Keywords: Operation Research, Logistics and Planning
Abstract: Supply chains are less robust than we generally believed in the past decades. How robust is the economy, how could we quantify that? For the first time we can now observe national supply chain networks on the firm-level, involving hundred thousands firms and millions of supply relations that constantly change over time. By assigning production functions to these firms and by estimating the re-linking dynamics of the economy, we are able to represent national economies as a 1:1 agent based model. On the basis of this model, we can rethink the big questions of economics and in particular make predictive statements about the robustness and resilience of the present economy. We discuss new ways to optimally transform production networks towards a green and—at the same time—socially acceptable economy.

Keywords: ODE, DAE, SODE, SDAE Systems, Numerical Simulation and Co-Simulation
Abstract: Due to its slender boom structure, the knuckle boom crane often undergoes significant elastic deformation when transporting heavy payloads in its fully extended configuration, adversely affecting operational efficiency and safety. Therefore, analyzing the crane's strong geometrical nonlinear dynamic behavior is crucial for engineering applications. This paper presents a dynamic modeling and numerical integration method for a rigid-flexible coupling knuckle boom crane, which is subjected to structural constraints and actuated by hydraulic cylinders. In terms of dynamic modeling, the dynamic equations of the crane’s flexible boom are derived based on the geometrically exact Euler-Bernoulli beam theory while integrating the crane's rigid multibody dynamic equations, structural constraint equations, and hydraulic state equations. This approach results in a comprehensive dynamic model of the crane. For numerical integration, we adopt the Newmark method and the implicit single-step trapezoidal discretization scheme to establish the discrete formulation for the mechanical structure and hydraulics, and derive the Jacobian matrix required for the Newton-Raphson iteration. Numerical simulations verify the effectiveness of the integration algorithm through a comparative analysis with the results obtained from ordinary differential equation solvers, and a dynamic analysis of a representative case study was subsequently conducted. This work contributes to the optimization of crane structures and the design of control systems.

Keywords: Automotive, Aerospace, Transportation Systems, Modelling for Control and Real-Time Applications, Fitting Models to Real Processes, incl. Identification and Calibration
Abstract: Fuel cell electric vehicles hold a significant promise for reducing the carbon footprint in the automotive sector by leveraging H2 as a clean fuel source. Maintaining a consistent H2 supply to the fuel cell system is vital. N2 crossover can lead to an inert gas built-up on the H2 supply side, adversely affecting fuel cell performance and durability. Through purging, gases are released, and a N2 built-up in the H2 supply system can be prevented, yet this also leads to fuel loss. This fuel loss can be minimized by keeping an optimal N2 molar fraction. We developed a dynamic model for effectively designing, controlling, and diagnosing fuel cell systems by predicting the N2 molar fraction in the H2 supply. This model considers factors such as N2 distribution throughout the fuel cell stack, N2 crossover, and the purge process. The model is simplified to a differential equation of first order and solved using the explicit Euler method at a typical automotive time step of 0.01 s. The proposed model was validated by a H2 measurement in a fuel cell system with passive recirculation.

Keywords: Manufacturing and Process Engineering, Data-Driven Models, Neural Networks, Modelling for Control and Real-Time Applications
Abstract: Cavity pressure control can enhance the repeatability of injection molding processes. While extensive research has focused on thermoplastic cavity pressure control, there is a notable gap in models and control strategies for thermoset injection molding. This study aims to develop a model structure for thermoset injection molding suitable for integration into a model-based control scheme. The modeling approach is intended to be as generalizable as possible and sufficiently flexible to adapt to various process conditions. At the same time, it should be easy to parameterize or to train. To address this challenge, we first derive a first-principles process model. In the second step, we integrate a feed-forward artificial neural network into this model, which learns parameters and source terms from past injection molding cycles, resulting in a gray-box model. The neural network outputs replace the initial model parameters with functions of system inputs, states, and time. We validate both models against experimental data from a thermoset injection molding machine using a flat-plate mold geometry and a phenolic resin compound. We identify limitations of the proposed approach and suggest potential solutions.

Keywords: Manufacturing and Process Engineering, Modelling for Control and Real-Time Applications, Fitting Models to Real Processes, incl. Identification and Calibration
Abstract: In the continuous casting of steel slabs, a constant mold level is crucial for the quality of the final products. However, mold level fluctuations may be caused by unsteady bulging, i.e., a time-varying bending of the solidified strand shell between the rolls of the roll array due to variations in the strand shell thickness. A control-oriented model of unsteady bulging is needed to design controllers that should suppress unsteady bulging systematically. Most existing models use complex, detailed, nonlinear formulations, typically requiring high computational costs. Therefore, these models are unsuitable for closed-loop simulations or applications in real-time control. As an alternative, this work presents a novel empirical model that allows parametrization based on usually available measurements from industrial continuous slab casters. The model facilitates fast dynamic simulations of unsteady bulging and its results accurately match measurements.

