Fed-Joint: Joint Modeling of Nonlinear Degradation Signals and Failure Events for Remaining Useful Life Prediction using Federated Learning

TL;DR

The paper addresses RUL prediction in environments where condition-monitoring data and failure times are siloed across sites. It introduces Fed-Joint, a federated framework that jointly models nonlinear degradation signals via a nonparametric multi-output Gaussian process and time-to-failure data via a CoxPH survival model, all trained without sharing raw data. A two-stage federated inference scheme combines stochastic variational inference for the MGP and federated maximum likelihood for the CoxPH model, with central aggregation to improve predictive accuracy while preserving privacy. Simulation and a turbofan engine case study show Fed-Joint achieving comparable or superior performance to centralized benchmarks, particularly in highly nonlinear settings and under data scarcity. The approach offers a scalable, privacy-preserving path for collaborative predictive maintenance across distributed assets.

Abstract

Many failure mechanisms of machinery are closely related to the behavior of condition monitoring (CM) signals. To achieve a cost-effective preventive maintenance strategy, accurate remaining useful life (RUL) prediction based on the signals is of paramount importance. However, the CM signals are often recorded at different factories and production lines, with limited amounts of data. Unfortunately, these datasets have rarely been shared between the sites due to data confidentiality and ownership issues, a lack of computing and storage power, and high communication costs associated with data transfer between sites and a data center. Another challenge in real applications is that the CM signals are often not explicitly specified \textit{a priori}, meaning that existing methods, which often usually a parametric form, may not be applicable. To address these challenges, we propose a new prognostic framework for RUL prediction using the joint modeling of nonlinear degradation signals and time-to-failure data within a federated learning scheme. The proposed method constructs a nonparametric degradation model using a federated multi-output Gaussian process and then employs a federated survival model to predict failure times and probabilities for in-service machinery. The superiority of the proposed method over other alternatives is demonstrated through comprehensive simulation studies and a case study using turbofan engine degradation signal data that include run-to-failure events.

Figures (7)

• Figure 1: Distributed CM and survival data.
• Figure 2: Parameter estimation procedure for Fed-Joint.
• Figure 3: Examples of 10 randomly generated degradation signals for each scenario.
• Figure 4: Examples of trajectories for each fitted model in Scenario I (Note: gray dots represent observations and the rightmost end of dots are prediction times; gray dotted lines represent the true underlying degradation signals; red solid lines represent fitted values using each model; shaded areas represent 95% confidence bands for each model except for LMM-Joint whose confidence band is omitted).
• Figure 5: Examples of trajectories for each fitted model in Scenario II (Note: gray dots represent observations and the rightmost end of dots are prediction times; gray dotted lines represent the true underlying degradation signals; red solid lines represent fitted values using each model; shaded areas represent 95% confidence bands for each model except for LMM-Joint whose confidence band is omitted).