Multiphase Batch Processes Research Articles

Multiphase time-varying batch process monitoring based on stage moving model migration

To improve product qualities and obtain maximum comprehensive economic benefits from batch process production, it is of great practical significance to optimize the operation of batch production processes. Considering the multiphase and slow time-varying characteristics, a multiphase time-varying batch process monitoring method is proposed based on stage moving model migration technology. Firstly, the sliding windows are constructed with moving phases, where the moving of different phases is decided by the influence of the process variables to the final product. And time slices are the basic units for building the regression models. Secondly, to analyze and capture the relationship between the process variables of both the old mode and new mode and the final quality variable, the JY-PLS algorithm is utilized on each time slice within sliding windows for quality prediction. Then, monitoring indexes and corresponding control limits are calculated and used for process monitoring. The application to a real multiphase time-varying batch process, the start-up process of injection molding process, proved the effectiveness of the proposed method.

Two-dimensional iterative learning hybrid robust fuzzy predictive control for nonlinear multi-phase batch processes with asynchronous switching

For nonlinear multi-phase batch processes with uncertainties, time-varying delays, and unknown bounded disturbances, an iterative learning hybrid robust fuzzy predictive control approach is developed within the context of two-dimensional systems. First, a two-dimensional T-S fuzzy Fornasini-Marchesini comprehensive feedback error model is constructed, which includes a state increment and an output error. Based on the established model and considering an asynchronous switching situation between a controller and a system state, a feedback error switching model, including match and mismatch cases, is developed. Then, a two-dimensional iterative learning hybrid robust fuzzy predictive controller is built, based on the established switching model. Second, building on related theories and methodologies, the stability conditions are derived by a linear matrix inequality form, while the system's asymptotic and exponential stability are analyzed. Next, the stability conditions are calculated to get the control law gains, minimum and maximum dwelling times. The acquired gains of control law greatly minimize the controller's learning cycle, while the advanced switching signal based on the obtained dwelling times is dynamically adjusted to ensure a smooth transition and the system's stability during switching. Ultimately, a simulation case is utilized to validate the proposed method's effectiveness and feasibility.

Pseudo-model-based iterative learning control for nonlinear multi-phase batch processes

In this article, a pseudo-model-based iterative learning control (ILC) is exploited for multi-phase batch processes which can be described as a nonlinear switched system with unknown functions and identical states in different phases. The nonlinear switched system is converted into a linear model whose system parameter matrix is approximated by minimizing the discrepancy from the real system output increment to the approximated system output increment. A data-driven ILC is constructed in an interactive form with system parameter matrix approximate algorithm. Meanwhile, the signs of the diagonal elements of system lower triangular parameter matrix are introduced into the construction of control input law. Theoretical analysis shows that the pseudo-model-based ILC (PM-ILC) concept can be extended to multi-phase batch processes with non-identical states in different phases. Furthermore, the approximation error of the system parameters matrix is bounded and the proposed PM-ILC is robust if the parameter is appropriately chosen. Simulation results illustrate the effectiveness and practicability of the proposed PM-ILC.

An improved transfer learning approach based on geodesic flow kernel for multiphase batch process soft sensor modeling

For multiphase batch process, the characteristics of process data under various batches differ. Consequently, the soft sensor model built for a particular working condition is inapplicable to other working conditions. Besides, each batch can be divided into several phases whose characteristics are probably different. To address the above problems, a soft sensor model based on phase division and transfer learning strategy is proposed. First, transfer learning strategy is adopted to construct a soft sensor model applicable to various working conditions. Specifically, geodesic flow kernel based on linear local tangent space alignment (LLTSA-GFK) algorithm is designed. By projecting process data to the common manifold subspace, the distribution difference of data between various batches is reduced and the performance of the soft sensor model is enhanced. In addition, sequence-based fuzzy clustering and just-in-time learning (JITL) are adopted to solve the multistage characteristic for batch process. The root-mean-square error ( RMSE), coefficient of determination [Formula: see text], and mean absolute error ( MAE) are adopted to compare the conventional soft sensing approach (i.e., partial least-square regression based on JITL, support vector regression, and back propagation neural network) with the proposed approach. The superiority of the proposed model is verified by a fed-batch penicillin fermentation process.

