Deducing effective light transport parameters in optically thin systems

We present an extensive Monte Carlo study on light transport in optically thin slabs, addressing both axial and transverse propagation. We completely characterize the so-called ballistic-to-diffusive transition, notably in terms of the spatial variance of the transmitted/reflected profile. We test the validity of the prediction cast by diffusion theory, that the spatial variance should grow independently of absorption and, to a first approximation, of the sample thickness and refractive index contrast. Based on a large set of simulated data, we build a freely available look-up table routine allowing reliable and precise determination of the microscopic transport parameters starting from robust observables which are independent of absolute intensity measurements. We also present the Monte Carlo software package that was developed for the purpose of this study

Keeping it Together: Interleaved Kirigami Extension Assembly

Traditional origami structures can be continuously deformed back to a flat sheet of paper, while traditional kirigami requires glue or seams in order to maintain its rigidity. In the former, non-trivial geometry can be created through overfolding paper while, in the latter, the paper topology is modified. Here we propose a hybrid approach that relies upon overlapped flaps that create in-plane compression resulting in the formation of "virtual" elastic shells. Not only are these structures self-supporting, but they have colossal load-to-weight ratios of order 10000

The Parallelized Large-Eddy Simulation Model (PALM) version 4.0 for atmospheric and oceanic flows: model formulation, recent developments, and future perspectives

In this paper we present the current version of the Parallelized Large-Eddy Simulation Model (PALM) whose core has been developed at the Institute of Meteorology and Climatology at Leibniz Universität Hannover (Germany). PALM is a Fortran 95-based 5 code with some Fortran 2003 extensions and has been applied for the simulation of a variety of atmospheric and oceanic boundary layers for more than 15 years. PALM is optimized for use on massively parallel computer architectures and was recently ported to general-purpose graphics processing units. In the present paper we give a detailed description of the current version of the model and its features, such as an embedded 10 Lagrangian cloud model and the possibility to use Cartesian topography. Moreover, we discuss recent model developments and future perspectives for LES applications.DFG/RA/617/3DFG/RA/617/6DFG/RA/617/16DFG/RA/617/27-

Quantification d’incertitude sur fronts de Pareto et stratégies pour l’optimisation bayésienne en grande dimension, avec applications en conception automobile

This dissertation deals with optimizing expensive or time-consuming black-box functionsto obtain the set of all optimal compromise solutions, i.e. the Pareto front. In automotivedesign, the evaluation budget is severely limited by numerical simulation times of the considered physical phenomena. In this context, it is common to resort to “metamodels” (models of models) of the numerical simulators, especially using Gaussian processes. They enable adding sequentially new observations while balancing local search and exploration. Complementing existing multi-objective Expected Improvement criteria, we propose to estimate the position of the whole Pareto front along with a quantification of the associated uncertainty, from conditional simulations of Gaussian processes. A second contribution addresses this problem from a different angle, using copulas to model the multi-variate cumulative distribution function. To cope with a possibly high number of variables, we adopt the REMBO algorithm. From a randomly selected direction, defined by a matrix, it allows a fast optimization when only a few number of variables are actually influential, but unknown. Several improvements are proposed, such as a dedicated covariance kernel, a selection procedure for the low dimensional domain and of the random directions, as well as an extension to the multi-objective setup. Finally, an industrial application in car crash-worthiness demonstrates significant benefits in terms of performance and number of simulations required. It has also been used to test the R package GPareto developed during this thesis.Cette thèse traite de l’optimisation multiobjectif de fonctions coûteuses, aboutissant à laconstruction d’un front de Pareto représentant l’ensemble des compromis optimaux. En conception automobile, le budget d’évaluations est fortement limité par les temps de simulation numérique des phénomènes physiques considérés. Dans ce contexte, il est courant d’avoir recours à des « métamodèles » (ou modèles de modèles) des simulateurs numériques, en se basant notamment sur des processus gaussiens. Ils permettent d’ajouter séquentiellement des observations en conciliant recherche locale et exploration. En complément des critères d’optimisation existants tels que des versions multiobjectifs du critère d’amélioration espérée, nous proposons d’estimer la position de l’ensemble du front de Pareto avec une quantification de l’incertitude associée, à partir de simulations conditionnelles de processus gaussiens. Une deuxième contribution reprend ce problème à partir de copules. Pour pouvoir traiter le cas d’un grand nombre de variables d’entrées, nous nous basons sur l’algorithme REMBO. Par un tirage aléatoire directionnel, défini par une matrice, il permet de trouver un optimum rapidement lorsque seules quelques variables sont réellement influentes (mais inconnues). Plusieurs améliorations sont proposées, elles comprennent un noyau de covariance dédié, une sélection du domaine de petite dimension et des directions aléatoires mais aussi l’extension au casmultiobjectif. Enfin, un cas d’application industriel en crash a permis d’obtenir des gainssignificatifs en performance et en nombre de calculs requis, ainsi que de tester le package R GPareto développé dans le cadre de cette thèse

Structural analysis of microsatellites

Satellite design, development, fabrication, testing and entry into service is a complex process. Each step of this process involves intricate steps to achieve the desired objective. This thesis summarizes a study relating to the area of development and testing of microsatellites to support qualification and eventually preparing a spacecraft for spaceflight. Students in the Space Systems Engineering laboratory (SSE Lab) in the Aerospace Engineering Program are in the process of developing a pair of microsatellites for a technology demonstration in space. After the initial design of the spacecraft is completed in the design phase a significant amount of time is spent on gaining confidence in the design. Various mathematical models are developed to represent the system and to verify its functionality. In the case of the primary structure of microsatellite a finite element model (FEM) is used to predict the behavior of the satellite structure and to verify strength requirements of design before its fabrication. Finite element model its application and results obtained form the majority of this thesis after which concentration is given to the testing phase of the microsatellite. After gaining confidence in the design and fabrication of the components it is important to validate the structure by subjecting it to structural testing. Structural testing is the only means to gain confidence in the design and certifying it for spaceflight. The results obtained from testing show how closely mathematical model (FEM) represents the physical system and provides an important learning experience for the satellite team and to help better understand and improve the design of the next generation of satellites on campus --Abstract, page iii

