Pub Date : 2026-04-01Epub Date: 2026-02-14DOI: 10.1016/j.jprocont.2026.103656
Yan Wang , Hao-Yuan Sun , Hong-Gui Han
Designing effective control strategies for wastewater treatment processes (WWTPs) is complicated by external disturbances and internal uncertainties, especially under the rigorous input and state constraints imposed by strict effluent standards and equipment limitations. To address this challenge, a data-driven soft constrained model predictive control (SCMPC) strategy with disturbance rejection is proposed. Firstly, a fuzzy neural network-based data-driven disturbance observer is constructed to quantify the lumped disturbances, which are then decomposed into the matched and unmatched disturbances. Furthermore, a composite control strategy is designed, in which the compensation controller neutralizes the matched disturbance directly, while the SCMPC strategy suppresses the unmatched disturbance by balancing constraint satisfaction with tracking performance. The feasibility and stability of the closed-loop system are proven theoretically. Finally, simulations on the Benchmark Simulation Model No. 1 (BSM1) demonstrate that the proposed approach can achieve superior tracking precision and robustness compared with existing methods.
由于外部干扰和内部不确定性，设计有效的污水处理过程控制策略非常复杂，特别是在严格的排放标准和设备限制所施加的严格输入和状态约束下。为了解决这一问题，提出了一种数据驱动的干扰抑制软约束模型预测控制策略。首先，构建基于模糊神经网络的数据驱动扰动观测器对集总扰动进行量化，然后将集总扰动分解为匹配扰动和不匹配扰动；在此基础上，设计了一种复合控制策略，补偿控制器直接中和匹配的干扰，而SCMPC策略通过平衡约束满足和跟踪性能来抑制不匹配的干扰。从理论上证明了闭环系统的可行性和稳定性。最后，在BSM1基准仿真模型（Benchmark Simulation Model No. 1, BSM1）上进行了仿真，结果表明，与现有方法相比，该方法具有更好的跟踪精度和鲁棒性。
{"title":"Data-driven soft constrained model predictive control with disturbance rejection for wastewater treatment processes","authors":"Yan Wang , Hao-Yuan Sun , Hong-Gui Han","doi":"10.1016/j.jprocont.2026.103656","DOIUrl":"10.1016/j.jprocont.2026.103656","url":null,"abstract":"<div><div>Designing effective control strategies for wastewater treatment processes (WWTPs) is complicated by external disturbances and internal uncertainties, especially under the rigorous input and state constraints imposed by strict effluent standards and equipment limitations. To address this challenge, a data-driven soft constrained model predictive control (SCMPC) strategy with disturbance rejection is proposed. Firstly, a fuzzy neural network-based data-driven disturbance observer is constructed to quantify the lumped disturbances, which are then decomposed into the matched and unmatched disturbances. Furthermore, a composite control strategy is designed, in which the compensation controller neutralizes the matched disturbance directly, while the SCMPC strategy suppresses the unmatched disturbance by balancing constraint satisfaction with tracking performance. The feasibility and stability of the closed-loop system are proven theoretically. Finally, simulations on the Benchmark Simulation Model No. 1 (BSM1) demonstrate that the proposed approach can achieve superior tracking precision and robustness compared with existing methods.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"160 ","pages":"Article 103656"},"PeriodicalIF":3.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192931","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}
Pub Date : 2026-04-01Epub Date: 2026-02-12DOI: 10.1016/j.jprocont.2026.103660
Shuo Tong , Han Liu , Runyuan Guo , Lin Zhang , Wenqing Wang , Ding Liu , Youmin Zhang
Data-driven soft sensors are widely used for estimating key quality variables in industrial processes. However, most existing models are task-specific and lack generalization, limiting their applicability in complex multi-task scenarios. Moreover, constraints on model and input capacity often lead to insufficient representational ability and degraded performance under sample-scarce settings. To address these, in this paper, a three-stage massively pretrained soft sensor (MPSS) is proposed for general industrial applications. Specifically, a spatial–temporal decoupled self-supervised learning framework and two distinct masked reconstruction strategies for representation learning are introduced for pretraining, aiming to acquire universal temporal dependency and spatial-variable coupling representations. To enhance model capacity and adaptivity to heterogeneous temporal-variable patterns, two sparsely structured routing modules—dual-branch temporal-aware routing (DTAR) and adaptive channel-aware routing (ACAR) are proposed, achieving adaptive allocation and specialized processing of heterogeneous inputs. Additionally, a prefix-enhanced time series embedding strategy is proposed, which encodes key statistical information as learnable conditional prefixes, increasing input information density and strengthening generalization. For downstream tasks, MPSS freezes pretrained parameters and integrates lightweight, task-specific adapters via parameter-efficient fine-tuning (PEFT), enabling plug-and-play adaptation across diverse soft sensing tasks. Experiments on four datasets demonstrate MPSS’s strong generality, transferability, and state-of-the-art (SOTA) performance under both full-data and few-shot settings.
