Reliable model identification for batch processes is difficult when the measured data contain both repetitive disturbances that recur at similar stages across batches and deterministic disturbances that vary from batch to batch. This study proposes a batch-process identification method that uses input–output data from the current batch and the immediately preceding batch. Differenced signals are formed to reduce the repeated effect of the repetitive disturbance on the output while preserving informative variation for nominal-model identification. A continuous-time nominal process model is then estimated from the differenced data by an integral-transform-based least-squares method. The residual component remaining in the differenced output is represented by Laguerre polynomials, and its coefficients and the model initial states are refined by the prediction error method. The proposed method is evaluated using four benchmark processes representing high-order, non-minimum-phase, and underdamped dynamics, supplemented by measurement-noise analyses and a nonlinear semi-batch case. Under the nominal benchmark configuration, the proposed method produced stable models in all four processes, whereas the previous method did so in only two cases. These results support the use of adjacent-batch differencing under the considered repetitive-disturbance conditions.
The growing reliance on state-of-the-art machine learning based models for engineering decision-making necessitates robust and systematic approaches for model selection. While high predictive accuracy at untrained points is necessary in the final model, other attributes such as model complexity, forecast ability, explainability, scalability, and physics-awareness may be equally important or relevant criteria depending on application context and user requirements. In this work, we propose a novel composite metric called Surrogate Quality Score (SQS) for model selection based on predictive accuracy and model complexity simultaneously. SQS heuristically integrates these two attributes through a weighted product of normalized measures, yielding a unified score to reflect overall model quality. A user-specified parameter in SQS enables explicit control over the accuracy-complexity trade-off, thereby incorporating human judgement and preference in the model selection process. We extensively discuss and justify the formulation of SQS, demonstrate its application through an illustrative example, and examine the sensitivity of its recommendations to user-specified parameters. We further demonstrate its applicability to real-life model selection problems through three engineering case studies. By combining predictive accuracy and model complexity, SQS offers a systematic, objective, and attractive approach for model selection based on a joint consideration of predictive accuracy and model complexity.
This paper proposes a data-driven robust moving horizon state estimation approach for a class of nonlinear systems using a learning-based deep probabilistic stable Koopman model. Different from conventional nonlinear estimation approaches that require the structure or parameter values of a mechanistic model of the underlying nonlinear system, a deep probabilistic stable Koopman operator is learned from noisy data to model the dynamic behavior of the nonlinear system. With the learned Koopman model, a linear robust moving horizon estimation method is proposed for the constrained state estimation of the considered nonlinear system. This method circumvents the challenges associated with non-convex optimization in nonlinear moving horizon estimation and offers an efficient data-based online estimation solution. We provide sufficient conditions that ensure the stability of the developed state estimation scheme in the presence of modeling errors. Finally, the proposed scheme is evaluated using a numerical example and a benchmark simulated chemical process example. The effectiveness and superiority of the proposed scheme are demonstrated.
Carbon dioxide produced in aluminum electrolysis greatly affects molten electrolyte flow, inter-electrode resistance and alumina dissolution, while the sealed high-temperature cell environment hinders real-time bubble monitoring. Traditional CFD simulation of this process requires high-precision meshes and therefore entails huge computational costs. This study adopts physics-informed neural networks (PINN) to combine physical governing equations with CFD data through loss functions, realizing mechanism-data fusion to explore gas-liquid flow characteristics in electrolyte melts. Driven by randomly sampled data, the model accurately predicts full-field internal flow fields using merely 2% of the original data, achieving relative RMSE and MAE both below 10%. Its prediction efficiency is about 3000 times higher than CFD. Simulation results indicate that bubbles drive electrolyte circulation. Rising bubble flow rate raises bubble volume fraction and layer thickness with a slowing growth trend. Bubble-induced extra resistance shows a nonlinear correlation with flow rate, with a critical value of 164.54 L/min; resistance surges rapidly once exceeding this point. Elevated current density also sharply increases extra resistance. Longitudinal-slot anodes can effectively reduce bubble resistance, reaching an 85.33% reduction at 180 L/min. Larger alumina particles present lower mass transfer efficiency and poorer dissolution performance. Rational regulation of bubble flow optimizes particle dissolution. The proposed bubble dynamic optimization method provides practical guidance for energy saving and output improvement in aluminum electrolysis industry.
