Keywords: Automotive, Aerospace and Flight Engineering, Mechanics, Mechatronics, incl. Robotics
Abstract: Model based development is seen as a key methodology for handling the complexity and guiding the development and optimization of future complex hybrid electric vehicles. It can help reduce the time to market and thus increase the pace of innovation, but a cornerstone for a high innovation pace is the availability and reusability of mathematical models. In this presentation, we will follow the initiation and development of a diesel engine model that has been much used and evolved over the years to become used in a wide range of applications beyond the initial intentions. Starting as a model for a long haulage truck it has been refitted to a passenger car, reused in a diesel electric powertrain in an off-highway application, reused as building blocks for a large marine engine model. Where analysis and adaptive control based on the model has been used to develop clean marine engines fulfilling the UN emission goals. It is now the cornerstone in a benchmark model for development of planning strategies in future connected vehicles as well as in a model for studying hybrid vehicles and how the powertrain interacts with the after-treatment system. Much of the success of the model, builds on the fact that it is component based, systematically developed, and adapted to a real-world engine with documented agreement with measurement data, in addition to that it was released as an open-source model that can be freely downloadable and modified.

Keywords: Model Reduction, Model Simplification and Optimization, ODE, DAE, SODE, SDAE Systems
Abstract: The problem of closed-loop control for for high dimensional nonlinear systems is considered. Three different types of kernel interpolation surrogates for the optimal feedback policy are compared. The data for this comes from open-loop controlled solutions. Here, additional information about the system originating from the Pontryagin Maximum Principle is exploited. The starting position for the open-loop control is adaptively selected by a geometric greedy selection criterion, and a so-called vectorial kernel orthogonal greedy algorithm is performed to set up the surrogate. With this procedure we can overcome the curse of dimensionality and still receive a very precise, robust and real-time capable feedback control.

Keywords: Model Reduction, Model Simplification and Optimization, Automation of Modelling and Software tools, incl. Computer Modelling
Abstract: pyMOR is a free and open source software library for writing model order reduction applications with the Python programming language. Implemented algorithms include both Reduced Basis and system-theoretic reduction methods, as well as non-intrusive approaches such as approximation with artificial neural networks. All these algorithms can be easily integrated with external high-performance PDE solver packages. In this poster contribution we give a brief overview on the design of pyMOR. Further, we will present in more details two main features of the upcoming 2022.1 release: 1. a new and unified model hierarchy, 2. new discretization routines to create these models from common analytical problem definitions using different PDE solver backends.

Keywords: Model Reduction, Model Simplification and Optimization, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Modelling for Control and Real-Time Applications
Abstract: We discuss nonlinear model predictive control (MPC) for multi-body dynamics via physics-informed machine learning methods. In more detail, we use a physics-informed neural networks (PINNs)-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator. PINNs are a promising tool to approximate (partial) differential equations but are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus follow the strategy of Antonelo et al. (arXiv:2104.02556, 2021) by enhancing PINNs with adding control actions and initial conditions as additional network inputs. Subsequently, the high-dimensional input space is reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms for the underlying optimal control problem.

Keywords: Model Reduction, Model Simplification and Optimization, ODE, DAE, SODE, SDAE Systems, Mechanics, Mechatronics, incl. Robotics
Abstract: We present a method to compute reduced models of second-order dynamical systems valid in a desired frequency range without specifying the order of the reduced models prior to the reduction process. The approach is based on a second-order variant of the iterative rational Krylov algorithm (SO-IRKA) and exploits the fact, that an eigenvalue decomposition of the reduced second-order system yields twice as many eigenvalues as its order. By selecting all eigenvalues whose mirror images lie in the frequency range in which the reduced model should be valid during each iteration of SO-IRKA, the order of the reduced model is growing (or shrinking) until a reasonable reduced order is found. Additionally, we show that performing the SO-IRKA optimization steps on an intermediate-sized model yields accurate reduced-order models while the computational cost of the reduction phase is reduced. We show the effectiveness of the proposed method by applying it to numerical models of a vibro-acoustic system.

Keywords: Numerical Simulation and Co-Simulation, Multiscale Modelling, Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: We propose a novel poroelastic model for the formation of extracellular oedema and infectious myocarditis valid in large deformations. This is expressed as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. In this work, we address the model sensitivity to its parameters and then perform a complete numerical analysis of the time-discrete problem, meaning that we study its well-posedness, numerical convergence and preconditioning. Our analyses rest at the multi-physics nature of the poblem: on one hand, the poroelastic system exhibits a saddle point structure which requires the use of higher order elements for the displacement, whereas the chemotaxis model is parabolic-like. The results show that the proposed model is adequate for modeling the formation of oedema in realistic geometries, as well as for its use in large scale simulations. The main application that we envision for our model is that of replacing the invasive endomyocardial biopsy, used for the detection of oedema formation, with computational models hinging only on an MRI.

Keywords: Medicine, Physiology and Biology, Automation of Modelling and Software tools, incl. Computer Modelling, Fluidics and Thermodynamics
Abstract: Positron emission particle tracking (PEPT) enables us to track a single particle in a complicated flow through an opaque environment. Despite its potential application in medical imaging and diagnosis, the uncertainties of the measurement of PEPT are yet to be fully understood. We have investigated the errors associated with the blood velocity measurement in a stenosed coronary artery. We analysed the error between the velocity profile calculated using computational fluid dynamic (CFD) techniques and the reconstructed velocity profile using the information of limited trials of single-particle tracking. The results show that the particle tracking time step and the number of particles, significantly affect the accuracy of the velocity reconstruction downstream of the stenosis. For instance, in a case with 50% blockage and a Reynold number of 250, the maximum acceptable tracking time step (with less than 10% error) was 2.5 ms. Such analyses are necessary to determine the range of the error of PEPT measurement in the cardiovascular system for potential clinical application in the future.

Keywords: Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, Medicine, Physiology and Biology, Numerical Simulation and Co-Simulation
Abstract: Radiofrequency catheter ablation is a minimally invasive procedure commonly used for the treatment of cardiac arrhythmias. Several models have been introduced to simulate the RF ablation procedure, which provide lesion size estimations at the end of the ablation. Typically, either the 50oC isotherm is considered as an estimation for the lesion, or an Arrhenius type model, which accounts for the time at which the tissue is at an altered state. In this work a three-state cell death model is considered for the estimation of the lesion, which captures the shrinkage of the damage region after the completion of the ablation. At first, the model is calibrated for the thermal death of cardiac myocytes. Then, the calibrated model is incorporated in a 3D computational framework of radiofrequency catheter ablation to estimate the resulting lesion. A comparison against experimental results and against previous lesion size estimations is also provided.

Keywords: Modelling in Manufacturing and Process Engineering, Modelling Uncertainties and Stochastic Systems
Abstract: In today’s chemical industries commercial software tools employing state-of-the-art models and advanced optimization and control algorithms are used at different stages of the project life cycle, from early stages performing scale-up and conceptual process design, front-end engineering design to retrofitting and optimization studies at the plant commissioning/operation stage. The impact of advanced process modeling and simulation, optimization and control is profound and has become mainstream in the chemical industries due to the significant economic benefits achieved. These are amongst crown achievements of the process systems engineering community in Chemical Engineering discipline through research in mathematical programming, modeling, process synthesis and design and process control that has been performed in the past decades. Today there are new driving forces affecting the bottom line of chemical industries but also universities alike namely digitalization, machine learning/Artificial Intelligence (AI), climate change, decarbonization, sector coupling through renewable energy, etc. These technologies open up new horizons for industry to become more efficient, to decrease CO2 footprint and to develop innovative products and services. As model-based engineering becomes more established as enabling technology to address these challenges, in this talk we review the critical role of uncertainty and sensitivity analysis methods starting from the fundamental theory of Monte Carlo integration to sensitivity analysis using variance decomposition methods. Here an important distinction between when a study is about uncertainty and when it is about sensitivity analysis will be discussed. A number of applications from process systems engineering which employs largely first principles models but also machine/deep learning models are covered. These examples include a range of engineering problems related to model identification/parameter estimation (in process/property modeling) to process synthesis and design and optimization. From these experiences, a critical analysis of the theory and pitfalls encountered in the application of uncertainty & sensitivity analysis in wider process systems engineering is given.