{"title":"MPSS: A spatiotemporal-decoupled massively pretrained soft sensor for general industrial scenarios with heterogeneous data robustness","authors":"Shuo Tong , Han Liu , Runyuan Guo , Lin Zhang , Wenqing Wang , Ding Liu , Youmin Zhang","doi":"10.1016/j.jprocont.2026.103660","DOIUrl":"10.1016/j.jprocont.2026.103660","url":null,"abstract":"<div><div>Data-driven soft sensors are widely used for estimating key quality variables in industrial processes. However, most existing models are task-specific and lack generalization, limiting their applicability in complex multi-task scenarios. Moreover, constraints on model and input capacity often lead to insufficient representational ability and degraded performance under sample-scarce settings. To address these, in this paper, a three-stage massively pretrained soft sensor (MPSS) is proposed for general industrial applications. Specifically, a spatial–temporal decoupled self-supervised learning framework and two distinct masked reconstruction strategies for representation learning are introduced for pretraining, aiming to acquire universal temporal dependency and spatial-variable coupling representations. To enhance model capacity and adaptivity to heterogeneous temporal-variable patterns, two sparsely structured routing modules—dual-branch temporal-aware routing (DTAR) and adaptive channel-aware routing (ACAR) are proposed, achieving adaptive allocation and specialized processing of heterogeneous inputs. Additionally, a prefix-enhanced time series embedding strategy is proposed, which encodes key statistical information as learnable conditional prefixes, increasing input information density and strengthening generalization. For downstream tasks, MPSS freezes pretrained parameters and integrates lightweight, task-specific adapters via parameter-efficient fine-tuning (PEFT), enabling plug-and-play adaptation across diverse soft sensing tasks. Experiments on four datasets demonstrate MPSS’s strong generality, transferability, and state-of-the-art (SOTA) performance under both full-data and few-shot settings.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"160 ","pages":"Article 103660"},"PeriodicalIF":3.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146154231","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}
In this paper, a novel causal inference model, called temporal supervised generative adversarial functional causal model (TSGA-FCM), is established for root cause diagnosis of industrial processes. First, a causal generation module (CGM) for multivariate time-series data is developed to infer causal relationships through a functional causal mechanism loss. Moreover, a temporal supervised generative adversarial network is established for joint training of the CGM. The parameters of the CGM are optimized via a combination of functional causal mechanism loss, reconstruction loss, and temporal supervised loss. The capability in temporal feature extraction is enhanced by reducing temporal distribution feature differences between generated data and original data. Using both the extracted static and temporal features, a directed acyclic causality graph is derived to pinpoint the root cause. Finally, a benchmark process and a real industrial process are utilized to validate the effectiveness of the proposed TSGA-FCM. Using the temporal supervised generative adversarial network, the proposed TSGA-FCM effectively extracts temporal feature-based causal inference to avoid unnecessary symmetry assumption of the traditional autoregressive-based root cause diagnosis (RCD) methods. The proposed method makes novel contributions to data-driven causal inference and demonstrates practical application value in an important heavy-plate rolling process.