Two-Dimensional Iterative Learning Robust Asynchronous Switching Predictive Control for Multiphase Batch Processes With Time-Varying Delays

Two-Dimensional Iterative Learning Robust Asynchronous Switching Predictive Control for Multiphase Batch Processes With Time-Varying Delays

Robust fuzzy predictive switching control for nonlinear multi-phase batch processes with synchronous vs asynchronous cases

Multi-phase batch processes (MPBP) have the characteristics of nonlinearity and various cases of switching, where the switching between two adjacent phases can be divided into synchronous vs asynchronous cases. The present study introduces a robust fuzzy predictive method for switching control to ensure that an MPBP can still operate stably in the above two cases. First, considering the multi-phase characteristics of MPBP, multiple stable sub-models are established under the synchronous case. On this basis, unstable sub-models are established between adjacent phases under the asynchronous case. Second, in order to deal with the inherent nonlinearity of MPBP, each sub-model is locally linearized and a mixed Takagi-Sugeno (T-S) model is established. Third, using a mapping relationship between controller and local subsystem including direct mapping and fully associative mapping, a global output control law is designed. By combining the Lyapunov stability theory, linear matrix inequality (LMI) theory, mode-dependent average dwell time method, etc., corresponding LMI conditions are derived by the mapping relationship of different cases, making each phase asymptotically stable and each batch exponentially stable. Then, the distribution compensation gains of the corresponding controllers, the shortest operating time of the stable subsystem and the longest operating time of the unstable subsystem can be obtained by solving corresponding LMI conditions in a synchronous or an asynchronous case. Finally, if the MPBP is in an asynchronous case, according to the longest operating time of the unstable subsystem, a time compensation method based on the obtained operating time is proposed to avoid the occurrence of an unstable subsystem. The simulation results demonstrate that the proposed method has greater advantages than the reference methods.

Nonlinear multiphase batch process monitoring and quality prediction using multi-way concurrent locally weighted projection regression

The batch process has the characteristics of nonlinear and multiphase due to variation operation conditions. Nonlinear and multiphase modeling of the batch process is very important to understand the running state of a process and improve the monitoring effect. In this work, a multiphase multi-way concurrent locally weighted projection regression algorithm is proposed. Firstly, the entire process is partitioned into phases according to local quality-related characteristics and time sequence. Secondly, the nonlinear process is modeled with locally linear models in each partitioned phase, the global approximation results are obtained by weighting all the local models. Thirdly, the complete monitoring indices of quality-related and process related are built, and the quality variables are predicted while exploiting the regression structure for quality and process monitoring. Finally, a nonlinear numerical process and the penicillin fermentation process are used to verify the effectiveness of the proposed algorithm.

Iterative Learning Hybrid Robust Predictive Control for Multi-Phase Batch Processes with Asynchronous Switching via a Lyapunov-Razumikhin Approach

Iterative Learning Hybrid Robust Predictive Control for Multi-Phase Batch Processes with Asynchronous Switching via a Lyapunov-Razumikhin Approach

Soft sensor based on localized semi-supervised relevance vector machine for penicillin fermentation process with asymmetric data

Due to operating conditions and on-site measurement instrument performance, the obtained batch process data present asymmetric characteristics. Compared with the symmetric data, it is more than a challenge to establish an effective soft sensor model for batch process with asymmetric data due to the following issues: (1) weak model performance due to the small amount of labeled data and (2) lack of an effective similarity evaluation between labeled data and unlabeled data with multiphase characteristics. To address these issues, a localized semi-supervised relevance vector machine-based soft sensor is proposed for multiphase batch processes with asymmetric data. First, a sequence-constrained fuzzy c-means algorithm is used to divide asymmetric data into phases. Then, a localized semi-supervised-based algorithm is proposed to estimate the label for unlabeled data of each phase. This algorithm consists of similar dataset construction based on a designed comprehensive similarity and label estimation based on just-in-time learning. On this basis, the soft sensor model for each phase is constructed based on relevance vector machine. Finally, an experiment of the penicillin fermentation process illustrates the effectiveness of the proposed method.

Data‐based iterative learning control for multiphase batch processes

AbstractIn order to cope with the problem of the robustness conditions dependence on system parameters information, this paper investigates a data‐based iteration learning control (ILC) for multiphase batch processes with different dimensions and system uncertainty. Firstly, by minimizing the residual between the actual subsystem output and the approximated subsystem output, a gradient‐type approximation law is designed to approximate the system lower triangular parameters matrix and initial state. Secondly, by minimizing the approximated tracking error between the desired trajectory and the approximated output, a data‐based ILC is constructed in an interactive mode with the approximation law. Finally, the boundedness of the approximation error of the real system parameters from the approximated parameters is derived by means of vector norm theory, while the unconditional robustness of the proposed data‐based ILC is proved. Simulation results illustrate the effectiveness and practicability of the proposed data‐based ILC.

