A two-phase differential evolution for uniform designs in constrained experimental domains

open access articleIn many real-world engineering applications, a uniform design needs to be conducted in a constrained experimental domain that includes linear/nonlinear and inequality/equality constraints. In general, these constraints make the constrained experimental domain small and irregular in the decision space. Therefore, it is difficult for current methods to produce a predefined number of samples and make the samples distribute uniformly in the constrained experimental domain. This paper presents a two-phase differential evolution for uniform designs in constrained experimental domains. In the first phase, considering the constraint violation as the fitness function, a clustering differential evolution is proposed to guide the population toward the constrained experimental domain from different directions promptly. As a result, a predefined number of samples can be obtained in the constrained experimental domain. In the second phase, maximizing the minimum Euclidean distance among samples is treated as another fitness function. By optimizing this fitness function, the samples produced in the first phase can be scattered uniformly in the constrained experimental domain. The performance of the proposed method has been tested and compared with another state-of-the-art method. Experimental results suggest that our method is significantly better than the compared method in the uniform designs of a new type of automotive crash box and five benchmark test problems. Moreover, the proposed method could be considered as a general and promising framework for other uniform designs in constrained experimental domains

Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter

This paper investigates the state estimation of a high-fidelity spatially resolved thermal- electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the pseudo-2D model is then used in combination with an extended Kalman filter algorithm for differential-algebraic equations to estimate the states of the model. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1 % in less than 200 s despite a 30 % error on battery initial state-of-charge and additive measurement noise with 10 mV and 0.5 K standard deviations.Comment: Submitted to the Journal of Power Source

Optimal configuration of microstructure in ferroelectric materials by stochastic optimization

An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differ significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited and hence the choice of the optimal solution which maximizes the piezoelectricity is complicated. Thus a stochastic global optimization combined with homogenization is employed for the identification of the optimal granular configuration of the FE ceramic microstructure with optimum piezoelectric properties. The macroscopic equilibrium piezoelectric properties of polycrystalline FE is calculated using mathematical homogenization at each iteration step. The configuration of grains characterised by its orientations at each iteration is generated using a randomly selected set of orientation distribution parameters. Apparent enhancement of piezoelectric coefficient $d_{33}$ is observed in an optimally oriented BaTiO$_3$ single crystal. A configuration of crystallites, simultaneously constraining the orientation distribution of the c-axis (polar axis) while incorporating ab-plane randomness, which would multiply the overall piezoelectricity in ceramic BaTiO$_{3}$ is also identified. The orientation distribution of the c-axes is found to be a narrow Gaussian distribution centred around ${45^\circ}$. The piezoelectric coefficient in such a ceramic is found to be nearly three times as that of the single crystal.Comment: 11 pages, 7 figure

Direct visualization of the magnetostructural phase transition in nanoscale FeRh thin films using differential phase contrast imaging

To advance the use of thermally activated magnetic materials in device applications it is necessary to examine their behavior on the localized scale operando conditions. Equiatomic FeRh undergoes a magnetostructural transition from an antiferromagnetic (AF) to a ferromagnetic (FM) phase above room temperature (∼350–380 K), and hence is considered a very desirable material for the next generation of nanomagnetic or spintronic devices. For this to be realized, we must fully understand the intricate details of the AF to FM transition and associated FM domain growth on the scale of their operation. Here we combine in situ heating with a comprehensive suite of advanced transmission electron microscopy techniques to investigate directly the magnetostructural transition in nanoscale FeRh thin films. Differential phase contrast imaging visualizes the stages of FM domain growth in both cross-sectional and planar FeRh thin films as a function of temperature. Small surface FM signals are also detected due to interfacial strain with the MgO substrate and Fe deficiency after HF etching of the substrate, providing a directional bias for FM domain growth. Our work provides high resolution imaging and quantitative measurements throughout the transition, which were previously inaccessible, and offers fundamental insight into their potential use in magnetic devices

Stress-Constrained Topology Optimization with Application to the Design of Electrical Machines

