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.     

Between‐phase‐based statistical analysis and modeling for transition monitoring in multiphase batch processes

Between‐phase transition analysis and monitoring are a critical problem in multiphase (MP) batch processes. An improved statistical analysis, modeling, and monitoring strategy are proposed for MP processes with between‐phase transition. It is realized that between‐phase transition may show complex “irregular dynamics” over different batches. That is, transition patterns may follow different trajectories with different durations and reveal different characteristics in different batch cycles. Phase centers are defined to capture the transition irregularity, and the relationship between two neighboring phase centers is analyzed by performing between‐phase analysis. Two different subspaces are thus separated in each phase, driven by the phase‐common and dependent correlations, respectively. The basic assumption is that despite their different operation patterns, the two neighboring phases share a certain common correlations immune to phase shift. Then, reconstruction‐based transition identification algorithm is designed, by which, between‐phase transition can be supervised automatically and dynamically without the need of transition model development. The proposed method captures the between‐phase transition from a new viewpoint. Its feasibility and performance are illustrated with a practical case. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Multivariate statistical monitoring of multiphase batch processes with between‐phase transitions and uneven operation durations

In order to achieve satisfactory monitoring, multivariate statistical process models should well reflect process nature. In manufacturing systems, many batch processes are inherently multiphase. Usually, different phases have different characteristics, while gradual transitions are often observed between phases. Another important feature of batch processes is the unevenness of operation durations. Especially, in multiphase batch processes, the situation becomes more complicated. In this study, a batch process modelling and monitoring strategy is proposed based on Gaussian mixture model (GMM), which can automatically extract phase and transition information for uneven‐duration batch processes. The application results verify the effectiveness of the proposed method. © 2011 Canadian Society for Chemical Engineering     

Discrete element reduced‐order modeling of dynamic particulate systems

One of the key technical challenges associated with modeling particulate processes is the ongoing need to develop efficient and accurate predictive models. Often the models that best represent solids handling processes, like discrete element method (DEM) models, are computationally expensive to evaluate. In this work, a reduced‐order modeling (ROM) methodology is proposed that can represent distributed parameter information, like particle velocity profiles, obtained from high‐fidelity (DEM) simulations in a more computationally efficient fashion. The proposed methodology uses principal component analysis (PCA) to reduce the dimensionality of the distributed parameter information, and response surface modeling to map the distributed parameter data to process operating parameters. This PCA‐based ROM approach has been used to model velocity trajectories in a continuous convective mixer, to demonstrate its applicability for pharmaceutical process modeling. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3184–3194, 2014     

基于多动态核聚类的间歇过程在线监控

针对传统的多元统计监测方法不能有效检测工业过程中由于初始条件波动较大所引发的弱故障问题,提出一种基于多动态核聚类的核主元分析(DKCPCA)监控策略,实现多阶段间歇过程的弱故障在线监控.该方法首先针对过程中各阶段每一批次数据结合自回归移动平均时间序列模型(ARMAX)和核主成分分析(KPCA)方法分别建立动态核PCA模型,然后根据各批次模型间载荷的相似性采用分层次聚类方法进行聚类,最后将聚在一起的批次数据进行展开重新再建立动态核PCA模型,随着聚类数目的不同从而建立多个类模型.当在线应用时给出了多模型选择策略,以提高监测精度.将此方法应用于青霉素发酵过程的监控中,监测结果表明此方法取得了比DKPCA和MKPCA更好的监测性能.     

A computational framework and solution algorithms for two‐stage adaptive robust scheduling of batch manufacturing processes under uncertainty

A novel two‐stage adaptive robust optimization (ARO) approach to production scheduling of batch processes under uncertainty is proposed. We first reformulate the deterministic mixed‐integer linear programming model of batch scheduling into a two‐stage optimization problem. Symmetric uncertainty sets are then introduced to confine the uncertain parameters, and budgets of uncertainty are used to adjust the degree of conservatism. We then apply both the Benders decomposition algorithm and the column‐and‐constraint generation (C&CG) algorithm to efficiently solve the resulting two‐stage ARO problem, which cannot be tackled directly by any existing optimization solvers. Two case studies are considered to demonstrate the applicability of the proposed modeling framework and solution algorithms. The results show that the C&CG algorithm is more computationally efficient than the Benders decomposition algorithm, and the proposed two‐stage ARO approach returns 9% higher profits than the conventional robust optimization approach for batch scheduling. © 2015 American Institute of Chemical Engineers AIChE J, 62: 687–703, 2016     

Recovering spectral reflectance based on natural neighbor interpolation with model‐based metameric spectra of extreme points