{"title":"Temporal supervised generative adversarial functional causal model for root cause diagnosis","authors":"Qiang Liu, Fengnian Zhao, Chao Yang, Jinliang Ding","doi":"10.1016/j.jprocont.2026.103652","DOIUrl":"10.1016/j.jprocont.2026.103652","url":null,"abstract":"<div><div>In this paper, a novel causal inference model, called temporal supervised generative adversarial functional causal model (TSGA-FCM), is established for root cause diagnosis of industrial processes. First, a causal generation module (CGM) for multivariate time-series data is developed to infer causal relationships through a functional causal mechanism loss. Moreover, a temporal supervised generative adversarial network is established for joint training of the CGM. The parameters of the CGM are optimized via a combination of functional causal mechanism loss, reconstruction loss, and temporal supervised loss. The capability in temporal feature extraction is enhanced by reducing temporal distribution feature differences between generated data and original data. Using both the extracted static and temporal features, a directed acyclic causality graph is derived to pinpoint the root cause. Finally, a benchmark process and a real industrial process are utilized to validate the effectiveness of the proposed TSGA-FCM. Using the temporal supervised generative adversarial network, the proposed TSGA-FCM effectively extracts temporal feature-based causal inference to avoid unnecessary symmetry assumption of the traditional autoregressive-based root cause diagnosis (RCD) methods. The proposed method makes novel contributions to data-driven causal inference and demonstrates practical application value in an important heavy-plate rolling process.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103652"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190710","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}
Pub Date : 2026-03-01Epub Date: 2026-01-29DOI: 10.1016/j.jprocont.2026.103631
Fernando Aarón Ortiz-Ricárdez , Karla María Muñoz-Páez , Alejandro Vargas
To upgrade biogas to biomethane, a mathematical model approach for a hydrogenotrophic methanation process is formulated in a biotrickling filter (BTF) reactor. The model partitions the trickling bed (TB) space in arbitrary levels of possibly different volumes and uses the first Fickian diffusion law along the vertical axis and through the biofilm layer attached to the inert bed material. To calculate gas flows among TB levels, the model is subject to the ideal gas law and to the partial pressures Dalton’s law, assuming a fixed amount of gaseous moles in each TB level. In addition to the available control variables, such as the liquid recirculation rate and the gaseous inflow rate, the gaseous effluent recirculation rate is tested as a new control variable for the model. The simulations performed of the model accurately describe experimental results of an ex-situ hydrogenotrophic methanation in a BTF. Finally, an optimal steady-state operation study for BTFs with certain physicochemical parameters is provided for any TB reactor size, and other operational improvements for the model, such as additional gaseous influent injections along the TB, are outlined.
{"title":"Mathematical model for optimal operation of an ex-situ hydrogenotrophic methanation bio-trickling filter reactor","authors":"Fernando Aarón Ortiz-Ricárdez , Karla María Muñoz-Páez , Alejandro Vargas","doi":"10.1016/j.jprocont.2026.103631","DOIUrl":"10.1016/j.jprocont.2026.103631","url":null,"abstract":"<div><div>To upgrade biogas to biomethane, a mathematical model approach for a hydrogenotrophic methanation process is formulated in a biotrickling filter (BTF) reactor. The model partitions the trickling bed (TB) space in arbitrary levels of possibly different volumes and uses the first Fickian diffusion law along the vertical axis and through the biofilm layer attached to the inert bed material. To calculate gas flows among TB levels, the model is subject to the ideal gas law and to the partial pressures Dalton’s law, assuming a fixed amount of gaseous moles in each TB level. In addition to the available control variables, such as the liquid recirculation rate and the gaseous inflow rate, the gaseous effluent recirculation rate is tested as a new control variable for the model. The simulations performed of the model accurately describe experimental results of an ex-situ hydrogenotrophic methanation in a BTF. Finally, an optimal steady-state operation study for BTFs with certain physicochemical parameters is provided for any TB reactor size, and other operational improvements for the model, such as additional gaseous influent injections along the TB, are outlined.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103631"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090754","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}
Pub Date : 2026-03-01Epub Date: 2026-02-03DOI: 10.1016/j.jprocont.2026.103641
Lipe Carmel, Giacomo Sartori, Chinmay Patwardhan, Christopher Sørmo, Nadav Bar
Precise biomass control is critical in microbial fermentation processes, particularly under continuous and cascade production conditions where physiological stability is essential. This work presents an experimental implementation of a supervisory layer to a nonlinear model predictive control (NMPC) for real-time regulation of biomass in Corynebacterium glutamicum fermentations. Two NMPC strategies were developed: a single-inflow control (SIC) system that feeds a concentrated substrate and a multi-inflow control (MIC) system that also adds a sugar-free medium for dynamic dilution. An Extended Kalman Filter (EKF) was employed, providing real-time estimates of biomass, substrate, and CO concentrations to enhance predictive control accuracy. Using a proportional substrate setpoint cost-shaping layer, the controller successfully tracked three biomass setpoints ( and ) within a single fermentation run. Both NMPC strategies delivered tight setpoint tracking while sustaining exponential growth and preventing substrate limitation stress. MIC reduced overshoot by up to 78.0 % and the integral of absolute error by up to 41.1 % relative to SIC. These findings demonstrate the feasibility and effectiveness of NMPC for robust biomass regulation and provide a foundation for future applications in adaptive, multi-phase fermentation processes.
