Titel Deelnemers "Korte inhoud" "Model Reduction Techniques to Improve the Efficiency of Flexible Multibody Simulations (Ontwikkeling en validatie van modelreductietechnieken voor de efficiënte simulatie van flexibele meerlichamendynamica)" "Gert Heirman" "The ever-increasing trend to design machines and processes to befaster, more lightweight, more energy-efficient and more reliablecauses virtual prototyping to gain importance over physicalprototyping. Accurate numerical modeling techniques for flexiblemultibody systems are needed in the different stages of thedesign. Furthermore, numerical models are not only used in thedesign phase; certain applications rely on simulation results ofnumerical models computed in real-time. Real-time targets arecurrently only met for highly simplified multibody models.However, in industry a strong desire exists to extend real-timecapabilities to more advanced models.In model reduction, the evolution of the system state is decomposedin dominant and negligible motion patterns. In the currentstate-of-the-use in flexible multibody modeling mainly body-levelmodel reduction is used. Body-level model reduction refers tomodel reduction applied to the flexibility description ofindividual bodies, i.e. mechanism components. These reduced bodyflexibility models are then incorporated in the model equations ofthe overall system. In case of a multitude of possible loadingpoints on a flexible body, its reduced body flexibility model willbe of significant size, such that time integration of the overallmultibody model becomes expensive. A first goal of this researchis to develop and validate efficient modeling techniques for therepresentation of flexibility in multibody dynamics, especiallytargeting this flaw in the state-of-the-use.A first solution to this problem is interface reduction, in which component interaction is approximated by a limited set of interaction patterns.An alternative interface reduction scheme is proposed and the associated computational hurdles are solved. This offers the user an alternative to model intercomponent interaction, without the numerically introduced artificial stiffness of conventional techniques. In a numerical experiment the effect of this artificial stiffness is illustrated.However, accuracy requirements can impose the use of more detailed body flexibility models. Quite often, many DOFs can be loaded during simulation, but few are loaded simultaneously. The multitude of possibly loaded DOFs imposes an expensive body flexibility description, but at any moment in time only a low-dimensional part of this description contributes to the solution. An innovative methodology is proposed, called Static Modes Switching, which at every time step only includes the strictly needed deformation patterns, so that at every time step an accurate body flexibility description of minimal size is obtained. Considerable simulation speed gains are obtained with an acceptable loss of accuracy.A second goal of this research is to develop and validate system-level model reduction techniques which enable real-time simulation of flexible multibody systems.The presence of both differential and algebraic equations in the model equations, and the number of degrees of freedom needed to accurately represent flexibility prohibit real-time simulation of these systems. Most current model reduction techniques for non-linear systems project the model equations on a set of invariable motion patterns. Only by using configuration-dependent motion patterns, one can transform the model equations from a set of differential-algebraic equations into a set of ordinary differential equations, and achieve a maximal dimension reduction. This is done in Global Modal Parameterization (GMP), for which this research proposes a generalization. Global Modal Parameterization divides the computational load over an expensive preparation phase and a cheap simulation phase. This research focuses on applications where fast online simulation capabilities justify an expensive offline preparation, such as real-time applications.In a first step, modal motion patterns are used. The sources of approximation error of a GMP-description are investigated. The effect of the configuration space discretization coarseness on the different approximation error sources is illustrated. The trade-offs to be defined by the user to control these approximation errors are explained. It was observed that the eigenmodes with eigenfrequencies near or within the frequency range of the excitation should be included in the motion patterns for model reduction. Furthermore, additional motion patterns are required to compensate for the quasi-static contribution of the omitted eigenmodes.Mode veering and mode crossing cause abrupt changes in mode shapes. As a modal GMP approach is based on describing the motion by the contributions of these rapidly changing motion patterns, the degrees of freedom of a GMP-description can vary abruptly for moderate system changes. It is theoretically proven that this even results in singularities for mode veering.Although the individual eigenmodes vary abruptly, the vector space spanned by a pair of veering/crossing modes has limited variability.To exploit this, linear combinations of eigenmodes are proposed to generate smoothly varying motion patterns. This requires an automatic