In this article, we proposed a new method based on natural neighbor interpolation to recover the spectral reflectance of objects from an image captured by a traditional Red‐Green‐Blue (RGB) digital camera. The concept of model‐based metameric spectra of eight extreme points in the standard RGB (sRGB) color gamut was further introduced to ensure that almost all test samples in the entire gamut can be simply and properly recovered without needing the extrapolation or any other auxiliary techniques. The quasi‐Newton method was used to estimate iteratively the optimal parameters of these metameric spectra, satisfying the constraints of the gamut extreme points. Several experiments were performed. The effectiveness of the method with and without the metameric spectra was evaluated, including some performance comparisons with the principal component analysis (PCA) method of transformational type (classic PCA and weighted PCA) and that of interpolation type. The results showed that the proposed method greatly enlarged the accurately applicable domain of the interpolation strategy and offered spectra with feasibility and naturalness much superior to the PCA‐based methods. The proposed method was obviously better than the conventional interpolation ones, and had a similar performance with the weighted PCA method in terms of color difference.     

Efficient scheduling method of complex batch processes with general network structure via agent‐based modeling

A novel efficient agent‐based method for scheduling network batch processes in the process industry is proposed. The agent‐based model is based on the resource‐task network. To overcome the drawback of localized solutions found in conventional agent‐based methods, a new scheduling algorithm is proposed. The algorithm predicts the objective function value by simulating another cloned agent‐based model. Global information is obtained, and the solution quality is improved. The solution quality of this approach is validated by detailed comparisons with the mixed‐integer programming (MIP) methods. A solution close to the optimal one can be found by the agent‐based method with a much shorter computational time than the MIP methods. As a scheduling problem becomes increasingly complicated with increased scale, more specifications, and uncertainties, the advantages of the agent‐based method become more evident. The proposed method is applied to simulated industrial problems where the MIP methods require excessive computational resources. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2884–2906, 2013     

输入训练神经网络的维数约简算法及其在化工过程建模中的应用

Many applications of principal component analysis （PCA） can be found in dimensionality reduction. But linear PCA method is not well suitable for nonlinear chemical processes. A new PCA method based on improved input training neural network （IT-NN） is proposed for the nonlinear system modelling in this paper. Momentum factor and adaptive learning rate are introduced into learning algorithm to improve the training speed of IT-NN. Contrasting to the auto-associative neural network （ANN）, IT-NN has less hidden layers and higher training speed. The effectiveness is illustrated through a comparison of IT-NN with linear PCA and ANN with experiments. Moreover, the IT-NN is combined with RBF neural network （RBF-NN） to model the yields of ethylene and propylene in the naphtha pyrolysis system. From the illustrative example and practical application, IT-NN combined with RBF-NN is an effective method of nonlinear chemical process modelling.     

基于主元相似度的间歇过程操作曲线递推优化

针对一类较长周期的间歇过程操作优化问题，提出了一种基于正常运行批次的数据驱动型操作曲线递推优化方法。首先采用分段离散化方法将原非线性优化问题转化为线性优化问题，再利用主元分析对离散化后的高维时段变量进行降维处理，然后在降维后的主元平面中，基于时段变量与最终产品指标间的余弦相似度，实现对原操作曲线的摄动优化。考虑到时段变量方差和相似度随批次会发生变化，建立了递推算法以实现操作曲线的递推更新。最后将该方法应用于某化工产品的间歇结晶过程中，结果验证了所提方法的有效性。     

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。     

MULTILEVEL PCA AND INDUCTIVE LEARNING FOR KNOWLEDGE EXTRACTION FROM OPERATIONAL DATA OF BATCH PROCESSES

A new methodology for monitoring batch processes is presented which is based on analysis of historical operational data using both principal component analysis (PCA) and inductive learning. Historical data of batch operations are analysed according to stages. For each stage, PCA is employed to analyse the trajectories of each variable over all batch runs and groups the trajectories into clusters. The first one or two PCs for all variables at a stage are then used in further PCA analysis to project the operation of the stage onto operational spaces. Production rules are generated to summarise the operational routes to produce product recipes, and to describe variables' contributions to stage-wise state spaces. A method for automatic identification of stages using wavelet multi-scale analysis is also described. The methodology is illustrated by reference to a case study of a semi-batch polymerisation reactor.     

