Multiphase Batch Processes Research Articles

Robust Asynchronous Switching Fault-Tolerant Control for Multi-Phase Batch Processes With Time-Varying Delay

A robust asynchronous switching fault-tolerant control method is proposed to solve the problems of uncertainties, unknown disturbances, time-varying delays and partial actuator failures in multi-phase batch processes. Firstly, an asynchronous system composed of subsystems with different dimensions including stable and unstable case is established to describe such multi-phase batch processes more accurately. Then introducing the output tracking error, the established switching model of different dimensions is extended. On this basis, a robust asynchronous switching fault-tolerant control law is designed, which improves the system’s ability to cope with negative factors such as actuator failure and can obtain greater adjustment freedom. Secondly, by using relevant theories and methods, the sufficient conditions in the form of linear matrix inequality (LMI) are given to ensure the exponential stability of the system and the asymptotic stability at each phase. By solving these LMIs conditions, the shortest running time under stable case, the longest running time under unstable case and the control law gain of each phase are obtained. Finally, the effectiveness and feasibility of the proposed method are verified with injection molding process.

Improved Mahalanobis Distance Based JITL-LSTM Soft Sensor for Multiphase Batch Processes

To predict key variables of complicated batch processes, the long short-term memory (LSTM) soft sensor is developed to deal with both data nonlinearity and dynamics. To extract proper historical samples and implement the real-time modeling scheme with model updating strategy, the just-in-time learning (JITL) algorithm is widely used at the data selection stage of LSTM soft sensor. However, the multiphase issue of batch processes are not considered for the conventional JITL-LSTM soft sensor. In this paper, a multiphase Mahalanobis distance based JITL framework is developed to integrate the phase recognition strategy into the similarity measurement and data selection scheme, by which an extra step of phase identification can be avoided and the accuracy of JITL can be significantly improved. Thus, batch samples from different operating phases can be recognized without an additional phase identification step. By the use of the Mahalanobis Distance based JITL-LSTM Soft Sensor, the probability of data mismatch can be significantly reduced so that the accuracy of quality prediction can be promoted. Two simulation cases are provided to verify the effectiveness of the proposed method consisting of a fed-batch reactor process and the penicillin fermentation process.

Development of Soft Sensor Based on Sequential Kernel Fuzzy Partitioning and Just-in-Time Relevance Vector Machine for Multiphase Batch Processes

Batch processes are important manufacturing approaches widely used in modern industry. During the manufacturing process, quality prediction is essential. Data-driven-based soft sensors have widely used for quality prediction because of the advantages of simple application and high flexibility. However, they do not perform well due to the characteristics of dynamic, nonlinear, and multiphases in batch processes. To address these issues, a soft sensor based on sequential kernel fuzzy partitioning (SKFP) and just-in-time relevance vector machine (JRVM), named SKFP-JRVM, is proposed in this work. First, an SKFP algorithm is proposed to divide batches into phases. In the SKFP algorithm, the inner and the sequential membership are constructed and compared to obtain highly accurate phase partitioning results. Meanwhile, a partitioning evaluation index is applied to automatically determine the optimal number of phases. Moreover, a soft sensor model based on the JRVM is built for each phase. The JRVM model not only considers the modeling samples of adjacent phases but also effectively addresses the problem of soft sensor modeling of process data with highly nonlinear and dynamic characteristics. The effectiveness of the SKFP-JRVM method is demonstrated on a numerical simulation and a penicillin fermentation process.

Robust switched predictive control for multi-phase batch processes with uncertainties and unknown disturbances

A robust switched predictive control method is designed to deal with the multi-phase batch processes with the inevitable uncertainties, time-varying delay and unknown disturbances. Firstly, the output tracking errors are augmented into the state variables and then the improved robust switched predictive control law is established using the new augmented state variables. To this end, the novel switched system is built to represent the different phases of multi-phase batch processes. Secondly, making full use of the robust predictive control theory, Lyapunov function theory, switched system theory, linear matrix inequality (LMI) theory and mode-dependent average dwell time method, the sufficient conditions in terms of LMI constraints are derived to ensure that the switching system is asymptotically controllable and stable. During the process of derivation, based on the traditional performance indicators, the H-infinite performance index is introduced, so that the system in different phases can still operate stably under the uncertainty and external interference. The average dwell time and the control law gain of each phase are thus calculated by solving these LMI constrains. Ultimately, the simulation results on the injection molding process show that the proposed method can make the controlled system run stably.

