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Force field (FF) based molecular modeling is an often used method to investigate and study structural and dynamic properties of (bio-)chemical substances and systems. When such a system is modeled or refined, the force field parameters need to be adjusted. This force field parameter optimization can be a tedious task and is always a trade-off in terms of errors regarding the targeted properties. To better control the balance of various properties’ errors, in this study we introduce weighting factors for the optimization objectives. Different weighting strategies are compared to fine-tune the balance between bulk-phase density and relative conformational energies (RCE), using n-octane as a representative system. Additionally, a non-linear projection of the individual property-specific parts of the optimized loss function is deployed to further improve the balance between them. The results show that the overall error is reduced. One interesting outcome is a large variety in the resulting optimized force field parameters (FFParams) and corresponding errors, suggesting that the optimization landscape is multi-modal and very dependent on the weighting factor setup. We conclude that adjusting the weighting factors can be a very important feature to lower the overall error in the FF optimization procedure, giving researchers the possibility to fine-tune their FFs.
Quality diversity algorithms can be used to efficiently create a diverse set of solutions to inform engineers' intuition. But quality diversity is not efficient in very expensive problems, needing 100.000s of evaluations. Even with the assistance of surrogate models, quality diversity needs 100s or even 1000s of evaluations, which can make it use infeasible. In this study we try to tackle this problem by using a pre-optimization strategy on a lower-dimensional optimization problem and then map the solutions to a higher-dimensional case. For a use case to design buildings that minimize wind nuisance, we show that we can predict flow features around 3D buildings from 2D flow features around building footprints. For a diverse set of building designs, by sampling the space of 2D footprints with a quality diversity algorithm, a predictive model can be trained that is more accurate than when trained on a set of footprints that were selected with a space-filling algorithm like the Sobol sequence. Simulating only 16 buildings in 3D, a set of 1024 building designs with low predicted wind nuisance is created. We show that we can produce better machine learning models by producing training data with quality diversity instead of using common sampling techniques. The method can bootstrap generative design in a computationally expensive 3D domain and allow engineers to sweep the design space, understanding wind nuisance in early design phases.
Electric vehicles (EVs) are rapidly growing in popularity, but range variability has become an important research area with significant implications for EV performance, usability, and overall market adoption. This study aims to unravel the complexities of range variability by examining the contributing factors and offering innovative strategies to mitigate these differences during pack design. Through a detailed analysis of cell parameter deviation, cell connections, battery configuration, battery pack size, and driving behavior, the research illuminates their impact on extractable energy and driving range. The study employed a comprehensive approach and conducted systematic simulation-based experimentation to identify the optimal battery pack configuration based on maximum extractable energy, minimal variability and maximum range. The results reveal insights into the relationship between discharge rate and battery pack performance, and the impact of cell parameter variations on pack energy output. This research advances the understanding of EV performance optimisation, reduces pack-to-pack variability, and extends battery pack lifespan.
Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauss-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauss-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor-Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor-Green vortex flows with Mach numbers Ma={0.5;1.0;1.5;2.0} on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.
The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. While it is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques, recent studies have not addressed possible connections between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch's deep learning and automatic differentiation facility. As a proof of concept for combining machine learning with the LBM, a neural collision model is developed, trained on a doubly periodic shear layer and then transferred to a different flow, a decaying turbulence. We also exemplify the added benefit of PyTorch's automatic differentiation framework in flow control and optimization. To this end, the spectrum of a forced isotropic turbulence is maintained without further constraining the velocity field.
