Temporal sequence data, such as event logs collected from industrial operations, often contain both sequential and time interval information. These two types of information can be used to define periodic patterns. Due to random disturbance, the occurrence of such periodic patterns may be drifted from their expected positions or time, resulting in asynchronous periodic patterns (APPs). The major limitation of existing studies on APPs is their reliance on subjective and case-specific determination of tolerance to the asynchrony. In real-world practice, however, knowledge on such tolerance values may be extremely limited, if not unavailable. To address this limitation, this paper formulates the asynchrony tolerating as a hierarchical clustering of time intervals embedded in the temporal sequence data. The clustering method is improved to balance the trade-off between data similarity and pattern interpretability. Based on the symbol sequence generated by the improved clustering method, APPs are detected with the proposed convolution-based periodicity detection algorithm. The effectiveness of the proposed approach is demonstrated with both numerical simulation experiment and real-world case study.