Enhanced high‐order information extraction for multiphase batch process fault monitoring

AbstractConventional independent component analysis (ICA) monitoring methods extract the feature information of process data by selecting more important independent components (ICs), which discard a small part of ICs that may contain useful information for faults, leading to unsatisfactory monitoring results. However, when the number of sampling points is greater than that of process variables, the ICA monitoring model does not work well. To address the aforementioned problems, a novel monitoring method, multiphase enhanced high‐order information extraction (MEHOIE), is proposed in this paper. The entire production process was first divided into several steady phases and transition phases by the affinity propagation (AP) phase partitioning method. The enhanced high‐order information extraction (EHOIE) model was then built in each phase for fault monitoring. Finally, the algorithm was applied in the penicillin simulation platform and industrial microbial pharmaceutical process. The flexibility and superiority of this algorithm were verified by comparing it with other conventional methods.

Phase partition and identification based on kernel entropy component analysis and multi-class support vector machines-fireworks algorithm for multi-phase batch process fault diagnosis

For the characteristics of nonlinear and multi-phase in the batch process, a self-adaptive multi-phase batch process fault diagnosis method is proposed in this paper. Firstly, kernel entropy component analysis (KECA) method is used to achieve multi-phase partition adaptively, which makes the process data mapped into the high-dimensional feature space and then constructs the core entropy and the angular structure similarity. Then a multi-phase KECA failure monitoring model is developed by using the angular structure similarity as the statistic, which is based on the partitioned phases and the effective failure features by the KECA feature extraction method. A multi-phase batch process fault diagnosis method, which applies the multi-class support vector machines (MSVM) and fireworks algorithm (FWA), is proposed to recognize each sub-phase fault diagnosis automatically. The effectiveness and advantages of the proposed multi-phase fault diagnosis method are illustrated with a case study on a fed-batch penicillin fermentation process.

A New Minimax Optimization Design of H∞ LQ Fault-Tolerant Tracking Control for Multi-Phase Batch Processes

For multi-phase batch processes with partial failure of the actuator and unknown disturbance, this paper proposes a minimax optimization design method for H ∞ linear quadratic fault-tolerant tracking control based on switching strategy. Firstly, a non-minimum state space model is constructed based on the input-output model given by the batch process, and then a discrete switched model consisting of state errors, tracking errors and new state variables containing tracking errors is constructed. In this model, the antidisturbances performance index function with terminal constraint is selected, and the controller and the external disturbances are obtained by using the optimization theory. Then, under the acquired control law, the switching signal is designed and the range of uncertainty caused by the fault is given to realize the robustness of the system. The advantage of this design is that the system is tracking fast and the tracking error is small. Finally, by taking the parameters such as speed and pressure in the process of injection molding as examples, and comparing with the traditional control methods, the method presented in this paper is proved to be effective.

Nonlinear Fault Detection Based on Fault-related Multiphase Principle Polynomial Analysis for Al Stack Etch Process

In integrated circuit manufacturing industry, etch process is a complex nonlinear batch process. Al stack etch is the penultimate layer of dry etch. Based on the specific steps of the recipe, it has the multiphase characteristic and the can exhibit significantly different behaviors over different phases. However, conventional fault detection methods cannot effectively monitor Al stack etch process due to nonlinear and multiphase characteristics. Moreover, they are usually modeled by normal process data. In Al stack etch process, fault process data can be obtained from the datalog of equipments. In order to utilize these data, a novel nonlinear fault detection method called fault-related multistage principal polynomial analysis (FMPPA) is proposed in this work. FMPPA is efficient to deal with nonlinearity of the multiphase batch process. Furthermore, it can make full use of fault data by decomposing original feature space into three subspaces. FMPPA is applied to monitoring the Al stack etch process. Simulation results demonstrate that FMPPA is superior to other methods.

