Handling multi‐rate and missing data in variable duration economic model predictive control of batch processes

In the present work, we consider the problem of variable duration economic model predictive control of batch processes subject to multi‐rate and missing data. To this end, we first generalize a recently developed subspace‐based model identification approach for batch processes to handle multi‐rate and missing data by utilizing the incremental singular value decomposition technique. Exploiting the fact that the proposed identification approach is capable of handling inconsistent batch lengths, the resulting dynamic model is integrated into a tiered EMPC formulation that optimizes process economics (including batch duration). Simulation case studies involving application to the energy intensive electric arc furnace process demonstrate the efficacy of the proposed approach compared to a traditional trajectory tracking approach subject to limited availability of process measurements, missing data, measurement noise, and constraints. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2705–2718, 2017     

Integrating data‐based modeling and nonlinear control tools for batch process control

A data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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     

Data‐driven model predictive quality control of batch processes

The problem of driving a batch process to a specified product quality using data‐driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this “missing data” problem by integrating a previously developed data‐driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed‐loop simulations of a nylon‐6,6 batch polymerization process with limited measurements. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2852–2861, 2013     

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     

Dynamic nonlinear batch process fault detection and identification based on two‐directional dynamic kernel slow feature analysis

The batch process generally covers high nonlinearity and two‐directional dynamics: time‐wise dynamics, which correspond to inherently time‐varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch‐wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch‐wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two‐directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time‐wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch‐wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling's T² and SPE statistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo‐sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA‐based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.     

Safe‐steering of batch process systems

This work considers the problem of controlling batch processes to achieve a desired final product quality subject to input constraints and faults in the control actuators. Specifically, faults are considered that cannot be handled via robust control approaches, and preclude the ability to reach the desired end‐point, necessitating fault‐rectification. A safe‐steering framework is developed to address the problem of determining how to utilize the functioning inputs during fault rectification to ensure that after fault‐rectification, the desired product properties can be reached upon batch termination. To this end, first a novel reverse‐time reachability region (we define the reverse time reachability region as the set of states from where the desired end point can be reached by batch termination) based MPC is formulated that reduces online computations, as well as provides a useful tool for handling faults. Next, a safe‐steering framework is developed that utilizes the reverse‐time reachability region based MPC in steering the state trajectory during fault rectification to enable (upon fault recovery) the achieving of the desired end point properties by batch termination. The proposed controller and safe‐steering framework are illustrated using a fed‐batch process example. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Modeling and simulation of fiber‐reinforced polymer mold‐filling with phase change

A gas‐solid‐liquid three‐phase model for the simulation of fiber‐reinforced composites mold‐filling with phase change is established. The influence of fluid flow on the fibers is described by Newton's law of motion, and the influence of fibers on fluid flow is described by the momentum exchange source term in the model. A revised enthalpy method that can be used for both the melt and air in the mold cavity is proposed to describe the phase change during the mold‐filling. The finite‐volume method on a non‐staggered grid coupled with a level set method for viscoelastic‐Newtonian fluid flow is used to solve the model. The “frozen skin” layers are simulated successfully. Information regarding the fiber transformation and orientation is obtained in the mold‐filling process. The results show that fibers in the cavity are divided into five layers during the mold‐filling process, which is in accordance with experimental studies. Fibers have disturbance on these physical quantities, and the disturbance increases as the slenderness ratio increases. During mold‐filling process with two injection inlets, fiber orientation around the weld line area is in accordance with the experimental results. At the same time, single fiber's trajectory in the cavity, and physical quantities such as velocity, pressure, temperature, and stresses distributions in the cavity at end of mold‐filling process are also obtained. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42881.     

Control‐relevant decomposition of process networks via optimization‐based hierarchical clustering

A systematic method is proposed for control‐relevant decomposition of complex process networks. Specifically, hierarchical clustering methods are adopted to identify constituent subnetworks such that the components of each subnetwork are strongly interacting while different subnetworks are loosely coupled. Optimal clustering is determined through the solution of integer optimization problems. The concept of relative degree is used to measure distance between subnetworks and compactness of subnetworks. The application of the proposed method is illustrated using an example process network. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3177–3188, 2016     

Integrated B2B‐NMPC control strategy for batch/semibatch crystallization processes