Temperature Inferential Control of Heat‐Integrated Distillation Column Based on Variable Sensitive Stage Temperature Set‐point

Heat‐integrated distillation is an improved distillation technique with remarkable energy‐saving potential. A control scheme with a variable sensitive stage temperature set‐point is proposed to solve the control problem of a heat‐integrated distillation column (HIDiC). An online estimator is designed to support the variation of the set‐point. The locations of the stage temperature measurements are carefully selected based on a combination strategy with three steps. First, the sensitive stages are selected. Then, the following stages are determined by a PCA‐based method. Finally, a maximum differentiation method provides the remaining measurement selections. According to the profile parameters estimated by the proposed estimator, the set‐point of the sensitive stage temperature is adjusted adaptively to reduce the influence of the disturbances. Two commonly‐used PID controllers, the sensitive temperature control and the temperature differential control, are developed as the comparative study. The simulation results show that the proposed control scheme has a distinct advantage in restraining different disturbances.     

Multivariate statistical process monitoring of batch‐to‐batch startups

In batch processes, multivariate statistical process monitoring (MSPM) plays an important role for ensuring process safety. However, despite many methods proposed, few of them can be applied to batch‐to‐batch startups. The reason is that, during the startup stage, process data are usually nonstationary and nonidentically distributed from batch to batch. In this article, the trajectory signal of each process variable is decomposed into a series of components corresponding to different frequencies, by adopting a nonparametric signal decomposition technique named ensemble empirical mode decomposition. Then, through instantaneous frequency calculation, these components can be divided into two groups. The first group reflects the long‐term trend between batches, which extracts the batch‐wise nonstationary drift information. The second group corresponds to the short‐term intrabatch variations. The variable trajectory signals reconstructed from the latter fulfills the requirements of conventional MSPM. The feasibility of the proposed method is illustrated using an injection molding process. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3719–3727, 2015     

Covariance‐oriented qualitative and quantitative calibration analysis for multistage batch processes

An improved stage‐specific multivariate calibration scheme is developed for multistage batch processes based on the covariance analysis unit. First, the process duration is automatically and properly divided into different stages, which reveals the changes of quality‐related process correlation characteristics. The concept of stage‐representative average process behaviour is then introduced, which is comprehensibly realized by averaging all covariance patterns within the same stage based on different weights. In this way, it stacks the cumulative effects of process variations on quality within each stage and meanwhile considers their time‐varying characteristics. Subsequently, covariance‐oriented OSC and variable selection are effectively combined, which can simplify the calibration model structure and enhance the causal relationship between predictors and quality by excluding the redundant latent factors and input variables. Finally, stage‐representative PLS regression models are developed focusing on the critical‐to‐quality stages for online quality prediction. It shows that a complete multistage calibration solution is readily achieved from an “overall” stage perspective by smartly making use of covariance. The illustration study to injection molding shows the effectiveness of the proposed method for improving process comprehension and quality prediction.     

MPCA在间歇反应过程故障诊断中的应用

将多方向主元分析(MPCA)理论应用到一个实际的PVC间歇反应过程的性能监测与故障诊断中。由于间歇反应的特点,数据具有多维性,应用传统的主元分析将使过程的统计建模与故障诊断难以实现。MPCA可将间歇过程的多维数据沿时间轨迹分割,使得多批次的数据可以在各时间序列轨迹上建立相应的PCA模型,从而完成对间歇过程的实时监视及故障诊断。     

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.     

Quality‐relevant fault diagnosis with concurrent phase partition and analysis of relative changes for multiphase batch processes

Multiplicity of phases as indicated by changes of process characteristics is an inherent nature of many batch processes for both normal and fault cases. To more efficiently perform online fault diagnosis via reconstruction for multiphase batch processes, the phase nature and the relationship between normal and fault cases within each phase should be deeply addressed. This article proposes a quality‐relevant fault diagnosis strategy with concurrent phase partition and analysis of relative changes for multiphase batch processes. First, a concurrent phase partition algorithm is developed. The basic idea is to track the changes of process characteristics at normal and fault statuses jointly so that multiple sequential modeling phases are identified simultaneously for both normal and fault cases. Then, the relative changes from the normal status to each fault case are analyzed in each phase to reveal the specific fault effects more efficiently. The fault effects are decomposed in two different monitoring subspaces, principal subspace, and residual subspace, by capturing their different roles in removing out‐of‐control signals. The significant increases relative to the normal case are judged to be responsible for the concerned alarm monitoring statistics in each phase. The others are composed of general variations that are deemed to still follow normal rules and thus insignificant to remove alarm monitoring statistics. Those alarm‐responsible fault deviations are then used to develop reconstruction models which can more efficiently recover the fault‐free part for online fault diagnosis. The proposed algorithm is illustrated with a typical multiphase batch process with one normal case and three fault cases. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2048–2062, 2014