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In this paper, we use the Hawkes process to model the sequence of failure,i.e., events of compressor station and conduct survival analysis on variousfailure events of the compressor station. However, until now, nearly allrelevant literatures of the Hawkes point processes assume that the baseintensity of the conditional intensity function is time-invariant. Thisassumption is apparently too harsh to be verified. For example, in thepractical application, including financial analysis, reliability analysis,survival analysis and social network analysis, the base intensity of the truthconditional intensity function is very likely to be time-varying. The constantbase intensity will not reflect the base probability of the failure occurringover time. Thus, in order to solve this problem, in this paper, we propose anew time-varying base intensity, for example, which is from Weibulldistribution. First, we introduce the base intensity from the Weibulldistribution, and then we propose an effective learning algorithm by maximumlikelihood estimator. Experiments on the constant base intensity syntheticdata, time-varying base intensity synthetic data, and real-world data show thatour method can learn the triggering patterns of the Hawkes processes and thetime-varying base intensity simultaneously and robustly. Experiments on thereal-world data reveal the Granger causality of different kinds of failures andthe base probability of failure varying over time.

Survival Analysis of the Compressor Station Based on Hawkes Process with Weibull Base Intensity