The uncertainty in crystallization kinetics is of major concern in manufacturing processes, which can result in deterioration of most model‐based control strategies. In this study, uncertainties in crystallization kinetic parameters were characterized by Bayesian probability distributions. An integrated B2B‐NMPC control strategy was proposed to first update the kinetic parameters from batch to batch using a multiway partial least‐squares (MPLS) model, which described the variances of kinetic parameters from that of process variables and batch‐end product qualities. The process model with updated kinetic parameters was then incorporated into an NMPC design, the extended prediction self‐adaptive control (EPSAC), for online control of the final product qualities. Promising performance of the proposed integrated strategy was demonstrated in a simulated semibatch pH‐shift reactive crystallization process to handle major crystallization kinetic uncertainties of L‐glutamic acid, wherein smoother and faster convergences than the conventional B2B control were observed when process dynamics were shifted among three scenarios of kinetic uncertainties. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Real‐time economic model predictive control of nonlinear process systems

Closed‐loop stability of nonlinear systems under real‐time Lyapunov‐based economic model predictive control (LEMPC) with potentially unknown and time‐varying computational delay is considered. To address guaranteed closed‐loop stability (in the sense of boundedness of the closed‐loop state in a compact state‐space set), an implementation strategy is proposed which features a triggered evaluation of the LEMPC optimization problem to compute an input trajectory over a finite‐time prediction horizon in advance. At each sampling period, stability conditions must be satisfied for the precomputed LEMPC control action to be applied to the closed‐loop system. If the stability conditions are not satisfied, a backup explicit stabilizing controller is applied over the sampling period. Closed‐loop stability under the real‐time LEMPC strategy is analyzed and specific stability conditions are derived. The real‐time LEMPC scheme is applied to a chemical process network example to demonstrate closed‐loop stability and closed‐loop economic performance improvement over that achieved for operation at the economically optimal steady state. © 2014 American Institute of Chemical Engineers AIChE J, 61: 555–571, 2015     

A new framework and a simpler method for the development of batch crystallization recipes

We use a new generalized dimensionless model of a seeded batch crystallization process to compare results from four crystal growth rate/concentration trajectories: a numerically‐computed optimal trajectory, a constant growth rate trajectory, a trajectory proposed by Mullin and Nyvlt [Chem Eng Sci. 1971;26:369–377] that can be calculated without a kinetic model, and a linear concentration‐time trajectory. Because the model is generalized and dimensionless it is not specific to any particular solute–solvent system. We show that if seed properties are good, all trajectories achieve a good result, whereas if seed properties are poor all trajectories achieve a poor result. If seed properties are intermediate, the linear concentration trajectory performs much worse than the other trajectories. On the basis of this, we conclude: (1) Linear trajectories and natural cooling trajectories are poor and should be avoided. When evaluating the benefit derived from an optimization of a temperature/saturation concentration trajectory, the appropriate benchmark should be the Mullin‐Nyvlt trajectory, which typically performs much better than the linear trajectory and can be calculated knowing only the mass of seeds at the beginning of the batch. (2) Changing seed properties is more likely to improve batch crystallizer performance than optimizing the growth/saturation concentration trajectory. (3) For rapid process development, the most reasonable approach is to use the Mullin‐Nyvlt trajectory and seek to improve process performance by adjusting seed properties. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A full‐condition monitoring method for nonstationary dynamic chemical processes with cointegration and slow feature analysis

Chemical processes are in general subject to time variant conditions because of load changes, product grade transitions, or other causes, resulting in typical nonstationary dynamic characteristic. It is of a considerable challenge for process monitoring to consider all possible operation conditions simultaneously including multifarious steady states and dynamic switchings. In this work, a novel full‐condition monitoring strategy is proposed based on both cointegration analysis (CA) and slow feature analysis (SFA) with the following considerations: (1) Despite that the operation conditions may vary over time, they may follow certain equilibrium relations that extend beyond the current time, and (2) there may exist certain dynamic relations that stay invariant under normal process operation despite process may operate at different operating conditions. To monitor both equilibrium and dynamic relations, in the proposed method, nonstationary variables are separated from stationary variables first. Then by CA and SFA, the long‐term equilibrium relation is distinguished from the specific relation held by the current conditions from both static and dynamic aspects. Various monitoring statistics are designed with clear physical interpretation. It can distinguish between the changes of operation conditions and real faults by checking deviations from equilibrium relation and deviations from the specific relation. Case study on a chemical industrial scale multiphase flow experimental rig shows the validity of the proposed full‐condition monitoring method. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1662–1681, 2018     

