Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15

Using the Sharp Operator for edge detection and nonlinear diffusion

In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement

An Optimization Platform for High Speed Propellers

To improve the efficiency by which current power plants translate jet energy into useful thrust the use of turboprop and in particular open rotor aircraft are being revisited. One challenge in association with developing new powerplants for such aircraft is high speed propeller design in general and noise prediction in particular. The Boxprop was invented in 2009 by GKN Aerospace in order to mitigate the effects of the tip vortex on noise and to improve upon the aerodynamics of a conventional propeller blade. The Boxprop is composed of a double-bladed propeller joined at the tips, and the design has the potential to eliminate the tip vortex, and thereby decrease that particular noise source. The complex and highly three-dimensional shape of an advanced propeller blade is challenging to model with classical propeller design methods, requiring instead more sophisticated optimization methods. This paper presents an optimization platform developed for high speed propellers, and illustrates its use by performing a reduced aerodynamic optimization of the Boxprop. The optimization process starts by performing a Latin Hypercube Sampling of the design space, and analyzes the resulting geometries using CFD. A meta-model employing radial basis functions is then used to interpolate on the obtained CFD results, which the GA uses to find optimal candidates along the obtained Pareto front. These designs are then evaluated using CFD, and their data added to the meta-model. The process iterates until the meta-model converges. The results of this paper demonstrate the capability of the presented optimization platform, and applying it on the Boxprop has resulted in valuable design improvements and insights. The obtained designs show less blade interference, more efficiently loaded blades, and less produced swirl. The methodology for geometry generation, meshing and optimizing is fast, robust, and readily extendable to other types of optimization problems, and paves the way for future collaborative research in the area of turbomachinery

Parallelization Strategies for Markerless Human Motion Capture

Markerless Motion Capture (MMOCAP) is the problem of determining the pose of a person from images captured by one or several cameras simultaneously without using markers on the subject. Evaluation of the solutions is frequently the most time-consuming task, making most of the proposed methods inapplicable in real-time scenarios. This paper presents an efficient approach to parallelize the evaluation of the solutions in CPUs and GPUs. Our proposal is experimentally compared on six sequences of the HumanEva-I dataset using the CMAES algorithm. Multiple algorithm’s configurations were tested to analyze the best trade-off in regard to the accuracy and computing time. The proposed methods obtain speedups of 8× in multi-core CPUs, 30× in a single GPU and up to 110× using 4 GPU

TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the entangled geometric complexity and biological complexity. We introduce topology, i.e., element specific persistent homology (ESPH), to untangle geometric complexity and biological complexity. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains crucial biological information via a multichannel image representation. It is able to reveal hidden structure-function relationships in biomolecules. We further integrate ESPH and convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the limitations to deep learning arising from small and noisy training sets, we present a multitask topological convolutional neural network (MT-TCNN). We demonstrate that the present TopologyNet architectures outperform other state-of-the-art methods in the predictions of protein-ligand binding affinities, globular protein mutation impacts, and membrane protein mutation impacts.Comment: 20 pages, 8 figures, 5 table

Comparison of genetic and tabu search algorithms in aerodynamic design of S-ducts

Confronto delle ottimizzazioni di un diffusore aeronautico utilizzando due diversi algoritmi: tabu search e un algoritmo genetico

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

A Parallel Genetic Algorithm for Optimizing Multicellular Models Applied to Biofilm Wrinkling

Multiscale computational models integrating sub-cellular, cellular, and multicellular levels can be powerful tools that help researchers replicate, understand, and predict multicellular biological phenomena. To leverage their potential, these models need correct parameter values, which specify cellular physiology and affect multicellular outcomes. This work presents a robust parameter optimization method, utilizing a parallel and distributed genetic-algorithm software package. A genetic algorithm was chosen because of its superiority in fitting complex functions for which mathematical techniques are less suited. Searching for optimal parameters proceeds by comparing the multicellular behavior of a simulated system to that of a real biological system on the basis of features extracted from each which capture high-level, emergent multicellular outcomes. The goal is to find the set of parameters which minimizes discrepancy between the two sets of features. The method is first validated by demonstrating its effectiveness on synthetic data, then it is applied to calibrating a simple mechanical model of biofilm wrinkling, a common type of morphology observed in biofilms. Spatiotemporal convergence of cellular movement derived from experimental observations of different strains of Bacillus subtilis colonies is used as the basis of comparison

Adaptive parameterization for Aerodynamic Shape Optimization in Aeronautical Applications

