{"title":"Interpretable Dynamic Modelling and Prediction of Free Acid in Zinc Leaching Process","authors":"Jainish Nareshkumar Rajput , Vamsi Krishna Puli , Graham Slot , Biao Huang","doi":"10.1016/j.jprocont.2025.103407","DOIUrl":"10.1016/j.jprocont.2025.103407","url":null,"abstract":"<div><div>In the metallurgical processing industry, the leaching process converts a concentrated slurry of zinc sulphide to zinc sulphate solution. The leaching process occurs within a multi-compartment autoclave in the presence of sulphuric acid and oxygen at high temperatures and pressure. The amount of unreacted acid (free acid) within each autoclave compartment is crucial for achieving high zinc recovery but is not directly measured, necessitating an efficient model. This work involves developing a dynamic model utilizing both the first principles and machine learning techniques to predict the free acid, making the model physically interpretable. Due to the dependency of free acid on upstream process variables, several sub-models were built for each preceding unit. The main challenge was the unavailability of several measurements required for the mass balance model, while some available measurements were sampled at a slower rate. Moreover, bias correction was performed, considering delays in receiving laboratory analysis results and the lack of exact timestamps for samples provided by the field operator. The proposed model is validated with integrated zinc and lead smelter process data. The model successfully predicts free acid at a fast rate despite several practical constraints. It performs well under various process conditions, detects abnormalities, and enhances stability in the leaching process.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"149 ","pages":"Article 103407"},"PeriodicalIF":3.3,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marcus Vinicius de Paula , Rodrigo Augusto Ricco , Bruno Otávio Soares Teixeira
{"title":"Subspace identification of Hammerstein models with interval uncertainties","authors":"Marcus Vinicius de Paula , Rodrigo Augusto Ricco , Bruno Otávio Soares Teixeira","doi":"10.1016/j.jprocont.2025.103412","DOIUrl":"10.1016/j.jprocont.2025.103412","url":null,"abstract":"<div><div>This work presents a novel method for identifying uncertain Hammerstein models in the state-space. The uncertainties of both the nonlinear static and linear dynamic blocks are represented by intervals. The limits of the model’s uncertain parameters are estimated by solving a nonlinear optimization problem, generated from the combination of subspace identification methods with interval arithmetic techniques. Unlike methodologies based on orthonormal functions, the proposed method does not require prior knowledge of the system dynamics. Additionally, the proposed methodology reduces the number of optimization problems and constraints needed to estimate the model parameters, compared to the technique that uses orthonormal functions. Simulated and experimental results illustrate the accuracy and precision of the estimates obtained by the proposed method.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"149 ","pages":"Article 103412"},"PeriodicalIF":3.3,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Adaptive design of delay timers for non-stationary process variables based on change detection and Bayesian estimation","authors":"Shuo Shi, Jiandong Wang","doi":"10.1016/j.jprocont.2025.103410","DOIUrl":"10.1016/j.jprocont.2025.103410","url":null,"abstract":"<div><div>In industrial alarm systems, delay timers are embedded modules to deal with nuisance alarms. However, most existing approaches for the design of delay timers make an assumption that process variables are stationary distributed, so that designed delay timers may not achieve the desired performance on false alarm rates (FAR) and missed alarm rates (MAR) for non-stationary process variables. Motivated by such a problem, this paper proposes an adaptive approach that updates delay timer parameters to control the number of nuisance alarms. Two main technical issues are addressed. For the first issue of whether delay timer parameters need to be updated, three cases of updating delay timer parameters are formulated according to the changes in alarm durations or intervals and the conditions of process variables. For the second issue of determining time instants to update delay timer parameters, the Bayesian estimation technique is exploited based on confidence intervals of FAR or MAR to be achieved. The proposed approach is illustrated by industrial and numerical examples, showing its necessity via a comparison with conventional delay timers whose parameters are fixed.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"149 ","pages":"Article 103410"},"PeriodicalIF":3.3,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Min Ji , Hai sheng Deng , Weiming Zhang , Hasan Rastgoo