Keywords: Fitting Models to Real Processes, incl. Identification and Calibration, Modelling for Control and Real-Time Applications, Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: Output sensitivities to parameters underly a highly efficient sensitivity based algorithm to compute local structural identifiability of possibly large-scale nonlinear dynamic systems. By means of simple examples, this paper explores exceptional cases where this algorithm fails. That is, if one applies the common definition of local structural identifiability. As also shown in this paper, when applying a closely related definition of identifiability, based on sensitivities, the sensitivity based algorithm always provides the correct answer. The subtle difference between these two definitions, that seems to have been overlooked in the literature, is further explored and explained in this paper. For the common definition of local structural identifiability, an extension of the sensitivity based algorithm is presented that approximately doubles the computation time. This extension is shown to work along nonsingular trajectories.

Keywords: Modelling Uncertainties and Stochastic Systems, Model Reduction, Model Simplification and Optimization, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing
Abstract: This work is concerned with learning the dynamics of technical systems from data within a sparse Bayesian framework. The approach employs a basis representation of the unknown dynamics function, similar to the sparse identification of nonlinear dynamics (SINDy) approach, which is combined with a Bayesian procedure for parameter estimation. We propose to use the recently introduced neuronized priors as a unified approach to enforce sparsity in a dynamical systems context, and illustrate the method with an academic example.

Keywords: Modelling Uncertainties and Stochastic Systems, Numerical Simulation and Co-Simulation, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: The quality of molecular dynamics (MD) simulations critically depends on the employed potential energy model. Accurate uncertainty quantification (UQ) of these models could increase trust in MD simulation predictions and promote progress in the field of active learning of neural network (NN) potentials. Bayesian methods promise reliable uncertainty estimates, but the high computational cost of training via classical Markov Chain Monte Carlo (MCMC) schemes has prevented their application to deep NN potentials. In this work, we propose stochastic gradient MCMC methods as a computationally efficient option for Bayesian UQ of MD potentials. The stochastic gradient Langevin dynamics method yields promising results for a tabulated coarse-grained water model and could thus be a feasible approach for NN potentials. Additionally, we illustrate the inherent limit of Bayesian UQ imposed by the functional form of the employed model.

Keywords: Automotive, Aerospace and Flight Engineering, Modelling for Control and Real-Time Applications, Modelling Uncertainties and Stochastic Systems
Abstract: Currently, the field of vehicle safety systems can be divided into active and passive systems. According to this definition, active systems ideally prevent an accident from happening, while passive systems mitigate the crash consequences for the occupants. Each actuator has its own operating time, activation logic, and operating principle. It is beneficial in many critical driving situations if the individual safety systems do not operate separately but pursue a joint strategy to protect the occupants. The increasing number of sensors on and inside the vehicle and the improved data accessibility in the vehicle make a holistic intervention strategy possible. A mathematical description of the whole driving scene is necessary to decide model-based later when and which actuator should intervene.

This paper presents an approach for a mathematical framework that combines different sensor data, states, correlations, probabilities, and uncertainties in one mathematical framework. The various variables and their relationships are represented by using a bipartite graph as a basis. In this work, one exemplary branch represents the states of the ego vehicle and one neighboring road user detected by perception. From the available states and the resulting path prediction, the time-to-collision (TTC) is derived.

This framework aims to be later extended and used for decision-making to deploy the safety actuators in the best possible way to optimally protect the occupants depending on the driving scenario, occupant occupancy, and seating positions.

Keywords: Modelling for Control and Real-Time Applications, Model Reduction, Model Simplification and Optimization, Fluidics and Thermodynamics
Abstract: Air conditioning systems are indispensable in all modern production cars, as they ensure thermal comfort for the passengers. Besides that, extended air conditioning systems allow for additional tasks like tempering the battery in hybrid and electric vehicles. To fulfill these multiple tasks, an advanced control structure has to be applied. Since the components of the air conditioning system are constantly optimized and new structures are developed, an efficient controller design requires a model-based approach to handle the diversity and allow for a fast adaptation to different structures.

This paper considers such an approach: For the usage in a two degree of freedom control structure a feedforward controller is derived. This controller is designed as a multiple-input-multiple-output controller with a flatness based approach. To apply the concept on the model of the air conditioning system, a nonlinear model order reduction is performed. The presented reduction method is extended by a frequency scaling on the reduction data and the reduced model is validated with experimental data.

Keywords: Modelling for Control and Real-Time Applications, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: Recent progress in model predictive control (MPC) has shown great potential to control complex nonlinear systems in real-time. However, if parts of the controlled system cannot be modeled exactly by differential equations, the performance of MPC can decrease significantly. This paper approaches this problem by combining MPC with deep reinforcement learning (DRL) to a hierarchical control system, which is applied to control the motion of an autonomous vehicle. While the DRL algorithm is responsible for the decision-making with regard to obstacles on the street, the model predictive controller deals with the nonlinear dynamics of the vehicle. To this end, the vehicle dynamics are modeled by differential equations and the decision-making problem is modeled as a Markov decision process (MDP). The decisions are considered in the optimization problem of the controller, whose cost function, in turn, is considered in the reward function of the MDP. The performance of the hierarchical vehicle control is evaluated in scenarios with static and moving obstacles. Furthermore, it is examined whether adding information about the predicted trajectory to the state space of the MDP can increase the convergence speed.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Medicine, Physiology and Biology, Computing Systems, Discrete and Discrete-Event Systems, incl. Discretisation of Continuous Systems, Petrinets
Abstract: Using the i-Tree software, this paper provides an overview of the ecosystem services of urban trees in Berlin. The purpose of this study is to determine the feasibility of research studies concerning the ecosystem ser-vices of Berlin's urban trees based on the Berlin Geoportal. The results of the analysis should highlight which further information on urban trees would be necessary to improve the informative value of future studies and, based on this, to improve the structure of the tree population and to enable the continuous provision of benefits by urban trees.

Keywords: Medicine, Physiology and Biology, Automation of Modelling and Software tools, incl. Computer Modelling, Model Reduction, Model Simplification and Optimization
Abstract: To provide a tool for the generation and evaluation of crop rotations in organic farming systems, the Leibniz-Centre for Agricultural Landscape Research ZALF e.V. has developed the software tool ROTOR in Microsoft (MS) Access beginning in 1997. Its database contains information on crops and crop production activities (CPAs). These CPAs obtained through expert knowledge are sets of crops and their cultivation methods, the resulting nitrogen (N) delivery as well as the N-need, describing the time range from stubble tillage until the harvest. They facilitate the generation of crop rotations crucial to organic farming based on a static rule-based model. It allows furthermore to evaluate nutrient-balances and yield projections, taking site-specific factors into account. The fact that ROTOR runs within the commercial software MS Access and the software’s structure and database that have grown over the years, becoming less maintainable, made a software re-engineering indispensable. The newly developed version of ROTOR is a standalone software written in Python with a PostgreSQL database. Although the core principles of the underlying models have remained, the calculations of nutrient-balances were refined, whereas the generation of crop rotations was comprehensively revised. Its modular structure allows for better maintainability and scalability.

Keywords: Education in/for/with Modelling, Fitting Models to Real Processes, incl. Identification and Calibration, Computing Systems, Discrete and Discrete-Event Systems, incl. Discretisation of Continuous Systems, Petrinets
Abstract: Student analytics relates student characteristics (e.g. gender, country of origin, prior education) to Key Performance Indicators such as length of study and drop-out quota. In that context, work has been largely based on Data Analytics and statistical analysis. Dynamic aspects of studying - such as individual factors affecting study success, student-student and student-lecture interactions - cannot be captured in that manner, which is why this paper argues for the employment of Agent-Based and Discrete Event Simulation in addition to the aforementioned approaches. Apart of being novel, our contribution lies in the conception of a simulation model called PASSt-A, which defines the data semantics and procedures used for study analytics in an extensible manner.