Fundamental hydrogen storage properties of TiFe-alloy with partial substitution of Fe by Ti and Mn
(2020)
TiFe intermetallic compound has been extensively studied, owing to its low cost, good volumetric hydrogen density, and easy tailoring of hydrogenation thermodynamics by elemental substitution. All these positive aspects make this material promising for large-scale applications of solid-state hydrogen storage. On the other hand, activation and kinetic issues should be amended and the role of elemental substitution should be further understood. This work investigates the thermodynamic changes induced by the variation of Ti content along the homogeneity range of the TiFe phase (Ti:Fe ratio from 1:1 to 1:0.9) and of the substitution of Mn for Fe between 0 and 5 at.%. In all considered alloys, the major phase is TiFe-type together with minor amounts of TiFe2 or \b{eta}-Ti-type and Ti4Fe2O-type at the Ti-poor and rich side of the TiFe phase domain, respectively. Thermodynamic data agree with the available literature but offer here a comprehensive picture of hydrogenation properties over an extended Ti and Mn compositional range. Moreover, it is demonstrated that Ti-rich alloys display enhanced storage capacities, as long as a limited amount of \b{eta}-Ti is formed. Both Mn and Ti substitutions increase the cell parameter by possibly substituting Fe, lowering the plateau pressures and decreasing the hysteresis of the isotherms. A full picture of the dependence of hydrogen storage properties as a function of the composition will be discussed, together with some observed correlations.
This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.
During the dawn of chemistry when the temperature of the young Universe had fallen below ∼4000 K, the ions of the light elements produced in Big Bang nucleosynthesis recombined in reverse order of their ionization potential. With its higher ionization potentials, He++ (54.5 eV) and He+ (24.6 eV) combined first with free electrons to form the first neutral atom, prior to the recombination of hydrogen (13.6 eV). At that time, in this metal-free and low-density environment, neutral helium atoms formed the Universe's first molecular bond in the helium hydride ion HeH+, by radiative association with protons (He + H+ → HeH+ + hν). As recombination progressed, the destruction of HeH+ (HeH+ + H → He + H+2) created a first path to the formation of molecular hydrogen, marking the beginning of the Molecular Age. Despite its unquestioned importance for the evolution of the early Universe, the HeH+ molecule has so far escaped unequivocal detection in interstellar space. In the laboratory, the ion was discovered as long ago as 1925, but only in the late seventies was the possibility that HeH+ might exist in local astrophysical plasmas discussed. In particular, the conditions in planetary nebulae were shown to be suitable for the production of potentially detectable HeH+ column densities: the hard radiation field from the central hot white dwarf creates overlapping Strömgren spheres, where HeH+ is predicted to form, primarily by radiative association of He+ and H. With the GREAT spectrometer onboard SOFIA, the HeH+ rotational ground-state transition at λ149.1 μm is now accessible. We report here its detection towards the planetary nebula NGC7027.
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
(2018)
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.
Since being introduced in the sixties and seventies, semi-implicit RosenbrockWanner (ROW) methods have become an important tool for the timeintegration of ODE and DAE problems. Over the years, these methods have been further developed in order to save computational effort by regarding approximations with respect to the given Jacobian [5], reduce effects of order reduction by introducing additional conditions [2, 4] or use advantages of partial explicit integration by considering underlying Runge-Kutta formulations [1]. As a consequence, there is a large number of different ROW-type schemes with characteristic properties for solving various problem formulations given in literature today.
We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model depends on the inverse temperature β and the interaction strength K. The rates of convergence results are obtained as (β,K) converges along appropriate sequences (βn,Kn) to points belonging to various subsets of the phase diagram which include a curve of second-order points and a tricritical point. We apply Stein's method for normal and non-normal approximation avoiding the use of transforms and supplying bounds, such as those of Berry-Esseen quality, on approximation error. We observe an additional phase transition phenomenon in the sense that depending on how fast Kn and βn are converging to points in various subsets of the phase diagram, different rates of convergences to one and the same limiting distribution occur.
In this article we introduce the concept and the first implementation of a lightweight client-server-framework as middleware for distributed computing. On the client side an installation without administrative rights or privileged ports can turn any computer into a worker node. Only a Java runtime environment and the JAR files comprising the workflow client are needed. To connect all clients to the engine one open server port is sufficient. The engine submits data to the clients and orchestrates their work by workflow descriptions from a central database. Clients request new task descriptions periodically, thus the system is robust against network failures. In the basic set-up, data up- and downloads are handled via HTTP communication with the server. The performance of the modular system could additionally be improved using dedicated file servers or distributed network file systems. We demonstrate the design features of the proposed engine in real-world applications from mechanical engineering. We have used this system on a compute cluster in design-of-experiment studies, parameter optimisations and robustness validations of finite element structures.