Un cadre holistique de la modélisation de la dégradation pour l’analyse de fiabilité et optimisation de la maintenance de systèmes de sécurité nucléaires

Components of nuclear safety systems are in general highly reliable, which leads to a difficulty in modeling their degradation and failure behaviors due to the limited amount of data available. Besides, the complexity of such modeling task is increased by the fact that these systems are often subject to multiple competing degradation processes and that these can be dependent under certain circumstances, and influenced by a number of external factors (e.g. temperature, stress, mechanical shocks, etc.). In this complicated problem setting, this PhD work aims to develop a holistic framework of models and computational methods for the reliability-based analysis and maintenance optimization of nuclear safety systems taking into account the available knowledge on the systems, degradation and failure behaviors, their dependencies, the external influencing factors and the associated uncertainties.The original scientific contributions of the work are: (1) For single components, we integrate random shocks into multi-state physics models for component reliability analysis, considering general dependencies between the degradation and two types of random shocks. (2) For multi-component systems (with a limited number of components):(a) a piecewise-deterministic Markov process modeling framework is developed to treat degradation dependency in a system whose degradation processes are modeled by physics-based models and multi-state models; (b) epistemic uncertainty due to incomplete or imprecise knowledge is considered and a finite-volume scheme is extended to assess the (fuzzy) system reliability; (c) the mean absolute deviation importance measures are extended for components with multiple dependent competing degradation processes and subject to maintenance; (d) the optimal maintenance policy considering epistemic uncertainty and degradation dependency is derived by combining finite-volume scheme, differential evolution and non-dominated sorting differential evolution; (e) the modeling framework of (a) is extended by including the impacts of random shocks on the dependent degradation processes.(3) For multi-component systems (with a large number of components), a reliability assessment method is proposed considering degradation dependency, by combining binary decision diagrams and Monte Carlo simulation to reduce computational costs.Composants de systèmes de sûreté nucléaire sont en général très fiable, ce qui conduit à une difficulté de modéliser leurs comportements de dégradation et d'échec en raison de la quantité limitée de données disponibles. Par ailleurs, la complexité de cette tâche de modélisation est augmentée par le fait que ces systèmes sont souvent l'objet de multiples processus concurrents de dégradation et que ceux-ci peut être dépendants dans certaines circonstances, et influencé par un certain nombre de facteurs externes (par exemple la température, le stress, les chocs mécaniques, etc.).Dans ce cadre de problème compliqué, ce travail de thèse vise à développer un cadre holistique de modèles et de méthodes de calcul pour l'analyse basée sur la fiabilité et la maintenance d'optimisation des systèmes de sûreté nucléaire en tenant compte des connaissances disponibles sur les systèmes, les comportements de dégradation et de défaillance, de leurs dépendances, les facteurs influençant externes et les incertitudes associées.Les contributions scientifiques originales dans la thèse sont:(1) Pour les composants simples, nous intégrons des chocs aléatoires dans les modèles de physique multi-états pour l'analyse de la fiabilité des composants qui envisagent dépendances générales entre la dégradation et de deux types de chocs aléatoires.(2) Pour les systèmes multi-composants (avec un nombre limité de composants):(a) un cadre de modélisation de processus de Markov déterministes par morceaux est développé pour traiter la dépendance de dégradation dans un système dont les processus de dégradation sont modélisées par des modèles basés sur la physique et des modèles multi-états; (b) l'incertitude épistémique à cause de la connaissance incomplète ou imprécise est considéré et une méthode volumes finis est prolongée pour évaluer la fiabilité (floue) du système; (c) les mesures d'importance de l'écart moyen absolu sont étendues pour les composants avec multiples processus concurrents dépendants de dégradation et soumis à l'entretien; (d) la politique optimale de maintenance compte tenu de l'incertitude épistémique et la dépendance de dégradation est dérivé en combinant schéma volumes finis, évolution différentielle et non-dominée de tri évolution différentielle; (e) le cadre de la modélisation de (a) est étendu en incluant les impacts des chocs aléatoires sur les processus dépendants de dégradation.(3) Pour les systèmes multi-composants (avec un grand nombre de composants), une méthode d'évaluation de la fiabilité est proposé considérant la dépendance dégradation en combinant des diagrammes de décision binaires et simulation de Monte Carlo pour réduire le coût de calcul

