Piecewise Deterministic Markov Processes for Condition-based Maintenance Modelling: Applications to Critical Infrastructures

Abstract

This thesis focuses on Piecewise deterministic Markov process (PDMP), a general class of non-diffusion stochastic models, as a framework for modelling condition-based maintenance (CBM) decision problems of critical infrastructures. This model allows to simulate different maintenance strategies for a stochastic deteriorating system and to assess the associated effects, the maintenance costs and the operational performance, in order to determine the best maintenance strategy to implement. From a stochastic models perspective, PDMP represents a canonical model that includes a wide variety of applications as special cases, virtually covering all non-diffusion applications, under a process that combines random jumps and deterministic motion. For CBM modelling, it presents a framework capable of handling a very large number of problems, with different modelling assumptions for both the deterioration and the intervention process, such as non-constant transition rates between discrete states, maintenance delays, different frequency regimes and quality of monitoring and system dependencies. The application of PDMP as a framework is studied and presented for models of single items and for multi-component systems, describing the formalism of the process and its evolution while developing a numerical approach for the calculation of quantities of interest such as the probability for the maintained system, to be in a critical or unacceptable state at any time or the maintenance strategy mean cost over a period of time. A simulation approach is also developed for comparison and validation of results of the numerical scheme. The scientific basis of the framework proposed in this thesis is supported by relevant solid theory published in recognized peer-reviewed journals. The proposed framework is applied to relevant case studies of critical infrastructures to illustrate the modelling and quantification approach. The presented modelling assumptions are based on both literature review and discussions with experts from the critical infrastructures sectors. One case is related to the transport sector with road bridges modelled as a single-unit system, and another case is related to the energy sector with gas compressors, exploring the capabilities for modelling of multi-component systems. Through the case studies, guidelines on how to account for different assumptions such as inspection frequency and quality, system dependencies, as well as maintenance policies are discussed. The thesis could serve as a basis for further research or engineering applications. A combination of physics-based and data-driven approaches for deterioration modelling and prognostics can be studied with PDMP as framework. Designing and presenting efficient algorithms for the computation of PDMP could allow the development of more advanced simulators than those available today for maintenance planning. Another interesting direction of research could be studying reinforced learning approaches with PDMP as base model, for estimation of model parameters when dealing with limited data characterized by a mixture of qualitative and quantitative information, important problems of censoring, incompleteness, and pollution by maintenance actions.