{"title":"Mixed logical dynamical (MLD)-based Kalman filter for hybrid systems fault diagnosis","authors":"Min Ji , Hai sheng Deng , Weiming Zhang , Hasan Rastgoo","doi":"10.1016/j.jprocont.2025.103411","DOIUrl":"10.1016/j.jprocont.2025.103411","url":null,"abstract":"<div><div>The Mixed Logical Dynamical (MLD) model framework is used in this paper to develop a novel algorithm for state estimation and fault diagnosis in hybrid systems. These systems, with both continuous and discrete dynamics, present challenges for accurate state estimation and timely fault detection. The proposed method integrates the constrained Kalman filter, MLD modeling, and mixed integer programming for robust state monitoring and fault diagnosis. It leverages the MLD model to represent system dynamics while handling discrete and continuous states, offering a flexible framework for hybrid system analysis. The constrained Kalman filter estimates the system state in real time, ensuring the estimation stays within constraints that reflect physical or operational limits. This enhances robustness, especially in noisy environments. Mixed integer programming efficiently manages discrete events and logical decisions, capturing the hybrid system's nature. The technique, called the Hybrid Kalman Filter (HKF), combines Kalman filtering with MLD models to detect and isolate sensor faults. A bank of HKFs monitors specific sensors or subsystems for precise fault isolation. When a fault occurs, the corresponding HKF detects it, providing critical information about its location and nature. The proposed method is tested on hybrid systems, both simulated and real-world, demonstrating its effectiveness in estimating system states and detecting sensor faults, even in complex environments. The results show its potential to improve hybrid system reliability and performance in industries such as automotive, aerospace, and industrial automation.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"148 ","pages":"Article 103411"},"PeriodicalIF":3.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jiayi Zhang , Xiang Liu , Yan Wang , Shenglin Zhang , Tuanjie Wang , Zhicheng Ji
{"title":"A novel explainable propagation-based fault diagnosis approach for Clean-In-Place by establishing Boolean network model","authors":"Jiayi Zhang , Xiang Liu , Yan Wang , Shenglin Zhang , Tuanjie Wang , Zhicheng Ji","doi":"10.1016/j.jprocont.2025.103405","DOIUrl":"10.1016/j.jprocont.2025.103405","url":null,"abstract":"<div><div>Industrial processes usually exhibit the strong logical relationships between different components, which can be accomplished and exhibited by Boolean functions. On this foundation, we develop an approach based on Boolean network (BN) to achieve fault diagnosis for binary industrial processes by applying the semi-tensor product (STP). At first, Boolean control network model for the binary industrial process and the corresponding fault propagation BN model are established. A fault propagation observer is introduced to select out the component nodes from the fault propagation BN and obtain the fault propagation path. Based on this, the definition of fault diagnosability is given, and a novel fault diagnosis approach is proposed to trace the fault source and predict the final state of fault propagation. After that, a novel metric based on the logical complexity of fault propagation is introduced to evaluate the explainability of proposed fault diagnosis approach. Finally, the proposed approach is applied in traditional Chinese medicine concentration tank Clean-In-Place to demonstrate its effectiveness and explainability.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"148 ","pages":"Article 103405"},"PeriodicalIF":3.3,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Real-time chlorate by-product monitoring through hybrid estimation methods","authors":"E.A. Ross , R.M. Wagterveld , M.J.J. Mayer , J.D. Stigter , K.J. Keesman","doi":"10.1016/j.jprocont.2025.103404","DOIUrl":"10.1016/j.jprocont.2025.103404","url":null,"abstract":"<div><div>Since the strict regulations regarding chlorate concentrations in drinking water and in food, there exists a need to monitor this by-product stemming from electrochlorination. Since, currently, there are no chlorate-specific sensors, Sensor Data Fusion is proposed as an alternative.</div><div>The objective of this paper is to investigate and design Sensor Data Fusion algorithms that are accurate over a broader set of circumstances.