基于隐变量空间载荷余弦相似度的间歇过程递推优化

针对间歇过程基于主元相似度优化方法中存在的变量相关性信息损失问题,提出一种单位化隐变量空间下利用载荷余弦相似度进行递推优化的新策略。首先将各时段变量与指标变量构成的扩展矩阵进行主元分解,通过信息的重新分配使得由主元构成的隐变量空间是单位正交的,从而得到包含更多变量相关信息的非单位化载荷矩阵,进一步计算隐变量空间下各时段变量与指标变量之间载荷余弦相似度和批次间指标增量,并对操作曲线进行递推修正。这种非单位化载荷矩阵的主元分解形式,不仅降低了隐变量空间下变量相关性信息损失,也使得更新操作曲线的递推算法更为简化。最后,通过间歇过程某一化工产品结晶纯度的优化研究,验证了所提方法的有效性。     

Probabilistic slow feature analysis‐based representation learning from massive process data for soft sensor modeling

Latent variable (LV) models provide explicit representations of underlying driving forces of process variations and retain the dominant information of process data. In this study, slow features (SFs) as temporally correlated LVs are derived using probabilistic SF analysis. SFs evolving in a state‐space form effectively represent nominal variations of processes, some of which are potentially correlated to quality variables and hence help improving the prediction performance of soft sensors. An efficient expectation maximum algorithm is proposed to estimate parameters of the probabilistic model, which turns out to be suitable for analyzing massive process data. Two criteria are also proposed to select quality‐relevant SFs. The validity and advantages of the proposed method are demonstrated via two case studies. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4126–4139, 2015     

Incorporating setting information for maintenance‐free quality modeling of batch processes

Typically, the operation condition of the batch process is changed frequently, following different recipes or manufacturing various production grades. For quality prediction purpose, the prediction model should also be updated or rebuilt, which leads to a significant model maintenance effort, especially for those processes which have various phases. To reduce such effort, a maintenance‐free method is proposed in this article, which incorporates the setting information of the batch process for modeling. The whole process variations are separated into two parts: setting information related and other quality related variations. By constructing a relationship between setting variables and other process variables, the data variations explained by the setting information can be efficiently removed. Then, a robust regression model connecting process variables to the quality variable is developed in different phases of the batch process. The feasibility and effectiveness of the proposed method is evaluated through an industrial injection molding process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 772–779, 2013     

Regression‐based analysis of multivariate non‐Gaussian datasets for diagnosing abnormal situations in chemical processes

This article presents a regression‐based monitoring approach for diagnosing abnormal conditions in complex chemical process systems. Such systems typically yield process variables that may be both Gaussian and non‐Gaussian distributed. The proposed approach utilizes the statistical local approach to monitor parametric changes of the latent variable model that is identified by a revised non‐Gaussian regression algorithm. Based on a numerical example and recorded data from a fluidized bed reactor, the article shows that the proposed approach is more sensitive when compared to existing work in this area. A detailed analysis of both application studies highlights that the introduced non‐Gaussian monitoring scheme extracts latent components that provide a better approximation of non‐Gaussian source signal and/or is more sensitive in detecting process abnormities. © 2013 American Institute of Chemical Engineers AIChE J, 60: 148–159, 2014     

Concurrent phase partition and between‐mode statistical analysis for multimode and multiphase batch process monitoring

The exiting automatic phase partition and phase‐based process monitoring strategies are in general limited to single‐mode multiphase batch processes. In this article, a concurrent phase partition and between‐mode statistical modeling strategy (CPPBM) is proposed for online monitoring of multimode multiphase batch processes. First, the time‐varying characteristics of batch processes are concurrently analyzed across modes so that multiple sequential phases are simultaneously identified for all modes. The feature is that both time‐wise dynamics and mode‐wise variations are considered to get the consistent phase boundaries. Then within each phase, between‐mode statistical analysis is performed where one mode is chosen for the development of reference monitoring system and the relative changes from the reference mode to each alternative mode are analyzed. From the between‐mode perspective, each of the original reference monitoring subspaces, including systematic subspace and residual subspace, are further decomposed into two monitoring subspaces for each alternative mode, which reveal two kinds of between‐mode relative variations. The part which shows significant increases represents the variations that will cause alarm signals if the reference models are used to monitor the alternative modes, whereas the part that shows no increases will not issue alarms. By modeling and monitoring different types of between‐mode relative variations, the proposed CPPBM method can not only efficiently detect faults but also offer enhanced process understanding. It is illustrated with a typical multiphase batch process with multiple modes. © 2013 American Institute of Chemical Engineers AIChE J 60: 559–573, 2014