Data-driven fault detection (FD) has attracted considerable attention both in research communities and engineering applications in response to the ever-growing demands for high levels of safety and reliability of modern industrial processes. In the framework of data-driven FD for stochastic dynamic systems, process operating information is extracted completely from data without sophisticated system models. The probability distribution for stochastic noises is traditionally assumed to be known exactly. Due to the inaccessible precise distribution knowledge of noises and faults in practical applications, data-driven FD subject to distributional ambiguity of random noises and faults remains an active and challenging topic.

This work is devoted to addressing the design and performance analysis issues of data-driven FD systems for stochastic linear discrete-time dynamic processes without exact distributional information of noises and faults. In the first part of the thesis, distribution independent optimization (DIO) methods are proposed to address design issues of the data-driven dynamic FD systems. On the basis of the subspace technique aided residual generation, the mean-covariance based ambiguity sets are introduced to characterize the probability distributions of residuals in fault-free and different faulty cases. In the context of minimizing the missed detection rate (MDR) for an acceptable false alarm rate (FAR), the design of FD systems is formulated as DIO problems without posing specific distribution assumptions on noises and faults, providing a performance-oriented synthesis of the residual generator, residual evaluation function, threshold and FD performance criteria. Vector- and matrix-valued solutions to the DIO problems are derived achieving quantitative upper bounds of FAR and MDR in the probabilistic context.

The second part of the thesis focuses on the performance assessment of the developed FD systems under estimation uncertainties in means and covariance matrices in the predefined ambiguity sets. The robustness of the FD systems is discussed, and the confidence levels of the derived FAR and MDR criteria are suggested in the statistic context. A benchmark study on a three-tank system is demonstrated to show the applicability of the proposed FD approaches.