Keywords: Fitting Models to Real Processes, incl. Identification and Calibration, Computing Systems, Discrete and Discrete-Event Systems, incl. Discretisation of Continuous Systems, Petrinets, Electrical, Electronic and Power Systems
Abstract: Creating behavioral models for radio frequency (RF) devices is a challenging task. Most approaches require a substantial prior knowledge of the physical structure in order to be able to generate suitable mathematical models for the desired characteristics. However, since it is usually not attractive for manufacturers to pass on extensive knowledge about internal components to third parties, one has to rely mainly on black- or gray-box models. An approach is to fit a parameterized model based on representative measurement data, following the example of the Hammerstein-Wiener models. With this approach, only simple linear least squares problems have to be solved and special structures encourage the use of efficient solution methods. In this paper, the general fitting procedure will be discussed and suggestions for successful device modeling will be provided

Keywords: Electrical, Electronic and Power Systems, Modelling for Control and Real-Time Applications, Model Reduction, Model Simplification and Optimization
Abstract: Power converters employ high-frequency switching between multiple switch states, each of which causes the system to exhibit a different dynamic behavior. Averaged models are a common simplification used for describing the behavior in one or two specific cycles of switch states, also called operating modes. In this context, we propose extending the method of Sun et al. (2001, Averaged modeling of PWM converters operating in discontinuous conduction mode. IEEE Trans. Power Electron., 16(4), 482-492), which allows averaging in two operating modes, to a converter model with four operating modes. We show in simulations that our model results in a reasonable approximation of the true moving average of the original switching converter model during large transients that pass through multiple operating modes.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Comparison of Methods for Modelling, Alternative Modelling Methods (Fuzzy, CAS, NN, etc.)
Abstract: This paper addresses the problem of data-based optimization of electric arc furnace (EAF) energy consumption. In the steel industry, optimization of production processes could lead to savings in energy and material consumption. Using data from EAF batches produced at the SIJ Acroni steel plant, the consumption of electrical energy during melting was analysed. For each batch, different parameters and signals were measured, such as the weight of the scrap, injected oxygen, added carbon, energy consumption, etc. After the preprocessing phase (detection of anomalies and outliers), the most influential regressors were analysed and selected for further modelling and prediction. In the modelling phase, we focused on evolving fuzzy modelling method in comparison with some established machine learning methods. The obtained static models were used to predict the total energy consumption of the current batch. All models were trained with 70% of data and validated and compared with 30% of data. The experimental results show that the proposed models can efficiently predict the energy consumption, which can be used to reduce the energy consumption and increase the overall efficiency of the electric steel mill.

Keywords: Model Reduction, Model Simplification and Optimization, Electrical, Electronic and Power Systems, ODE, DAE, SODE, SDAE Systems
Abstract: In this work, we present topology optimization of a piezoelectric energy harvester device for broadband energy harvesting. Common design goal of such multi-resonant devices is having constant, usable power output over a large range of operational frequencies. The presented folded beam energy harvester aims for having its first two resonance frequencies in close proximity. In order to achieve this goal, we consider topology optimization with different goal functions: compliance-based and frequency-based. Both approaches result in promising designs, which show sufficient performance over a considered frequency range.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Medicine, Physiology and Biology, First Principles Modelling
Abstract: Mathematical metabolic modelling is a systematic endeavour to allow identifying the main causes of an observed metabolic change and to estimate the consequences of an imposed metabolic perturbation regarding a biosystem. Dynamic Constraint-based modelling (DCBM) has delivered promising results in metabolic engineering and in bioprocess design by providing mechanistically relevant systems-level knowledge of a network of bioreactions. Here, we seek to establish a DCBM approach that leverages convex optimization and nonlinear regression mathematical toolkit to estimate dynamic intracellular metabolic flux distributions in stored Red Blood Cells (RBCs) for transfusion purposes. First, we developed an ad-hoc metabolic network including 77 reactions and 74 metabolites, second, we adapted Flux Variability Analysis (FVA) technique to quantify the connection between exometabolomic dynamics and the dynamics of feasible intracellular reaction flux ranges. We have obtained fine-grained flux range dynamics of the intracellular reactions for the benchmark data published in Bordbar et al. (2016). Then, we defined four objective functions regarding the accumulation of oxidative stress in stored RBCs for performing a dynamic Flux Balance Analysis (DFBA). In all four cases, time-resolved flux predictions were obtained respecting the imposed equality and inequality constraints. Last, we adapted a quadratic programming (QP) approach to calculate the Euclidean distance between the dynamic optimum flux vectors. The DCBM approach we have developed herein along with the developed metabolic network showed being suitable for the computational analysis of RBCs metabolic behaviour, and it is thought to be useful for other biosystems.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, Modelling for Control and Real-Time Applications
Abstract: This paper describes the extension of a baker's yeast growth model to account for the intracellular trehalose storage and mobilization. Trehalose is a reserve carbohydrate that is accumulated and converted back to intracellular glucose when the yeast cells face certain stresses. This is modeled by a new macroscopic reaction, which is coupled to an existing macroscopic reaction scheme describing the coordinated uptake of glucose and ammonium by the yeast cells. The dynamics of the trehalose concentration is described by a delay differential equation as the available experimental data used to fit the model exhibits a time-delayed correlation between trehalose storage and glucose uptake as well as a time-delayed correlation between trehalose mobilization and ethanol respiration phases. The proposed extension contains 6 parameters of which 5 are estimated via nonlinear least squares identification. The proposed model predicts accurately the dynamics of trehalose storage and mobilization and can be used to optimize the intracellular trehalose accumulation in Saccharomyces cerevisiae, which is valuable for obtaining reinforced yeast cells, able to better withstand drying operations.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Bio-Technical, Bio-Chemical and Chemical Engineering Processes, First Principles Modelling
Abstract: In bioprocesses, it is important to model the kinetics of the macroscopic rates of reactions since these are required to catch the dynamical aspects of a process. In [Wang et al.2020], a modeling method involving Gaussian processes has been developed, using a kernel especially designed for the modeling of Monod-type kinetics (activation, inhibition, double component, neutral effect). However, as will be illustrated in this paper, when the number of training data is limited or the metabolite concentration data do not have large variations (which is generally the case for real-life data), this kernel can yield inaccurate models for the kinetics. In this paper, we develop a new kernel better tailored for the modelling of Monod-type kinetics and we show that it has good modeling performances in the case of limited number of data. The idea is to use the particular structure of Monod-type functions in the design of the kernel, i.e., we incorporate prior knowledge in the modeling.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Fitting Models to Real Processes, incl. Identification and Calibration, Modelling for Control and Real-Time Applications
Abstract: Anaerobic digestion is a widely employed technique that converts waste into biogas, which can be employed as renewable energy. To improve its efficiency, but also to treat recalcitrant waste, mixes involving several types of feedstock with different biodegradability rates are fed to the process. Finding the proper mix is difficult and involves extensive, long-lasting experimental work. This paper presents an approach which allows determining the mix with desired properties based on Biochemical Methane Potential (BMP) tests, chemical composition of the feedstocks and optimization. This procedure is illustrated based on experimental data gathered from BMP tests on leaves of linden, oak and maple, and meadow. Subsequently, a simple model is used to simulate the continuous operation of the process converting the proposed mixes into methane.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Modelling Uncertainties and Stochastic Systems, Model Reduction, Model Simplification and Optimization
Abstract: Multi-objective optimization is used when a system needs to be optimized for multiple conflicting objectives. However, the solution of such a problem is not one point but a set of equally optimal points called Pareto points which highlight the trade-off required to achieve optimization of one objective over another. As any computer aided approaches depend on the model, any uncertainties in the model have a large influence on the solution of the optimization. Thus, the uncertainty needs to be incorporated into the optimization methodology. In this paper, along with incorporating uncertainty in the optimization, an ellipsoid based filter is described to select points in the Pareto set which are significantly different from each other. This filter is applied to the case study of beer fermentation. Fermentation is a key step in brewing which affects the flavour and stability of beer. Along with operating parameters like yeast pitching, dissolved oxygen, etc., fermentation temperature has a large influence on beer flavour and fermentation progression. In this paper, this temperature profile is optimized using multi-objective optimization for conflicting objectives. The novel Pareto ellipsoid based filter is used to discriminate between Pareto points and generate a Pareto set that contains only the relevant solutions.