Keywords: Modelling for Control and Real-Time Applications, Automotive, Aerospace, Transportation Systems
Abstract: The paper focuses on reducing computational time when solving optimal control problems by expressing them within a flat coordinate system. To demonstrate and discuss this approach, two case studies are presented: time-optimal velocity trajectory planning and torque control of permanent magnet synchronous motors. The reformulated optimal control problems show significant reductions in computational time without affecting the resulting trajectories. Additionally, analyses were performed to investigate the impact of prediction horizons and solver starting values on the observed computational advantages. The results clearly show the potential of the presented method for developing computationally efficient optimization-based control strategies.

Keywords: Mechanics, Mechatronics, incl. Robotics, Automation of Modelling and Software tools, incl. Computer Modelling
Abstract: A Modelica library for battery sizing of underground mining electric vehicles is presented. The library, named UGMiningBEV, facilitates modelling underground mining electric vehicles with different design parameters and architectures, under varying working scenarios. UGMiningBEV includes models of vehicle transmission, auxiliary driving-related systems (steering and braking), mixer drum, lighting, HVAC (heating, ventilation and air conditioning), cooling, battery and battery charging. It also includes validation examples of relevant components and the model of an electric concrete mixer for underground mining and its typical working cycle. The technical contribution of the library lies in the variety of subsystems that can be integrated, combined with a working cycle that allows the simulation of vehicle mission profiles based on distance travelled or time elapsed. The UGMiningBEV library has been developed using Dymola 2021x and is freely available under the Modelica License 2 terms.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, ODE, DAE, SODE, SDAE Systems, Medicine, Physiology, Health Care and Biology
Abstract: We enhance machine learning algorithms for learning model parameters in complex systems represented by differential equations with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, the FBPINN approach better captures the overall dynamical behavior compared to the vanilla PINN approach, even in cases with data only from a time domain with quasi-stationary dynamics.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Modelling Uncertainties and Stochastic Systems, Electrical, Electronic and Power Systems
Abstract: Efficient energy management in building energy systems (BES) is essential for reducing energy consumption while maintaining thermal comfort. One effective approach is Model Predictive Control (MPC), which optimizes control actions based on a model of the building; however, deriving such models can be costly and time-consuming. This paper combines Gaussian Processes (GP) with parametric mean functions which can be viewed as Physics Informed Gaussian Processes (PIGP). The PIGP is evaluated against other approaches to identify the thermal dynamics of BES, showing that the PIGP provides the best predictive accuracy. Furthermore, these models are integrated into a nonlinear MPC to compare energy demand and constraint violations in a sample BES, with simulations indicating that the PIGP results in lower energy demand.

Keywords: Data-Driven Models, Neural Networks, Modelling for Control and Real-Time Applications, Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: This study presents a mathematical modeling framework that leverages recurrent neural networks (RNNs), specifically echo state networks (ESNs) and long short-term memory (LSTM) architectures, for the predictive modeling of electrical submersible pumps (ESPs) in offshore oil extraction operations. Utilizing real operational data from an offshore oil field, the research addresses the inherent complexity and nonlinear dynamics of ESP systems by employing these recurrent structures to capture and represent the temporal dependencies within the data. Key challenges, such as data noise, variability, and limited diversity, are systematically tackled to ensure robust dynamic modeling. A comparative analysis evaluates the performance of ESN and LSTM models under these constrained data conditions, aiming to identify the superior model in terms of predictive accuracy and resilience. The modeling approach emphasizes the formulation, parameterization, and validation processes essential for effective ESP optimization and control in real-world industrial settings. Findings reveal the distinct strengths and limitations of each RNN variant when applied to offshore operational data.

Keywords: Data-Driven Models, Neural Networks, Modelling for Control and Real-Time Applications, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: A virtual representation of a complete cyber-physical system introduces several opportunities, such as enabling real-time monitoring of physical systems and ongoing learning to deliver accurate and dependable information. This approach is often referred to as the creation of a digital twin (DT). Nevertheless, challenges emerge, particularly with the computational requirements of implementing AI-driven models in real-time data exchange contexts, as is common with DTs. This research presents a DT framework tailored for optimal and autonomous decision-making within a gas-lift process, with a focus on increasing the adaptability of the DT system. The proposed solution integrates Bayesian inference, Monte Carlo (MC) simulations, transfer learning, and online learning alongside techniques for dimensionality reduction and cognitive modelling. These approaches contribute to the development of a reliable and efficient DT. The framework aims to deliver a system that can adapt to dynamic environments, account for prediction uncertainties, and improve decision-making processes in complex, real-world applications.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Data-Driven Models, Neural Networks, Operation Research, Logistics and Planning
Abstract: Efficiently allocating limited resources in classification problems is an important task in many real-world applications. We propose a two-phase framework consisting of machine learning and optimization models to address this challenge. In the first phase, a machine learning model is used to obtain a probability matrix for potential classifications. In the second phase, the probability matrix is used as input for a linear programming model, which is designed to minimize misclassification costs while considering resource constraints. This study addresses both local and global resource availability constraints, which we define in the context of classification problems as: target-based constraints—limiting the total number of entities that can be assigned to various classes; and feature-based constraints—limiting the number of entities from each subgroup, defined by a specific feature value, that can be assigned to various classes (e.g., geographic-based limitations). We prove that the coefficient constraint matrix in the linear programming model is totally unimodular, guaranteeing that integer optimal solutions can be obtained using efficient linear programming algorithms. An experimental study illustrates the effectiveness of the proposed framework in terms of time and performance in resource allocation compared to the commonly used conventional method. This two-phase approach advances the application of machine learning and operations research in resource-constrained environments, offering a scalable framework for solving complex classification problems under various constraints.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Numerical Simulation and Co-Simulation
Abstract: This study introduces a transferable approach for solving partial differential equations (PDEs) on metric graphs, often called quantum graphs, employing Physics-Informed Neural Networks (PINNs). Unlike traditional solvers constrained by specific graph structures, our method utilizes a Neumann-Neumann domain decomposition technique, offering adaptability across various network topologies. By incorporating edge-wise surrogates, this approach achieves experimental results comparable to those obtained with FEM across diverse network configurations.