The Convergence of Data-Driven Optimal Iterative Learning Control for Linear Multi-Phase Batch Processes

For multi-phase batch processes with different dimensions whose dynamics can be described as a linear discrete-time-invariant system in each phase, a data-driven optimal ILC was explored using multi-operation input and output data that subordinate a tracking performance criterion. An iterative learning identification was constructed to estimate the system Markov parameters by minimizing the evaluation criterion that consists of the residual of the real outputs from the predicted outputs and two adjacent identifications. Meanwhile, the estimated Markov parameters matrix was embedded into the learning control process in the form of an interaction. By virtue of inner product theory, the monotonic descent of the estimation error was derived, which does not restrict the weighting factor at all. Furthermore, algebraic derivation demonstrates that the tracking is strictly monotonically convergent if the estimation error falls within an appropriate domain. Numerical simulations were carried out to illustrate the validity and the effectiveness of the proposed method.

Two-dimensional multiphase batch process monitoring based on sparse canonical variate analysis

Most industrial batch processes involve inherent dynamic characteristics in both within-batch time direction and batch-wise direction. In order to ensure process safety and improve process performance, the two-dimensional dynamics should be analyzed during batch process monitoring. In this work, two-dimensional region of support (2D-ROS) is first constructed to select and preserve the relevant samples for the current measured sample by calculating autoregressive orders with Akaike information criterion (AIC) in time direction and measuring the similarity with the weighted Euclidean distance in batch-wise direction. Afterwards, sparse canonical variate analysis (SCVA) algorithm is performed to yield sparse canonical vectors, which is especially advantageous for eliminating the irrelevant variables and facilitating the interpretation of underlying relationships of process variables. Meanwhile, given most measurements are subject to the non-Gaussian distribution, the upper control limits (UCLs) in 2D-SCVA can be estimated using kernel density estimation (KDE). The achieved results obtained from a numerical dynamic example and the benchmark fed-batch penicillin fermentation process clearly verify that the proposed method performs well for detecting abnormal operation for the batch processes.

Slow‐varying batch process monitoring based on canonical variate analysis

AbstractMost industrial batch processes display normal slow changes over batches because of the influence of external factors. The question of how to take this slow‐varying behaviour into account during dynamic process monitoring remains a challenge for researchers. To address the above issue, a slow‐varying batch process monitoring method is proposed for multiphase batch processes. It makes subtraction between two different batches with a certain interval for pre‐treating the original data and subsequently utilizes a canonical variate analysis (CVA) algorithm with kernel density estimation (KDE) for fault detection. For each subphase, the proposed method can extract a variable‐wise dynamic characteristic with the time evolution for every single batch and capture statistical features of slow variations along batch direction simultaneously. It is less sensitive to normal gradual changes with a low false‐positive rate. The performance of the proposed method for batch process monitoring was tested on a numerical simulation system and penicillin fermentation production process with comparison to multiphase CVA, multiphase slow feature analysis (SFA), multiphase principal component analysis (PCA), and traditional CVA without phase division. The achieved results clearly demonstrate the effectiveness of the proposed method, which is a remarkable and promising tool for modelling and monitoring batch processes with regular slow‐varying characteristics.

Quality-related fault monitoring for multi-phase batch process based on multiway weighted elastic network

A quality-related fault monitoring method of multi-phase batch process based on multiway weighted elastic network is proposed in this paper. Firstly, to make the phase division for batch process more accurately, an improved affinity propagation clustering algorithm is developed. Secondly, a multiway weighted elastic network model is developed in each phase. On the one hand, quality-related subspace and quality-unrelated subspace are constructed in each phase to achieve dual monitoring of process fault and quality anomalies. On the other hand, kernel density estimation is used to measure the contribution of each element in each subspace to the fault. According to the difference of the contribution of each element to the fault, different weight is assigned to enhance the fault features and eliminate irrelevant features such as noise. Finally, support vector data description is used to establish monitoring indexes in both quality-related subspace and quality-unrelated subspace. Compared with traditional methods, the superiority and effectiveness of the proposed method have been verified by monitoring the penicillin fermentation process and the hot strip mill process.