{"title":"Model predictive control with supervisory substrate targeting for multi-setpoint biomass control in continuous bioprocesses","authors":"Lipe Carmel, Giacomo Sartori, Chinmay Patwardhan, Christopher Sørmo, Nadav Bar","doi":"10.1016/j.jprocont.2026.103641","DOIUrl":"10.1016/j.jprocont.2026.103641","url":null,"abstract":"<div><div>Precise biomass control is critical in microbial fermentation processes, particularly under continuous and cascade production conditions where physiological stability is essential. This work presents an experimental implementation of a supervisory layer to a nonlinear model predictive control (NMPC) for real-time regulation of biomass in <em>Corynebacterium glutamicum</em> fermentations. Two NMPC strategies were developed: a single-inflow control (SIC) system that feeds a concentrated substrate and a multi-inflow control (MIC) system that also adds a sugar-free medium for dynamic dilution. An Extended Kalman Filter (EKF) was employed, providing real-time estimates of biomass, substrate, and CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> concentrations to enhance predictive control accuracy. Using a proportional substrate setpoint cost-shaping layer, the controller successfully tracked three biomass setpoints (<span><math><mrow><mn>7</mn><mo>.</mo><mn>0</mn><mo>,</mo><mn>13</mn><mo>.</mo><mn>0</mn><mo>,</mo></mrow></math></span> and <span><math><mrow><mn>15</mn><mo>.</mo><mn>7</mn><mspace></mspace><mi>g</mi><mspace></mspace><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>) within a single fermentation run. Both NMPC strategies delivered tight setpoint tracking while sustaining exponential growth and preventing substrate limitation stress. MIC reduced overshoot by up to 78.0 % and the integral of absolute error by up to 41.1 % relative to SIC. These findings demonstrate the feasibility and effectiveness of NMPC for robust biomass regulation and provide a foundation for future applications in adaptive, multi-phase fermentation processes.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103641"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190702","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}
Pub Date : 2026-03-01Epub Date: 2026-01-27DOI: 10.1016/j.jprocont.2026.103637
Piotr Tatjewski
Design of offset-free model predictive control (MPC) with parametric process models is concerned in the paper, in the presence of deterministic constant or asymptotically constant external and internal (modeling errors) disturbances. For linear state-space models, two established methods assuring offset-free control and relations between them are briefly recalled, including very recent results. It yields also a new result concerning disturbance estimation when full-state is measured. This is needed for presentation of the main result of the paper, but jointly, yields also a unified approach to the mentioned design problem, for linear parametric models (state-space models, difference equations models). The main new result of the paper is formulation of the augmented formula for unmeasured disturbance estimate assuring offset-free control in the GPC (generalized predictive control) algorithm. The new formula is parametrized, which gives possibility to tune dynamics of the estimate and influence substantively sensitivity to noise of the control system. It is essential, as the GPC algorithm in existing formulation is known to be sensitive to noise. Theoretical foundation of the proposed algorithm is given. Theoretical results are validated and illustrated by simulation results of a MIMO control system. In particular, it is shown that tuning the augmented disturbance estimate reduces sensitivity to noise of the GPC algorithm. Finally, formulae for new, augmented and parametrized unmeasured disturbance estimates in the MPC algorithms with nonlinear parametric models are proposed.