Keywords: Model Reduction, Model Simplification and Optimization, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing
Abstract: In analysing the observability, identifiability, and controllability of smooth (possibly non-linear) dynamic control systems, the authors identified numerous ways to improve both the accuracy and efficiency of their computations. We summarize a few techniques that help to pinpoint exactly what kind of linear dependencies exist between parametric output sensitivities. These relations, in turn, can be traced back with the help of computer algebra software to an exact re-parametrizations of the original model. The suggested techniques to increase the accuracy of results will be presented on the basis of a few examples.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, ODE, DAE, SODE, SDAE Systems, Numerical and Symbolical Methods for Modelling, incl. Inverse Problems, Aspects in Scientific Computing
Abstract: In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensor-train method by performing inference tasks such as smoothing and parameter inference using the tensor-train framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensor-train format, a significant reduction of the computational time is observed as well.

Keywords: Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, ODE, DAE, SODE, SDAE Systems, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: In (bio)chemical process engineering, first-principles process models have played a central role for some time in better understanding, monitoring, and controlling these complex processes. Dynamic process models have become even more critical in the context of Industry 4.0 and the use of digital twins in the last decade. However, the quality and the technology readiness level of digital process models depend crucially on the reliability of the model predictions. In addition to a suitable model structure/hypothesis, the model parameters of the implemented kinetics are of paramount importance. The accuracy of the parameter estimation, in turn, depends on the quantity and quality of the data as well as on the employed parameter identification solving strategies, where ordinary least squares concepts are still the standard. We propose a novel parameter identification concept that combines systems theory and machine learning principles. The parameter identification problem is formulated as a total least squares optimization problem that uses neural ordinary differential equations for surrogate modeling and recalculates the model control inputs with the algebraic differential flatness framework for model inversion. The usefulness of the proposed concept for more precise kinetic parameters is demonstrated with a simulation study of an enzyme-catalyzed biochemical process, where the total least squares approach leads to lower parameter uncertainties compared to the standard concept based on ordinary least squares using the same amount of data.

Keywords: Model Reduction, Model Simplification and Optimization, First Principles Modelling, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs)
Abstract: This paper shows that a tree-like network with damage can be modeled as the product of a fractional- order (FO) nominal plant and a FO multiplicative disturbance, which is well structured and completely characterized by the damage amount at each damaged component. Such way of modeling brings insight about that damaged network’s behavior and helps us design robust controllers under uncertain damages and identify the damage.

Keywords: Mechanics, Mechatronics, incl. Robotics
Abstract: The application of a recent beam model requires the evaluation of a suitably defined shear deformability tensor in order to ensure both energetic and geometric consistency with the 3D Saint Venant model subjected to non-uniform flexure and torsion. Actually, whatever is the position of the shearing force, the beam model provides the same elastic energy and the same tip displacement of the barycentric axis of the 3D Saint Venant model. The expression of the shear deformability tensor is rather involved since it depends upon three harmonic functions, namely the warping and the warpage functions associated, respectively, with torsion and shear. For this reason, in order to promote its use and shed some light on its properties, we derive explicit expressions of the shear deformability tensor for circular, elliptical and rectangular sections exploiting the relevant analytical formulas of the warping and warpage functions.

Keywords: Automotive, Aerospace and Flight Engineering, Mechanics, Mechatronics, incl. Robotics, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: Integrated vehicle safety - a combination of active and passive vehicle safety systems has the potential to increase occupant safety dramatically. To adapt the passive safety components such as belt and airbag to a given collision scenario, the system requires a priori knowledge of the collision consequences, i.e. via a camera, radar or lidar system. Therefore, real-time capable surrogate models are needed, that predict the vehicle decelerations during a crash with high accuracy. To combine the strength of both data-driven and physics-based surrogate modeling techniques, a hybrid surrogate model consisting of a machine learning-enhanced spring-damper-mass model is developed in this work. Thereby, the spring-damper-mass model describes the deformation behavior of the vehicle structure. A neural network is then trained to predict the stiffness and damping parameters of the simplified physical model based on the impact angle, the velocity and the offset of the vehicles.

Keywords: Medicine, Physiology and Biology, Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Numerical Simulation and Co-Simulation
Abstract: Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields elementary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the number of uninfected people may be taken into account. Those formulae might therefore be useful to decision makers. A feedback loop stemming from model-free control leads to a remarkable robustness with respect to severe uncertainties of various kinds. Although an identification procedure is presented, a good knowledge of the recovery rate is not necessary for our control strategy. Several convincing computer experiments are displayed.

Keywords: Medicine, Physiology and Biology, Fitting Models to Real Processes, incl. Identification and Calibration, ODE, DAE, SODE, SDAE Systems
Abstract: In spring 2021, it became eminent that the emergence of higher infectious virus mutants of SARS-CoV-2 is an unpredictable and omnipresent threat for fighting the pandemic and has wide-ranging implications on containment policies and herd immunity goals. To quantify the risk related to a more infectious virus variant, extensive surveillance and proper data analysis are required. Key observable of the analysis is the excess infectiousness defined as the quotient between the effective reproduction rate of the new and the previous variants. A proper estimate of this parameter allows forecasts for the epidemic situation after the new variant has taken over and enables estimates by how much the new variant will increase the herd immunity threshold. Here, we present and analyse methods to estimate this crucial parameter based on surveillance data. We specifically focus on the time dynamics of the ratio of mutant infections among the new confirmed cases and discuss, how the excess infectiousness can be estimated based on surveillance data for this ratio. We apply a modified susceptible-infectious-recovered approach and derive formulas which can be used to estimate this parameter. We will provide adaptations of the formulas which are able to cope with imported cases and different generation-times of mutant and previous variants and furthermore fit the formulas to surveillance data from Austria. We conclude that the derived methods are well capable of estimating the excess infectiousness, even in early phases of the replacement process. Yet, a high ratio of imported cases from regions with higher variant prevalence may cause a major overestimation of the excess infectiousness, if not considered. Consequently, the analysis of Austrian data allowed a proper estimate for the Alpha variant, but results for the Delta variant are inconclusive.

Keywords: ODE, DAE, SODE, SDAE Systems, Medicine, Physiology and Biology
Abstract: Once an infectious disease developed, the main goal is containing its spread. Several control strategies may be applied in order to control a disease, such as detection and isolation of infectious individuals or vaccination. However, the detection of infectious individuals is far from being easy:indeed, various diseases, such as influenza, cholera, shigella or Covid-19, often do not show symptoms. The presence of asymptomatic cases allows a wide circulation of a disease in the population,since they often remain unidentified. Hence, the contribution of the so called “silent spreaders” to the infection transmission dynamics should be considered in mathematical epidemic models. Unlike the more famous and studied epidemic models, much less attention has been paid to the SAIR(S)-type models. Thus, we think that a deeper understanding of these kind of models is needed, and could prove to be very useful in the epidemiological field.

