Quantification de l'incertitude paramétrique dans le calcul de débit d'absorption spécifique d'un téléphone mobile

This thesis focuses on parameter uncertainty quantification (UQ) in specific absorptionrate (SAR) calculation using a computer-aided design (CAD) mobile phone model.The impact of uncertainty, e.g., lack of detailed knowledge about material electricalproperties, system geometrical features, etc., in SAR calculation is quantified by threecomputationally efficient non-intrusive UQ methods: unscented transformation (UT),stochastic collocation (SC) and non-intrusive polynomial chaos (NIPC). They are callednon-intrusive methods because the simulation process is simply considered as a blackboxwithout changing the code of the simulation solver. Their performances for thecases of one and two random variables are analysed. In contrast to the traditionaluncertainty analysis method: Monte Carlo method, the time of the calculation becomesacceptable. To simplify the UQ procedure for the case of multiple uncertain inputs, it isdemonstrated that uncertainties can be combined to evaluate the parameter uncertaintyof the output. Combining uncertainties is an approach generally used in the field ofmeasurement, in this thesis, it is used in SAR calculations in the complex situation. Oneof the necessary steps in the framework of uncertainty analysis is sensitivity analysis (SA)which aims at quantifying the relative importance of each uncertain input parameterwith respect to the uncertainty of the output. Polynomial chaos (PC) based Sobol’indices method whose SA indices are evaluated by PC expansion instead of Monte Carlomethod is used in SAR calculation. The results of the investigations are presented anddiscussed.In order to make the reading easier, elementary notions of SAR, modelling, uncertaintyin modelling, and probability theory are given in introduction (chapter 1). Thenthe main content of this thesis are presented in chapter 2 and chapter 3. In chapter 4,another approach to use PC expansion is given, and it is used in the finite-differencetime-domain (FDTD) code. Since the FDTD code in the simulation solver should bechanged, it is so-called intrusive PC expansion. Intrusive method already investigatedin details in other people’s thesis. In chapter 5, conclusions and future work are given.La thèse porte sur la quantification d'incertitude de paramètres (Uncertainty Quantification ou UQ) dans le calcul du débit d'absorption spécifique (Specific Absorption Rate ou SAR) de téléphones mobiles. L'impact de l'incertitude, ainsi le manque de connaissances détaillées sur les propriétés électriques des matériaux, les caractéristiques géométriques du système, etc., dans le calcul SAR est quantifiée par trois méthodes de calcul efficaces dites non-intrusives : Transformation non parfumée (Unscented Transformation ou UT), collocation stochastique (Stochastic Collocation ou SC) et polynômes de chaos non-intrusifs (Non-Intrusive Polynomial Chaos ou NIPC).Ces méthodes sont en effet appelées méthodes non intrusives puisque le processus de simulation est tout simplement considéré comme une boîte noire sans que ne soit modifié le code du solveur de simulation. Leurs performances pour les cas de une et deux variables aléatoires sont analysées dans le présent travail. En contraste avec le procédé d'analyse d'incertitude traditionnel (la méthode de Monte Carlo ou MCM), le temps de calcul devient acceptable. Afin de simplifier la procédure UQ pour le cas de plusieurs entrées incertaines, il est démontré que des incertitudes peuvent être combinées de manière à évaluer l'incertitude sur les paramètres de la sortie.Combiner des incertitudes est une approche généralement utilisée dans le domaine des mesures, et ici, il est utilisé dans le calcul du SAR pour la situation complexe. Une des étapes nécessaires dans le cadre de l'analyse d'incertitude est l'analyse de sensibilité (Sensitivity Analysis ou SA), qui vise à quantifier l'importance relative de chaque paramètre d'entrée incertain par rapport à l'incertitude de la sortie. La méthode reposant sur le calcul des indices de sensibilité de Sobol est employée, ces indices étant évalués par un développement en polynômes de chaos, au lieu d'utiliser la méthode de Monte-Carlo dans le calcul SAR. Les résultats des investigations sont présentés et discutés.Afin de faciliter la lecture, des notions élémentaires de débit d'absorption spécifique, de modélisation, d'incertitude dans la modélisation, de théorie des probabilités, et de calcul SAR par l'un des solveurs de simulation sont proposés dans l'Introduction (chapitre 1). Puis l'usage des méthodes non-intrusives UQ telles que UT, SC et NIPC, et l'application de la méthode des indices de Sobol pour l'analyse de sensibilité dans le calcul SAR est présentée dans les chapitres 2 et 3. Dans le chapitre 4, une autre approche d'utilisation des polynômes de chaos est fournie, et elle est utilisée dans le domaine temporel par l'intermédiaire d'un code de différences finies (Finite Difference-Time Domain ou FD-TD). Puisque le code FD-TD dans le solveur de simulation peut en effet être modifié, c'est le développement en polynômes de chaos intrusifs, étudié en détail par un certain nombre de scientifiques déjà, qui est considéré. Dans le chapitre 5, les conclusions et un aperçu des travaux futurs sont fournis

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Worst-Case Analysis of Electrical and Electronic Equipment via Affine Arithmetic

In the design and fabrication process of electronic equipment, there are many unkown parameters which significantly affect the product performance. Some uncertainties are due to manufacturing process fluctuations, while others due to the environment such as operating temperature, voltage, and various ambient aging stressors. It is desirable to consider these uncertainties to ensure product performance, improve yield, and reduce design cost. Since direct electromagnetic compatibility measurements impact on both cost and time-to-market, there has been a growing demand for the availability of tools enabling the simulation of electrical and electronic equipment with the inclusion of the effects of system uncertainties. In this framework, the assessment of device response is no longer regarded as deterministic but as a random process. It is traditionally analyzed using the Monte Carlo or other sampling-based methods. The drawback of the above methods is large number of required samples to converge, which are time-consuming for practical applications. As an alternative, the inherent worst-case approaches such as interval analysis directly provide an estimation of the true bounds of the responses. However, such approaches might provide unnecessarily strict margins, which are very unlikely to occur. A recent technique, affine arithmetic, advances the interval based methods by means of handling correlated intervals. However, it still leads to over-conservatism due to the inability of considering probability information. The objective of this thesis is to improve the accuracy of the affine arithmetic and broaden its application in frequency-domain analysis. We first extend the existing literature results to the efficient time-domain analysis of lumped circuits considering the uncertainties. Then we provide an extension of the basic affine arithmetic to the frequency-domain simulation of circuits. Classical tools for circuit analysis are used within a modified affine framework accounting for complex algebra and uncertainty interval partitioning for the accurate and efficient computation of the worst case bounds of the responses of both lumped and distributed circuits. The performance of the proposed approach is investigated through extensive simulations in several case studies. The simulation results are compared with the Monte Carlo method in terms of both simulation time and accuracy