Robust Model Predictive Control for Multi-phase Batch Processes with Asynchronous Switching

Robust Model Predictive Control for Multi-phase Batch Processes with Asynchronous Switching

Robust asynchronous switching predictive control for multi-phase batch processes with time-varying tracking trajectory and delay

To solve the delay condition of the controller during adjacent phases and the change of the set value in multi-phase batch processes, a robust asynchronous switching predictive control scheme is proposed based on the mode-dependent average dwell time method. Firstly, the model of multi-phase batch processes including stable and unstable subsystems is established. Secondly, the LMI conditions to ensure that the system is asymptotically stable at each phase and exponentially stable at each batch are given. By solving these LMI conditions, not only the control law can be calculated, but also the shortest running time in the stable subsystems and the longest running time in the unstable subsystems can be obtained. Finally, according to these times, the controller is switched ahead of time to avoid the appearance of unstable subsystems. The comparison results of the injection moulding processes with the existing switching methods verifies the feasibility of the proposed method.

Online quality prediction based on the double cumulative model for multiphase batch processes with transitions

In multiphase batch processes, the final product quality prediction results depend on the common cumulative effects of all the critical phases with transitions on quality rather than a separated one. However, the common cumulative effect are rarely considered at the same time. To address this issue, a double cumulative model is proposed in this paper. The double model includes the internal cumulative model and the external cumulative model. On one hand, the critical local cumulative quality is introduced to isolate the local cumulative effect of different phases and transitions in the internal cumulative model. Especially, for transitions modeling, an average process trajectories method based on the dominant phase identification is developed to deal with the dynamic and uncertainty. On the other hand, the correlation of different cumulative models is extracted by constructing the external cumulative model. In this way, the cumulative effect of all the phases and transitions are considered simultaneously. The proposed method is applied to penicillin fermentation. The simulation results demonstrate the effectiveness and superiority of the proposed method over the competing models.

Real-time synchronization with expected distribution of synchronized index for on-line monitoring of uneven multiphase batch process

Because of the inconsistent batch duration, identifying the progress of an ongoing batch highly affects the performance of the on-line monitoring. In this paper, a real-time synchronization scheme is proposed based on relative proceeding rates, newly defined as the time difference between the trajectory of an ongoing batch and the nominal trajectory. As the relative proceeding rate indicates how early the point attains its desired value compared to the nominal trajectory, the synchronized index is obtained on-line by estimating the relative proceeding rate. Compared with the conventional methods that optimize the synchronized index with local constraints, the proposed method can estimate its distribution using the relative proceeding rate without applying local constraints. It can reduce synchronization errors and increase the accuracies of the state estimation and fault detection. The utility of the proposed method is verified via a case study of industrial penicillin production with a real-time unmeasurable variable.

Quality-Analysis-Based Process Monitoring for Multi-Phase Multi-Mode Batch Processes

In batch processing, not only the characteristics of different phases are different, but also there may be different characteristics between batches. These characteristics of different phases and batches will have different effects on the final product quality. In order to enhance the safety of batch processes, it is necessary to establish an appropriate monitoring system to monitor the production process based on quality-related information. In this work, based on multi-phase and multi-mode quality prediction, a new quality-analysis-based process-monitoring strategy is developed for batch processes. Firstly, the time-slice models are established to determine the critical-to-quality phases. Secondly, a multi-phase residual recursive model is established using each quality residual of the phase mean models. Subsequently, a new process-monitoring strategy based on quality analysis is proposed for a single mode. After that, multi-mode quality analysis is carried out to judge the relevance between the historical modes and the new mode. Further, online quality prediction is achieved applying the selected model based on multi-mode quality analysis, and an according process-monitoring strategy is developed. The simulation results show the availability of this method for multi-phase multi-mode batch processes.

Iterative Learning Control for Multiphase Batch Processes With Asynchronous Switching

Asynchronous switching between the controller and the active subsystems in multiphase batch processes may cause the systems to be unstable around the switching instants. In view of this, an average dwell-time method-based iterative learning control (ILC) scheme is proposed in this paper. First, the multiphase process is represented as an equivalent closed-loop two-dimensional (2-D) switched system composed of stable and unstable subsystems, based on which new relevant concepts on the stability of the switched system are given. Second, using an average dwell-time method, the ILC law is designed to guarantee the system exponentially stable. Minimum running time for the stable subsystems and maximum running time for the unstable ones are obtained. Lastly, depending on the maximum time for the unstable subsystems, the idea of putting the controller switching step forward is proposed. In this way, the asynchronous switching is removed such that the unstable subsystem can be avoided. The case study on an injection molding process demonstrates the effectiveness and superiority of the proposed method in comparison with the existing 2D-MPC and one-dimensional traditional control methods.