscopy in this context including limitations have been discussed. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2013