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     

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     

Error‐triggered on‐line model identification for model‐based feedback control

In industry, it may be difficult in many applications to obtain a first‐principles model of the process, in which case a linear empirical model constructed using process data may be used in the design of a feedback controller. However, linear empirical models may not capture the nonlinear dynamics over a wide region of state‐space and may also perform poorly when significant plant variations and disturbances occur. In the present work, an error‐triggered on‐line model identification approach is introduced for closed‐loop systems under model‐based feedback control strategies. The linear models are re‐identified on‐line when significant prediction errors occur. A moving horizon error detector is used to quantify the model accuracy and to trigger the model re‐identification on‐line when necessary. The proposed approach is demonstrated through two chemical process examples using a model‐based feedback control strategy termed Lyapunov‐based economic model predictive control (LEMPC). The chemical process examples illustrate that the proposed error‐triggered on‐line model identification strategy can be used to obtain more accurate state predictions to improve process economics while maintaining closed‐loop stability of the process under LEMPC. © 2016 American Institute of Chemical Engineers AIChE J, 63: 949–966, 2017     

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     

Robust model predictive control and fault handling of batch processes

This work considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient nonlinear robust Model Predictive Control (MPC) is designed. The robust MPC scheme uses robust reverse‐time reachability regions (RTRRs), which we define as the set of process states that can be driven to a desired neighborhood of the target end‐point subject to input constraints and model uncertainty. A multilevel optimization‐based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR‐based MPC as the main tool, a robust safe‐steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end‐point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR‐based controller and safe‐steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed‐batch reactor system. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Nonlinear process identification in the presence of multiple correlated hidden scheduling variables with missing data

Identification of nonlinear processes in the presence of noise corrupted and correlated multiple scheduling variables with missing data is concerned. The dynamics of the hidden scheduling variables are represented by a state‐space model with unknown parameters. To assure generality, it is assumed that the multiple correlated scheduling variables are corrupted with unknown disturbances and the identification dataset is incomplete with missing data. A multiple model approach is proposed to formulate the identification problem of nonlinear systems under the framework of the expectation‐maximization algorithm. The parameters of the local process models and scheduling variable models as well as the hyperparameters of the weighting function are simultaneously estimated. The particle smoothing technique is adopted to handle the computation of expectation functions. The efficiency of the proposed method is demonstrated through several simulated examples. Through an experimental study on a pilot‐scale multitank system, the practical advantages are further illustrated. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3270–3287, 2015     

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     

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.     

Handling sensor faults in economic model predictive control of batch processes

The problem of sensor fault detection and isolation (FDI) and fault-tolerant economic model predictive control (FT-EMPC) for batch processes is addressed. To this end, we first model batch processes using subspace-based system identification techniques. The analytical redundancy within the identified model is subsequently exploited to detect, isolate, and handle the faulty measurements. The reconciled fault-free measurements are then incorporated in an economic model predictive controller formulation. Simulation case studies involving the application of the proposed data-driven FDI and FT-EMPC algorithms to the energy intensive electric arc furnace process illustrate the improvement in economic performance under various fault scenarios. © 2018 American Institute of Chemical Engineers AIChE J, 65: 617–628, 2019     

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.     

Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

A novel data‐driven adaptive robust optimization framework that leverages big data in process industries is proposed. A Bayesian nonparametric model—the Dirichlet process mixture model—is adopted and combined with a variational inference algorithm to extract the information embedded within uncertainty data. Further a data‐driven approach for defining uncertainty set is proposed. This machine‐learning model is seamlessly integrated with adaptive robust optimization approach through a novel four‐level optimization framework. This framework explicitly accounts for the correlation, asymmetry and multimode of uncertainty data, so it generates less conservative solutions. Additionally, the proposed framework is robust not only to parameter variations, but also to anomalous measurements. Because the resulting multilevel optimization problem cannot be solved directly by any off‐the‐shelf solvers, an efficient column‐and‐constraint generation algorithm is proposed to address the computational challenge. Two industrial applications on batch process scheduling and on process network planning are presented to demonstrate the advantages of the proposed modeling framework and effectiveness of the solution algorithm. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3790–3817, 2017     

A data‐driven multistage adaptive robust optimization framework for planning and scheduling under uncertainty

