Constrained latent variable model predictive control for trajectory tracking and economic optimization in batch processes

A constrained latent variable model predictive control (LV-MPC) technique is proposed for trajectory tracking and economic optimization in batch processes. The controller allows the incorporation of constraints on the process variables and is designed on the basis of multi-way principal component analysis (MPCA) of a batch data array rearranged by means of a regularized batch-wise unfolding. The main advantages of LV-MPC over other MPC techniques are: (i) requirements for the dataset are rather modest (only around 10–20 batch runs are necessary), (ii) nonlinear processes can efficiently be handled algebraically through MPCA models, and (iii) the tuning procedure is simple. The LV-MPC for tracking is tested through a benchmark process used in previous LV-MPC formulations. The extension to economic LV-MPC includes an economic cost and it is based on model and trajectory updating from batch to batch to drive the process to the economic optimal region. A data-driven model validity indicator is used to ensure the prediction’s validity while the economic cost drives the process to regions with higher profit. This technique is validated through simulations in a case study.     

Latent variable MPC for trajectory tracking in batch processes

A novel multivariate empirical model predictive control strategy (LV-MPC) for trajectory tracking and disturbance rejection for batch processes is presented. The strategy is based on dynamic principal component analysis (PCA) models of the batch process. The solution to the control problem is computed in the low dimensional latent variable space of the PCA model. The trajectories of all variables over the future horizon are then computed from the latent variable solution of the controller. The excellent control performance and the modest closed-loop data requirements for identification are illustrated for the temperature tracking in simulations of an emulsion polymerization process, an exothermic chemical reaction system and for MIMO temperature and pressure tracking in a nylon polymerization autoclave.     

Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .     

Latent variable model predictive control for trajectory tracking in batch processes: Alternative modeling approaches

Several Latent Variable Model (LVM) structures for modeling the time histories of batch processes are investigated from the view point of their suitability for use in Latent Variable Model Predictive Control (LV-MPC) [1] for trajectory tracking and disturbance rejection in batch processes. The LVMs are based on Principal Component Analysis (PCA). Two previously proposed approaches (Batch-Wise Unfolding (BWU) and Observation-Wise with Time-lag Unfolding (OWTU)) for modeling of batch processes [2] are incorporated in the LV-MPC and the benefits and drawbacks of each are explored. Furthermore, a new modeling approach (Regularized Batch-Wise Unfolding (RBWU)) is proposed to overcome the shortcomings of each of the previous modeling approaches while keeping the major benefits of both. The performances of the three latent variable modeling approaches in the course of LV-MPC for trajectory tracking and disturbance rejection are illustrated using two simulated batch reactor case studies. It is seen that the RBWU approach models the nonlinearity and time-varying properties of the batch almost as accurately as BWU approach, but needs fewer observations (batches) for model identification and results in a smoother PCA model. Recommendations are then given on which modeling approach to use under different scenarios.     

Optimal genetic manipulations in batch bioreactor control

Advances in metabolic engineering have enabled bioprocess optimization at the genetic level. Large-scale systematic models are now available at a genome level for many biological processes. There is, thus, a motivation to develop advanced control algorithms, using these complex models, to identify optimal performance strategies both at the genetic and bioreactor level. In the present paper, the bilevel optimization framework previously developed by the authors is coupled with control algorithms to determine the genetic manipulation strategies in practical bioprocess applications. The bilevel optimization includes a linear programming problem in the inner level and a nonlinear optimization problem in the outer level. Both gradient-based and stochastic methods are used to solve the nonlinear optimization problem. Ethanol production in an anaerobic batch fermentation of Escherichia coli is considered in case studies that demonstrate optimization of ethanol production, batch time, and multi-batch scheduling.     

