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    Item type:Publication, Access status: with files ,
    Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor.
    Lagrangian sensors have shown promise to improve operator awareness of conditions inside a chemical reactor but three-dimensional tracking remains a mostly unsolved challenge. We explore a setup where in-silico sensors, based on a recently proposed real-world design, are tracked using data from an accelerometer and magnetometer available from a built-in inertial measurement unit. Filtering algorithms, using a bespoke dynamical model, are used to process these readings into position estimates. We compare tracking performance of an extended Kalman filter, a particle filter and the unscented Kalman filter implemented in the pykalman library. Our numerical experiments track in-silico particles moving in an analytically given threedimensional vortex as well as in the experimentally measured flow-field of a lab-scale stirred tank reactor. Using the Maxey-Riley-Gatignol equations for the movement of inertial particles as ground-truth, we demonstrate that the extended Kalman filter and the particle filter reconstruct trajectories from noisy synthetic data with mean relative errors below 3%.
    Publicationtype: Journal Article
      52  27
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    Koopman–PCE-based confidence-bounded fault diagnosis and recovery for hydrogen demand tracking in a membrane reactor
    (Elsevier, 2026-06-01)
    Actuator loss-of-effectiveness (LOE) faults and matched disturbances can severely degrade tracking performance in nonlinear control affine systems, especially when the fault severity and disturbance bounds are unknown. This paper develops a fault recovery framework that combines (i) a Koopman based predictor for data-driven fault detection and identification (FDI), (ii) polynomial chaos expansion (PCE) to quantify uncertainty and provide confidence bounds on the estimated fault parameters, and (iii) an adaptive deep neural network (DNN) augmentation that compensates residual fault and disturbance effects in closed loop. We first rewrite the plant under the standard matched disturbance assumption into an effective input form, which exposes LOE faults and disturbances as a single input channel uncertainty. Using this structure, we derive the faulted tracking error dynamics under a nominal controller and a DNN augmentation. In the offline phase, we generate expert demonstrations across fault and disturbance scenarios and train a baseline DNN fault compensator by supervised learning. To decide which part of the network should be adapted online, we evaluate the average causal effect (ACE) of each layer on the closed-loop tracking error and select a single layer for online updates. During operation, a Koopman–PCE assisted FDI module estimates the actuator effectiveness matrix and supplies a confidence bound that is used to reconfigure the nominal controller. We then propose a single layer adaptive update law and prove uniform ultimate boundedness (UUB) of the tracking and weight errors. Finally, we show that the FDI estimates tighten the residual bound and reduce the ultimate tracking error bound, with an explicit dependence on estimation accuracy. We validate these claims numerically by evaluating FDI accuracy, confidence-band behavior, residual tightening, and closed-loop recovery under out-of-distribution fault scenarios, showing that FDI alone gives the lowest RMSE while the combined FDI with adaptive NN scheme reduces worst-case tracking excursions.
    Publicationtype: Journal Article
      70
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    Reproducibility of GPU-based Large Eddy Simulations for mixing in stirred tank reactors
    CFD simulations are widely used to quantify the mixing performance of stirred tanks for various applications in chemical engineering and biotechnology. Due to advances in GPU computing, these simulations increasingly employ Large Eddy Simulation (LES), which explicitly resolves the dynamics of large-scale turbulence. Although such simulations are fully deterministic and therefore theoretically reproducible, small numerical variations induced by round-off errors, floating-point arithmetic, and differences in the distribution and ordering of operations in parallel computing lead to separation of trajectories i.e., different flow-field evolutions and consequently to significant run-to-run variability in predicted mixing times, even on the same hardware architecture. This work investigates the impact of repeated simulations, in the form of a case study, on the mixing-time distribution observed in a (Formula presented) stirred tank reactor using two commercial CFD packages operating with representative, production-level solver configurations. The analysis does not aim to assess the general performance of numerical method classes, but rather to quantify run-to-run variability under fixed solver settings and to compare the resulting numerical distributions to experimental variability. The results demonstrate that numerical variability is of comparable magnitude to the experimental spread, highlighting the necessity to treat LES-derived metrics as statistical ensembles rather than deterministic values. It is concluded that the reporting of confidence intervals is essential for methodological rigour in LES-based mixing studies.
    Publicationtype: Journal Article
      36  61
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    Optimization-based process synthesis by phenomena-based building blocks and an MINLP framework featuring structural screening
    An existing approach for optimization-based process synthesis with abstracted phenomena-based building blocks (PBB) is extended by implementing it into a novel MINLP framework with structural screening. Consistency across the multilayer MINLP framework is guaranteed by creating a MathML/XML data model and subsequently exporting the code to the different program parts. The novel framework focuses both on fidelity by implementing thermodynamically sound models and on generality by employing a state-space superstructure that spans a large search space. In order to retain tractability, we insert a structural screening layer which pre-screens based on binary decision variables of the superstructure by graph- and rule-based analyses, penalizing non-physical instances without solution of the underlying MINLP. The MINLP framework is successfully applied on two challenging synthesis tasks to determine the separation of the feed streams of benzene and toluene, as well as of n-pentane, n-hexane, and n-heptane utilizing superstructures with two, respectively four PBB.