detection of mode veering. A numerical experiment shows that this is unfeasible for systems with multiple parameters defining the dynamics.As a second solution, Krylov subspaces are proposed for the motion patterns of the GMP model reduction. A Krylov subspace also spans the dominant dynamics near a chosen frequency, without singularities due to mode veering.The maximal variability with respect to the system configuration of the first Krylov vector is one order of magnitude lower than the first eigenmode. However, due to the recursive definition and the orthogonalization in the Arnoldi computational process, variability is propagated and amplified through the series of Krylov vectors. By omitting this orthogonalization step, this propagation and amplification of variability vanishes. However, a singularity-free GMP-simulation using Krylov seems to be infeasible.Finally, several future research tracks are proposed." "Development of System-level Model Reduction Techniques for Flexible Multibody Simulation (Ontwikkeling van system-niveau modelreductietechnieken voor flexibele meerlichamensystemen)" "Frank Naets" "In recent years, flexible multibody simulation has become an essential tool in the computer aided design of many systems. However, current formalisms require a very large computational load, and these techniques are not feasible for many applications which require models to be run at a high rate. In order to address this limitation, this doctoral research investigates a novel system level reduction technique for flexible multibody models: Global Modal Parameterization (GMP). This approach allows a considerable reduction in the number of degrees-of-freedom and eliminates the constraint equations from the equations of motion, leading to compact ordinary differential models.The research mainly focusses on improvements of the formalism for hard real-time systems and reduction of computational load for complex mechanism. The basic GMP formulation is also extended in order to facilitate the reduction of complicated systems. By combining GMP reduced models of sub-systems these complicated system can be efficiently simulated. Finally, the GMP methodology is also extended to generalized geometric nonlinearities. This allows the treatment of a more general set of mechanisms.The presented methods will contribute to the development of a wide array of model based engineering techniques in optimization, state-estimation and control, which were previously infeasible." "EFFICIENT TRANSIENT ANALYSIS OF THE HIGH-SPEED STAGE OF A WIND TURBINE GEARBOX BY ADVANCED MODEL REDUCTION TECHNIQUES AND MEMORY-EFFECTIVE DISCRETIZATION" "Tommaso Tamarozzi, Bart Blockmans, Wim Desmet" "Modern wind turbines are designed to cope with their increased size and capacity. One of the most expensive components of these machines is the gearbox. Its design is more complex than a mere upscaling exercise from predecessors. The stress levels experienced by the different gear stages, the dynamic effects induced by their size and the unparalleled loads transmitted are some of the challenges that design engineers face. Moreover, unexpected events that load the wind turbines such as voltage dips, wind gusts or emergency breaking are expected to be major contributors to the premature failure of these gearboxes. The lack of engineering experience at this scale calls for accurate and efficient simulation tools thereby enabling reliable gearbox design. Standard lumped-parameters models or rigid multibody approaches do not provide a sufficient level of details to study the dynamic effects induced by e.g. gear design modifications (micro-geometry) or to analyze local stress concentrations. More advanced numerical tools are available such as flexible multibody or non-linear FE and allow to model complex contact interactions including all the relevant dynamic effects. Unfortunately the level of mesh refinement needed for an accurate analysis causes these simulations to be computationally expensive with time scales of several weeks to perform a single full rotation of a gear pair. This work introduces a novel efficient simulation tool for dynamic analysis of transmissions. This tool adopts a flexible multibody paradigm but incorporates several advanced features that allows to run simulations up to two orders of magnitudes faster as compared to non-linear FE with the same level of accuracy. A unique non-linear parametric model order reduction technique is used to develop a simulation strategy that is quasi mesh-independent allowing the usage of very fine FE meshes. Finally, in order to limit the memory consumption, a technique is developed to be able to finely mesh only a few of the gears teeth while the remaining gears are coarsely meshed. The main novelty of this approach lies in the possibility to perform full gear rotations without losing spatial resolution as compared to a finely meshed gear. After an accuracy check performed with a sample pair of helical gears, the framework is used to simulate the high speed stage of a three-stage wind turbine gearbox. The combined efficiency and accuracy of the approach is demonstrated by performing a dynamic stress analysis of the high-speed stage with and without a tip-relief modification. Accuracy of the results, simulation time, and memory usage are assessed." "Coordinate