Cryptographic approaches to security and optimization in machine learning

Modern machine learning techniques have achieved surprisingly good standard test accuracy, yet classical machine learning theory has been unable to explain the underlying reason behind this success. The phenomenon of adversarial examples further complicates our understanding of what it means to have good generalization ability. Classifiers that generalize well to the test set are easily fooled by imperceptible image modifications, which can often be computed without knowledge of the classifier itself. The adversarial error of a classifier measures the error under which each test data point can be modified by an algorithm before it is given as input to the classifier. Followup work has showed that a tradeoff exists between optimizing for standard generalization error versus for adversarial error. This calls into question whether standard generalization error is the correct metric to measure. We try to understand the generalization capability of modern machine learning techniques through the lens of adversarial examples. To reconcile the apparent tradeoff between the two competing notions of error, we create new security definitions and classifier constructions which allow us to prove an upper bound on the adversarial error that decreases as standard test error decreases. We introduce a cryptographic proof technique by defining a security assumption in a simpler attack setting and proving a security reduction from a restricted black-box attack problem to this security assumption. We then investigate the double descent curve in the interpolation regime, where test error can continue to decrease even after training error has reached zero, to give a natural explanation for the observed tradeoff between adversarial error and standard generalization error. The second part of our work investigates further this notion of a black-box model by looking at the separation between being able to evaluate a function and being able to actually understand it. This is formalized through the notion of function obfuscation in cryptography. Given some concrete implementation of a function, the implementation is considered obfuscated if a user cannot produce the function output on a test input without querying the implementation itself. This means that a user cannot actually learn or understand the function even though all of the implementation details are presented in the clear. As expected this is a very strong requirement that does not exist for all functions one might be interested in. In our work we make progress on providing obfuscation schemes for simple, explicit function classes. The last part of our work investigates non-statistical biases and algorithms for nonconvex optimization problems. We show that the continuous-time limit of stochastic gradient descent does not converge directly to the local optimum, but rather has a bias term which grows with the step size. We also construct novel, non-statistical algorithms for two parametric learning problems by employing lattice basis reduction techniques from cryptography

Evaluating Models for Metallic Honeycomb Structures

Sandwich panels with metallic honeycomb cores have been utilized in many industrial applications where structures with high specific modulus or stiffness to weight ratios are required, most notably in the aerospace industry. Sandwich panels with square honeycomb cores have been found to exhibit a slightly higher strength to weight ratio than their more common hexagonal counterparts, and are also easier to manufacture when high core densities are required. The majority of research on square honeycomb sandwich panels has been aimed at characterizing the structure\u27s dynamic blast performance, as well as its response to out-of-plane shear, bending, and in-plane/out-of-plane compression. In this work, several analytical models for the failure of metallic square honeycomb structures under three-point-bending loading are evaluated. Failure modes of interest include face-buckling, face-yielding, core-buckling, and core-yielding. In contrast to traditional models, in which the moment is resisted entirely by the face sheets and the shear is resisted entirely by the core, several alternative analytical models are assessed. These account for the axial stress caused by the bending moment in the core as well as the face sheets, and for the shear in the face sheets. Accounting for the portion of the moment resisted by the core becomes especially important as the relative core density increases. Finite element analysis is used to verify and compare with the analytical models. Post-processing of the finite element models is focused on determining when local yielding and buckling occur in the structure, and on analyzing the effects of local failure on the global force-displacement behavior of the honeycomb structure. A parametric study with a range of honeycomb geometries is conducted in order to assess how accurately the analytical models predict failure. The intent is to develop simplified analytical models that reliably predict the onset of failure for a broad range of loading levels, geometries, and relative densities. These analytical models are then incorporated in structural optimization protocols to aid designers in selecting combinations of materials and geometries under competing performance constraints

Robotic Trajectory Tracking: Position- and Force-Control

This thesis employs a bottom-up approach to develop robust and adaptive learning algorithms for trajectory tracking: position and torque control. In a first phase, the focus is put on the following of a freeform surface in a discontinuous manner. Next to resulting switching constraints, disturbances and uncertainties, the case of unknown robot models is addressed. In a second phase, once contact has been established between surface and end effector and the freeform path is followed, a desired force is applied. In order to react to changing circumstances, the manipulator needs to show the features of an intelligent agent, i.e. it needs to learn and adapt its behaviour based on a combination of a constant interaction with its environment and preprogramed goals or preferences. The robotic manipulator mimics the human behaviour based on bio-inspired algorithms. In this way it is taken advantage of the know-how and experience of human operators as their knowledge is translated in robot skills. A selection of promising concepts is explored, developed and combined to extend the application areas of robotic manipulators from monotonous, basic tasks in stiff environments to complex constrained processes. Conventional concepts (Sliding Mode Control, PID) are combined with bio-inspired learning (BELBIC, reinforcement based learning) for robust and adaptive control. Independence of robot parameters is guaranteed through approximated robot functions using a Neural Network with online update laws and model-free algorithms. The performance of the concepts is evaluated through simulations and experiments. In complex freeform trajectory tracking applications, excellent absolute mean position errors (<0.3 rad) are achieved. Position and torque control are combined in a parallel concept with minimized absolute mean torque errors (<0.1 Nm)