Improved H-Infinity Hybrid Model Predictive Fault-Tolerant Control for Time-Delayed Batch Processes Against Disturbances

An H-infinity model predictive fault-tolerant control strategy is proposed for multi-phase batch processes with interval delay and actuator failures. First, state variables, state errors and output tracking errors are introduced to establish an extended-state-space switched system model. Then, based on this model, a predictive fault-tolerant control law is designed for tracking the set point by the output that satisfies the requirements of the optimal performance index under input and output constraints. The feasibility conditions for the solvability of the control law are presented in the form of linear matrix inequalities. In addition, the designed switching law is constructed, and the gain of the control law is obtained via the optimization algorithm. This design has several advantages: the output tracking is faster, the tracking performance is superior, and the trace is smoother at the switching time. Finally, through a comparison with traditional methods, the effectiveness and feasibility of this method are demonstrated via injection molding simulation.

Phase division and transition modeling based on the dominant phase identification for multiphase batch process quality prediction

Batch processes are carried out from one steady phase to another one, which may have multiphase and transitions. Modeling in transitions besides in the steady phases should also be taken into consideration for quality prediction. In this paper, a quality prediction strategy is proposed for multiphase batch processes. First, a new repeatability factor is introduced to divide batch process into different steady phases and transitions. Then, the different local cumulative models that considered the cumulative effect of process variables on quality are established for steady phases and transitions. Compared with the reported modeling methods in transitions, a novel just-in-time model can be established based on the dominant phase identification. The proposed method can not only consider the dynamic characteristic in the transition but also improve the accuracy and the efficiency of transitional models. Finally, online quality prediction is performed by accumulating the prediction results from different phases and transitions. The effectiveness of the proposed method is demonstrated by penicillin fermentation process.

Multiphase batch process monitoring based on higher‐order cumulant analysis

AbstractIn this paper, a two‐step phase partitioning strategy is proposed. Firstly, the number of phases is automatically determined according to the intra‐class and inter‐class similarity of feature space data, thus avoiding excessive manual intervention. Secondly, the phases are partitioned by step‐wise adding the kernel entropy extended load matrix (KEELM), avoiding the wrong division of phases caused by unstable state of working condition conversion. A process monitoring model based on multiway kernel entropy independent component analysis (MKEICA) is constructed in each sub‐phase to deal with complex batch processes with nonlinear and non‐Gaussian properties. A new statistics index based on the idea of high order cumulant analysis (HCA) is constructed in each sub‐phase for process monitoring. Compared with the traditional second‐order statistics, it can obtain high‐order statistical information. Finally, the proposed method is applied to the penicillin simulation platform process and compared with the traditional multiway kernel independent components analysis (MKICA) and HCA methods to verify the effectiveness of the method that is mentioned above.

Robust Hybrid Controller Design for Batch Processes with Time Delay and Its Application in Industrial Processes

A new design method of two-dimensional (2D) controller for multi-phase batch processes with time delay and disturbances is proposed to ensure the stability of the control system and realize efficient production in industry. The batch process is first converted to an equivalent but different dimensional 2D-FM switched system. Based on the 2D system framework, then sufficient conditions of a controller existence expressed by linear matrix inequalities (LMIs) that stabilizing system is given by means of the average dwell time method. Meanwhile, robust hybrid 2D controller design containing extended information is proposed and the minimum runtime lower bound of each sub-system is accurately calculated. The design advantages of the controller depend on the size of the time delay so it has a certain degree of robustness. At the same time, considering the exponential stability, the system can have a faster rate of convergence. In addition, the introduction of extended information has improved the control performance of the system to some extent. The acquisition of minimum time at different phases will promote certain production efficiency and thus reduce energy consumption. Finally, an injection process in industrial production process has been taken as an example to verify effectiveness of the proposed method.

