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

arXiv: https://arxiv.org/abs/2112.13581 · HTML: https://mlsanity.com/paper/2112.13581/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 55 references that are in the map.
- First posted on arXiv 27 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [A Kernel Independence Test for Random Processes](https://mlsanity.com/paper/1402.4501/) (2014)
- [Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm](https://mlsanity.com/paper/1405.2936/) (2014)
- [Shaping Social Activity by Incentivizing Users](https://mlsanity.com/paper/1408.0406/) (2014)
- [Tracking Dynamic Point Processes on Networks](https://mlsanity.com/paper/1409.0031/) (2014)
- [Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes](https://mlsanity.com/paper/1410.6834/) (2014)

## Abstract (arXiv)

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.