{"title":"Offset-free Model Predictive Control with parametric models: Augmented disturbance estimates with tunable dynamics and impact on noise sensitivity","authors":"Piotr Tatjewski","doi":"10.1016/j.jprocont.2026.103637","DOIUrl":"10.1016/j.jprocont.2026.103637","url":null,"abstract":"<div><div>Design of offset-free model predictive control (MPC) with parametric process models is concerned in the paper, in the presence of deterministic constant or asymptotically constant external and internal (modeling errors) disturbances. For linear state-space models, two established methods assuring offset-free control and relations between them are briefly recalled, including very recent results. It yields also a new result concerning disturbance estimation when full-state is measured. This is needed for presentation of the main result of the paper, but jointly, yields also a unified approach to the mentioned design problem, for linear parametric models (state-space models, difference equations models). The main new result of the paper is formulation of the augmented formula for unmeasured disturbance estimate assuring offset-free control in the GPC (generalized predictive control) algorithm. The new formula is parametrized, which gives possibility to tune dynamics of the estimate and influence substantively sensitivity to noise of the control system. It is essential, as the GPC algorithm in existing formulation is known to be sensitive to noise. Theoretical foundation of the proposed algorithm is given. Theoretical results are validated and illustrated by simulation results of a MIMO control system. In particular, it is shown that tuning the augmented disturbance estimate reduces sensitivity to noise of the GPC algorithm. Finally, formulae for new, augmented and parametrized unmeasured disturbance estimates in the MPC algorithms with nonlinear parametric models are proposed.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103637"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045296","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}
Pub Date : 2026-03-01Epub Date: 2026-01-27DOI: 10.1016/j.jprocont.2026.103638
Andrea Wu , Andres Cordoba-Pacheco , Senem Ozgen , Fredy Ruiz
Waste-to-energy plants have become a strategic resource to reduce the volume of non-recyclable solid waste in municipalities. Flue gas treatment is a key component in making these plants clean and sustainable. In particular, acid gas abatement is a fundamental process for complying with emission standards. However, developing models of the abatement process is challenging due to the complexity of the phenomena and reactions occurring inside the pollutant abatement system. In this work, a predictive control strategy is proposed to regulate the concentration of hydrogen chloride in the flue gas of a waste-to-energy plant by manipulating the reactant flow rate. Black-box models for simulation and prediction tasks are derived from experimental data from a real WtE plant in Italy. A learning strategy is proposed to update an autoregressive model of the process in real-time using Set Membership identification techniques, and a Model Predictive Controller is formulated to optimally manipulate the reactant feed rate, guaranteeing that emissions comply with regulatory constraints while minimizing the reactant dosage. The performance of the resulting control strategy is compared with a standard PI plus FeedForward controller, currently employed in this kind of process. The results show that the adaptive MPC improves the tracking performance, reducing the Mean Integrated Absolute Error by up to 57.1% and reactant consumption by 3%, while ensuring better compliance with emission regulations.
{"title":"Efficient learning-based predictive control for acid gas abatement in waste to energy processes","authors":"Andrea Wu , Andres Cordoba-Pacheco , Senem Ozgen , Fredy Ruiz","doi":"10.1016/j.jprocont.2026.103638","DOIUrl":"10.1016/j.jprocont.2026.103638","url":null,"abstract":"<div><div>Waste-to-energy plants have become a strategic resource to reduce the volume of non-recyclable solid waste in municipalities. Flue gas treatment is a key component in making these plants clean and sustainable. In particular, acid gas abatement is a fundamental process for complying with emission standards. However, developing models of the abatement process is challenging due to the complexity of the phenomena and reactions occurring inside the pollutant abatement system. In this work, a predictive control strategy is proposed to regulate the concentration of hydrogen chloride in the flue gas of a waste-to-energy plant by manipulating the reactant flow rate. Black-box models for simulation and prediction tasks are derived from experimental data from a real WtE plant in Italy. A learning strategy is proposed to update an autoregressive model of the process in real-time using Set Membership identification techniques, and a Model Predictive Controller is formulated to optimally manipulate the reactant feed rate, guaranteeing that emissions comply with regulatory constraints while minimizing the reactant dosage. The performance of the resulting control strategy is compared with a standard PI plus FeedForward controller, currently employed in this kind of process. The results show that the adaptive MPC improves the tracking performance, reducing the Mean Integrated Absolute Error by up to 57.1% and reactant consumption by 3%, while ensuring better compliance with emission regulations.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103638"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045294","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}