Batch Process Modeling and Monitoring With Local Outlier Factor

Batch processes are commonly involved by a succession of working phases with implicit non-Gaussian behaviors. Besides, in most cases, batch-to-batch processes also show similar but yet not identical running trajectory variations. To deal with these issues, this paper introduces a systematic analysis flowchart based on local outlier factor (LOF) for monitoring multiphase batch processes. First, a step-wise phase dividing algorithm is proposed with LOF to conduct phase dividing for a better understanding of batch process. Afterward, we develop the multiphase LOF for similar batch data modeling and then fault detection. The fault isolation method is proposed, where variable contributions with LOFs are induced, also with the analysis of isolability. The developed method is validated on a numerical example and the fed-batch fermentation benchmark process, both of which are compared with the multiphase principal component analysis method. Results demonstrate the feasibility and superiority of the proposed method.

Slow-Feature-Analysis-Based Batch Process Monitoring With Comprehensive Interpretation of Operation Condition Deviation and Dynamic Anomaly

In order to provide more sensitive monitoring results, the time dynamics and steady-state operating conditions should be separately monitored by distinguishing time information from the steady-state counterpart. However, it is a more challenging task for batch processes because they vary from phase to phase presenting multiple steady states and complex dynamic characteristics. To address the above issue, a concurrent monitoring strategy of multiphase steady states and process dynamics is developed for batch processes in this paper. On one hand, multiple local models are constructed to identify a steady derivation from the normal operating condition for different phases. On the other hand, based on the recognition that the process dynamics can be considered to be irrelevant with the steady states, a global model is built to detect the dynamics anomalies by monitoring the time variations. Corresponding to alarms issued by different statistics, different operating statuses are indicated with meaningful physical interpretation and deep process understanding. To illustrate the feasibility and efficacy, the proposed algorithm is applied to the injection molding process, which is a typical multiphase batch process.

Data-Driven Dynamic Modeling and Online Monitoring for Multiphase and Multimode Batch Processes with Uneven Batch Durations

Batch processes are often characterized by piecewise linear dynamics due to varying operating conditions. Multiphase and multimode modeling of batch processes is a common technique that offers insi...

KECA Similarity-Based Monitoring and Diagnosis of Faults in Multi-Phase Batch Processes.

Multiple phases with phase to phase transitions are important characteristics of many batch processes. The linear characteristics between phases are taken into consideration in the traditional algorithms while nonlinearities are neglected, which can lead to inaccuracy and inefficiency in monitoring. The focus of this paper is nonlinear multi-phase batch processes. A similarity metric is defined based on kernel entropy component analysis (KECA). A KECA similarity-based method is proposed for phase division and fault monitoring. First, nonlinear characteristics can be extracted in feature space via performing KECA on each preprocessed time-slice data matrix. Then phase division is achieved with the similarity variation of the extracted feature information. Then, a series of KECA models and slide-KECA models are established for steady and transitions phases respectively, which can reflect the diversity of transitional characteristics objectively and preferably deal with the stage-transition monitoring problem in multistage batch processes. Next, in order to overcome the problem that the traditional contribution plot cannot be applied to the kernel mapping space, a nonlinear contribution plot diagnosis algorithm is proposed, which is easier, more intuitive and implementable compared with the traditional one. Finally, simulations are performed on penicillin fermentation and industrial application. Specifically, the proposed method detects the abnormal agitation power and the abnormal substrate supply at 47 h and 86 h, respectively. Compared with traditional methods, it has better real-time performance and higher efficiency. Results demonstrate the ability of the proposed method to detect faults accurately and effectively in practice.