transformation techniques for efficient model reduction in flexible multibody dynamics" "Gert Heirman, Wim Desmet, Paul Sas" "Computational efficiency is important for all numerical simulation tools. For real-time and faster-than-real-time applications, which rely on a strong interaction between simulation results and other subsystems, it is vital. This paper proposes a theoretical framework for coordinate transformations to recast the differential-algebraic system equations of a flexible mechanism into a simpler set of equations, which is cheaper to solve. Desirable properties of the coordinate transformation to minimize the computational burden of the simulation are discussed, as well as some assumptions that can be made for further simplification. A methodology to make practical use of coordinate transformation techniques to speed up simulation speed for real-time and faster-than-real-time applications is presented." "Coordinate transformation techniques for efficient model reduction in flexible multibody dynamics" "Gert Heirman, Olivier Brüls, Wim Desmet, Paul Sas" "Computational efficiency is important for all numerical simulation tools. For real-time and faster-than-real-time applications, which rely on a strong interaction between simulation results and other subsystems, it is vital. This paper proposes a theoretical framework for coordinate transformations to recast the differential-algebraic system equations of a flexible mechanism into a simpler set of equations, which is cheaper to solve. Desirable properties of the coordinate transformation to minimize the computational burden of the simulation are discussed, as well as some assumptions that can be made for further simplification. A methodology to make practical use of coordinate transformation techniques to speed up simulation speed for real-time and faster-than-real-time applications is presented." "Reduction techniques for model checking and learning in MDPs" "Suda Bharadwaj, Stephane Le Roux, Guillermo Alberto Perez, Ufuk Topcu" "Novel Reduction Techniques for Exterior Vibro-acoustic Models and their use in Model-based Sensing and Identification" "Sjoerd van Ophem" "The physical interaction between vibrating structures and acoustics is of paramount importance in modern society. It is encountered in many products of daily use, such as vehicles, home appliances, and musical instruments but also in industrial environments, such as an assembly line in a factory. On the one hand, sound can be considered pleasant or useful in the context of music or communication. On the other hand, undesired sound, or noise, can cause health issues and is hence regarded as a problem. The physical principles behind sound waves and their mathematical description are known since a long time, but the analytical solution for problems with a moderate to high geometrical complexity is too difficult to obtain. Therefore, engineers make use of numerical computer models that approximately solve the underlying physics to predict and prevent the resulting noise from a vibrating structure. Besides the assessment of acoustic comfort, additional fields of application arise for vibro-acoustic models that are combined with physical measurements. For example, material properties and boundary conditions, or the health of a structure can be derived by doing an inverse identification. Another possibility is to combine them in a state-estimator to get an accurate prediction of the unmeasured field variables, thus to create a virtual vibro-acoustic sensor. For low-frequency noise and vibration modeling deterministic element based numerical approximation schemes, such as the finite element method, are most often used. The expectations and desires from academia and industry on what should be calculated with these models have increased throughout the years. Thus, although the available computing power is larger than before, solving such models remains a demanding task. Especially when a series of solutions is desired, for example when an optimization is performed, or when simulation results are desired in near-real time, the required time and calculation resources might be unacceptable. Therefore, this dissertation's main focus is on model order reduction techniques. Its main contributions are split into two parts. The first part is focused on the advancement of model order reduction techniques for vibro-acoustic systems to reduce the calculation complexity of these models. Specifically, the focus is on exterior vibro-acoustic problems in the time domain. Since they require the inclusion of the Sommerfeld radiation condition to correctly model the wave propagation to infinity, which is not included in the weak form of the finite element method, an additional stable boundary condition has to be introduced. Therefore, a conjugated infinite element description is chosen and it is shown how the resulting model can be reduced in size effectively with several examples. Furthermore, a parametric model order reduction scheme is derived that allows for low-rank parametric changes in the reduced order model of the second order system without sampling of the parameter space. A potential disadvantage of the shown algorithm is that it can lead to large reduced order models when an extensive set of parameters is considered. Hence, the first part concludes with the