Cette thèse est consacré aux tests d'adéquation basés sur la fonction caractéristique. Nous débutons en présentant et en complétant les résultats probabilistes nécessaires à la construction de statistiques de test prenant la fonction caractéristique et son pendant la fonction caractéristique empirique comme représentations respectives des lois de référence et de la loi inconnue de l'échantillon de vecteurs aléatoires à tester. Nous poursuivons le travail en faisant la revue et en classant les tests basés sur la fonction caractéristique existants. Nous élaborons ensuite une classe de statistiques de test s'appuyant sur le calcul d'une distance intégrale. Le cas de la distance L2 est étudié plus à fond, car nous avons pu établir des résultats asymptotiques dans ce dernier cas. Ceux-ci font intervenir les éléments propres inconnus d'un opérateur intégral. Nous présentons, puis utilisons, une méthode d'approximation spectrale basée sur une projection de l'opérateur sur une base orthonormée.Finalement, nous construisons une nouvelle classe de tests appartenant au paradigme des tests lisses de Neyman. L'étude précédente nous permet de simplifier considérablement la construction de ces tests, dont différentes versions sont proposées tant pour le test d'une hypothèse simple que pour le test d'une hypothèse composite. / This PhD thesis consists in building goodness-of-fit tests using the characteristic function (CF) as a prefered representation for the probability laws involved.We start with listing and improving results in probability theory necessary to build test statistics using the characteristic function and its conterpart the empirical characteristic function.We list and classify existing characteristic function based goodness-of-fit tests published by varions authors since 1977.Then, we build a class of tests based on integral metrics. We take particular attention to the case where the statistics are build using a L2 distance. More specifically, we give asymptotic results in this case. However, these results reveal the need for information on the unknown eigenelements of an integral operator. Thus, we present and implement an approximation method using a sequence of projections on orthonormal bases ofan hilbertian functional space.Finally, we will build another class of tests using the Neyman smooth test paradigm. This study is based on our previous results, that fit well into the construction of characteristic function based smooth tests. We give various applications, presenting tests for both a simple hypothesis and a composite hypothesis.

Indiana University-Purdue University Indianapolis (IUPUI) / This paper presents a novel approach of particulate material (soot) measurement in a Diesel particulate filter using Electrical Capacitance Tomography. Modern Diesel Engines are equipped with Diesel Particulate Filters (DPF), as well as on-board technologies to evaluate the status of DPF because complete knowledge of DPF soot loading is very critical for robust efficient operation of the engine exhaust after treatment system. Emission regulations imposed upon all internal combustion engines including Diesel engines on gaseous as well as particulates (soot) emissions by Environment Regulatory Agencies. In course of time, soot will be deposited inside the DPFs which tend to clog the filter and hence generate a back pressure in the exhaust system, negatively impacting the fuel efficiency. To remove the soot build-up, regeneration of the DPF must be done as an engine exhaust after treatment process at pre-determined time intervals. Passive regeneration use exhaust heat and catalyst to burn the deposited soot but active regeneration use external energy in such as injection of diesel into an upstream DOC to burn the soot. Since the regeneration process consume fuel, a robust and efficient operation based on accurate knowledge of the particulate matter deposit (or soot load)becomes essential in order to keep the fuel consumption at a minimum. In this paper, we propose a sensing method for a DPF that can accurately measure in-situ soot load using Electrical Capacitance Tomography (ECT). Simulation results show that the proposed method offers an effective way to accurately estimate the soot load in DPF. The proposed method is expected to have a profound impact in improving overall PM filtering efficiency (and thereby fuel efficiency), and durability of a Diesel Particulate Filter (DPF) through appropriate closed loop regeneration operation.