Incipient Fault Detection for Multiphase Batch Processes With Limited Batches

Sufficient batches are in general, required for fault detection of batch processes. However, sometimes, it is difficult and may be impractical to conduct multiple cycles and wait until enough batches are available. Without batch-wise normalization step, the nonstationary cannot be efficiently removed by time-wise normalization. The mean values of the nonstationary variables are still time varying and the interval of fault-free data is very wide in each phase. Therefore, the incipient fault, which has a small magnitude including early changing and the slow developing, may be buried by nonstationary trends resulting in low fault detection rate. To address the above issue, a two-layer fault detection method is proposed to detect the incipient fault for multiphase batch processes with limited batches. First, a concurrent variable separation strategy is proposed to distinguish nonstationary variables from stationary variables for multiple batches in each phase. Second, a two-layer fault detection model is constructed to detect the incipient fault. Cointegration analysis-based fault detection model is built to investigate the relationship between nonstationary variables, which can effectively distinguish the incipient fault from the normal trend of the nonstationary variables. Principal component analysis is adopted to describe the correlation of stationary variables. Afterward, a total fault detection model is constructed to monitor the relation between nonstationary variables and stationary variables. To illustrate the feasibility and effectiveness, the proposed algorithm is applied to two multiphase batch processes including fed-batch penicillin fermentation process and semiconductor etch process.

Between-Phase Nonlinear Correlation Analysis-Based Modeling and Online Monitoring for Multiphase Batch Process With Transitions

In order to provide better monitoring performance, between-phase nonlinear correlations and differences should be considered and separately monitored in multiphase batch processes. However, it is a more challenging task for batch processes to extract the nonlinear correlation information because the large-size samples may bring the computational complexity and high-dimensional kernel instability. To address the above issue, a feature vector selection with kernel vector correlation analysis (FVS-KVCA) method is developed for batch processes. In this paper, a novel two-level phase division method is firstly proposed to divide batch processes into the steady phases and the transitions. Then, the local phase models are constructed based on the FVS-KVCA method to separate process information into the common information and the specific information, which represent the nonlinear correlation between two neighboring phases and within only one phase, respectively. Based on such an information separation, the transition can be further divided into the transitional phases and the mixing phases by the second-level division. Also, a dynamic transition modeling method is introduced to solve the transition monitoring problem. Finally, online process monitoring can be conducted based on the defined score features to select the right model. The proposed algorithm is applied to the penicillin fermentation process to illustrate the effectiveness and feasibility.

Design of Optimal Hybrid Controller for Multi-Phase Batch Processes With Interval Time Varying Delay

Concerning two dimensional (2D) multi-phase batch processes, a delay-range-dependent optimal hybrid iterative learning control (2D-OILC) scheme is presented. Firstly, the process is converted into a 2D-FM time delay switched system in different dimensions by introduction of state errors and system output tracking errors among batches. According to this model, hybrid iterative learning control is combined with feedback control and a 2D optimal hybrid controller is designed. Secondly, the average dwell time method is adopted to give sufficient conditions for system robust stability in terms of linear matrix inequalities and the upper bound for system's optimal performance index is provided. Besides, the issue of optimal controller design is presented to draw the minimum upper limit of the closed-loop system performance index. The presented control law not only can make the closed-loop system preserving good tracking performance but also ensures its $H_{\infty }$ performance. Last but not least, the validity of the above strategies is proved by the simulation on an injection molding process.

Robust Predictive Fault-Tolerant Control for Multi-Phase Batch Processes With Interval Time-Varying Delay

In view of multi-phase batch processes with interval time-varying delay, uncertainties, unknown disturbances, partial actuator failures and input and output constrains in real-world industrial production, a robust predictive fault-tolerant control (RPFTC) method is proposed in this paper. First, a multi-phase batch process considering the above process dynamics is described by a switching model that consists of different dimensional sub-systems. Then the switching model is transformed into the extended switching state space model by the introduction of output tracking error. On basis of this extended model, a robust predictive fault-tolerant control law is designed to improve the control performance and to obtain more degrees of freedom of the adjustment for the controller. Second, by the utilization of Lyapunov function theory, switching system theory and average dwell time approach, the sufficient conditions in terms of linear matrix inequality (LMI) constraints and minimum running time at each phase are given to make the corresponding discrete-time switching closed-loop system robustly exponential stable and the running time of each phase shortest. At the same time, the optimal cost function and H-infinity performance index are considered in the derivation of stable conditions, which can obtain the optimized control performance and suppress the unknown disturbances. Finally, the gain of the control law and the minimum running time of each phase are calculated by solving these LMIs. Taking the injection molding process as a simulation object, the control results verify the effectiveness and feasibility of the proposal.