Cílem mé disertační práce je analyzovat a vyvinout parametrizační metodu pro 2D a 3D tvarové optimalizace v kontextu průmyslového aerodynamického návrhu letounu založeném na CFD simulacích. Aerodynamická tvarová optimalizace je efektivní nástroj, který si klade za cíl snížení nákladů na návrh letounů. Nástroj založený na automatickém hledání optimálního tvaru. Klíčovou částí úspěšného optimalizačního procesu je použití vhodné parametrizační metody, metody schopné garantovat možnost dosažení optimálního tvaru. Parametrizační metody obecně používané v oblasti aerodynamické tvarové optimalizace momentálně nejsou připravený na komplikované průmyslové aplikace vyskytující se u moderních dopravních letounů, které mají šípová zalomená křídla s winglety a motorovými gondolami, přechodové prvky spojující např. trup s křídlem atd.. Existuje tedy potřeba nalezení obecné parametrizační metody, která bude aplikovatelná na širokou škálu různých geometrických tvarů. Free-Form Deformation (FFD[1]) parametrizace může, vzhledem ke svým schopnostem při zacházení s geometrií, být odpovědí na tuto potřebu. Adaptivní parametrizace by se měla být schopna automaticky přizpůsobit danému tvaru tak, aby byly její kontrolní body vhodně rozmístěny. Což umožní dostatečnou kontrolu deformací objektu, která zaručí možnost vytvoření optimálního tvaru objektu a splnění geometrických omezení. Primární aplikací takové parametrizační metody je deformace tvaru objektu. Dalším navrhovaným cílem je modifikace FFD parametrizační metody pro současné deformace tvaru objektu a CFD výpočetní sítě, umožnující velké deformace objektu při zachování kvality výpočetní sítě.The goal of this doctoral thesis is to analyze and develop parameterization algorithms for 2D and 3D shape optimization in the context of industrial aircraft aerodynamic design based on simulations with CFD. Aerodynamic shape optimization is an efficient tool that aims at reducing the cost of the process of aircraft design. A tool that is based on automatization of the search for the optimum shape. Key part of successful aerodynamic shape optimization is the use of appropriate parameterization method, a method that should guarantee the possibility of reaching optimum shape. The parameterization methods used in aerodynamic shape optimizations are still not ready for complex industrial applications, which are present on modern passenger aircrafts with swept cranked wings with winglets and engine pylons, fuselage-wing interactions etc. So there is a need for general parameterization method that applies on wide variety of different geometries.The Free-Form Deformation (FFD[1]) parameterization can, thanks to its geometry handling qualities, be the answer to this need. Adaptive parameterization should automatically modify parameterization grid (lattice) to get appropriate lattice in regions of interest. Such that will allow sufficient control of deformations of the object with respect to reaching optimum shape and fulfilling optimization constraints. First application is in the surface deformation. The other proposed goal is development of the FFD parameterization that can do both surface deformations and CFD mesh deformations, while enabling large object deformations and preserving the level of mesh quality during the process.

pymooCFD - A Multi-Objective Optimization Framework for CFD

Modern computational resource have solidified the use of computer modeling as an integral part of the engineering design process. This is particularly impressive when it comes to high-dimensional models such as computational fluid dynamics (CFD) models. CFD models are now capable of producing results with a level of confidence that would previously have required physical experimentation. Simultaneously, the development of machine learning techniques and algorithms has increased exponentially in recent years. This acceleration is also due to the widespread availability of modern computational resources. Thus far, the cross-over between these fields has been mostly focused on computer models with low computational costs. However, this is slowly changing through the continued rapid development of both fields. The pymooCFD platform seeks to unite these fields of study by connecting a state-of-the-art library of optimization algorithms with industry leading CFD solvers. To begin with, this platform is important for testing the effectiveness of applying new optimization algorithms to CFD. Additionally, machine learning has been shown to help improve CFD models; this platform could serve to facilitate the development of better CFD models. In this paper, the pymooCFD platform is applied to three different optimization problems. First, for validation purposes, the platform was used to conduct a well documented optimization problem, the reduction of drag around a circular cylinder through oscillating rotation around it\u27s central axis. Second, the platform was applied to a Large Eddy Simulation (LES) to Reynolds-Average Navier-Stokes (RANS) model simplification. Lastly, the platform was applied to optimizing the direction, power and location of portable air purifiers in a room with six computer simulated persons (CSPs). The results show that the pymooCFD is a powerful tool for applying optimization algorithms to CFD. The validation of the platform was successful. A novel approach to CFD model simplification, called boundary condition calibration, is proposed. Finally, conclusions were drawn about optimal configuration of portable air purifiers within indoor spaces. These conclusions should serve to inform the experiments need to draw qualitative conclusion and create health advisories. Code Repository: https://github.com/gmclove/pymooCF