Modèle bayésien d'agrégation des avis d'experts en exploitation d'équipements, application à l'optimisation de la disponibilité

RÉSUMÉ : Le travail proposé dans ce mémoire traite le problème de la prise en compte des avis d’experts en exploitation des équipements industriels dans les modèles statistiques de fiabilité, de maintenance et de disponibilité. Les avis d’experts sont formulés sous forme de distributions a priori sur des paramètres inconnus de ces derniers modèles. L’inférence bayésienne est proposée comme une méthode de construction des distributions a postériori de ces mêmes paramètres en tenant compte des données de vraisemblance collectées lors de l’exploitation d’un équipement. Ainsi, trois modèles sont développés et résolus à l’aide des méthodes de simulation de chaînes de Markov de type MCMC. Le premier modèle concerne l’agrégation des avis d’experts issus d’un même domaine d’expertise formulés sur un seul paramètre. Le second propose un modèle d’agrégation des avis formulés sur deux paramètres, les experts proviennent de deux domaines d’expertises différentes. Ces deux premiers modèles sont validés à l’aide de trois critères statistiques : le DIC (Deviance information criterion), le p-value bayésien et le test non paramétrique de mesure de tendance des données. Le troisième modèle concerne l’optimisation de la disponibilité d’un équipement avec une actualisation du taux de défaillance et du taux de réparation sur plusieurs périodes. Les trois modèles ainsi que les algorithmes de résolution sont programmés sous Matlab. Des données de simulation ont été exploitées afin de tester la logique de modélisation et d’analyser la performance des modèles proposés.----------ABSTRACT : The work proposed in this document addresses the problem of combining different opinions of experts about unknown parameters within the reliability, maintenance and availability models. Expert opinions are characterised using a prior distribution functions of these unknown parameters. The Bayesian inference is proposed as a modeling approach to establish the posterior distribution functions of the same unknown parameters with respect to the likelihood data collected during the operation time of the equipment. Thus, three models are developed and solved using Markov Chains Monte Carlo (MCMC). The first model concerns the aggregation of expert opinions from the same area of expertise made on a single unknown parameter. The second provides an aggregation of opinions on two unknown parameters. The experts belong to two different areas of expertise. These first two models are validated using three statistical criteria: DIC (Deviance information criterion), the bayesian p-value and the nonparametric test of Fisher which measures the data trend. The third model concerns the optimization of the availability of equipment with a discount of the failure and repair rates over several periods of time. These three models as well as the solving algorithms are programmed using Matlab software. Simulation data were used to test the logic of modeling and to analyze the performance of the proposed models

A Bayesian-Based Framework for Making Inspection and Maintenance Decisions from Data and Expert Knowledge

PhDIt is estimated that more than one-third of current infrastructure maintenance expenditure is wasted through poor decision-making. To make better decisions about maintenance, there is a need to provide better predictions of asset deterioration, and further, to use this information to plan inspections and appropriate repair actions. A number of statistical modelling techniques have been proposed to predict deterioration. However, these approaches can be difficult to apply in practice, for example when the time of deterioration is only known approximately from periodic inspections. Also, these approaches lack an easy way to incorporate knowledge about the deterioration process that can readily be considered when judgements are made by experienced maintainers. Moreover, in practice, the size of available datasets on deterioration is often limited; hence there is a need to blend data with knowledge. This thesis presents a framework for predicting deterioration and reasoning about the effects of repair using both the available data and expert knowledge that can support inspection and maintenance-related decisions. The framework uses Bayesian modelling, combining two types of Bayesian approaches: Bayesian statistical models and Bayesian Networks (BNs). Bayesian statistical models are used to estimate the parameter of statistical distributions, modelled as continuous variables. On the other hand, BNs model causal or influential relationships between (primarily) discrete variables to make predictions and can be based on elicited knowledge. This thesis builds on earlier work that combines these two forms of model, with both the continuous variables from Bayesian statistical models and the discrete variables of BNs. We refer this type of model to as a hybrid BN. The use of hybrid BNs is possible using an already existing algorithm that dynamically discretises continuous variables in a BN. BNs within the framework can be combined to model the different aspects of deterioration needed in different circumstances. The rate of deterioration can be learnt from censored deterioration data inferred from inspection records and knowledge elicited from engineers. Asset sharing similar characteristics can be grouped, and when a group contains only a few instances in the available data, data from related groups can be used to constrain the parameter learning. Deterioration through multiple condition states can be modelled. The deterioration of different components of complex structures can be combined. Finally, we model the effect of repair actions and show how to plan maintenance. A case study using data from the US National Bridge Inventory is used to validate the deterioration prediction models. We show how real-world inspection records can be integrated with engineering knowledge to predict the deterioration. Compared with other published approaches, the proposed models show better performance, especially when the group of similar assets is small. We then apply the models to reason about inspection and maintenance-related decisions. We use case studies of maintenance practices in the GB and US to show how the models can be used to assist both operational and strategic maintenance decision making. Many features of the proposed framework need to be adapted and combined to create a maintenance model applicable in a particular circumstance. Examples include the number of deterioration states, the decomposition of assets into components and the grouping of assets. The challenge is to create a complex and large-scale asset management system to allow a maintenance analyst to apply the framework, without needing expertise in Bayesian modelling. By representing our framework as a set of generic models using an extended form of BN – a probabilistic relational model – we show, with a simple prototype, how such a system could be realised