Algorithms are developed for the quickest detection of a change in statistically periodic processes. These are processes in which the statistical properties are nonstationary but repeat after a fixed time interval. It is assumed that the pre-change law is known to the decision maker but the post-change law is unknown. In this framework, three families of problems are studied: robust quickest change detection, joint quickest change detection and classification, and multislot quickest change detection. In the multislot problem, the exact slot within a period where a change may occur is unknown. Algorithms are proposed for each problem, and either exact optimality or asymptotic optimal in the low false alarm regime is proved for each of them. The developed algorithms are then used for anomaly detection in traffic data and arrhythmia detection and identification in electrocardiogram (ECG) data. The effectiveness of the algorithms is also demonstrated on simulated data.

翻译：针对统计周期过程中变化的快速检测问题，本文开发了相应算法。此类过程的统计特性虽为非平稳状态，但会在固定时间间隔后重复出现。假设决策者已知变化前分布规律，但变化后分布未知。在此框架下，本文研究了三类问题：鲁棒快速变化检测、联合快速变化检测与分类、以及多时隙快速变化检测。在多时隙问题中，一个周期内可能发生变化的具体时隙是未知的。针对每个问题均提出了相应算法，并证明了每种算法在低虚警机制下具有精确最优性或渐近最优性。最后，将所开发算法应用于交通数据异常检测以及心电图数据中的心律失常检测与识别。通过模拟数据验证了算法的有效性。