Keywords: Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Medicine, Physiology, Health Care and Biology, Numerical Simulation and Co-Simulation
Abstract: Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux boundary conditions at the cell boundaries. Such a model will become computationally inefficient and analytically complex when there are many cells, even more so when they are moving. We propose to consider instead a point source model. Each cell is virtually reduced to a point and appears in the diffusion equation for the compound on the full spatial domain as a singular reaction term in the form of a Dirac delta ‘function’ (measure) located at the cell’s centre. In this model, it has an amplitude that is a non-local function of the concentration of compound on the (now virtual) cell boundary. We prove the well-posedness of this particular parabolic problem with non-local and singular reaction term in suitable Sobolev spaces. We show for a square bounded domain and for the plane that the solution cannot be H^1-smooth at the Dirac point. Further, we show a preliminary numerical comparison between the solutions to the two models that suggests that the two models are highly comparable to each other.

Keywords: Mechanics, Mechatronics, incl. Robotics, Physical and Multiport Modelling, Bondgraphs, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs)
Abstract: A crucial factor in achieving high efficiency during second-harmonic generation is maintaining a constant temperature along the beam propagation in the nonlinear crystal, despite a significant non-homogeneous heat input through absorption. In this context, we present a theoretical approach to determine the necessary longitudinal oven temperature profile applied to the crystal's shell surface to ensure a constant temperature at the center along the propagation axis. The approach is validated through simulations for an exemplary case, followed by a discussion of the results.

Keywords: Comparison of Methods for Modelling, Fluidics and Thermodynamics, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs)
Abstract: This paper deals with system-identification for a distributed parameter heating process where a solid substrate is moving through a spatially extended heating zone and heated up by applying hot air to its surface. The temperature distribution inside the substrate is modeled in a spatial plane, where heat conduction is considered in the direction, perpendicular to the direction of movement. In contrast to previous work, where scalar model parameters (e.g. the thermal parameters of the substrate) have been identified, here, the quantities for the heat transfer (heat transfer coefficient and air temperature) are identified as functions yielding a significantly improved fit to the measurement data. This improved system-identification is performed for two early-lumping modeling approaches, which differ in the way the advection term in the governing Partial Differential Equation is discretized: one uses Eulerian coordinates, where the computational grid is stationary, whereas the second employs Lagrangian coordinates where the grid is moving with the substrate. The differences of the two approaches are discussed with the main focus on numerical diffusion. Especially its impact on the system-identification is investigated: although the fit to the measurement is comparably good in both cases, very different solutions are obtained for the identified functions which, we argue, is due to the optimizer counteracting the smoothing effect of numerical diffusion.

Keywords: Electrical, Electronic and Power Systems, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), ODE, DAE, SODE, SDAE Systems
Abstract: The Cuk converter is a particularly interesting converter, as it can be used to generate voltages which could be above or below the supply voltage. The chokes take up the most space when setting up such a converter. In this article, the chokes are replaced by transmission lines. This approach leads to a new converter topology and other mathematical models. The new distributed converter model can later on be discretized for a physical implementation to replace the two large inductances with numerous smaller inductances as suggested by Sander (2012).

Keywords: Model Reduction, Model Simplification and Optimization, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs)
Abstract: In the present paper, we introduce a new approach for the numerical calculation of the transfer function of linear time-invariant partial differential equations in a non-parametric form, e.g. for a subsequent approximation using (non-) rational transfer functions. With the approach, the closed-form solution of the transfer function is represented using a state transition matrix. Thus, the value of the transfer function at explicit values of the complex frequency can be determined by numerically solving the matrix differential equation of the former. The idea is illustrated using an example. In addition, a comparison with the system’s closed-form solution is carried out and the advantages of the new approach over an established one based on a finite-dimensional approximation are shown.