We provided a global stability analysis for a SAIRS epidemic model with vaccination, answering to an open problem proposed in Ansumali et al. (2020). In particular, we study the global asymptotic stability (GAS) of the disease-free equilibrium (DFE) and provide results related to the global asymptotic stability of the endemic equilibrium (EE) for many variations of the model. We determine the value of the basic reproduction number R0 and prove that the DFE is globally asymptotically stable if R0<1 and unstable if R0>1, condition under which a positive endemic equilibrium (EE) exists.

Currently, we are working on a generalization of the SAIRS model, which takes into account different groups of individual among which an epidemic can spread.

Keywords: Computing Systems, Discrete and Discrete-Event Systems, incl. Discretisation of Continuous Systems, Petrinets, Medicine, Physiology and Biology, Fitting Models to Real Processes, incl. Identification and Calibration
Abstract: Since the outbreak of the COVID-19 pandemic in spring 2020, the concept of test, trace, and isolate (TTI) was used as a non-pharmaceutical intervention against further spreading of the disease. Hereby, recent contact partners of newly confirmed SARS-CoV-2 infected persons were identified and isolated along with the originally detected case to avoid potential secondary infections. While the policy is, given the compliance of the traced persons, generally deemed efficient, not much is known about network-specific impact factors.

In this work, we aim to evaluate the effectiveness of the TTI strategy when used (1) for diseases with different infectiousness levels and (2) on different contact networks. For the prior, we vary the infection probability per contact, for the latter, we analyse different clustering coefficients. Our goal is to test the validity of two hypotheses: First, we expect the policy to be more efficient if the infectiousness of the disease is small, since the time delay for isolating persons is crucial. Second, due to the implications of the friendship paradox, we expect the policy to be more effective if the clustering coefficient of the underlying contact network is high.

We make use of an agent-based network model consisting of three intertwined model parts: an epidemiological SEIR model, a quarantine model and a contact-tracing model. To test the hypotheses, the disease parameters and the clustering coefficient of the underlying contact network are varied.

The simulation results show that, indeed, tracing seems to have a slightly larger containment impact for networks with higher clustering, in particular for fast-spreading diseases. Yet, the effects are small compared to the impact of the infectiousness of the disease. Therefore, we find a significant decrease of the policy effectiveness the higher the transmission probability. The latter implies that the containment impact of tracing and isolating contacts becomes more efficient, if supported by additional measures that limit the infection probability or if applied in periods with low negative seasonality effects.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Model Reduction, Model Simplification and Optimization, Numerical Simulation and Co-Simulation
Abstract: We consider machine-learning of time-dependent quantities of interest derived from solution trajectories of parabolic partial differential equations. For large-scale or long-time integration scenarios, where using a full order model (FOM) to generate sufficient training data is computationally prohibitive, we propose an adaptive hierarchy of intermediate Reduced Basis reduced order models (ROM) to augment the FOM training data by certified ROM training data required to fit a kernel model.

Keywords: Model Reduction, Model Simplification and Optimization, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Modelling for Control and Real-Time Applications
Abstract: Classical projection-based model order reduction methods, like the reduced basis method, are popular tools for getting efficiently solvable reduced order models for parametric PDEs. However, for some problems, the error-decay with respect to the dimension of the linear projection space is predetermined to be slow, e.g., for parameterized wave equations with jump discontinuities. In order to cope with this issue, we consider approximations formed by a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly solution of a parameter-dependent problem, we reformulate finding a best Linear/Ridge expansion in terms of an optimization problem that we solve with a particle grid algorithmn. The linear functions as well as the ridge profiles are build offline with a greedy-type algorithmn. By training the directions offline, we can achieve an efficient online evaluation to solve the projected parametric PDE.

Keywords: Model Reduction, Model Simplification and Optimization, Numerical Simulation and Co-Simulation, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly nonlinear behaviors like shock formation or shock interaction. In the case of parametrized hyperbolic equations, where, for instance, varying transport velocities are considered, these nonlinearities and strong transport effects result in a highly nonlinear solution manifold. This solution manifold cannot be approximated properly by linear subspaces. To this end, nonlinear approaches for model order reduction of hyperbolic conservation laws are required.

We propose a new method for nonlinear model order reduction that is especially well-suited for hyperbolic equations with discontinuous solutions. The approach is based on a space-time discretization and employs diffeomorphic transformations of the underlying space-time domain to align the discontinuities. To derive a reduced model for the diffeomorphisms, the Lie group structure of the diffeomorphism group is used to associate diffeomorphisms with corresponding velocity fields via the exponential map. In the linear space of velocity fields, standard model order reduction techniques, such as proper orthogonal decomposition, can be applied to extract a reduced subspace. For a parametrized Burgers' equation with two merging shocks, numerical experiments show the potential of the approach.

Keywords: Model Reduction, Model Simplification and Optimization, ODE, DAE, SODE, SDAE Systems
Abstract: Classical model reduction methods disregard the special symplectic structure associated with Hamiltonian systems. A key challenge in projection-based approaches is to construct a symplectic basis that captures the essential system information. This necessitates the computation of a so-called proper symplectic decomposition (PSD) of a given sample data set. The PSD problem allows for a canonical formulation as an optimization problem on the symplectic Stiefel manifold. However, as with their Euclidean counterparts, symplectic projectors only depend on the underlying symplectic subspaces and not on the selected symplectic bases. This motivates to tackle the PSD problem as a Riemannian optimization problem on the symplectic Grassmann manifold, i.e., the matrix manifold of symplectic projectors. Initial investigations on this manifold feature in a recent preprint of the authors. In this work, we investigate the feasibility and performance of this approach on two academic numerical examples. More precisely, we calculate an optimized PSD for snapshot matrices that stem from solving the one-dimensional linear wave equation and the one-dimensional nonlinear Schrödinger equation.

Keywords: Model Reduction, Model Simplification and Optimization, Physical and Multiport Modelling, Bondgraphs, ODE, DAE, SODE, SDAE Systems
Abstract: Symplectic model order reduction is a structure-preserving reduction technique for Hamiltonian systems. Apart from theoretical results like the preservation of stability, it has been demonstrated to give improved numerical results compared to classical MOR techniques. A key element in this procedure is the choice of a good symplectic reduced order basis (ROB). In our work, we introduce so-called canonizable Hamiltonian systems in energy coordinates. For such systems with the assumption of a periodic solution, we derive a globally optimal symplectic ROB in the sense of the proper symplectic decomposition (PSD). To this end, we show that the proper orthogonal decomposition (POD) of a canonizable Hamiltonian system is automatically symplectic from which we deduce optimality of the PSD. To verify our findings numerically, we consider a reproduction experiment for the linear wave equation.

Keywords: Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Modelling Uncertainties and Stochastic Systems, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant.

Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem.