derivation of an automatic reduction algorithm for second order systems with many inputs, where the aim is to arrive at a model of acceptable size. The second part of this dissertation investigates the possibilities to use the aforementioned model order reduction techniques for efficient vibro-acoustic sensing and modeling. The effectiveness of the derived reduced order models is shown by constructing a virtual sensor that accurately estimates both the pressure and acoustic intensity of a complex radiating structure with the inclusion of only a small amount of measurements. Additionally, it is shown with an experimental setup how the derived parametric model order reduction scheme can be used for fast inverse identification of structural boundary conditions. The required reduced order model is obtained with the proposed automatic reduction algorithm. The potential of this algorithm is also assessed in a substructuring context, which could be beneficial for the modeling of unit cells, for example to evaluate the performance of metamaterials. The second part concludes by presenting a time reversed version of the conjugated infinite element description that works as an acoustic sink, which can be used in a time reversal simulation for scatterer and source identification." "Simulations of Advanced Combustion Modes Using Detailed Chemistry Combined with Tabulation and Mechanism Reduction Techniques" "Francesco Contino, Tommaso Lucchini, Gianluca D'errico, Véronique Dias, Herve Jeanmart" "Multi-dimensional models represent today consolidated tools to simulate the combustion process in HCCI and Diesel engines. Various approaches are available for this purpose, it is however widely accepted that detailed chemistry represents a fundamental prerequisite to obtain satisfactory results when the engine runs with complex injection strategies or advanced combustion modes. Yet, integrating such mechanisms generally results in prohibitive computational cost. This paper presents a comprehensive methodology for fast and efficient simulations of combustion in internal combustion engines using detailed chemistry. For this purpose, techniques to tabulate the species reaction rates and to reduce the chemical mechanisms on the fly have been coupled. In this way, the computational overheads related to the use of these mechanisms are significantly reduced since tabulated reaction rates are re-used for cells with similar compositions and, when it becomes necessary to perform direct integration, only the relevant set of species and reactions is taken into account. The proposed approach named tabulation of dynamic adaptive chemistry (TDAC) has been implemented in the Lib-ICE code, which is a set of libraries and applications for IC engine modeling developed using the OpenFOAM® technology. In particular, a modified version of the in-situ adaptive tabulation (ISAT) algorithm has been developed for systems with variable temperature and pressure, and the directed relation graph (DRG) method has been used to reduce the mechanism at run-time. The validation has been carried out with HCCI and Diesel cases both using a simplified case to compare the results obtained with and without TDAC, and a detailed case that is validated with experimental data. For each tested condition, a detailed comparison between computed and experimental data is provided along with the achieved speed-up factors compared to the use of direct-integration." "Towards better understanding of feature-selection or reduction techniques for Quantitative Structure-Activity Relationship models" "Mohammad Goodarzi, S. Funar-Timofei" "A system-level model reduction technique for efficient simulation of flexible multibody dynamics" "Gert Heirman, Wim Desmet" "In flexible multibody dynamics, body-level model reduction is typically used to decrease the computational load of a simulation. Body-level model reduction is generally performed by means of Component Mode Synthesis. This offers an acceptable solution for many applications, but does not result in significant model reduction for systems with moving connection points, e.g. due to a flexible sliding joint. In this research, Global Modal Parametrization, a model reduction technique initially proposed for real-time control of flexible mechanisms, is further developed to speed up simulation of multibody systems. The reduction is achieved by a system-level modal description, as opposed to the classic body-level modal description. As the dynamics is configuration-dependent, the system-level modal description is chosen configuration-dependent in such a way that the system dynamics are optimally described with a minimal number of degrees of freedom. Moving connection points do not pose a problem to the proposed model reduction methodology. The complexity of simulation of the reduced model equations is estimated. The applicability to systems with moving connection points is highlighted. In a numerical experiment, simulation results for the original model equations are compared with simulation results for the model equations obtained after model reduction, showing a good match. The approximation errors resulting from the model reduction techniques are investigated by comparing results for different mode sets. The mode set affects the approximation error similarly as it does in linear modal synthesis."