Reliability analysis for multi-component systems subject to multiple dependent competing failure processes

For complex multi-component systems with each component experiencing multiple failure processes due to simultaneous exposure to degradation and shock loads, we developed a new multi-component system reliability model, and applied two different preventive maintenance policies. This new model extends previous research, and is different from related previous research by considering an assembled system of degrading components with $s$-dependent failure times resulting from shared shock exposure. Previous research primarily pertained to a single component or simple system, or systems with $s$-independent failure processes and failure times. In our new system model, the individual failure processes for each component and the component failure processes are all $s$-dependent. These models can be applied directly, or customized for many complex systems with multiple components that experience $s$ -dependent competing failure processes. In this model, each component can fail due to a soft failure process, or a hard failure process. These two component failure processes are mutually competing and $s$-dependent. If one component fails relatively frequently, it is likely that the number of shocks is relatively large, and these shocks impact all components potentially causing them to fail more often as well. Therefore, failure processes of all components are also $s$-dependent. An age replacement policy and an inspection-based maintenance policy are applied for a system with multiple components. The optimal replacement interval or inspection times are determined by minimizing a cost ra- e function. The model is demonstrated on several examples

Reliability analysis for multi-component systems subject to multiple dependent competing failure processes

For complex multi-component systems with each component experiencing multiple failure processes due to simultaneous exposure to degradation and shock loads, we developed a new multi-component system reliability model, and applied two different preventive maintenance policies. This new model extends previous research, and is different from related previous research by considering an assembled system of degrading components with $s$-dependent failure times resulting from shared shock exposure. Previous research primarily pertained to a single component or simple system, or systems with $s$-independent failure processes and failure times. In our new system model, the individual failure processes for each component and the component failure processes are all $s$-dependent. These models can be applied directly, or customized for many complex systems with multiple components that experience $s$ -dependent competing failure processes. In this model, each component can fail due to a soft failure process, or a hard failure process. These two component failure processes are mutually competing and $s$-dependent. If one component fails relatively frequently, it is likely that the number of shocks is relatively large, and these shocks impact all components potentially causing them to fail more often as well. Therefore, failure processes of all components are also $s$-dependent. An age replacement policy and an inspection-based maintenance policy are applied for a system with multiple components. The optimal replacement interval or inspection times are determined by minimizing a cost ra- e function. The model is demonstrated on several examples

Maintenance optimisation for systems with multi-dimensional degradation and imperfect inspections

In this paper, we develop a maintenance model for systems subjected to multiple correlated degradation processes, where a multivariate stochastic process is used to model the degradation processes, and the covariance matrix is employed to describe the interactions among the processes. The system is considered failed when any of its degradation features hits the pre-specified threshold. Due to the dormancy of degradation-based failures, inspection is implemented to detect the hidden failures. The failed systems are replaced upon inspection. We assume an imperfect inspection, in such a way that a failure can only be detected with a specific probability. Based on the degradation processes, system reliability is evaluated to serve as the foundation, followed by a maintenance model to reduce the economic losses. We provide theoretical boundaries of the cost-optimal inspection intervals, which are then integrated into the optimisation algorithm to relieve the computational burden. Finally, a fatigue crack propagation process is employed as an example to illustrate the effectiveness and robustness of the developed maintenance policy. Numerical results imply that the inspection inaccuracy contributes significantly to the operating cost and it is suggested that more effort should be paid to improve the inspection accuracy

Non-intrusive load management system for residential loads using artificial neural network based arduino microcontroller