Plant-wide simulation in biopharmaceutical manufacturing heavily relies on mechanistic models that are costly to develop, while data-driven approaches are typically confined to single unit operations and lack plant-wide integration. This work presents a modular, data-driven modeling framework for plant-wide simulation, where interconnected predictive models represent different sections of the process and enable systematic propagation of predicted outputs and process variables across the entire plant without relying on mechanistic constraints. The framework supports flexible reconfiguration across process topologies and scales, allowing rapid prediction and scenario analysis. A sensitivity analysis is integrated to quantify the impact of intermediate outputs and process parameters on final product yield. A case study on an end-to-end industrial-scale vaccine biopharmaceutical plant, involving 12 manufacturing steps and 665 batches, is used herein to demonstrate the approach. The plant-wide model achieves a yield prediction RMSE of 0.141 and maintains stable predictive performance under ±5% input perturbations. Results reveal highly uneven cross-stage influence, with downstream operations dominating final yield variability. The proposed framework provides a practical and scalable tool for plant-wide modeling and early-stage prediction, as well as a basis for process optimization in biopharmaceutical systems.
Continuous zeolite crystallization in tubular reactors presents major control challenges due to nonlinear kinetics, distributed temperature fields, and multiple heating sources. This work introduces a new thermal model for a pilot-scale continuous oscillatory baffled reactor equipped with conventional and microwave heating for continuous zeolite crystallization. The model extends existing formulations by explicitly incorporating thermostat dynamics and a coaxial microwave heating system, and is validated against experimental data from the pilot plant. Building on this validated process representation, we develop a methodological framework for robust model predictive control (MPC) under uncertainty. High-dimensional partial-differential equation models are replaced by data-driven surrogate models based on nonlinear autoregressive networks with exogenous inputs and dimensionality reduction via principal component analysis and autoencoders. Parametric uncertainty in crystallization kinetics is captured through conformalized quantile regression, providing uncertainty bounds for robust constraint handling in MPC. The resulting framework achieves real-time robust MPC of continuous zeolite crystallization, coordinating multiple heat sources to meet varying throughput targets and product quality constraints while minimizing energy consumption.Closed-loop simulations against a high-fidelity process model show accurate tracking, robustness to uncertain kinetics, and real-time computational feasibility, providing a basis for future deployment on the pilot plant.
The transition toward electrified transportation may reduce the long-term demand for fuel ethanol, creating both challenges and opportunities for the Brazilian bioeconomy. This study evaluates the strategic valorization of ethanol through the production of high-value bioproducts. A multi-criteria mixed integer nonlinear programming model is developed to design an integrated supply chain comprising representative biorefineries, ethanol-derived production plants, maritime hubs, and local and international markets. Economic performance, greenhouse gas emissions, water and energy consumption, and social equity are evaluated across 30 weighting scenarios. The results indicate that export-oriented configurations can generate positive economic returns and support the use of ethanol as a chemical feedstock. Road freight is the main source of modeled emissions, whereas water and energy requirements strongly influence technology selection, production scale, and product portfolios. Under the assumed redistribution mechanism, the model projects population-weighted regional reductions of approximately 0.1-2.4% in the Gini index and 0.2-3.7% in social vulnerability, depending on the region and scenario. Overall, the results demonstrate that, under the adopted assumptions, ethanol-derived value chains can support a sustainable and socially inclusive bioeconomy while providing alternative valorization pathways for ethanol under changing market conditions.
Eco-industrial parks (EIPs) offer significant potential for improving industrial resource efficiency and reducing emissions, yet practical deployment requires transparent monitoring of resource exchanges and verifiable emissions accounting among participating plants. This study presents a framework that enables verifiable emissions and resource tracking in EIPs by coupling a mixed-integer linear programming (MILP) superstructure optimization model with a private permissioned blockchain. The MILP model determines optimal process selection, production capacities, and mass-balanced flows of energy, water, materials, and CO₂ while accounting for Scope 1 and Scope 2 emissions. A binding CO₂ cap is imposed, and alternative compliance pathways are evaluated including capture, utilization, storage, carbon taxation, and credit purchases. Free allowances and credit eligibility are allocated proportionally to baseline emissions, and coalition surplus is distributed using Shapley values. Optimization outputs are subsequently operationalized on a private permissioned blockchain that registers entities, records resource exchanges and emissions reports, and enforces policy rules and financial settlements through smart contracts, thereby providing an auditable link between design decisions and operational outcomes. A case study EIP consisting of seven plants and multiple carbon capture routes demonstrates the framework. Across emission caps of 10 %, 62 %, and 95 % below baseline, optimal profits are 277, 272, and 243 million USD yr⁻¹, with captured CO₂ of 270, 1660, and 1946 kt yr⁻¹, respectively. Under very stringent caps, the system relies on CO₂ credits and carbon taxation to close the remaining compliance gap. The proposed framework generates complete ledgers of resource exchanges and net emissions while maintaining MRV-aligned records suitable for verification, auditing, and settlement. Blockchain energy demand remained negligible for daily to hourly logging and increased materially only under real-time reporting frequencies. The results highlight how explicit policy representation and cooperative profit allocation influence technology selection, trading patterns, and financial outcomes within low-carbon industrial ecosystems.
