Joint Model for Multi-Type Failure Event Prediction from Multi-Sensor Time Series and Survival Data

Modern industrial systems often have multiple components subject to multiple types of failure, and their conditions are monitored by multiple sensors, generating multiple time-series signals. Additionally, time-to-failure data are commonly available. Predicting multiple components' remaining useful life (RUL) is crucial by leveraging multi-sensor time series and multi-type failure event data. In most existing models, failure mode identification and RUL prediction are performed independently, ignoring the inherent relationship between these two tasks. Some models integrate multiple failure modes classification and event prediction using black-box machine learning approaches, which lack statistical rigor and cannot characterize the inherent uncertainty in the system and data. This paper introduces a unified approach to jointly model the multi-sensor time-series data and RUL prediction concerning multiple failures. We integrate a Cox proportional hazards model with a Multi-output Convolutional Gaussian Process (MCGP) in a hierarchical Bayesian framework. We employ a Dirichlet prior to account for multiple failure modes to precisely capture distinct degradation paths specific to each failure mode and accurately predict the failures within the Cox proportional hazard model. Variational Bayes are used for inference, where we derive an Evidence Lower Bound (ELBO). Due to the unified framework that characterizes the associations between multiple sensor signals and multi-type failure events and their uncertainties, the proposed method outperforms existing methods.