Keywords: First Principles Modelling, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Fitting Models to Real Processes, incl. Identification and Calibration
Abstract: Given the recent increase in wildfires, developing a better understanding of their dynamics is crucial. For this purpose, the advection-diffusion-reaction model has been widely used to study wildfire dynamics. In this study, we introduce the previously unconsidered influence of topography through an additional advective term. Furthermore, we propose a linear term for the combustion function, comparing it with the commonly used Arrhenius law to offer a simpler model for further analysis. Our findings on the model's dynamics are supported by numerical simulations showing the differences of model extensions and approximations.

Keywords: Manufacturing and Process Engineering, Modelling for Control and Real-Time Applications
Abstract: Flexible, metal forming processes such as flow forming are exposed to many disturbances that affect geometry and material properties during forming and reduce the reproducibility of those processes. In this context, closed-loop property control is a feasible solution for process improvement. To include advanced controllers and observers in closed-loop property control concepts, mathematical models in terms of state-space models are advantageous. However, especially in case of flow forming these models are not spread due to the complex process kinematics, nonlinearity of the process and spatial dimensions of the workpiece. This makes mathematic state-space modelling challenging. Thus, a model has to be newly developed. This paper therefore presents a novel discrete-time state-space model for flow forming. The model treats the workpiece geometry as discrete and represents the complex process kinematics in the form of a local sampling of the roller trajectory. It can be shown that the model is valid and that the resulting system dynamics especially results the from the displacement between roller and sensor which is considered in the model. Thus, the result of this paper is a valid state-space model that can be prospectively used in a model-based state observer for flow forming. This state observer could later extent a closed-loop property control to enable more complex property structures than before.

Keywords: Data-Driven Models, Neural Networks, Manufacturing and Process Engineering
Abstract: Freeform bending is a technique used to bend different tube profiles into complex structures. In the realm of Aritificial Intelligence and Machine Learning, data-driven approaches in modeling and in optimization based control contribute to the job being executed, by increasing product quality and reducing energy consumption and material waste. In previous works, soft-sensors as well as different factors affecting the geometry and the residual stresses have been investigated and been utilized in a preliminary closed-loop control structure. Later on, this control structure has been replaced with a control strategy called Residual Strategy Algorithm, that could, based on previous deviations in the geometry, proactively react in order to reduce their effects. In this paper, the previously developed Residual Strategy Algorithm is extended to include both, the geometry as well as the residual stresses of the tube being bent. Also the modelling of both will be discussed altogether. The validation of the algorithm is done using simulation results.

Keywords: Modelling for Control and Real-Time Applications, Data-Driven Models, Neural Networks, Numerical and Symbolical Methods for Modelling, incl. Inverse Problems, Aspects in Scientific Computing
Abstract: Impedance spectrum modelling requires parameter extraction by solving the corresponding inverse identification problem, for which both gradient-based and stochastic methods have been proposed. Stochastic methods are more robust and have a lower risk of getting trapped in local minima but need a long calculation time. In this study, we examine the implementation of artificial neural networks (ANNs) in solving inverse identification problems in inductance spectroscopy, contrasting their performance with robust stochastic methods. In order to overcome the shortage of a representative amount of experimental data, we propose to use the analytically based model to generate accurate enough labelled data for the training process of the ANN. The artificial data have been structured in a homogeneous and tightly spaced grid in the parameter space, thus supporting the model's generalisation and suppressing overfitting. ANNs with varied degrees of complexity have been investigated by modifying the number of neurons and evaluated by training and comparison with stochastic parameter extraction methods. The investigation concludes that, for the presented application in inductive spectroscopy, the neural networks can provide comparable parameter extraction results with a relative deviation of 0.03 % of the parameter value and a significant reduction in runtime from 60 s to 8 ms.

Keywords: Manufacturing and Process Engineering, Modelling for Control and Real-Time Applications, Mechanics, Mechatronics, incl. Robotics
Abstract: New machine concepts, such as the 3D Servo Press, make it possible to implement and study new forming processes like the flexible hole-rolling. In combination with the ongoing development of models, new control concepts can be developed and thus increase productivity of manufacturing systems. As part of this work, a softsensor was developed to predict the part geometry of a polygon profile during the process of hole rolling based on the process forces and the ram position. This prediction was used in an experimental investigation to set up an inline geometry control to compensate for the geometric error due to roller deflection during the process.

Keywords: Fitting Models to Real Processes, incl. Identification and Calibration, Mechanics, Mechatronics, incl. Robotics, Modelling for Control and Real-Time Applications
Abstract: During a multi-stage press hardening process, where a metal sheet undergoes rapid austenitization, tempering, and forming, the spatial-temporal temperature development is a driving factor and its control enables it to reach desired product properties. A two-dimensional model extension is proposed, which enables a precise and computationally efficient temperature modeling along the whole metal sheet. Thereupon, a Kalman filter with a time-varying stage dependent output matrix is used to estimate the spatial-temporal temperature development of the sheet based on measurements from a thermal imaging camera. Both the proposed modeling approach and the estimation scheme are validated experimentally.