Monitoring and prediction of big process data with deep latent variable models and parallel computing

Process monitoring and quality prediction are crucial for maintaining favorable operating conditions and have received considerable attention in previous decades. For majority complicated cases in chemical and biological industrial processes with particular nonlinear characteristics, traditional latent variable models, such as principal component analysis (PCA), principal component regression (PCR), partial least squares (PLS), may not work well. In this paper, various nonlinear latent variable models based on autoencoder (AE) are developed. In order to extract deeper nonlinear features from process data, the basic shallow AE models are extended to the deep latent variable models, which provides a deep generative structure for nonlinear process monitoring and quality prediction. Meanwhile, with the ever increasing scale of industrial data, the computational burden for process modeling and analytics has becoming more and more tremendous, particularly for large-scale processes. To handle the big data problem, the parallel computing strategy is further applied to the above model, which partitions the whole computational task into a few sub-tasks and assigns them to parallel computing nodes. Then the parallel models are utilized for process monitoring and quality prediction applications. The effectiveness of the developed methods are evaluated through the Tennessee Eastman (TE) benchmark process and a real-life industrial process in an ammonia synthesis plant (ASP).     

Multiphase two-dimensional time-slice dynamic system for batch process monitoring

In this work, a multiphase 2D time-slice dynamic system approach has been proposed to characterize the batch-wise and variable-wise dynamics of batch processes simultaneously. First, in each phase, the 2D latent representation has been developed for time slice matrices so as to extract informative features from both batch-wise and variable-wise variations. Afterward, the first-order Markov chains are introduced for capturing the underlying 2D latent dynamics across time-slice evolutions. In this way, batch process dynamic behaviors in each working phase can be captured from both single batch run and batch-to-batch evolutions, while process noise can also be explained in the probabilistic modeling framework. Last, in order to carry out online monitoring with the proposed 2D dynamic system, an effective 2D online-monitoring mechanism is established. The feasibility of the dynamic batch process monitoring method is validated on the fed-batch penicillin fermentation benchmark.     

Quality relevant nonlinear batch process performance monitoring using a kernel based multiway non-Gaussian latent subspace projection approach

Multiway kernel partial least squares method (MKPLS) has recently been developed for monitoring the operational performance of nonlinear batch or semi-batch processes. It has strong capability to handle batch trajectories and nonlinear process dynamics, which cannot be effectively dealt with by traditional multiway partial least squares (MPLS) technique. However, MKPLS method may not be effective in capturing significant non-Gaussian features of batch processes because only the second-order statistics instead of higher-order statistics are taken into account in the underlying model. On the other hand, multiway kernel independent component analysis (MKICA) has been proposed for nonlinear batch process monitoring and fault detection. Different from MKPLS, MKICA can extract not only nonlinear but also non-Gaussian features through maximizing the higher-order statistic of negentropy instead of second-order statistic of covariance within the high-dimensional kernel space. Nevertheless, MKICA based process monitoring approaches may not be well suited in many batch processes because only process measurement variables are utilized while quality variables are not considered in the multivariate models. In this paper, a novel multiway kernel based quality relevant non-Gaussian latent subspace projection (MKQNGLSP) approach is proposed in order to monitor the operational performance of batch processes with nonlinear and non-Gaussian dynamics by combining measurement and quality variables. First, both process measurement and quality variables are projected onto high-dimensional nonlinear kernel feature spaces, respectively. Then, the multidimensional latent directions within kernel feature subspaces corresponding to measurement and quality variables are concurrently searched for so that the maximized mutual information between the measurement and quality spaces is obtained. The I² and SPE monitoring indices within the extracted latent subspaces are further defined to capture batch process faults resulting in abnormal product quality. The proposed MKQNGLSP method is applied to a fed-batch penicillin fermentation process and the operational performance monitoring results demonstrate the superiority of the developed method as apposed to the MKPLS based process monitoring approach.     

Latent‐variable Nonlinear Model Predictive Control Strategy for a pH Neutralization Process

Linear model predictive control (MPC) is a widely‐used control strategy in chemical processes. Its extension to nonlinear MPC (NMPC) has drawn increasing attention since many process systems are inherently nonlinear. When implementing the NMPC based on a nonlinear predictive model, a nonlinear dynamic optimization problem must be calculated. For the sake of solving this optimization problem efficiently, a latent‐variable dynamic optimization approach is proposed. Two kinds of constraint formulations, original variable constraint and Hotelling T² statistic constraint, are also discussed. The proposed method is illustrated in a pH neutralization process. The results demonstrate that the latent‐variable dynamic optimization based the NMPC strategy is efficient and has good control performance.     