The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, ODE, DAE, SODE, SDAE Systems
Abstract: This paper discusses a model of two interconnected chemostats in series, characterized by biomass mortality. A comparison is established with a single chemostat of the same total volume in two different cases, that are with or without mortality rate. The outlet substrate concentration and the biogas flow rate are the main criteria for comparison. According to conditions depending on the operating parameters and the distribution of the total volume, our results show which structure, the series of the two chemostats or the single chemostat, performs better in terms of minimizing the outlet substrate concentration or maximizing the biogas flow rate, and this with or without account of mortality. Moreover, the differences and similarities in the results corresponding to the case with mortality and the one without mortality, are highlighted.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, ODE, DAE, SODE, SDAE Systems, Numerical Simulation and Co-Simulation
Abstract: The deterministic model developed by Graham et al. [2020], which is the approximation in large population of a stochastic model, allowed the authors to propose a `macroscopic description' of metabolic heterogeneity of Escherichia coli growing on glucose and xylose. However, none mechanistic modeling was proposed to explain the variations of the duration of the `lag-phase' observed when the glucose is exhausted and before the xylose is being consumed. Here, we propose a deterministic mechanistic model to explain how E. coli switches its consumption of a sugar to another one depending on the dynamic of intracellular XylR molecules. The model is developed and investigated numerically. It reveals some observability issues.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Modelling in Manufacturing and Process Engineering, Automation of Modelling and Software tools, incl. Computer Modelling
Abstract: In this study, a software sensor monitoring a viral amplification process is developed and validated. First, a dynamic model structure is proposed, describing Vero cell growth as well as the impact of viral infection, in accordance with the considered industrial application. A parameter identification procedure is set up based on a nonlinear least-square optimization criterion using several data sets provided by Sanofi Pasteur (Lyon, France). Second, an extended Kalman filter is designed considering a specific measurement configuration including a Raman probe sensing biomass, glucose, lactate and glutamine concentrations, and the estimation of exogenous variables such as the cell growth rate and viral amplification parameters. The obtained results validate the possibility to consider the EKF software sensor as a useful tool to monitor and report on viral amplification dynamics.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Numerical Simulation and Co-Simulation, ODE, DAE, SODE, SDAE Systems
Abstract: In this paper, we propose an interval observer-based fault detection strategy for a hydrogen production bioreactor in occurrence of sensor faults. Based on the dark fermenter model in presence of disturbances, we design a robust interval observer to: (i) estimate the glucose and biomass concentrations from hydrogen flow rate measurements, (ii) attenuate the influence of a disturbance, and (iii) detect the occurrence of the sensor faults by adaptive thresholds. The features of the proposed observer are assessed by numerical simulations.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: A dynamic model consisting of a system of partial differential equations, was created in order to describe and simulate the behaviour of a continuous immobilised-cell fermentation system for the production of succinic acid from glycerol. The model can confidently predict the steady state output of the process under a range of different initial and operating conditions. Moreover the model results, are verified by experimental results, further strengthening the credibility of the model. Then the constructed model was utilised to build a model reduction based stochastic optimal control strategy for the complex bio-process. Proper Orthogonal Decomposition and artificial neural networks were employed to address the high dimensionality of the model, in a 2-step reduction scheme, and polynomial chaos expansion to address model uncertainty. Computational results show that the reduced model-based stochastic control policy can efficiently improve production satisfying process requirements for byproduct concentrations.

Keywords: Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs)
Abstract: In this contribution, we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the variational problem based on the principle of virtual power, with both the Dirichlet (velocity) and Neumann (stress) boundary conditions imposed in a weak sense. As a consequence, the formal skew-adjointness of the system operator becomes directly visible after integration by parts, and, after compatible FE discretization, the boundary degrees of freedom of both causalities appear as explicit inputs in the resulting state space model. The rationale behind our formulation is illustrated using a lumped parameter example, and numerical experiments on a one-dimensional rod show the properties of the approach in practice.

Keywords: Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs)
Abstract: We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian fashion and show that the system is semi-uniformly stable.

Keywords: Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Physical and Multiport Modelling, Bondgraphs, First Principles Modelling

Keywords: ODE, DAE, SODE, SDAE Systems, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Fluidics and Thermodynamics

Keywords: Operation Research, Logistics and Planning, Comparison of Methods for Modelling, Alternative Modelling Methods (Fuzzy, CAS, NN, etc.), Model Reduction, Model Simplification and Optimization
Abstract: In this paper we present two alternative models for the Stochastic Guaranteed Service Model with Demand Propagation (SGSM-DP) in multi-echelon inventory theory. While the original SGSM-DP could so far not be solved for standard networks with more than 15 nodes in 1000 seconds, the new equivalent model F-SGSM-DP based on dynamic flows with arcs going backwards in time can be solved even for heavy instances with up to around 50 nodes.

Keywords: Electrical, Electronic and Power Systems, Financial, Economic and Macroeconomic Systems, Modelling in Manufacturing and Process Engineering
Abstract: This paper proposes a model to analyze, assess and forecast the viability of Electronic Design Automation (EDA) companies that operate in a dynamic environment. Due to the technological advancements and the specific characteristics of this industry, companies that operate in the market are under continuous pressure to innovate their products, to find new policies of investment, strategies and forms of business model organization to maintain viability. Knowledge-intensive industries, like EDA, are known for needing continuous access to new knowledge, talents, and experts and a lot of research and development activity. Not all companies can provide in time the necessary results and innovation to compete in the market, so most of them dissolve, merge, or are being acquired.

Keywords: Modelling in Manufacturing and Process Engineering, Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs)
Abstract: Nowadays, control strategies are a crucial part of the industrial domain. A challenging aspect in production lines therein is the mismatch between the total desired lots and the total lots of the system output due to the system limitations, the so-called backlog problem. In this paper, optimal control approaches are investigated to address this problem in terms of conservation laws coupled with ordinary differential equations (ODEs) in different interconnection topologies that correspond to dispersing and merging networks. The problem is optimized utilizing open-loop optimal control according to discretize-then-optimize and optimize-then-discretize mechanisms. In addition, model predictive control is designed to solve the problem by using a suitable forward shifting technique to suppress disturbances also taking into account constraints. The numerical results show solvability and associated features for each approach depending on the requirement of the corresponding use case.

Keywords: Modelling in Manufacturing and Process Engineering, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, Automation of Modelling and Software tools, incl. Computer Modelling
Abstract: For cause-effect analysis in productions on account of failures, it is usually difficult to identify all influencing factors and to analyze the relationships between them. This paper presents a method to combine production process, cause-effect and process data representation into one model named Structure Graph of Production (SGP). It uses the concept of causal graph to represent variables and relationships in the production system, can document and visualize process and product variables as well as relationships, and structures the graph elements using four types of clusters – products, processes, machines and measuring systems. Another aspect is data accessing and integration. The SGP provides a method for associating the stored data in database and the variables in the SGP model in order to enable a direct interpretation with an easier data access. This paper formally defines the model elements of SGP using UML class diagrams and demonstrates the modelling approach on an example taken from a laboratory plant. The SGP is implemented and validated in a pilot project in cooperation with manufacturing companies. It establishes the basis for an automated data integration and interpretation for causal analysis in production area.

Keywords: Operation Research, Logistics and Planning, Computing Systems, Discrete and Discrete-Event Systems, incl. Discretisation of Continuous Systems, Petrinets
Abstract: Earthworks in infrastructure construction are dominated by extensive logistics operations. They have to be planned thoroughly, even in a very early phase of a project. The industry standard approach includes coarse estimations and tedious, error prone manual work. With the models presented here, an optimal allocation of transports can be achieved even for large scale projects. Practically usable models have solution times in the range of minutes. With our approach, complexity is split and computation time sufficient for real-world problems. In the first step, material flow is calculated, the second step separates the flow into transport relations, the third step breaks the plan down to the level of single truck transports. The first two steps are implemented using linear programming. The third step is realized by an agent-based simulation model, implemented using AnyLogic.

Keywords: Computing Systems, Discrete and Discrete-Event Systems, incl. Discretisation of Continuous Systems, Petrinets, Modelling in Manufacturing and Process Engineering, Operation Research, Logistics and Planning
Abstract: Petri nets (PN) are a versatile modelling tool that can also be used to represent scheduling problems. In this paper, a PN-based representation of schedules is investigated in the context of optimization by genetic algorithms (GA). A new sequence repair scheme is proposed, integrated into the GA optimizer, and applied to standard benchmark instances of the flexible job shop scheduling problem. The results are compared with other state-of-the-art approaches. The main contribution of the paper is a step towards bridging the gap between PN modelling and advanced scheduling algorithms. The results motivate further research on the use of Petri net models in solving complex scheduling problems.