Pub Date : 2026-03-01Epub Date: 2026-02-08DOI: 10.1016/j.jprocont.2026.103654
Lifeng Cao , Gaowei Yan , Hang Liu , Suxia Ma , Guanjia Zhao , Zhongyuan Liu
Under deep peak-shaving conditions, the dynamic complexity and the lag and uncertainty inherent in real-time monitoring do indeed pose challenges to traditional NO prediction models. This paper proposes a physics-informed deep operator network with hypergraph regularization for NO concentration prediction. First, use hypergraph regularization dimensionality reduction, construct hyperedges through temporal neighborhoods, preserve the local structure and temporal correlation of the data after dimensionality reduction, and address redundancy and nonlinearity in high-dimensional data. Subsequently, a physics-informed deep operator network is employed to establish a multi-step ahead prediction model for NO concentration under a multi-scale coupling mechanism, simulating operator mapping relationships during temporal evolution processes. Additionally, the NO mechanism model is discretized using numerical methods, and a physics-informed regularization term is formulated to enforce compliance with mechanistic constraints. Experimental studies conducted on pulverized coal boilers and circulating fluidized bed boilers demonstrate that the proposed method improves the prediction accuracy of NO emission concentrations. Among them, at the SCR outlet under typical conditions, HR_PI_DeepONet achieves an RMSE of 2.6199, R of 0.9579, and MAE of 1.662, outperforming comparison models. This method effectively improves the generalization ability of the model.
{"title":"Physics-informed deep operator network with hypergraph regularization for NOx emission prediction","authors":"Lifeng Cao , Gaowei Yan , Hang Liu , Suxia Ma , Guanjia Zhao , Zhongyuan Liu","doi":"10.1016/j.jprocont.2026.103654","DOIUrl":"10.1016/j.jprocont.2026.103654","url":null,"abstract":"<div><div>Under deep peak-shaving conditions, the dynamic complexity and the lag and uncertainty inherent in real-time monitoring do indeed pose challenges to traditional NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> prediction models. This paper proposes a physics-informed deep operator network with hypergraph regularization for NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> concentration prediction. First, use hypergraph regularization dimensionality reduction, construct hyperedges through temporal neighborhoods, preserve the local structure and temporal correlation of the data after dimensionality reduction, and address redundancy and nonlinearity in high-dimensional data. Subsequently, a physics-informed deep operator network is employed to establish a multi-step ahead prediction model for NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> concentration under a multi-scale coupling mechanism, simulating operator mapping relationships during temporal evolution processes. Additionally, the NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> mechanism model is discretized using numerical methods, and a physics-informed regularization term is formulated to enforce compliance with mechanistic constraints. Experimental studies conducted on pulverized coal boilers and circulating fluidized bed boilers demonstrate that the proposed method improves the prediction accuracy of NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> emission concentrations. Among them, at the SCR outlet under typical conditions, HR_PI_DeepONet achieves an RMSE of 2.6199, R<span><math><msup><mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span> of 0.9579, and MAE of 1.662, outperforming comparison models. This method effectively improves the generalization ability of the model.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103654"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190700","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}
Pub Date : 2026-03-01Epub Date: 2026-01-30DOI: 10.1016/j.jprocont.2026.103640
Lisbel Bárzaga-Martell , Francisco Ibáñez , Angel L. Cedeño , Maria Coronel , Francisco Concha , Norelys Aguila-Camacho , José Ricardo Pérez-Correa
Accurate state estimation in nonlinear chemical reactors is essential for advanced monitoring and control, yet sensor limitations and model uncertainties pose significant challenges. This paper presents a novel multi-observer switching framework that operates four state estimators in parallel—Extended Luenberger Observer, Extended Kalman Filter, Unscented Kalman Filter, and Particle Filter—and dynamically selects the most reliable estimate at each sampling instant. The switching mechanism employs a composite cost function combining and norms of the output estimation error: the component captures sustained deviations while the component enables rapid response to transient peaks, together providing robust adaptation to changing operating conditions. The framework is validated on continuous stirred-tank reactor networks with up to three reactors in series, under partial global observability where only downstream concentrations and temperatures are measured. Monte Carlo simulations demonstrate that the switching observer achieves superior estimation accuracy compared to individual estimators while maintaining computational efficiency suitable for real-time implementation. Parametric robustness analyses confirm reliable performance under kinetic and thermal uncertainties. The proposed approach offers a scalable solution for state estimation in complex chemical processes, with potential applications in fault detection and model predictive control.
