Bayesian Joint Model of Multi-Sensor and Failure Event Data for Multi-Mode Failure Prediction

📄 Overview

This repository contains the implementation of MFGPCox, a unified Bayesian framework for jointly modeling:

1. Time-to-event data (failure times)
2. Condition-monitoring signals from multiple sensors
3. Multiple Failure modes (categorical outcomes)

The model integrates:

• Convolved Multi-output Gaussian Process (CMGP) for modeling sensor signals
• Cox proportional hazards model for survival analysis
• Multinomial distribution for failure mode modeling

within a hierarchical Bayesian framework, enabling accurate prediction and uncertainty quantification.

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📄 Data Sources

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📄 Model Framework

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📄 Prediction Pipeline

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📄 Repository Structure

1. case_study/
   Files for the case study, including CMGP hyperparameter optimization code and outputs, ELBO optimization code, prediction code, evaluation code, benchmark comparison files, and associated data/results.

2. numerical_study/
   Files for the numerical study, including data generation, CMGP hyperparameter optimization code and outputs, ELBO optimization code, prediction code, evaluation code, benchmark comparison files, and associated data/results.

3. utils/
   Shared Python utility modules used across the case study and numerical study workflows.

4. requirements.txt
   Python dependency list for the main code environment.

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📄 Paper

This repository accompanies the following paper:

📌 https://arxiv.org/abs/2506.17036
(Accepted at Technometrics, 2026)

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📄 Citation

If you use this code or find it helpful, please cite:

@article{aghaee2025bayesian,
  title={Bayesian Joint Model of Multi-Sensor and Failure Event Data for Multi-Mode Failure Prediction},
  author={Aghaee Dabaghan Fard, Sina and Kim, Minhee and Deep, Akash and Lee, Jaesung},
  journal={arXiv e-prints},
  pages={arXiv--2506},
  year={2025}
}