Chemical process control is essential for safe and reliable operation under disturbances, nonlinear dynamics, and model uncertainties. In this context, data-driven deep reinforcement learning (DRL), particularly the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, has gained attention for learning optimal control policies for continuous processes without explicit models or historical data. This study proposes a Q-value adaptive evaluation TD3 (QAETD3) model to address the challenge of Q-value underestimation, which often arises in TD3 under policy fluctuations and can compromise stability and control performance. In QAETD3, an adaptive evaluation mechanism is developed based on a novel metric that integrates the current Q-value, immediate reward, and next-state Q-value to assess and detect underestimation. An adjusted Q-value is then computed for more stable policy updates. However, as this correction is computed online and varies across samples and training iterations, it introduces time-varying and sample-dependent behavior into the TD target, potentially leading to gradient sensitivity and oscillatory updates under fixed learning rates. To mitigate this, a Triangular Decay Cycle (TDC) learning rate strategy is introduced to dynamically adjust the step size, enhancing convergence and computational stability. The dynamic behavior of the QAETD3 model is described by a system of ordinary differential equations (ODE), and its convergence is verified by applying Lyapunov stability theory and the contraction property of the Bellman operator. The effectiveness of QAETD3 is demonstrated through application to a natural gas dehydration process, where its performance under various disturbances is compared with that of conventional PID and original TD3 controllers.
CFD-based design of hydrogen-capable non-premixed burners is governed by strong trade-offs between thermal performance and NOx emissions. At the same time, each design evaluation can require hours of runtime, and computational cost varies continuously with mesh resolution. We propose a multi-objective, multi-fidelity Bayesian optimization framework that jointly optimizes burner geometry and fuel composition while explicitly managing numerical fidelity and simulation time. Numerical fidelity is represented through a normalized coordinate derived from mesh size and included in an augmented Gaussian-process input space for modeling the mean chamber temperature Tmean and outlet NOx.New candidates are selected by maximizing a composite acquisition function that combines (i) q-log noisy expected hypervolume improvement, (ii) probabilistic feasibility with respect to an emission limit, (iii) a learned fidelity-shaping term, and (iv) a runtime-aware penalty based on an online-calibrated cost proxy. The framework is demonstrated on a confined, axisymmetric non-premixed CH4/H2 burner. Across 238 CFD evaluations, the proposed strategy reduces cumulative computational cost by more than 60% (from 313 to 122 CPU-hours) relative to a hypothetical single-fidelity baseline using only the highest resolution, while recovering a consistent Pareto set of high-temperature and low-emission designs. Flow-field analysis shows that NOx levels are largely dictated by the size and residence time of high-temperature zones, explaining the observed Tmean–NOx trade-off. In addition, re-simulating the best hydrogen-enriched geometry under pure methane yields a different performance ranking, indicating that optimal configurations depend on fuel composition and supporting joint design–operation optimization.
Phosphate ore blending is a chemically constrained decision problem in which contaminant control, grade preservation, sourcing feasibility, and logistics performance must be addressed simultaneously. In industrial practice, blending decisions are often made empirically, which limits the ability to quantify trade-offs between chemical compliance and operational efficiency. This study proposes an optimization-based decision-support framework for phosphate ore blending in a mine-to-plant supply chain under cadmium and P2O5 constraints. The framework combines lexicographic linear programming and multi-objective evolutionary optimization to support blending, sourcing, and transport decisions under stock, capacity, and logistics limitations. In the first stage, a lexicographic linear programming model identifies a chemically rigorous reference solution by sequentially minimizing cadmium content and maximizing phosphate grade. In the second stage, NSGA-II explores the broader set of feasible trade-offs between chemical quality and logistics cost. Computational experiments based on instances reflecting the Tunisian phosphate context show that strict cadmium minimization produces chemically robust but structurally rigid sourcing patterns, whereas controlled relaxation within the admissible chemical region can yield substantial logistics savings while preserving compliance. Beyond the application itself, the results provide an interpretable optimization perspective on chemically constrained blending and highlight the value of combining exact and evolutionary methods for process systems decisions involving quality, logistics, and environmental requirements.
