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

Abstract

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 by leveraging the well-quantified uncertainty estimates, allowing them to make well-informed maintenance decisions and avoid unnecessary operational expenses.