Zweitveröffentlichung, ursprünglich veröffentlicht: Jonas Holley: Stress-Constrained Topology Optimization with Application to the Design of Electrical Machines. München: Verlag Dr. Hut, 2023, 199 Seiten, Dissertation Humboldt-Universität Berlin (2023). ISBN 978-3-8439-5378-8Während des Designprozesses physischer Gegenstände stellt die mechanische Stabilität in nahezu jedem Anwendungsbereich eine essentielle Anforderung dar. Stabilität kann mittels geeigneter Kriterien, die auf dem mechanischen Spannungstensor basieren, mathematisch quantifiziert werden. Dies dient dem Ziel der Vermeidung von Schädigung in jedem Punkt innerhalb des Gegenstands. Die vorliegende Arbeit behandelt die Entwicklung einer Methode zur Lösung von Designoptimierungsproblemen mit punktweisen Spannungsrestriktionen. Zunächst wird eine Regularisierung des Optimierungsproblems eingeführt, die einen zentralen Baustein für den Erfolg einer Lösungsmethode darstellt. Nach der Analyse des Problems hinsichtlich der Existenz von Lösungen wird ein Gradientenabstiegsverfahren basierend auf einer impliziten Designdarstellung und dem Konzept des topologischen Gradienten entwickelt. Da der entwickelte Ansatz eine Methode im Funktionenraum darstellt, ist die numerische Realisierung ein entscheidender Schritt in Richtung der praktischen Anwendung. Die Diskretisierung der Zustandsgleichung und der adjungierten Gleichung bildet die Basis für eine endlich-dimensionale Version des Optimierungsverfahrens. Im letzten Teil der Arbeit werden numerische Experimente durchgeführt, um die Leistungsfähigkeit des entwickelten Algorithmus zu bewerten. Zunächst wird das Problem des minimalen Volumens unter punktweisen Spannungsrestriktionen anhand der L-Balken Geometrie untersucht. Ein Schwerpunkt wird hierbei auf die Untersuchung der Regularisierung gelegt. Danach wird das multiphysikalische Design einer elektrischen Maschine adressiert. Zusätzlich zu den punktweisen Restriktionen an die mechanischen Spannungen wird die Maximierung des mittleren Drehmoments berücksichtigt, um das elektromagnetische Verhalten der Maschine zu optimieren. Der Erfolg der numerischen Tests demonstriert das Potential der entwickelten Methode in der Behandlung realistischer industrieller Problemstellungen.In the process of designing a physical object, the mechanical stability is an essential requirement in nearly every area of application. Stability can be quantified mathematically by suitable criteria based on the stress tensor, aiming at the prevention of damage in each point within the physical object. This thesis deals with the development of a framework for the solution of optimal design problems with pointwise stress constraints. First, a regularization of the optimal design problem is introduced. This perturbation of the original problem represents a central element for the success of a solution method. After analyzing the perturbed problem with respect to the existence of solutions, a line search type gradient descent scheme is developed based on an implicit design representation via a level set function. The core of the optimization method is provided by the topological gradient, which quantifies the effect of an infinitesimal small topological perturbation of a given design on an objective functional. Since the developed approach is a method in function space, the numerical realization is a crucial step towards its practical application. The discretization of the state and adjoint equation provide the basis for developing a finite-dimensional version of the optimization scheme. In the last part of the thesis, numerical experiments are conducted in order to assess the performance of the developed algorithm. First, the stress-constrained minimum volume problem for the L-Beam geometry is addressed. An emphasis is put on examining the effect of the proposed regularization. Afterwards, the multiphysical design of an electrical machine is addressed. In addition to the pointwise constraints on the mechanical stress, the maximization of the mean torque is considered in order to improve the electromagnetic performance of the machine. The success of the numerical tests demonstrate the potential of the developed design method in dealing with real industrial problems

Proceedings of the FEniCS Conference 2017

Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg

Large Eddy Simulations of gaseous flames in gas turbine combustion chambers

Recent developments in numerical schemes, turbulent combustion models and the regular increase of computing power allow Large Eddy Simulation (LES) to be applied to real industrial burners. In this paper, two types of LES in complex geometry combustors and of specific interest for aeronautical gas turbine burners are reviewed: (1) laboratory-scale combustors, without compressor or turbine, in which advanced measurements are possible and (2) combustion chambers of existing engines operated in realistic operating conditions. Laboratory-scale burners are designed to assess modeling and funda- mental flow aspects in controlled configurations. They are necessary to gauge LES strategies and identify potential limitations. In specific circumstances, they even offer near model-free or DNS-like LES computations. LES in real engines illustrate the potential of the approach in the context of industrial burners but are more difficult to validate due to the limited set of available measurements. Usual approaches for turbulence and combustion sub-grid models including chemistry modeling are first recalled. Limiting cases and range of validity of the models are specifically recalled before a discussion on the numerical breakthrough which have allowed LES to be applied to these complex cases. Specific issues linked to real gas turbine chambers are discussed: multi-perforation, complex acoustic impedances at inlet and outlet, annular chambers.. Examples are provided for mean flow predictions (velocity, temperature and species) as well as unsteady mechanisms (quenching, ignition, combustion instabil- ities). Finally, potential perspectives are proposed to further improve the use of LES for real gas turbine combustor designs