Structural process-model mismatch represents a major challenge in process systems engineering, as it undermines the reliability of mechanistic models, even after precise parameter estimation. Identifying which modeling assumption or grouped terms most contribute to the observed mismatch remains nontrivial. To address this issue, we propose a novel approach based on Sobol’s global sensitivity analysis for diagnosing structural process-model mismatch. This approach is applied to the mismatch trajectory – which is defined as the difference between model predictions and process data – while predefined input channels (e.g., specific functional groups appearing in model equations) are perturbed within uncertainty ranges. Computed sensitivity indices quantify both individual and interaction effects on mismatch variance, thereby providing interpretable diagnostics of dominant structural sources and revealing potential inflation effects due to interactions. The proposed approach is demonstrated through two in-silico case studies: (i) a fed-batch bioreactor for yeast cultivation, and (ii) an ion-exchange chromatography process for biopharmaceutical manufacturing. Results show that our approach can pinpoint structural assumptions driving the mismatch, providing systematic support for model refinement and streamlining the development of more reliable mechanistic and hybrid models for process simulation.
Population balance equations (PBEs) are widely used to predict particle size distributions, but fixed-domain discretization can waste resolution in negligibly populated size ranges and may suffer numerical diffusion unless fine grids are used. This study presents the Flexible-Domain Population Balance Equation (FlexPBE), an adaptive crystallization PBE framework in which the size domain evolves with the PSD through a moving boundary. FlexPBE adopts established dynamic-domain mapping rather than introducing a new coordinate transformation.The boundary is updated using a Z-score criterion based on moment-derived PSD statistics, while an exponential moving average prevents abrupt motion and numerical stiffness. The mapping modifies the size-derivative terms, allowing FlexPBE to operate as a wrapper for conventional discretization schemes without changing their structure.FlexPBE is validated against analytical batch growth and nucleation–growth benchmarks. Nucleation and crystal growth are treated as the fundamental crystallization mechanisms, whereas aggregation and breakage are excluded to isolate the numerical effects of dynamic-domain mapping; a growth law linear in particle size is used. With first-order upwinding, FlexPBE reduces the error metric by ∼95% relative to its fixed-domain counterpart and outperforms fixed-grid second-order upwind and HR-Van Leer schemes under the same setup. At comparable computational cost, FlexPBE with 1000 grids achieves lower error than fixed-domain simulations with 14,000–15,000 grids.Finally, FlexPBE is integrated into an OpenFOAM-based MP-PIC-PBE solver. The coupled simulation remains numerically stable, and under the same 30-grid condition, FlexPBE 30 yields PSD shapes and moment characteristics closer to higher-resolution fixed-grid results than fixed-grid PBE 30.
This study presents a direct data-driven method for designing feedback controllers without requiring explicit process model identification. The method constructs a fictitious setpoint from measured input–output data based on a user-specified desired closed-loop behavior, then estimates controller parameters by solving a least-squares regression problem. The proposed formulation can be interpreted as a practical specialization of a VRFT-type tuning framework for process-control applications. A key feature is that only a single parameter, the desired response delay, needs to be specified. This parameter can be optimized automatically or adjusted manually to achieve desired performance trade-offs. The method accommodates various linearly parameterized controller structures and can use operating data when the data contain sufficient dynamic variation for the resulting regression problem. The effectiveness of the method is demonstrated through simulation studies, including comparison with standard VRFT, and experimental validation on a physical water-level control system. The results indicate improved tracking performance compared with conventional tuning approaches while clarifying the practical trade-offs associated with the pure-delay reference model and the unity weighting filter.
In green ammonia synthesis powered by intermittent renewables, frequent load fluctuations cause dynamic operations that alter statistical relationships among process variables. Under such conditions, accurate anomaly detection is critical for system safety and reducing false alarms. However, existing methods face three key challenges: (1) lacking causal logic to distinguish normal variations from true faults; (2) lacking interpretability for root cause analysis; (3) relying on fixed parameters that cannot accommodate distribution shifts, leading to high false alarms and poor generalization. To address these issues, this paper proposes a Causality-Guided LSTM-VAE (CG-LSTM-VAE) with three key mechanisms: PCMCI-based causal prior extraction, causality-constrained latent space embedding for physically consistent reconstruction, and adaptive training optimization combining dynamic KL annealing, causal regularization, and latent structural alignment. Validated on a green ammonia synthesis simulator, CG-LSTM-VAE achieves a test MSE of 0.045 and R² of 0.955. In two fault scenarios (synthesis tower leakage and heat exchanger failure), it attains true positive rates of 99.77% and 98.72% with false positive rates of 0.67% and 3.34%, respectively. The framework effectively reduces load-induced false alarms and provides a causally-informed, interpretable safety monitoring paradigm for green ammonia production under dynamic renewable energy supply.
