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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📄 Data Availability

Case Study Data

The dataset used in the case study is publicly available and was introduced in:

Z. Li, Y. Li, X. Yue, E. Zio, and J. Wu, "A Deep Branched Network for Failure Mode Diagnostics and Remaining Useful Life Prediction," IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1–11, 2022, Art no. 3519111.
DOI: 10.1109/TIM.2022.3195280

This dataset can be accessed at:

📌 https://github.com/kernelLZ/Turbofan-Engine-Degradation-Dataset-with-Multiple-Failure-Modes

Numerical Study Data

For the numerical study, the data are synthetically generated, and the corresponding data and data generation code is available in the numerical_study/Data_Generation/ folder.

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📄 Paper

This repository accompanies the following paper:

📌 https://doi.org/10.1080/00401706.2026.2653564
(Published in Technometrics, 2026)

📌 https://arxiv.org/abs/2506.17036
(This is a preprint version. The final, peer-reviewed version is available in Technometrics and should be considered the authoritative version.)

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📄 Citation

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

author = {Sina Aghaee Dabaghan Fard and Minhee Kim and Akash Deep and Jaesung Lee},
title = {Bayesian Joint Model of Multi-Sensor and Failure Event Data for Multi-Mode Failure Prediction},
journal = {Technometrics},
volume = {0},
number = {ja},
pages = {1--24},
year = {2026},
publisher = {Taylor \& Francis},
doi = {10.1080/00401706.2026.2653564},
}