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

TL;DR

This paper introduces a novel Hawkes process model with a Weibull-based time-varying base intensity for survival analysis of compressor station failures, demonstrating improved learning of failure patterns and causality in real-world data.

Contribution

It proposes a new Weibull-based time-varying base intensity for Hawkes processes and an effective maximum likelihood learning algorithm, addressing limitations of constant base intensity models.

Findings

The method accurately learns triggering patterns and base intensity variations.

It reveals Granger causality among failure types.

The approach is robust on synthetic and real-world data.

Abstract

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 various failure events of the compressor station. However, until now, nearly all relevant literatures of the Hawkes point processes assume 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 base intensity of the truth conditional intensity function is very likely to be time-varying. The constant base intensity will not reflect the base probability of the failure occurring over time. Thus, in order to solve this problem, in this paper, we propose a new time-varying base intensity, for example, which is from Weibull distribution. First, we introduce the base intensity from the Weibull distribution, and then we propose an effective learning algorithm by 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 the real-world data reveal the Granger causality of different kinds of failures and the base probability of failure varying over time.