A novel data‐driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M‐estimation is proposed. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over‐conservatism. Robust kernel density estimation with Hampel loss function is employed to extract probability distributions from uncertainty data via a kernelized iteratively reweighted least squares algorithm. A data‐driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, to organically integrate the multistage ARO framework with uncertainty data. Based on this uncertainty set, we further develop an exact robust counterpart in its general form for solving the resulting data‐driven multistage ARO problem. To illustrate the applicability of the proposed framework, two typical applications in process operations are presented: The first one is on strategic planning of process networks, and the other one on short‐term scheduling of multipurpose batch processes. The proposed approach returns 23.9% higher net present value and 31.5% more profits than the conventional robust optimization method in planning and scheduling applications, respectively. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4343–4369, 2017     

A geometric framework for monitoring and fault detection for periodic processes

Although cyclical operation systems are relatively widespread in practice (notably in the realm of physical separations, for example, pressure‐swing adsorption and chromatography), the development of specific fault detection mechanisms has received little attention compared to the extensive efforts dedicated to continuous or batch processes. Here, a novel geometric approach for process fault detection is proposed. Specifically, a time‐explicit multivariable representation of data collected from the process, which provides a natural framework for defining “normal” operation and the corresponding confidence regions is developed. On this basis, a two‐step fault detection approach is proposed, based on detecting intercycle variations to locate a faulty cycle, and intracycle changes to determine the exact timing of a fault. The theoretical developments are illustrated with two simulation case studies. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2719–2730, 2017     

Robust identification of piecewise/switching autoregressive exogenous process

A robust identification approach for a class of switching processes named PWARX (piecewise autoregressive exogenous) processes is developed in this article. It is proposed that the identification problem can be formulated and solved within the EM (expectation‐maximization) algorithm framework. However, unlike the regular EM algorithm in which the objective function of the maximization step is built upon the assumption that the noise comes from a single distribution, contaminated Gaussian distribution is utilized in the process of constructing the objective function, which effectively makes the revised EM algorithm robust to the latent outliers. Issues associated with the EM algorithm in the PWARX system identification such as sensitivity to its starting point as well as inability to accurately classify “un‐decidable” data points are examined and a solution strategy is proposed. Data sets with/without outliers are both considered and the performance is compared between the robust EM algorithm and regular EM algorithm in terms of their parameter estimation performance. Finally, a modified version of MRLP (multi‐category robust linear programming) region partition method is proposed by assigning different weights to different data points. In this way, negative influence caused by outliers could be minimized in region partitioning of PWARX systems. Simulation as well as application on a pilot‐scale switched process control system are used to verify the efficiency of the proposed identification algorithm. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

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     

Bayesian inference and joint probability analysis for batch process monitoring

A new probabilistic monitoring method for batch processes that have multiple operating conditions is described. Particularly, for multiphase batch processes, a phase‐based Bayesian inference strategy is introduced, which can efficiently combine the information of multiple operation modes together into a single model in each specific phase. Therefore, without any process knowledge, local monitoring results in different operation modes can be automatically integrated. Besides, the information of the operation mode can be obtained through joint probability analysis under the Bayesian monitoring framework. Potential extensions of the proposed method for fault diagnosis and identification are also discussed. A benchmark case study on the penicillin fermentation process is given to evaluate the feasibility and efficiency of the proposed method. It is demonstrated that the monitoring performance and the process comprehension have both been improved. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3702–3713, 2013     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

A Bayesian approach for control loop diagnosis with missing data

This article is concerned with determination of the underlying source of problematic control performance through a data‐driven Bayesian approach. This approach synthesizes information from different monitoring algorithms to isolate possible problem sources. A main issue encountered in the application of the data‐driven approach is the problem of missing data or missing monitor reading. By introducing the concept of missing pattern, data missing problems are classified into single and multi missing patterns. A novel method based on marginalization over underlying complete evidence matrix is proposed to circumvent missing data problems. Performance of the proposed Bayesian approach is examined through simulations as well as an industrial application example to verify its ability of information synthesis. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Robust batch‐to‐batch optimization in the presence of model‐plant mismatch and input uncertainty

In model‐based optimization in the presence of model‐plant mismatch, the set of model parameter estimates which satisfy an identification objective may not result in an accurate prediction of the gradients of the cost‐function and constraints. To ensure convergence to the optimum, the predicted gradients can be forced to match the measured gradients by adapting the model parameters. Since updating all available parameters is impractical due to estimability problems and overfitting, there is a motivation for adapting a subset of parameters for updating the predicted outputs and gradients. This article presents an approach to select a subset of parameters based on the sensitivities of the model outputs and of the cost function and constraint gradients. Furthermore, robustness to uncertainties in initial batch conditions is introduced using a robust formulation based on polynomial chaos expansions. The improvements in convergence to the process optimum and robustness are illustrated using a fed‐batch bioprocess. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2660–2670, 2017