Dissertation/ Thesis
Rare Event Simulation for Piecewise Deterministic Markov Processes, application in reliability assessment with PyCATSHOO tool. ; Simulation d'événements rares pour des processus de Markov déterministes par morceaux, application en fiabilité industrielle avec l'outil PyCATSHOO.
| العنوان: | Rare Event Simulation for Piecewise Deterministic Markov Processes, application in reliability assessment with PyCATSHOO tool. ; Simulation d'événements rares pour des processus de Markov déterministes par morceaux, application en fiabilité industrielle avec l'outil PyCATSHOO. |
|---|---|
| المؤلفون: | Chennetier, Guillaume |
| المساهمون: | Centre de Mathématiques Appliquées de l'Ecole polytechnique (CMAP), Institut National de Recherche en Informatique et en Automatique (Inria)-École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS), Institut Polytechnique de Paris, Josselin Garnier |
| المصدر: | https://theses.hal.science/tel-04904282 ; Methodology [stat.ME]. Institut Polytechnique de Paris, 2024. English. ⟨NNT : 2024IPPAX087⟩. |
| بيانات النشر: | CCSD |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | Rare event simulation, Piecewise deterministic Markov process, Monte Carlo, Reliability analysis, Importance sampling, Simulation d'événements rares, Processus de Markov déterministes par morceaux, Monte-Carlo, Analyse fiabiliste, Échantillonnage d'importance, [STAT.ME]Statistics [stat]/Methodology [stat.ME], [STAT.CO]Statistics [stat]/Computation [stat.CO], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] |
| الوصف: | The purpose of this thesis is to provide new methods for estimating rare event probabilities for Piecewise Deterministic Markov Processes (PDMPs). This very general class of stochastic processes offers the flexibility needed to accurately represent complex dynamic industrial systems. In particular, it allow for the joint modeling of the deterministic and continuous dynamics of the physical variables of the system (temperature, pressure, liquild levels, etc.), and the random jump dynamics that govern the change in status of its components (failures, repairs, control mechanisms, etc.). The industrial challenge is to enable the tool PyCATSHOO, used by the company Électricité de France for its probabilistic safety assessment studies, to efficiently estimate the failure probability of such systems with guaranteed accuracy. A classical Monte Carlo approach requires, for a fixed level of accuracy, a number of simulations inversely proportional to the probability sought. It is therefore not suitable for highly reliable systems with high simulation costs. Importance sampling is a popular variance reduction method in the rare event context. It consists of generating simulations under a biased distribution that favors the occurrence of the event, and correcting the bias a posteriori. Recent work has proposed a theoretical framework for implementing importance sampling of PDMPs, and has highlighted the connection between the optimal biased distribution and the so-called "committor function" of the process. Using tools from reliability analysis and the theory of random walks on graphs, new families of approximations of the committor function are introduced in this thesis. The proposed methodology is adaptive: an approximation of the committor function is constructed a priori and then refined during the simulations of a cross-entropy procedure. The simulations are then recycled to produce an importance sampling estimator of the target probability. Convergence results have been obtained, making it possible to overcome the ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| اللغة: | English |
| Relation: | NNT: 2024IPPAX087 |
| الاتاحة: | https://theses.hal.science/tel-04904282 https://theses.hal.science/tel-04904282v1/document https://theses.hal.science/tel-04904282v1/file/134114_CHENNETIER_2024_archivage.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.714EB291 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |