This thesis investigates the problem of fault detection and isolation in complex and distributed systems, with the aim of improving sustainability. The primary objective is to develop a theoretical framework for modelling, detecting and isolating faults. Presented models are capable of capturing nonlinear effects of a fault, and also are able to successfully incorporate multiple causes that might lead to the same fault, where each of the presumed causes is masked by conditions such as noise or model-reality mismatch. Next, a protocol is developed that allows local models to interact continuously to make a decision about the state of the system. Classification of neighbouring local models in autonomous groups and exchange of local model parameters within a group allow decentralised decision-making about the presence of faults.
To model a fault that may be caused by more than one source, a mixture of conditional Gaussian transitions is proposed. The conditional means are modelled by recurrent neural networks, thus permitting arbitrary nonlinearity, and the expectation-maximization algorithm is used to estimate model parameters. By grouping known types of faults, a bank of competing local fault models is formed. The mixture model is then extended to the case of a hidden Markov model to handle instances where the relationship between the various causes of fault changes with time. Recurrent neural networks are again used to model the conditional means.
For practical application of the methodology, asymptotic stability of the model is demonstrated. This is done by appealing to the theory of Markov chains on a general state space. Methods for model evaluation and parameter estimation are established by adapting the Baum-Welch procedure to autoregressive hidden Markov models. Finally, a procedure for distributed fault detection is proposed, which is based on consensus in a group of local agents/experts. Local models are represented by Markov chains, and modelling consensus as a mixture of these allows estimation of optimal ratings using the expectation-maximization framework. To deal with the unobservable case, the procedure is extended to accommodate hidden Markov models. Stability conditions for the algorithm are also determined.
In summary, this thesis helps answer some important questions concerning the detection of faults in complex and distributed systems. The problem of fault modelling, which is generally nonlinear and multi-modal, suggests the use of a mixture model. In contrast to previously proposed methods, the conditional mean of a mixture component is modelled by a continuous nonlinear function for which the Lipschitz condition holds. In the case where the contribution of the mixture component to the total fault dynamics changes with time, an autoregressive hidden Markov model is employed. Finally, to establish decentralized fault detection, a consensus algorithm is used in concert with hidden Markov models. The efficacy of the proposed methods is demonstrated using simulation.