The energy monitoring is one of the most important aspects of energy management. In fact there is a need to monitor the power consumption of a building or premises before planning technical actions to minimize the energy consumption. In traditional load monitoring method, a sensor or a group of sensors attached to every load of interest to monitor the system, which makes the system costly and complex. On the other hand, by Non-Intrusive Load Monitoring (NILM) the aggregated measurement of the building’s appliances can be used to identify and/or disaggregate the connected appliances in the building. Therefore, the method provides a simple, reliable and cost effective monitoring since it uses only one set of measuring sensors at the service entry. This thesis aims at finding a solution in the residential electrical energy management through the development of Artificial Neural Network Arduino (ANN-Arduino) NILM system for monitoring and controlling the energy consumption of the home appliances. The major goal of this research work is the development of a simplified ANN-based non-intrusive residential appliances identifier. It is a real-time ANN-Arduino NILM system for residential energy management with its performance evaluation and the calibration of the ZMPT101B voltage sensor module for accurate measurement, by using polynomial regression method. Using the sensor algorithm obtained, an error of 0.9% in the root mean square (rms) measurement of the voltage is obtained using peak-peak measurement method, in comparison to 2.5% when using instantaneous measurement method. Secondly, a residential energy consumption measurement and control system is developed using Arduino microcontroller, which accurately control the home appliances within the threshold power consumption level. The energy consumption measurement prototype has an accurate power and current measurement with error of 3.88% in current measurement when compared with the standard Fluke meter. An ANN-Arduino NILM system is also developed using steady-state signatures, which uses the feedforward ANN to identify the loads when it received the aggregated real power, rms current and power factor from the Arduino. Finally, the ANN-Arduino NILM based appliances’ management and control system is developed for keeping track of the appliances and managing their energy usage. The system accurately recognizes all the load combinations and the load controlling works within 2% time error. The overall system resulted into a new home appliances’ energy management system based on ANN-Arduino NILM that can be applied into smart electricity system at a reduced cost, reduced complexity and non-intrusively

(Batch) Markovian arrival processes: the identifiability issue and other applied aspects