Keywords: Fluidics and Thermodynamics, ODE, DAE, SODE, SDAE Systems, First Principles Modelling
Abstract: This paper presents three alternative dynamic models and a corresponding comparison by simulations for a vapor compression cycle. The first model is derived by first principles and uses both the mass and energy balances in finite-volume models of the evaporator and the condenser, whereas the compressor and the expansion-valve are modeled by means of algebraic equations. Assuming vanishing pressure losses along the evaporator and the condenser, a second model description is established. Additionally, a further simplification concerning the inner mass flows, which can be often found in the literature, leads to a third model. Both model variations are compared in simulations with the original model regarding model accuracy and simulation time. It becomes obvious that the second simplification leads to a significantly larger error. Moreover, the achievable increase in simulation speed of the simplified models is shown. Finally, the impact of a varying spatial resolution is discussed.

Keywords: Numerical Simulation and Co-Simulation, Fluidics and Thermodynamics
Abstract: To calculate the driving temperature difference between the hot and the cold side of a heat exchanger, the use of the logarithmic mean temperature difference is common practice. To provide high robustness in complex dynamic system models, a robust formulation of the logarithmic mean (logmean) function becomes vital. As the analytic definition of the logmean function naturally comes along with singularities and limitations for specific input conditions, it is essential to extend and modify it for heat exchanger modeling. This paper proposes how the logmean function can be extended to be valid in all four quadrants of the Cartesian coordinate system and how to bridge the resulting definition gaps. Special focus lies on the robust formulation in such a way that it can be easily handled by numerical solvers. This includes the numerical approximation of the logmean by use of its integral form by implicit ODE solvers with variable step width. Furthermore a way is presented to flatten the naturally steep gradients in the vicinity of the x- and y-axes without manipulating the function in the uncritical regions. All the modifications on the logmean are finally applied in a simple simulation model written in the object-oriented programming language Modelica to examine the robustness of the approach.

Keywords: Mechanics, Mechatronics, incl. Robotics, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, Physical and Multiport Modelling, Bondgraphs
Abstract: In this paper, we present a linear parameter-varying (LPV) model of an electrostatic loudspeaker driven by dielectric elastomer (DE) actuators. Because of its numerical simplicity, this LPV model represents a convenient tool to develop real-time control strategies for the speaker. Starting from a non-linear reduced model of the device, we assume that the control input can be broken into two components: a small-amplitude high-frequency component, responsible for the sound generation, and a slowly-varying bias component, which can be used as a free control parameter to tune and adjust the speaker response. We thus build an LPV model, treating the dynamic response to the high-frequency input component as linear, and parametrising the coefficients of such linear system with respect to the low-frequency input component. We present a validation of the model against experiments, and show that the proposed LPV formulation captures the most relevant non-linearities involved in the DE speaker operation.

Keywords: Mechanics, Mechatronics, incl. Robotics, Electrical, Electronic and Power Systems, Modelling in Manufacturing and Process Engineering
Abstract: Dielectric elastomers (DEs) are flexible active materials capable of large deformations when activated by high voltage. Because of this strong electromechanical conversion, they are considered as promising materials for loudspeakers membrane. Several prototypes have been developed and tested by several research groups, and models have been proposed to estimate their performance. Previous studies described the electro-elastoacoustic interactions occurring in a DE membrane with the help of an electromechanical model solved numerically using finite elements.The relation between the electrode shape and the dynamical and acoustical behavior of membranes was described for the first time with the perspective to control selectively the contribution of eigenmodes to the radiated sound. Although several progresses have been made in the field in these recent years, still a high actuating electric field is needed to induce large mechanical deformation of DEs, thus limiting their practical applications. A new approach based on the use of polymers loaded with conductive nano-inclusions is the subject of growing interest in scientific research. DE nanocomposites are generally made up of random dispersions of particles without any structural optimization. In this study, we propose to manufacture and formulate isotropic self-assembled networks of core-shell nano-inclusions composed of conductive carbon nanotubes (CNT) coated by a few nanometers of SiO2passivation layer uniformly dispersed in flexible polymer elastic matrix (PDMS) without compromising breakdown strength (Eb) and elasticity (Y) of membrane assuring high actuation strain under a low driving electric field. According to Maxwell stress equation, a substantial increase of the electromechanical sensitivity (β) obtained by a slight improvement of the dielectric constant of DEs nanocomposite keeping a reasonable elastic modulus represents a safe and reliable solution to reduce the driving electric field of dielectric elastomer loudspeakers. Based on actual measurements of the tensile-dielectric properties of nanofabricated nanocomposites, we aim for improvements beyond the state of the art by obtaining high actuation stress at halved applied electric field.

Keywords: Numerical Simulation and Co-Simulation, Modelling for Control and Real-Time Applications, Model Reduction, Model Simplification and Optimization
Abstract: Dielectric elastomers can be used to develop innovative mechatronic actuators (called DEA). In this paper, we consider the optimal control problem (OCP) of transitioning between an actuator's operating states. Following a model-based approach, a set of discrete-time state equations is derived for the DEA, which satisfy accuracy demands and, at the same time, can be solved efficiently by numerical methods. Due to numerical stiffness, the implicit midpoint rule is chosen as an integration method. Then, we discuss different classes of input signals to be considered in the OCP. In particular, zero-order-hold and first-order-hold parametrizations are compared within the OCP formulation. While we show equivalence of two OCP formulations from the theoretical point of view, numerical investigations show benefits of our proposed OCP model regarding the quality of computed solutions and the robustness w.r.t. initial guesses. Altogether, we derive a numerically treatable DEA optimal control set-up, which can be used for various control tasks.

Keywords: Mechanics, Mechatronics, incl. Robotics, Operation Research, Logistics and Planning, Numerical Simulation and Co-Simulation
Abstract: In this paper, we model the multi-objective optimisation problem for maximising the energetic performance while minimising the damage accumulation in ocean wave energy converters based on dielectric elastomer generators (DEGs). DEGs are electrostatic smart material-based transducers that are cheaper, lighter, and more adaptable to the marine environment than conventional power take-off systems. Because DEGs are prone to electrical breakdown upon cyclic loading, identifying trade-offs between achievable performance and lifetime is currently a crucial research question. Based on some assumptions on the system layout and material properties, and using the methods of Pareto optimisation, we prove that a suitably chosen control strategy can potentially achieve a dramatic reduction in the accumulated damage at the expense of a small reduction in the harvested energy. We further compare the Pareto optimal control solutions with commonly used control heuristics for DEGs, showing that optimal control can provide a reduction in the accumulated damage while preserving (or even improving) the energy performance.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, ODE, DAE, SODE, SDAE Systems
Abstract: The abundance of specific protein molecules in genetically identical cell populations exposed to the same external environment can show remarkable cell-to-cell variations as biochemical reactions are inherently stochastic and occur with low numbers of molecular copies. Such variations in gene products are commonly known as gene expression noise. One of the mechanisms for cells to reduce such noise is auto-regulatory negative feedback (auto-inhibition), commonly found across organisms. This auto-inhibition is subjected to unavoidable time-delays associated with transcriptional and translational processes. Sufficient time-delays and strong auto-inhibition can generate sustained oscillations in gene products, which is a common mechanism for precise timekeeping in many biomolecular clocks. While the importance of time-delays in the generation of oscillations is well appreciated, its role in stochastic dynamics is not well understood in the absence of sustained oscillations. Here, we investigate the interplay between the feedback strength and the time-delay to study the noise propagation in the non-oscillatory regime using linear stability analysis, the linear noise approximation, and stochastic simulations. From a simple auto-regulatory model with one protein species (no delay), we systematically introduce one-step and two-step time-delays by incorporating intermediate dynamics with additional second and third species, respectively. Interestingly, the negative feedback in the presence of time-delay can show counterintuitive noise behavior to our common perception about its role as a noise buffer.

Keywords: Fitting Models to Real Processes, incl. Identification and Calibration, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing
Abstract: Green roofs are a sustainable solution to manage water runoff from rain events in urban areas. Modeling hydrological phenomena of green roofs over long period is challenging because of the difficulties to both characterize the soil parameters and to take into account the dynamics of the vegetation and the meteorological variables. The water retention capacity is represented by the Van Genuchten - Mualem model implemented in Hydrus-1D©. For the calibration of the model, global sensitivity analysis is exploited to quantify the effects of parameter uncertainties on the water retention capacity. The results of this study highlight the most influential parameters on the water retention capacity and lead to an efficient reduction of the parameter uncertainties.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, ODE, DAE, SODE, SDAE Systems, First Principles Modelling
Abstract: High Rate Algal-Bacterial Ponds (HRABP) are often considered as an interesting solution for reducing the energy demand due to oxygenation in wastewater treatment, since oxygen is produced by the microalgae during photosynthesis. Modelling these complex dynamical processes is a challenging task since it is subjected to the solar fluxes imposing permanent fluctuations in light and temperature. The ALBA model was developed to represent this process, and validated with 623 days of outdoor measurements, in two different locations and for the four seasons. However, so far this model -as all the other existing models- was not fully predictive since it was requiring the measurement of the water temperature.

The objective of this work is to upgrade the ALgae-BActeria (ALBA) model, coupling it with a physical model predicting the evolution of temperature in the HRABP and presenting a novel structure for the pH submodel implementation. A heat-transfer model was developed and coupled to this model. It was able to accurately (with a standard error of 1.5^circ C) predict the temperature along the year. When coupled to the ALBA model, full predictions only based on meteorological data become possible. The predictions are hardly affected compared to using the actual measured temperature, resulting in an overall excellent capability to predict the process behaviour so that it can be further used for the system optimization, and for testing scenarios under very different operating and weather conditions.

Keywords: Medicine, Physiology and Biology, Numerical Simulation and Co-Simulation, Automation of Modelling and Software tools, incl. Computer Modelling
Abstract: Atrial fibrillation (AF) is a common comorbidity in left ventricular assist device (LVAD) patients and has been identified as a risk factor for stroke. Clinical studies in heart failure patients have shown reduced thromboembolic risk after occlusion of the left atrial appendage (LAA), however potential benefits in LVAD patients are not yet fully understood. This study aims to investigate the effect of left atrial appendage occlusion (LAAO) on thrombosis-related parameters using LVAD patient-specific hemodynamic simulations. Left ventricular and left atrial models of an LVAD patient with AF were obtained from computed tomography. Hemodynamics for LVAD patient with AF were generated by lumped parameter model and was applied for two CFD simulations with passive atrial contraction and active ventricular contraction for 8 cardiac cycles (CC); one for the atrium with LAA and a second one with LAAO. Stagnation regions (mean velocity <10mm/s), and blood residence time quantified with a virtual-ink technique were evaluated. Appendage occlusion results in +5% higher mean velocity within the atrium. The reduction of 64% in stasis volume (from 6.5 to 2.3 cm3) was observed post-LAAO. After 3 CC the entire old blood within the LA was replaced with new blood for LAAO simulation, while 4.3% of the old blood remained in the LAA for more than 8 CC. The results of this study showed a significant stasis volume within the left atrial appendage. These regions are known as potential sources for thrombus formation. Therefore, to reduce the stasis zones for LVAD patients with atrial fibrillation, occlusion of the appendage could be considered.

Keywords: Medicine, Physiology and Biology, Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: Impedance spectroscopy is a useful diagnostic tool in oncology to determine malignant and healthy tissue areas. However, since the electrical measurements are sensitive enough to detect structural changes in tissue, they are also prone to exterior influences such as the contact force of the sensor and mechanical stress in the tissue. These disturbances might predominate electrical properties and make tissue differentiation difficult. In this work, a multiphysical model for the electro-mechanical coupling during impedance spectroscopy is established. Increasing resistivity at rising compression levels is an often observed phenomena that can be explained by the extrusion of fluids from the compressed tissue. With fluids being important ion carriers, tissue conductivity heavily depends on the fluid content within the sample. Separate electrical and mechanical models for tissue are identified and linked through the fluid volume and its transfer to neighboring structures under compression. Measurements on both healthy urinary bladder wall and bladder tumors are carried out to identify the model parameters and to investigate if the changes induced by mechanical stress outweigh the pathological changes. The recorded data fits the electro-mechanical model and confirms that the impedance variations under compression originate from the fluid exodus. Furthermore, the electrical parameters for extracellular matrix resistivity and membrane capacity are found to differ significantly between healthy and malignant tissue, yielding to the conclusion that the apprehension of electromechanical factors prevailing over pathological changes is ungrounded for these parameters.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, ODE, DAE, SODE, SDAE Systems, Medicine, Physiology and Biology
Abstract: The paper addresses the problem of the unknown temperature reconstruction from the neuronal signal generated by networks of thermosensitive neurons modeled by the Hodgkin-Huxley formalism. We show that the instantaneous frequencies of the neurons do not provide sufficient information for the precise temperature reconstruction and that the temporal patterns of the instantaneous frequencies should be taken into account. For this purpose, we augment the considered network of thermosensitive neurons with a multi-layered artificial neural network (ANN) and train it to reconstruct the unknown piecewise-constant input temperature using a supervised learning technique. The input layer of the ANN receives the discretized (in time) trajectories of the instantaneous frequencies of neurons over a certain time interval. Interestingly, more rich information containing the time evolution of membrane potentials in the input layer does not lead to any improvement of the unknown input reconstruction. This observation is in accordance with one of the fundamental principles of neuroscience stating that, except for a few highly specific contexts, information in neural systems is encoded in the temporal rather than voltage characteristics of action potentials. Finally, we benchmark the performance of the proposed reconstruction scheme against different types of input signals.

Keywords: Medicine, Physiology and Biology, Numerical Simulation and Co-Simulation, ODE, DAE, SODE, SDAE Systems
Abstract: Neural oscillations are electrical activities of the brain measurable at different frequencies. This paper studies the interaction between the fast and slow processes in the brain. We recorded signals intracranially from the simple Wistar rats, performed the signal processing, and computed the correlation between envelopes of a high-frequency gamma rhythm and a low-frequency signal. The analysis shows that the low-frequency signal (delta rhythm) modulates the gamma rhythm with a small time delay. Further, we used simple excitable neuron models, namely FitzHugh-Nagumo and Hindmarsh-Rose, to simulate the gamma rhythm. The low-frequency signal delta rhythm can be used as the input to affect the threshold and simulate gamma rhythm using these neuron models.

Keywords: Modelling for Control and Real-Time Applications, Medicine, Physiology and Biology, ODE, DAE, SODE, SDAE Systems
Abstract: A dynamical model for an outbreak of dengue fever with countermeasures as control inputs is considered. We formulate an optimal control problem (OCP) for maintaining a hard infection cap with preferably low control effort and study different scenarios numerically. To this end, we solve the OCP in both open and closed loop using model predictive control (MPC).

Keywords: Fitting Models to Real Processes, incl. Identification and Calibration, Medicine, Physiology and Biology, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing
Abstract: A mathematical model for the spread of dengue is presented that is based on a Markov–like continuous–time process based on a simple six state automaton representing the mixed human–mosquito population. The reasonability of the model is shown by comparison of the numerical solutions with actual data from two different locations in the state of Morelos, Mexico. A central feature of the model is the potential of relating it with basic meteorological data to determine time windows of increased mosquito reproduction rates.

Keywords: Modelling for Control and Real-Time Applications, ODE, DAE, SODE, SDAE Systems, Fitting Models to Real Processes, incl. Identification and Calibration
Abstract: Seasonal influenza is an acute respiratory infection caused by several types of influenza viruses worldwide. Its outbreak exhibits a seasonal cycle in temperate climates. For public health decision-making and medical resource management during the time course of seasonal epidemics, a reliable real-time forecasting system is necessary. In this study, we introduce a novel approach combining two different data assimilation techniques to produce a real-time prediction of seasonal influenza governed by the standard SIR model. When applying our developed approach to Influenza-Like-Illness(ILI) data collected in Korea for 2016–2021, it successfully near-casted the upcoming week's flu incidence.