Keywords: Model Reduction, Model Simplification and Optimization, Modelling for Control and Real-Time Applications, Mechanics, Mechatronics, incl. Robotics
Abstract: Spanning applications from microsystems to passenger jets, finite element (FE) models play a crucial role in the design of a wide range of technical products. However, such models are not suited for applications at system-level or in control due to their large scale. While several schemes to obtain models and controllers based on FE models exist, they either require high-level access to the FE software, create black-box models without physical interpretation, or require specialist knowledge. This paper outlines a workflow to generate highly efficient models and appropriate controllers for nonlinear FE models at the push of a button. In a first step, model order reduction via proper orthogonal decomposition creates an accurate surrogate model of drastically smaller dimension. Nonlinearities are handled via the trajectory piecewise linear approximation (TPWL), maximizing compatibility with commercial FE software by exclusively relying on data produced by regular solutions. Complementing TPWL, gain-scheduling is deployed to establish a precise controller. The proposed workflow is demonstrated for a tunable prism, showcasing its efficacy.

Keywords: Fluidics and Thermodynamics, Model Reduction, Model Simplification and Optimization, Modelling for Control and Real-Time Applications
Abstract: Spray drying is a common technique in process engineering, involving analysis tasks for large-scale multiphysics mechanisms, typically addressed using Computational Fluid Dynamics (CFD) software based on Finite Element Model (FEM) simulation. To enable e.g. real-time control schemes to take into account spatio-temporal behavior, efficient Reduced Order Models (ROMs) need to be identified, which in the best case retain physical information and interpretability as much as possible. In this paper, this problem is approached for a simplified two-dimensional spray dryer CFD model. Two different versions of Dynamic Mode Decomposition with control (DMDc) are compared, namely a direct application of DMDc to snapshot data for temperature and humidity profiles, including droplet populations as moving and distributed inputs, and an adaptation exploring structure preservation based on the physical insight to the underlying mechanisms. It turns out that for the presented case study the structure preserving DMDc yields improved results for the same dimension of the ROM in comparison to direct DMDc.

Keywords: Electrical, Electronic and Power Systems, First Principles Modelling, Model Reduction, Model Simplification and Optimization
Abstract: A large-scale wind farm model is presented as a benchmark model for various model order reduction (MOR) methods. Firstly, the detailed mathematical description of a wind turbine generator is provided, including the aerodynamic and mechanical sub-blocks of the wind turbine, the electrical sub-block of the generator, and the associated controllers. Based on the wind turbine generator model, a large-scale wind farm model is created whose dimension can be easily changed to test MOR methods on different scales. Finally, the wind farm model is utilised as a benchmark model to show the performance of a nonlinear MOR method and a linear MOR method.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Model Reduction, Model Simplification and Optimization, ODE, DAE, SODE, SDAE Systems
Abstract: This work introduces a formal framework for model order reduction of an ion exchange process commonly used in water treatment for human consumption. The objective is to retrieve a finite dimension model to describe the advection-diffusion-reaction-equation governing the ion exchange process in a packed bed reactor. A state-space model is derived using a finite-difference scheme to explain the ion exchange process for ammonium removal. Further, a model order reduction step is incorporated to streamline the computational complexity while preserving the essential dynamics of the system. Three model order reduction criteria are established based on the breakthrough curve retrieved by numerical simulations. The results quantitatively demonstrate the influence of the reduction criteria on the behavior of the breakthrough curves. This proposal aims to serve as a reference framework for designing experiments in ion exchange processes for ammonium removal and further optimizing these processes using estimation and control strategies.

Keywords: Model Reduction, Model Simplification and Optimization, First Principles Modelling, Modelling for Control and Real-Time Applications
Abstract: This paper presents an effective single-mode model of laser cavity dynamics, focusing on pulsed lasers, which significantly improves the computational efficiency of state-of-the-art models while exhibiting a comparable model accuracy. The phenomenon of gain-narrowing is discussed starting from a spatially lumped model with a spectrum of multiple longitudinal modes. Based on this information, effective mode parameters are derived, which convert the multi-mode behavior to time-varying dynamics for the total intracavity power. A simulation study for a cavity-dumped Nd:YAG laser shows that the simple model agrees well with the original model. The results presented in this work can be utilized for laser optimization and controller design for a wide range of photonic systems where a compromise between model accuracy and complexity is desired.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Modelling for Control and Real-Time Applications, Data-Driven Models, Neural Networks
Abstract: In this contribution, the Dynamic Mode Decomposition with control (DMDc) is used to derive a surrogate model of a continuous PHA biopolymer production process based on a recently published complex process model. Here, snapshot simulation data of the original model is processed to obtain a linear surrogate model formulation using delay coordinates. The quality of the surrogate is statistically validated within simulation studies. Additionally, the influence of the of the order of delay coordinates is investigated. It is shown, that the highly nonlinear dynamics of the PHA-manufacturing process can be approximated accurately by the DMD- based model even for large variations of initial conditions and control variables. This offers the opportunity to apply well-studied and established tools from robust and optimal control in future investigations.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Modelling for Control and Real-Time Applications, First Principles Modelling
Abstract: This paper addresses the modeling of astaxanthin accumulation in the microalgae Haematococcus pluvialis, a well-known source of natural astaxanthin, under fluctuating environmental conditions. For biomass growth and astaxanthin accumulation first principles models under sufficient nutrient concentration and high incident light exposure are derived. The obtained models are validated using measurement data of an outdoor production plant, and are the basis for implementing an extended Kalman Filter (EKF) for state and unknown reaction rate estimation.