Mención Internacional en el título de doctorThis dissertation is mainly motivated by the problem of statistical modeling via a specific point process, namely, the Batch Markovian arrival processes. Point processes arise in a wide range of situations of our daily activities, such as people arriving to a bank, claims of an insurance company or failures in a system. They are defined by the occurrence of an event at a specific time, where the event occurrences may be understood from different perspectives, either by the arrival of a person or group of people in a waiting line, the different claims to the insurance companies or failures occurring in a system. Point processes are defined in terms of one or several stochastic processes which implies more versatility than mere single random variables, for modeling purposes. A traditional assumption when dealing with the analysis of point processes is that the occurrence of events are independent and identically distributed, which considerably simplifies the theoretical calculations and computational complexity, and again because of simplicity, the Poisson process has been widely considered in stochastic modelling. However, the independence and exponentiability assumptions become unrealistic and restrictive in practice. For example, in teletraffic or insurance contexts it is usual to encounter dependence amongst observations, high variability, arrivals occurring in batches, and therefore, there is a need of more realistic models to fit the data. In particular, in this dissertation we investigate new theoretical and applied properties concerning the (batch) Markovian arrival processes, or (B)MAP, which is well known to be a versatile class of point process that allows for dependent and non-exponentially distributed inter-event times as well as correlated batches. They inherit the tractability of the Poisson processes, and turn out suitable models to fit data with statistical features that differ from the classical Poisson assumptions. In addition, in spite of the large amount of works considering the BMAP, still there are a number of open problems which are of interest and which shall be considered in this dissertation. This dissertation is organized as follows. In Chapter 1, we present a brief theoretical background that introduces the most important concepts and properties that are needed to carry out our analyses. We give a theoretical background of point processes and describe them from a probabilistic point of view. We introduce the Markovian point processes and its main properties, and also provide some point process estimation backdrop with a review of recent works. An important problem to consider when the statistical inference for any model is to be developed is the uniqueness of its representation, the identifiability problem. In Chapter 2 we analyze the identifiability of the non-stationary two-state MAP. We prove that, when the sample information is given by the inter-event times, then, the usual parametrization of the process is redundant, that is, the process is nonidentifiable. We present a methodology to build an equivalent non-stationary two-state MAPs from any fixed one. Also, we provide a canonical and unique parametrization of the process so that the redundant versions of the same process can be reduced to its canonical version. In Chapter 3 we study an estimation approach for the parameters of the non-stationary version of the MAP under a specific observed information. The framework to be considered is the modelling of the failures of N electrical components that are identically distributed, but for which it is not reasonable to assume that the operational times related to each component are independent and identically distributed. We propose a moments matching estimation approach to fit the data to the non-stationary two-state MAP. A simulated and a real data set provided by the Spanish electrical group Iberdrola are used to illustrate the approach. Unlike Chapters 2 and 3, which are devoted to the Markovian arrival process, Chapters 4 and 5 focus on its arrivals-in-batches counterpart, the BMAP. The capability of modeling non-exponentially distributed and dependent inter-event times as well as correlated batches makes the BMAP suitable in different real-life settings as teletraffic, queueing theory or actuarial contexts, to name a few. In Chapter 4 we analyze the identifiability issue of the BMAP. Specifically, we explore the identifiability of the stationary two-state BMAP noted as BMAP2(k), where k is the maximum batch arrival size, under the assumptions that both the inter-event times and batches sizes are observed. It is proven that for k ≥ 2 the process cannot be identified. The proof is based on the construction of an equivalent BMAP2(k) to a given one, and on the decomposition of a BMAP2(k) into k BMAP2(2)s. In Chapter 5 we study the auto-correlation functions of the inter-event times and batch sizes of the BMAP. This chapter examines the characterization of both auto-correlation functions for the stationary BMAP2(k), for k ≥ 2, where four behavior patterns are identified for both functions for the BMAP2(2). It is proven that both auto-correlation functions decrease geometrically as the time lag increases. Also, the characterization of the autocorrelation functions has been extended for the general BMAPm(k) case, m ≥ 3. To conclude, Chapter 6 summarizes the most significant contributions of this dissertation, and also give a short description of possible research lines.Esta tesis está motivada por el problema de modelización estadística mediante un tipo específico de procesos puntuales, los procesos de llegada Markovianos en tandas. Los procesos