Periodicity is prevalent in physical world, and many events involve more than one periods, e.g., individual's mobility, tide paern, and massive transportation utilization. Knowing the true periods of events can benefit a number of applications, such as traffic prediction, time-aware recommendation and advertisement, and anomaly detection. However, detecting multiple periods is a very challenging task due to not only the interwoven periodic patterns but also the low quality of event tracking records. In this paper, we study the problem of discovering all true periods and the corresponded occurring patterns of an event from a noisy and incomplete observation sequence. We devise a novel scoring function, by maximizing which we can identify the true periodic patterns involved in the sequence. We prove that, however, optimizing the objective function is an NP-hard problem. To address this challenge, we develop a heuristic algorithm named Timeslot Coverage Model (TiCom), for identifying the periods and periodic patterns approximately. The results of extensive experiments on both synthetic and reallife datasets show that our model outperforms the state-of-the-art baselines significantly in various tasks, including period detection, periodic pattern identification, and anomaly detection.