{"title":"Observer switching strategy for enhanced state estimation in CSTR networks","authors":"Lisbel Bárzaga-Martell , Francisco Ibáñez , Angel L. Cedeño , Maria Coronel , Francisco Concha , Norelys Aguila-Camacho , José Ricardo Pérez-Correa","doi":"10.1016/j.jprocont.2026.103640","DOIUrl":"10.1016/j.jprocont.2026.103640","url":null,"abstract":"<div><div>Accurate state estimation in nonlinear chemical reactors is essential for advanced monitoring and control, yet sensor limitations and model uncertainties pose significant challenges. This paper presents a novel multi-observer switching framework that operates four state estimators in parallel—Extended Luenberger Observer, Extended Kalman Filter, Unscented Kalman Filter, and Particle Filter—and dynamically selects the most reliable estimate at each sampling instant. The switching mechanism employs a composite cost function combining <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> norms of the output estimation error: the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> component captures sustained deviations while the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> component enables rapid response to transient peaks, together providing robust adaptation to changing operating conditions. The framework is validated on continuous stirred-tank reactor networks with up to three reactors in series, under partial global observability where only downstream concentrations and temperatures are measured. Monte Carlo simulations demonstrate that the switching observer achieves superior estimation accuracy compared to individual estimators while maintaining computational efficiency suitable for real-time implementation. Parametric robustness analyses confirm reliable performance under kinetic and thermal uncertainties. The proposed approach offers a scalable solution for state estimation in complex chemical processes, with potential applications in fault detection and model predictive control.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103640"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090449","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}
Pub Date : 2026-03-01Epub Date: 2026-01-27DOI: 10.1016/j.jprocont.2026.103639
Arthur Lepsien , Lucas Holtorf , Alexander Schaum
The paper addresses the problem estimating the cell-mass distribution density, glucose and lactate concentration, as well as of the total biomass concentration in lactic-acid fermentation. The estimate is based on the combination of a cell population balance model with the available measurements. The model shows a cascade structure of a nonlinear finite-dimensional subsystem and a linear infinite-dimensional subsystem. The measurements are available on different time scales. On a quasi-continuous time scale optical density and conductivity are measured. The cell-size distribution is measured with a considerably lower frequency and is furthermore subject to non-uniform delays. The proposed estimation strategy exploits the cascade structure and consists of two cascaded discrete-time extended Kalman filters (EKFs). The performance of the proposed approach is demonstrated using experimental data from batch experiments with Streptococcus thermophilus. The estimation strategy improves the mean normalized root mean squared error of the distribution by approximately 41.6 % compared to a pure simulation.
{"title":"Observer design for lactic-acid bacteria population balances with non-uniformly delayed measurements","authors":"Arthur Lepsien , Lucas Holtorf , Alexander Schaum","doi":"10.1016/j.jprocont.2026.103639","DOIUrl":"10.1016/j.jprocont.2026.103639","url":null,"abstract":"<div><div>The paper addresses the problem estimating the cell-mass distribution density, glucose and lactate concentration, as well as of the total biomass concentration in lactic-acid fermentation. The estimate is based on the combination of a cell population balance model with the available measurements. The model shows a cascade structure of a nonlinear finite-dimensional subsystem and a linear infinite-dimensional subsystem. The measurements are available on different time scales. On a quasi-continuous time scale optical density and conductivity are measured. The cell-size distribution is measured with a considerably lower frequency and is furthermore subject to non-uniform delays. The proposed estimation strategy exploits the cascade structure and consists of two cascaded discrete-time extended Kalman filters (EKFs). The performance of the proposed approach is demonstrated using experimental data from batch experiments with <em>Streptococcus thermophilus</em>. The estimation strategy improves the mean normalized root mean squared error of the distribution by approximately 41.6<!--> <!-->% compared to a pure simulation.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103639"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045201","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}
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