Survival analysis of failures based on Hawkes process with Weibull base intensity

Abstract

In this paper, we construct a Hawkes process with time-varying base intensity to model the sequence of failure, i.e., failure events of the compressor station, and we combine survival analysis and point process model on various failure events of the compressor station based on Hawkes process. To our best knowledge, until now, nearly all relevant literature of the Hawkes point processes assumes that the base intensity of the conditional intensity function is time-invariant. This assumption is apparently too harsh to be verified. For example, in the practical application, including financial analysis, reliability analysis, survival analysis and social network analysis, the truth variation of the base intensity of the failure occurrence over time is not constant. The constant base intensity will not reflect the base intensity trend of the failure occurring over time. Thus, in order to solve this problem, in this paper, we propose a new time-varying base intensity, e.g. which is treated as obeying Weibull distribution. First, we introduce the base intensity into a Hawkes process that obeys the Weibull distribution, and then we propose an effective learning algorithm based on the maximum likelihood estimator. Experiments on the constant base intensity synthetic data, time-varying base intensity synthetic data, and real-world data show that our method can learn the triggering patterns of the Hawkes processes and the time-varying base intensity simultaneously and robustly. Experiments on real-world data also reveal the Granger causality of different types of failures and the base probability of failure varying over time. We put forward some suggestions for practical production based on the experimental results.