    Publicationtype: Journal Article
      27  84
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    Optimising bioreactor processes with in-situ product removal using mathematical programming: a case study for propionate production
    Designing and operating bioreactors with in-situ product removal (ISPR) can be challenging, particularly in discontinuous systems, where the ISPR and substrate feeding need to be effectively scheduled. Mathematical models can help assess different scheduling regimes in the fermentation medium and provide a means to optimise the process. Focusing on a propionate production case study, a model of a co-culture batch fermentation with electrodialysis (the ISPR system), was developed. Using this model, the product yield and/or the productivity were maximised by 1) single objective optimisation maximising the product yield (0.49 gpropionate /gglucose) or productivity (0.75 gpropionate/L/h), 2) multi objective optimisation to pursue trade-off solutions between the yield and productivity and 3) a stochastic optimisation maximising the productivity robustly (0.64 gpropionate/L/h) to account for uncertainties associated to the model parameters. With this contribution it is demonstrated that, through mathematical models, ISPR can be implemented and adapted to the user's objectives.
    Publicationtype: Journal Article
      53  164
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    Enabling optimization of complex distillation configurations in GAMS with CAPE-OPEN thermodynamic models
    Optimization of complex process models, e.g., those, resulting from conceptual design of distillation processes, with optimization environments such as GAMS, AMPL, or AIMMS is still thwarted by the manual implementation necessary for the interface to external thermo engines. In this contribution, we address this issue by automatically generating all code for interfacing GAMS with an external CAPE-OPEN thermodynamic property package. The distillation models in our approach are assembled in a modular way by combining multiple general vapor-liquid equilibrium stage models. A method, where all existing vapor-liquid-equilibria are relaxed is proposed and examined for enhanced model stability. The ability of our optimization approach is shown by the results of two examples that determine an optimum energy-targeted design of a fully thermally coupled dividing wall column for the separation of a zeotropic mixture of n-pentane, n-hexane, and n-heptane and an azeotropic mixture of acetone, methanol, and water.
    Publicationtype: Journal Article
      74
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    Advanced hybrid optimization methods for the design of complex separation processes
    While the need for more efficient and integrated processes for the separation of non-ideal and azeotropic mixtures mandates model-based design methods, the resulting mixed-integer problems are highly nonlinear and particularly hard to solve without proper initialization. In order to handle such complex design problems, two hybrid optimization methods are presented in the current contribution. Both methods rely on a nested approach, which integrates a polylithic modeling and solution strategy, based on the solution of successively refined nonlinear programming problems, with an upper level metaheuristic for the initialization and optimization of discrete design decisions. Both methods are evaluated for two case studies. The optimization of a simple column design problem allows for the direct comparison with an available global deterministic optimization solver for identifying the global optimal solution. The optimization of an extractive distillation process with simultaneous solvent selection and energy integration illustrates the potential complexity that can be handled effectively.
    Publicationtype: Journal Article
      74
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    Model compendium, data, and optimization benchmarks for sector-coupled energy systems
    (Elsevier, 2020-04-06)
    Sass, Susanne
    ;
    ;
    Hollermann, Dinah Elena
    ;
    Kappatou, Chrysoula Dimitra
    ;
    Sauer, Dominique
    Decarbonization and defossilization of energy supply as well as increasing decentralization of energy generation necessitate the development of efficient strategies for design and operation of sector-coupled energy systems. Today, design and operation of process and energy systems rely on powerful numerical methods, in particular, optimization methods. The development of such methods benefits from reproducible benchmarks including transparent model equations and complete input data sets. However, to the authors’ best knowledge and with respect to design and optimal control of sector-coupled energy systems, there is a lack of available benchmarks. Hence, this article provides a model compendium, exemplary realistic data sets, as well as two case studies (i.e., optimization benchmarks) for an industrial/research campus in an open-source description. The compendium includes stationary, quasi-stationary, and dynamic models for typical components as well as linearization schemes relevant for optimization of design, operation, and control of sector-coupled energy systems.
    Publicationtype: Journal Article
    Scopus© Citations 22  8  60
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    Model uncertainty-based evaluation of process strategies during scale-up of biopharmaceutical processes
    Reliable scale-up of biopharmaceutical production processes is key in Quality by Design. In this study, a model-based workflow is described to evaluate the bioprocess dynamics during process transfer and scale-up computationally. First, a mathematical model describes the bioprocess dynamics of different state variables (e.g., cell density, titer). Second, the model parameter probability distributions are de- termined at different scales due to measurement uncertainty. Third, the quantified parameter distribu- tions are statistically compared to evaluate if the process dynamics have been changed. This workflow was tested for the scale-up of an antibody-producing CHO fed-batch process. Significant differences were identified between the process development (30 ml) and implementation (250 ml) scale, and the feeding strategy was validated using model-assisted Design of Experiments. Then, the validated process strategy was successfully scaled up to 2 l laboratory and 50 l pilot scale. In summary, the proposed workflow enables a knowledge-driven evaluation tool for bioprocess development.
    Publicationtype: Journal Article
    Scopus© Citations 21  325  972
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    Efficient optimization-based design of energy-integrated azeotropic distillation processes
    The separation of azeotropic mixtures is frequently performed by extractive or heteroazeotropic distillation processes. The design of these processes requires careful selection of a suitable solvent and is specifically challenging since feasibility and optimality of the processes require consideration of the closed loop design including solvent recovery. Consideration of energy integration further complicates the design task and is usually conducted as post-evaluation step. The current publication proposes an efficient optimization-based design approach, which allows for the direct evaluation of several energy-integrated process concepts, while significantly reducing manual effort and computational time through a polylithic modeling and solution approach. The developed approach allows for a simultaneous evaluation of solvent selection and energy integration and is illustrated for different case studies, including the evaluation extractive and heteroazeotropic distillation for the dehydration of ethanol, as well as the evaluation of multiple solvent candidates for the extractive distillation of acetone and methanol.
    Publicationtype: Journal Article
      42