An Integrated Uncertainty Quantification Model for Longitudinal and Time-to-Event Data

We present a novel joint prognostic framework for the integrated analysis and uncertainty quantification of longitudinal (i.e., multi-sensor degradation signals) data and time-to-event data. Specifically, the proposed method models longitudinal data using a functional principal component analysis (FPCA), while the time-to-event data is characterized by a Bayesian neural network-based Cox (BNN-Cox) model. The proposed method delivers several unique advantages: 1) Providing accurate remaining useful life (RUL) predictions while seamlessly integrating the uncertainties of both the longitudinal and time-to-event sub-models; 2) Demonstrating great flexibility in modeling both data types; 3) Allowing online, real-time updates of the RUL distribution as new measurements are collected; and 4) Making reliable predictions under limited data availability. Compared to existing methods that provide limited uncertainty information restricted to a single sub-model, the proposed approach offers more accurate and comprehensive uncertainty information via uncertainty propagation. The numerical evaluations on simulated and real-world data suggest that the proposed method achieves outstanding performance compared to existing benchmarks. Note to Practitioners -This paper is motivated by the practical issue of extracting prognostic insights from longitudinal and time-to-event data. There are two fundamental research questions involved: 1) How to accurately model both types of data without resorting to restrictive parametric assumptions; and 2) how to seamlessly integrate the uncertainties from both sub-models into the final RUL predictions. The proposed method is particularly useful in cases when there are modeling uncertainties in both longitudinal and time-to-event data, such as complex manufacturing or energy systems with multiple sensors, such as aircraft engines. There are four main steps involved when implementing the proposed method: 1) fit the historical longitudinal data using an FPCA-based degradation sub-model; 2) construct a BNN-Cox sub-model using the fitted longitudinal data and time-to-event data; 3) predict the degradation status and remaining useful life of the in-service units based on their longitudinal data and time-to-event data; and 4) provide uncertainty quantifications of the RUL estimates by integrating the uncertainties across the two sub-models. A key advantage of the proposed method is that practitioners can assess the reliability of RUL predictions