puntuales surgen en una gran variedad de situaciones de la vida real, como las personas que llegan a un banco, reclamaciones en compañías de seguro o fallos en un sistema. Los procesos puntuales se definen como la ocurrencia de eventos en diferentes instantes temporales, donde las ocurrencias de eventos se pueden entender desde diferentes perspectivas, llegadas de personas o un grupo de personas a una cola, las distintas reclamaciones en una compañía de seguros o los fallos que ocurren en un sistema. Los procesos puntuales se definen en términos de uno o varios procesos estocásticos lo que implica más versatilidad, en términos de modelización, que la que se obtiene mediante variables aleatorias que no consideren la dimensión temporal. Una suposición tradicional en la literatura al estudiar y analizar procesos puntuales es que los tiempos entre la ocurrencia de eventos son independientes e idénticamente distribuidos, lo que simplifica considerablemente los cálculos teóricos y la complejidad computacional. Adicionalmente, por simplicidad, el proceso de Poisson ha sido ampliamente considerado en modelización estocástica. Sin embargo, las suposiciones de independencia y exponenciabilidad son poco realistas en la práctica. Por ejemplo, en el contexto teletráfico o de seguros es usual encontrar dependencia entre las observaciones, alta variabilidad, llegadas que ocurren en tandas, por lo que hay una necesidad de ajustar los datos a modelos más reales. En particular, en esta tesis investigamos nuevas propiedades teóricas y aplicadas sobre los procesos de llegada Markovianos (en tanda), denotados (B)MAP, que son conocidos por ser procesos puntuales versátiles que permiten la dependencia y no-exponenciabilidad de los tiempos entre eventos, así como la correlación entre las tandas. Ya que heredan la manejabilidad de los procesos de Poisson, son procesos adecuados para ajustar datos con características estadísticas que difieren de los supuestos clásicos de Poisson. Además, a pesar de la gran cantidad de trabajos que consideran los BMAP, todavía hay una serie de problemas abiertos que son de interés y que serán considerados en esta tesis. La estructura de esta tesis es la siguiente. En el Capítulo 1, se presenta una breve revisión teórica que introduce las definiciones y propiedades más importantes necesarias para el desarrollo de nuestros análisis. Se definen los procesos puntuales y se describen desde un punto de vista probabilístico. Se introducen los procesos puntuales Markovianos y sus propiedades principales, además se proporciona una revisión de la literatura sobre la estimación de los procesos puntuales. Un problema importante a considerar cuando se quieren desarrollar métodos de inferencia sobre cualquier modelo es la unicidad de su parametrización, o alternativamente, el problema de identificabilidad. En el Capítulo 2 estudiamos el problema de identificabilidad del MAP no estacionario con dos estados. Se demuestra que, cuando la información muestral está dada por los tiempos entre eventos, entonces, la parametrización usual del proceso es redundante, esto es, el proceso es no-identificable. Se presenta un procedimiento para construir un MAP no estacionario con dos estados equivalente a uno fijo. Además, se proporciona una parametrización canónica y única del proceso, de manera que las versiones redundantes o equivalentes de un mismo proceso se pueden reducir a su versión canónica. En el Capítulo 3 se estudia un método de estimación para los parámetros del MAP no estacionario con dos estados. El esquema que se considerará es la modelización de los fallos de N componentes eléctricos que son idénticamente distribuidos, pero que no es razonable considerar que los tiempos operacionales asociados a cada componente son independientes ni idénticamente distribuidos. Se propone un método de igualdad de momentos para ajustar datos a un MAP no estacionarios con dos estados. Se presenta un ejemplo simulado y un ejemplo con datos reales proporcionados por la compañía eléctrica Iberdrola para ilustrar la metodología propuesta. A diferencia de los capítulos 2 y 3, que están dedicados a los procesos de llegada Markovianos, los capítulos 4 y 5 se centran en su generalización para considerar llegadas en tandas, el BMAP. La capacidad de modelar tiempos entre eventos dependientes y no-exponenciales, así como llegadas en tandas correladas, hace que los BMAP sean modelos apropiados en problemas de la vida real, como en contextos teletráficos, de teoría de colas o actuariales, entre otros. En el Capítulo 4 se explora la identificabilidad para el BMAP estacionario de 2 estados, BMAP2(k), donde k es el tamaño máximo de las tandas, bajo la suposición de que los tiempos entre eventos y los tamaños de las tandas son los datos observados. Se demuestra que para k ≥ 2 el proceso no es único. La demostración se basa en la construcción de un BMAP2(k) equivalente a uno fijo, y en la descomposición de un BMAP2(k) en k BMAP2(2)s. En el Capítulo 5 se estudia las funciones de autocorrelación para los tiempos entre-eventos y las llegadas en tanda del BMAP. Además, también se examina la caracterización de ambas funciones de autocorrelación para el BMAP2(k), k ≥ 2, estacionario, donde se identifican cuatro patrones para el BMAP2(2). Se demuestra que ambas funciones de autocorrelación decrecen geométricamente. Finalmente, se extiende la caracterización de las funciones de autocorrelación para el caso general BMAPm(k), m ≥ 3. Finalmente, en el Capítulo 6 se resumen las contribuciones más importantes de esta tesis y futuras líneas de investigación.Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Rafael Pérez Ocón.- Secretario: D Auria , Bernardo.- Vocal: Mogens Blad