Keywords: Fitting Models to Real Processes, incl. Identification and Calibration, Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Data-Driven Models, Neural Networks
Abstract: In this paper, a practical modeling approach for a batch-operated, stirred reactor is investigated that shows significant deviations in system behavior to the same actuation applied over multiple batches. Starting from an easily identifiable, sub-optimal, linear dynamical model to describe the basic dynamic behavior of the system, an augmented model reformulation is defined. This is used to model observed, nonlinear drift effects and static differences that can be seen in the system response over multiple batches, which can finally be estimated using an extended Kalman filter (EKF). The quality of this adaptive model approach that can be used in an online fashion is further assessed using a prediction error for all performed experiments.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Manufacturing and Process Engineering, Fitting Models to Real Processes, incl. Identification and Calibration
Abstract: In this paper, liquid-liquid-mixer systems modelled by population balance equations are considered. As the control input / manipulated variable, the stirrer speed (and hence the energy dissipation rate) is used to control the distribution of the particle size. Three different measurement signals are considered. We investigate the observability and identifiability of the system for each measurement option and show that only in one scenario the model is observable and structurally identifiable. Further, it is shown that in this scenario, practical identifiability is generally challenging and particular care must be taken to ensure the model with identified parameter values is able to describe the dynamic behaviour of the system.

Keywords: Modelling Uncertainties and Stochastic Systems, Numerical Simulation and Co-Simulation, Medicine, Physiology, Health Care and Biology
Abstract: Crop protection science plays a role in responding to the challenge of food demand with growing population and climate change. Mathematical models able to predict the interactions between the biocides and the crops can be exploited to develop new products that are also safer for the environment. This project focuses on modelling the foliar uptake of pesticides, where the goal is to obtain a reliable predictive model for the system. Several sources of uncertainty are present when modelling this systems: intrinsic biological variability between leaves, experimental data variability, uncertainty on the physico-chemical phenomena in the systems, uncertainty in the parameters when calibrating the model. These effects contribute to the uncertainty in the model predictions, addressed in this paper. It is proposed use a systematic modelling approach to consider the different sources of uncertainty. The framework consists of 6 key steps: (1) formulation of different candidate models, (2) preliminary analyses on the identifiability of the model parameters and any identifiability issue is addressed, (3) characterise the variability in the experimental data, (4) application of Model-Based Design of Experiments (MBDoE) techniques for model discrimination and for parameter precision, (5) the model parameters are precisely estimated and validated statistically, (6) the model predictions are statistically validated based on new experimental data. In MBDoE there are methods that exploit directly the uncertainty in the model predictions instead of the variance in the parameters. To assess which MBDoE approach is more beneficial when building a predictive model for foliar uptake, here the study of error propagation from the parameters to predictions is presented. This analysis is conducted on a diffusion-based model by sampling the uncertainty region of the parameters. An uncertainty reduction scenario is considered, and the reduced parameter uncertainty allows to sensibility reduce the prediction uncertainty. This analysis paves the way to the application of MBDoE techniques in the context of biological systems, in particular for the foliar application of biocides.

Keywords: Mechanics, Mechatronics, incl. Robotics, ODE, DAE, SODE, SDAE Systems, Discrete and Discrete-Event Systems, incl. Petrinets
Abstract: In the present contribution, the possibilities of transferring vibration energy from lower to higher modes of vibration of a beam-like structure by applying impulsively shaped moments are investigated. It is shown that with this concept, the enhanced damping capacities of higher modes can be utilized more effectively, resulting in a faster decay of transient vibrations compared to the autonomous case. The impulsive excitation is designed to be state-dependent in a way that neither energy is extracted from the mechanical system, nor external energy is fed to the system across impulses. The applied modelling approach results in a non-smooth system description which allows to design the impulsive actuation a-priori.

