| The dissertation presents a novel approach to anomaly detection in complex systems based on the fundamental principles of Systems Sciences, Language Theory, and Computational Mechanics. The goal of the research is to detect anomalies to mitigate failures in complex dynamical systems as well as to enhance their performance and availability. However, solely based on the fundamental principles of physics, accurate and computationally tractable modelling of complex system dynamics is often infeasible. One may have to rely on semi-empirical models whose parameters can be identified using time series data generated from sensors and (possibly) additional sources of information such as operation history of the process.; This dissertation proposes a new, computationally simpler, alternative approach to Crutchfield's epsilon machine (epsilon-machine) for representing the pattern in a symbolic process. The proposed tool is called the D-Markov machine, which is motivated from the perspective of anomaly detection. Anomalies due to small faults, such as deviations of system parameters from their nominal values, are detected by identifying variations of patterns in symbol sequences. Time series data, observed under selected stimuli and/or self-excitation, are used to generate the symbol sequences.; The problem of anomaly detection, addressed in this dissertation, belongs to the class of non-linear non-autonomous dynamical systems in which anomalies occur at a slow time-scale while the inferences are made based on the time-series observation of selected system variable(s) at the fast time-scale. The proposed procedure of anomaly detection relies on two-time-scale analysis of the stationary response of the dynamical system. To possibly facilitate small change detection in system parameters, the system may be excited with a priori known stimuli and discovering anomaly patterns, if any, from the resulting responses at the fast time scale.; The proposed anomaly detection methodology is separated into two parts: (i) Forward problem; and (ii) Inverse problem. The objective in the forward problem is to learn, in an off-line setting, how the grammar underlying the system dynamics changes as an anomaly evolves. In contrast, the inverse problem is that of inferring a possible anomaly based on the on-line observations of the stationary behavior. The feasible range of anomaly parameter estimates can be narrowed down from the intersection of the information generated from responses under several stimuli chosen in the forward problem. (Abstract shortened by UMI.)... |
