Uncertainty quantification and its properties for hidden Markov models with application to condition based maintenance

Condition-based maintenance (CBM) can be viewed as a transformation of data gathered from a piece of equipment into information about its condition, and further into decisions on what to do with the equipment. Hidden Markov model (HMM) is a useful framework to probabilistically model the condition of complex engineering systems with partial observability of the underlying states. Condition monitoring and prediction of such type of system requires accurate knowledge of HMM that describes the degradation of such a system with data collected from the sensors mounted on it, as well as understanding of the uncertainty of the HMMs identified from the available data. To that end, this thesis proposes a novel HMM estimation scheme based on the principles of Bayes theorem. The newly proposed Bayesian estimation approach for estimating HMM parameters naturally yields information about model parametric uncertainties via posterior distributions of HMM parameters emanating from the estimation process. In addition, a novel condition monitoring scheme based on uncertain HMMs of the degradation process is proposed and demonstrated on a large dataset obtained from a semiconductor manufacturing facility. Portion of the data was used to build operating mode specific HMMs of machine degradation via the newly proposed Bayesian estimation process, while the remainder of the data was used for monitoring of machine condition using the uncertain degradation HMMs yielded by Bayesian estimation. Comparison with a traditional signature-based statistical monitoring method showed that the newly proposed approach effectively utilizes the fact that its parameters are uncertain themselves, leading to orders of magnitude fewer false alarms. This methodology is further extended to address the practical issue that maintenance interventions are usually imperfect. We propose both a novel non-ergodic and non-homogeneous HMM that assumes imperfect maintenances and a novel process monitoring method capable of monitoring the hidden states considering model uncertainty. Significant improvement in both the log-likelihood of estimated HMM parameters and monitoring performance were observed, compared to those obtained using degradation HMMs that always assumed perfect maintenance. Finally, behavior of the posterior distribution of parameters of unidirectional non- ergodic HMMs modeling in this thesis for degradation was theoretically analyzed in terms of their evolution as more data become available in the estimation process. The convergence problem is formulated as a Bernstein-von Mises theorem (BvMT), and under certain regularity conditions, the sequence of posterior distributions is proven to converge to a Gaussian distribution with variance matrix being the inverse of the Fisher information matrix. An example of a unidirectional HMM is presented for which the regularity conditions are verified, and illustrations of expected theoretical results are given using simulation. The understanding of such convergence of posterior distributions enables one to determine when Bayesian estimation of degradation HMMs is justified and converges toward true model parameters, as well as how much data one then needs to achieve desired accuracy of the resulting model. Understanding of these issues is of utmost important if HMMs are to be used for degradation modeling and monitoring.Operations Research and Industrial Engineerin

Semi-Markov and delay time models of maintenance

This thesis is concerned with modelling inspection policies of facilities which Qraduallv deteriorate in time. The context of inspection policies lends itself readily to probabilistic modelling. Indeed, many of the published theoretical models to be found in the literature adopt a Markov approach, where states are usually 'operating', 'operating but fault present', and 'failed'. However, most of these models fail to discuss the 'fit' of the model to data,a nd virtually no exampleso f actual applications or case-studiesa re to be found. hi a series of recent papers dating from 1984, a robust approach to solve these problems has been introduced and developed as the Delay Time Model (DTM). The central concept for this model is the delay time, h, of a fault which is the time lapse from when a fault could first be noticed until the time when its repair can be delayed no longer because of unacceptable consequences. The bottle neck in delay time modelling is how to estimate the delay time distribution parameters. Two methods for estimating these parameters have been developed. namely the subjective method and the objective method. Markov models have the advantage of an extensive body of theory. 'fliere are, however. difficulties of definition, measurement, and calculation when applying Markov models to real-world situations within a maintenance context. Indeed. this problem has motivated the current research which ainis to explore the two modelling methodologies in cases where comparison is valid, and also to gain an insight as to how robust Markov inspection models can be as decision-aids where Markovian properties are not strictly satisfied. It Nvill be seen that a class of inspection problems could be solved by a serni- Markov model using the delay time concept. In this thesis, a typical senii-i%Ia, rkov inspection model based upon the delay time concept is presented for a complex repairable systein that may fail during the course of its service lifetime and the results are compared. Finally, a case study of the senii-Markov inspection model and the delay time model is discussed

Addressing Complexity and Intelligence in Systems Dependability Evaluation

Engineering and computing systems are increasingly complex, intelligent, and open adaptive. When it comes to the dependability evaluation of such systems, there are certain challenges posed by the characteristics of “complexity” and “intelligence”. The first aspect of complexity is the dependability modelling of large systems with many interconnected components and dynamic behaviours such as Priority, Sequencing and Repairs. To address this, the thesis proposes a novel hierarchical solution to dynamic fault tree analysis using Semi-Markov Processes. A second aspect of complexity is the environmental conditions that may impact dependability and their modelling. For instance, weather and logistics can influence maintenance actions and hence dependability of an offshore wind farm. The thesis proposes a semi-Markov-based maintenance model called “Butterfly Maintenance Model (BMM)” to model this complexity and accommodate it in dependability evaluation. A third aspect of complexity is the open nature of system of systems like swarms of drones which makes complete design-time dependability analysis infeasible. To address this aspect, the thesis proposes a dynamic dependability evaluation method using Fault Trees and Markov-Models at runtime.The challenge of “intelligence” arises because Machine Learning (ML) components do not exhibit programmed behaviour; their behaviour is learned from data. However, in traditional dependability analysis, systems are assumed to be programmed or designed. When a system has learned from data, then a distributional shift of operational data from training data may cause ML to behave incorrectly, e.g., misclassify objects. To address this, a new approach called SafeML is developed that uses statistical distance measures for monitoring the performance of ML against such distributional shifts. The thesis develops the proposed models, and evaluates them on case studies, highlighting improvements to the state-of-the-art, limitations and future work