Latent variable based model predictive control: Ensuring validity of predictions

This paper presents a methodology to constrain the optimisation problem in LV-MPC so that validity of predictions can be ascertained. LV-MPC is a model-based predictive control methodology implemented in the space of the latent variables and is based on a linear predictor. Provided real processes are non-linear, there is model-process mismatch, and under tight control, the predictor can be used for extrapolation. Extrapolation leads to bad predictions which deteriorates control performance, hence the interest in validity of predictions. In the proposed approach first two validity indicators on predictions are defined. The novelty in the two indicators proposed is they neglect past data, and so validity of predictions is ascertained in terms of future moves which are actually the degrees of freedom in the optimisation. Second, the indicators are introduced in the optimisation as constraints. Provided the indicators are quadratic, recursive optimisation with linearised constraints is implemented. A MIMO example shows how ensuring validity of predictions neglecting past data can improve closed-loop performance, specially under tight control outside the identification region.     

基于递推非线性部分最小二乘模型的间歇过程批到批优化

针对间歇过程控制策略优化问题,提出一种基于递推非线性部分最小二乘(NLPLS)模型的批到批优化方法:首先采用非线性部分最小二乘方法建立软测量模型,根据过程的控制操作变量对最后的产品质量进行预测。然后基于该模型,计算出最优控制策略并在实际装置上实施。为了解决模型和对象失配并且存在未知扰动的问题,采用递推算法,在每个批次结束后根据新得到的数据和旧模型参数对原模型进行更新。然后,重新求解最优控制策略并在对象上实施。通常经过几个批次,控制策略将收敛到一个满意解。在一个间歇过程上进行仿真研究,同时与基于PLS模型的批到批优化算法进行对比,结果表明采用NLPLS模型取得了优于采用PLS模型的结果。     

Data-driven latent-variable model-based predictive control for continuous processes

A model-based predictive control methodology in the space of the latent variables for continuous processes is presented. Implementing identification and control in the latent variable space eases identification in the case of correlation in the data set, acts as a prefilter reducing the effect of noisy data, and reduces computational complexity. The proposed data-driven LV-MPC approach deals with setting the control horizon different to the prediction horizon, improves Hessian conditioning, and attains offset-free tracking. Additionally, a weighting matrix is introduced in the identification stage so that the performance of the predictor in the near horizon can be enhanced. A MIMO example shows how the proposed methodology can outperform conventional data-driven MPC in terms of computational complexity and reference tracking.     

Bridging systems theory and data science: A unifying review of dynamic latent variable analytics and process monitoring

This paper is concerned with data science and analytics as applied to data from dynamic systems for the purpose of monitoring, prediction, and inference. Collinearity is inevitable in industrial operation data. Therefore, we focus on latent variable methods that achieve dimension reduction and collinearity removal. We present a new dimension reduction expression of state space framework to unify dynamic latent variable analytics for process data, dynamic factor models for econometrics, subspace identification of multivariate dynamic systems, and machine learning algorithms for dynamic feature analysis. We unify or differentiate them in terms of model structure, objectives with constraints, and parsimony of parameterization. The Kalman filter theory in the latent space is used to give a system theory foundation to some empirical treatments in data analytics. We provide a unifying review of the connections among the dynamic latent variable methods, dynamic factor models, subspace identification methods, dynamic feature extractions, and their uses for prediction and process monitoring. Both unsupervised dynamic latent variable analytics and the supervised counterparts are reviewed. Illustrative examples are presented to show the similarities and differences among the analytics in extracting features for prediction and monitoring.     

间歇过程动态优化方法综述

间歇过程的动态优化近年来引起了广泛关注.针对近期主要的研究成果,综述了间歇过程动态优化中的数学模型、求解方法及控制架构等问题,介绍了间歇过程目前主要的操作优化方法,具体分析了含不确定性间歇过程的动态优化策略,总结了间歇过程常用的优化模拟计算工具.最后探讨了这一领域中值得进一步研究的问题和可能的发展方向.     

间歇过程动态潜结构阶段划分与在线监控

阶段划分是间歇过程准确建模和有效监控的前提.针对传统阶段划分方法未考虑间歇过程的动态性造成阶段划分不准确、影响监控精度,且具有参数选择难、鲁棒性差的局限,提出一种基于动态潜结构的动态间歇过程阶段划分与在线监控方法.首先,对间歇过程三维张量数据沿变量方向展开,并增加时滞变量构建增广矩阵来提取过程动态关系;然后,以增广矩阵...     