</div><div>Two different estimators are explored, both of which combine a first-principles model with a machine learning algorithm. The first-principles models are based on a nonlinear, reduced-order state-space model. The data-driven models investigated were multiple linear regression, K nearest neighbors, a gradient-boosting decision tree and support vector regression, with optimized hyperparameters and a two-stage validation process.</div><div>It was found that the addition of a first-principles model reduced the cross-validation mean squared error by 58%, and allows accurate scaling with the fluid flow rate, when used in combination with support vector regression. Furthermore, a relatively simple hybrid approach, with state-space and data-driven models in series, was sufficient in terms of accuracy, when compared to a more complex series–parallel hybrid version. The latter does provide information regarding the free chlorine concentration and current efficiencies in real-time, as well as an estimate of the uncertainties associated with the process states. The 1 <span><math><mi>σ</mi></math></span> confidence interval converged to 14% of the chlorate estimate.</div><div>The results indicate that a hybrid approach is viable in the design of a Sensor Data Fusion algorithm for chlorate monitoring, and preferable over a purely data-driven approach.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"148 ","pages":"Article 103404"},"PeriodicalIF":3.3,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ensemble Quality-Aware Slow Feature Analysis for decentralized dynamic process monitoring","authors":"Yuanhui Ni , Chao Jiang","doi":"10.1016/j.jprocont.2025.103400","DOIUrl":"10.1016/j.jprocont.2025.103400","url":null,"abstract":"<div><div>Slow Feature Analysis (SFA) has gained prominence in process monitoring due to its capability to capture inertial features in industrial systems. However, traditional SFA methods are predominantly unsupervised and often neglect output quality, limiting their effectiveness in large-scale, complex systems. To address these limitations, this paper introduces the Ensemble Quality-Aware Slow Feature Analysis (EQASFA) framework, which maximizes the correlation between quality variables and slow features. This decentralized monitoring framework generates fine-grained submodels by: (i) constructing a diverse set of submodels through different variable combinations, and (ii) selecting base submodels with the lowest false alarm rate on the validation dataset. The selection process utilizes a divisive hierarchical clustering algorithm, where probabilistic similarity is quantified using symmetric Kullback–Leibler divergence. In addition, novel static and dynamic metrics, derived from Bayesian inference, are proposed to distinguish routine operational fluctuations from significant anomalies. The performance of the EQASFA framework is validated through two benchmark case studies: the Tennessee Eastman process and a wastewater treatment process.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"148 ","pages":"Article 103400"},"PeriodicalIF":3.3,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiaoxia Chen, Yifeng Hu, Chengshuo Liu, Ao Chen, Zhengwei Chi
{"title":"Dynamic spatio-temporal graph network based on multi-level feature interaction for sinter TFe prediction","authors":"Xiaoxia Chen, Yifeng Hu, Chengshuo Liu, Ao Chen, Zhengwei Chi","doi":"10.1016/j.jprocont.2025.103401","DOIUrl":"10.1016/j.jprocont.2025.103401","url":null,"abstract":"<div><div>Sinter ore is one of the primary raw materials for blast furnace ironmaking, and the iron grade (TFe) is a crucial indicator for assessing the quality of sinter ore, as its concentration directly impacts the yield and quality of blast furnace production. The iron ore sintering is a complex industrial process characterized by inconsistent sampling frequency, variable time delays, and intricate spatio-temporal dependencies, making the prediction of TFe content particularly challenging. Previous research has often focused on extracting global features from the sintering process as a whole, neglecting the interactions between subprocess features and the integration of subprocess features with global features. To address these challenges, this paper proposes a dynamic spatio-temporal graph network for TFe prediction in sinter ore based on multi-level feature interactions (MLDSTGN). First, to effectively utilize high-frequency sampling data while accounting for variable time delays in the sintering process, a time delay feature reconstruction (TDFR) method is designed. This method serializes and extends the data through a delay window, facilitating alignment with low-frequency sampling data. Second, adaptive graph construction (AGC) employs an attention mechanism to learn the underlying spatial dependencies. This module constructs a global graph representing overall dependencies in the sintering process and a local graph for the dependencies within subprocesses. The proposed spatio-temporal graph learning (STGL) module captures long- and short-term temporal features at different levels, and the spatial information aggregation layer further extracts deep spatial features that encompass the synergistic effects among variables. Additionally, multi-level dynamic interactive learning (MDIL) is introduced to enhance information transfer between global and local features. Finally, simulation results based on actual operational data demonstrate that the proposed model outperforms all baseline methods in multi-step TFe prediction, with a reduction of at least 4.86% in MAE and at least 13.27% in RMSE.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"148 ","pages":"Article 103401"},"PeriodicalIF":3.3,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Design and repetitive control of a self-cycling ethanol fermentation bioreactor for ethanol production","authors":"Sichen Wu, Shilin Chen, Chi Zhai","doi":"10.1016/j.jprocont.2025.103403","DOIUrl":"10.1016/j.jprocont.2025.103403","url":null,"abstract":"<div><div>With breakthrough of cellulose pretreatment and enzyme hydrolysis technology, the fermentation process itself has become the main limiting factor for bio-ethanol manufacturing. Self-cycling fermentation (SCF) is an advanced configuration that could improve cell metabolic intensity, increase productivity and downsize substrate run-away. However, the modeling and monitoring techniques are in short that might hamper the realization of the SCF apparatus in industrial scale. In this work, a rigorous ethanol fermentation model considering the respiration effect of yeast <em>S. cerevisiae</em> is established; then, superiority and stability criterions under periodic load variations are developed for the SCF configuration; afterwards, repetitive control is proposed to stabilize the state trajectories related to SCF, the control laws include adaptive adjustment mechanisms for uncertainties of the input, nonlinear estimation of the unknown influential concentration through higher order sliding mode observer, and state observers and parameter estimators used to estimate the unknown states and kinetics. Since the temperature is an important factor for an efficient operation of the process, a split ranging control framework is also developed. As a conclusion, SCF demonstrates as a potential configuration when improvements in substrate conversion and productivity is pursued, but difficulty on proper monitoring of the triggering signals (for discharge-and-refill) might hamper its application, and the proposed feedback loops could be a solution to realize SCF under various scenarios.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"148 ","pages":"Article 103403"},"PeriodicalIF":3.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hongfeng Tao , Yuan Huang , Tao Liu , Wojciech Paszke
{"title":"Reinforcement learning based iterative learning control for nonlinear batch process with non-repetitive uncertainty via Koopman operator","authors":"Hongfeng Tao , Yuan Huang , Tao Liu , Wojciech Paszke","doi":"10.1016/j.jprocont.2025.103402","DOIUrl":"10.1016/j.jprocont.2025.103402","url":null,"abstract":"<div><div>To tackle the time and batchwise uncertainty often involved in nonlinear batch process, this paper proposes a deep reinforcement learning (DRL) based ILC scheme via Koopman operator. Using the Koopman operator, the original nonlinear system is reformulated into a high-dimensional linear space form. Then, a DRL agent with neural network is introduced into the 2D ILC framework to compensate for non-repetitive uncertainty. Correspondingly, a synthetic 2D ILC-DRL scheme is designed to improve the system tracking performance against time and batchwise uncertainty. Meanwhile, the convergence conditions of the proposed ILC scheme are analyzed with a proof through the linear matrix inequality. An illustrative example of continuous stirring tank reactor (CSTR) demonstrates that the established high-dimensional linear model can ensure good accuracy compared to the original nonlinear process model, with an output error of smaller than 5%. Moreover, the tracking error is significantly reduced over 90% by the reinforcement learning based ILC in comparison with the recently developed dynamic iterative linearization and PD-type ILC methods.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"148 ","pages":"Article 103402"},"PeriodicalIF":3.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}