Keywords: Automotive, Aerospace, Transportation Systems, Modelling for Control and Real-Time Applications, Comparison of Methods for Modelling
Abstract: The study of vehicle behavior for the development of guidance algorithms has been widely explored. In agriculture, tractor guidance systems are now standard features in premium machinery. The next step to further improve precision is to achieve centimeter-level guidance for connected implements, especially those equipped with additional steering capabilities. Compared to the tractor-only scenario, the complexity of model design increases, and there is no established consensus among manufacturers on the preferred modeling approach. To facilitate interoperability between implement and tractor manufacturers, a generalized approach is required and has been previously proposed. This work presents an enhanced model that features an abstracted control interface for actuated towed implements. This interface is designed to be extendable to hitched implements and can account for known tire side-slip. For more detailed simulations, a dynamic version of the model is derived, allowing for the use of advanced tire and force models. The paper includes a systematic derivation of both kinematic and dynamic models, as well as first simulation results.

Keywords: Mechanics, Mechatronics, incl. Robotics, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, Fitting Models to Real Processes, incl. Identification and Calibration
Abstract: Recently, research has focused on the ankle joint and pedal angles. Therefore, we measured the change in pedal angle in the horizontal plane, revealing a difference in pedaling characteristics. In this study, a computational model was proposed to accurately measure the rotation angles of both bicycle pedals. The system consisted of three wireless motion sensors with biaxial acceleration and an angular velocity sensor attached to the crank arm and both pedals. The rotational pedal angles measured by the motion sensors were compared with data from a motion-capture system. The root-mean-square error for the bicycle pedal angle was 0.429 ± 0.138° (mean ± SD), and the correlation coefficient was 0.9996 for the combined pedals. Using the proposed computational model, both pedal angles were measured with the same accuracy as that of the motion-capture system but with a higher frequency.

Keywords: Mechanics, Mechatronics, incl. Robotics
Abstract: To ensure structural stability of fire service turntable ladders, the working range and actuator velocities are usually limited based on static calculations with conservative safety factors. Considering dynamic effects through an online stability measure may potentially allow for a more efficient limitation of ladder movements in future, aiming to enhance the performance of turntable ladders.Within this work, a rigid body model of a turntable ladder is derived enabling the elevation and extraction of the ladder parts as well as the outrigger lifting off the ground in case of vanishing contact force. The dynamic equations are derived using the Lagrange formalism. Subsequently, the dynamic stability measure NTOPv3 from Bennett (2019) is applied to assess a margin for the tip-over stability of the manipulator. Two exemplary trajectories are analyzed to examine the respective stability measure. These simulations reveal that initiating an emergency stop based on the stability measure prevents a possible tip-over. Therefore, the NTOPv3 measure is shown to be a useful tool for determining the position and velocities limits of the manipulator actuators of the turntable ladder.

Keywords: Mechanics, Mechatronics, incl. Robotics, ODE, DAE, SODE, SDAE Systems, Electrical, Electronic and Power Systems
Abstract: By exploiting controllable asymmetries, consensus in networks can be adjusted. In case of coupled oscillators, the characteristic frequencies of the network can be controlled. This property is called {frequency tunability} and {it is, e.g., induced by changing the asymmetry between the damping of the oscillators or the coupling between the oscillators.} Subsequently, the frequency tunability of two diffusively coupled Andronov-Hopf oscillators is investigated by analyzing the emergence of Andronov-Hopf bifurcations. This is done by investigating the local dynamics of the corresponding system. It turns out that the number of critical points of the Andronov-Hopf bifurcation is determined by analyzing a polynomial whose degree changes based on the choice of the bifurcation parameter. Thus, this polynomial is analyzed in terms of two different bifurcation parameters: (i) symmetric damping and (ii) symmetric coupling. In case of (i), the system has two critical points, which correspond to Andronov-Hopf bifurcations. In contrast to this, for (ii) the number of critical points varies between one and three depending on the asymmetric damping.

Keywords: Discrete and Discrete-Event Systems, incl. Petrinets, Automation of Modelling and Software tools, incl. Computer Modelling
Abstract: Byzantine Fault Tolerance (BFT) is a key framework for improving the resilience of distributed systems, particularly in blockchain networks. However, a major drawback of current consensus mechanisms is their inability to adapt to changing validator behavior. This paper introduces a novel probabilistic opinion dynamics model aimed at analyzing and predicting validator behavior in BFT-based blockchain systems. The model simulates the evolution of validator states and opinions to detect security vulnerabilities and anomalies that could compromise the network’s integrity. By monitoring the proportion of validators exhibiting similar behaviors or voting patterns, the model enables early detection of suspicious activities, allowing timely interventions through appropriate countermeasures. Simulation results demonstrate the model’s effectiveness in identifying and mitigating various forms of attacks, including transient and persistent threats, thereby enhancing the security and overall resilience of the blockchain network.