人体运动的非线性降维及新运动生成

为了提高现有运动数据的可重用性,生成更为丰富的新运动,提出快速自适应比例高斯过程隐变量模型,以及基于该模型的人体运动数据降维及运动生成方法.通过对运动数据进行统计学习,获得运动数据在隐空间的一个低维映射来实现非线性降维,同时获得了该运动的姿态空间的概率分布,其大小反映了该姿态的自然逼真程度;在给定末端约束条件下求取满足约束的、同时概率最大的姿态,并将其作为逆向运动学的解,克服了传统逆向运动学算法计算烦琐、效果不逼真的缺点.实验结果表明,该模型具有更快的收敛速度和更高的收敛精度,同时能够自适应运动编辑的方向,有效地扩大运动的可编辑幅度.     

Nonlinear dynamical factor analysis for state change detection

Changes in a dynamical process are often detected by monitoring selected indicators directly obtained from the process observations, such as the mean values or variances. Standard change detection algorithms such as the Shewhart control charts or the cumulative sum (CUSUM) algorithm are often based on such first- and second-order statistics. Much better results can be obtained if the dynamical process is properly modeled, for example by a nonlinear state-space model, and then the accuracy of the model is monitored over time. The success of the latter approach depends largely on the quality of the model. In practical applications like industrial processes, the state variables, dynamics, and observation mapping are rarely known accurately. Learning from data must be used; however, methods for the simultaneous estimation of the state and the unknown nonlinear mappings are very limited. We use a novel method of learning a nonlinear state-space model, the nonlinear dynamical factor analysis (NDFA) algorithm. It takes a set of multivariate observations over time and fits blindly a generative dynamical latent variable model, resembling nonlinear independent component analysis. We compare the performance of the model in process change detection to various traditional methods. It is shown that NDFA outperforms the classical methods by a wide margin in a variety of cases where the underlying process dynamics changes.     

Gaussian process dynamical models for human motion

We introduce Gaussian process dynamical models (GPDM) for nonlinear time series analysis, with applications to learning models of human pose and motion from high-dimensionalmotion capture data. A GPDM is a latent variable model. It comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space. We marginalize out the model parameters in closed-form, using Gaussian process priors for both the dynamics and the observation mappings. This results in a non-parametric model for dynamical systems that accounts for uncertainty in the model. We demonstrate the approach, and compare four learning algorithms on human motion capture data in which each pose is 50-dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces.     

基于超图正则化的域适应偏最小二乘多工况软测量模型

针对流程工业中,因多工况导致数据分布变化引起传统软测量模型预测性能恶化问题,本文提出一种基于超图正则化的域适应多工况软测量回归模型框架.首先,采用非线性迭代偏最小二乘回归算法为基模型,在潜变量空间利用历史工况数据重构当前工况数据,以增强工况间的相关性,有效减小数据分布差异;同时,对重构系数施加低秩稀疏约束,保留了数据的局部和全局子空间结构;其次,通过超图拉普拉斯正则项对域适应潜变量求解过程进行约束,避免在寻找潜变量过程中破坏数据结构.最后,利用交替方向乘子法优化求解模型参数.在多个数据集上的实验表明,本文方法在多工况环境下可有效提高软测量模型的预测精度和泛化性能.     

A Constrained Multiple Raw Materials Manufacturing Batch Sizing Problem

The purpose of this research is to determine an optimal batch size for a product, and the purchasing policy of associated raw materials, for a manufacturing firm. Like any other practical situation, this manufacturing firm has a limited storage space, and transportation fleet of known capacity. The mathematical formulation of the problem indicates that the model is a constrained nonlinear integer program. Considering the complexity of solving such a model, we investigate the use of genetic algorithms (GAs) for solving this model. We develop both binary and real coded genetic algorithms with six different penalty functions. In addition, we develop a new procedure to solve constrained optimization models using penalty function based GAs. The real coded genetic algorithms work well for the batch sizing problems. The detailed computational experiences are presented.