Keywords: Modelling for Control and Real-Time Applications, Data-Driven Models, Neural Networks
Abstract: Artificial neural networks and their applications in deep learning have recently made an incursion into the field of control. Deep learning techniques in control are often related to optimal control, which relies on the Pontryagin maximum principle or the Hamilton-Jacobi-Bellman equation. They imply control schemes that are tedious to implement. We show here that the new HEOL setting, resulting from the fusion of the two established approaches, namely differential flatness and model-free control, provides a solution to control problems that is more sober in terms of computational resources. This communication is devoted to the synchronization of the popular Kuramoto's coupled oscillators, which was already considered via artificial neural networks by L. Böttcher et al. (Nature Commun., 2022), where, contrarily to this communication, only the single control variable case is examined. One establishes the flatness of Kuramoto’s coupled oscillator model with multiplicative control and develops the resulting HEOL control. Unlike many examples, this system reveals singularities that are avoided by a clever generation of phase angle trajectories. The results obtained, verified in simulations, show that it is not only possible to synchronize these oscillators in finite time, and even to follow angular frequency profiles, but also to exhibit robustness concerning model mismatches. To the best of our knowledge that has never been done before. Concluding remarks advocate a viewpoint, which might be traced back to Wiener's cybernetics: control theory belongs to AI.

Keywords: Medicine, Physiology, Health Care and Biology, ODE, DAE, SODE, SDAE Systems
Abstract: In this work, we propose an approach to determine the dosages of antithyroid agents to treat hyperthyroid patients. Instead of relying on a trial-and-error approach as it is commonly done in clinical practice, we suggest to determine the dosages by means of a model predictive control (MPC) scheme. To this end, we first extend a mathematical model of the pituitary-thyroid feedback loop such that the intake of methimazole, a common antithyroid agent, can be considered. Second, based on the extended model, we develop an MPC scheme to determine suitable dosages. In numerical simulations, we consider scenarios in which (i) patients are affected by Graves' disease and take the medication orally and (ii) patients suffering from a life-threatening thyrotoxicosis, in which the medication is usually given intravenously. Our conceptual study suggests that determining the medication dosages by means of an MPC scheme could be a promising alternative to the currently applied trial-and-error approach.

Keywords: ODE, DAE, SODE, SDAE Systems, Medicine, Physiology, Health Care and Biology, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing
Abstract: This paper presents an extensive local and global sensitivity analysis of a mathematical model describing the hypothalamus-pituitary-thyroid axis. The model is based on a system of differential equations describing the dynamic interactions between the key physiological variables: thyroid-stimulating hormone, free thyroxine, the functional size of the thyroid gland and anti-thyroid peroxidase antibodies. We employed the local sensitivity analysis to assess the response of the system to minor alternations in individual parameters, thereby providing insight into the immediate responsiveness of the hypothalamus-pituitary-thyroid axis. To extend the analysis, we also conducted a global sensitivity analysis using latin hypercube sampling combined with partial rank correlation coefficients. Latin hypercube sampling ensures efficient sampling, while partial rank correlation coefficients permit the examination of both linear and non-linear, but monotonic relationships between parameters and output. This dual approach provides a more comprehensive understanding of the impact of variations in key physiological factors on the system globally. Concluding, the findings of these sensitivity analyses have the potential to facilitate the development of patient-specific diagnostics, providing valuable insight into the individual variability in thyroid function.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: A brief review of existing medical dosage guidelines for Graves' disease is conducted. This motivates to derive a recommendation strategy and a performance assessment via limit cycle stability analysis. For this purpose, an existing mathematical treatment model is simplified by incorporating medical aspects. From an application point of view, this is related to suboptimal treatments which can be approximated by a proportional controller in combination with a time-discretization of the closed-loop model for incorporating the effect of regular appointments with a physician. The presented results highlight critical aspects to be considered during treatment.

Keywords: ODE, DAE, SODE, SDAE Systems, Medicine, Physiology, Health Care and Biology, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing
Abstract: This paper presents an extensive global sensitivity analysis of a mathematical model describing the female endocrine cycle. The model, based on a system of differential equations, captures the dynamics of Luteinizing Hormone, Follicle-Stimulating Hormone, Estrogen, and Progesterone, along with their regulatory feedback mechanisms. We employed three complementary methods – Latin Hypercube Sampling, Partial Rank Correlation Coefficient, and extended Fourier Amplitude Sensitivity Test – to analyze both linear and non-linear parameter-output relationships. The extended Fourier Amplitude Sensitivity Test method, in particular, revealed non-monotonic and non-linear interactions between input and output, highlighting the complexity of the hypothalamus-pituitary-ovary axis. Our findings offer significant insights for future model refinement and pave mathematical ways towards better understanding of the female endocrine cycle and potential clinical applications, especially in the diagnosis and treatment of reproductive disorders.

Keywords: First Principles Modelling
Abstract: Modern physics is facing a philosophical dilemma: its two main pillars, quantum theory and the theory of gravity, are rooted in world views that mutually exclude each other. If quantum physics is correct, we need to radically rethink our notions of space and time. If gravity theory is correct, quantum physics requires a dramatic revision. This is an experimental problem. However, up to this date there is no evidence that gravity requires a quantum description. Quantum experiments with increasingly massive particles may change that situation – by directly probing how gravity reacts to a quantum object.