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A Federated Data Fusion-Based Prognostic Model for Applications with Multi-Stream Incomplete Signals

Madi Arabi, Xiaolei Fang

TL;DR

The paper tackles the challenge of building reliable prognostic models when historical data are scarce and distributed across multiple organizations. It introduces a privacy-preserving federated framework that fuses multi-stream degradation signals via multivariate functional PCA to produce MFPC-scores, which are then used in a (log)-location-scale regression for failure-time prediction. A two-stage federated feature extraction algorithm—federated dominant subspace identification and federated MFPC-scores computation—enables joint learning without sharing raw data, while a federated LLS regression estimates model parameters. Extensive simulations and a NASA turbofan case study show the Federated Model achieves the same predictive accuracy as a centralized approach and outperforms models built by individual users, especially when local data are limited. The work demonstrates that privacy-preserving, distributed prognostics with incomplete multi-sensor signals can attain centralized-level performance and scale to many participants in industrial settings.

Abstract

Most prognostic methods require a decent amount of data for model training. In reality, however, the amount of historical data owned by a single organization might be small or not large enough to train a reliable prognostic model. To address this challenge, this article proposes a federated prognostic model that allows multiple users to jointly construct a failure time prediction model using their multi-stream, high-dimensional, and incomplete data while keeping each user's data local and confidential. The prognostic model first employs multivariate functional principal component analysis to fuse the multi-stream degradation signals. Then, the fused features coupled with the times-to-failure are utilized to build a (log)-location-scale regression model for failure prediction. To estimate parameters using distributed datasets and keep the data privacy of all participants, we propose a new federated algorithm for feature extraction. Numerical studies indicate that the performance of the proposed model is the same as that of classic non-federated prognostic models and is better than that of the models constructed by each user itself.

A Federated Data Fusion-Based Prognostic Model for Applications with Multi-Stream Incomplete Signals

TL;DR

The paper tackles the challenge of building reliable prognostic models when historical data are scarce and distributed across multiple organizations. It introduces a privacy-preserving federated framework that fuses multi-stream degradation signals via multivariate functional PCA to produce MFPC-scores, which are then used in a (log)-location-scale regression for failure-time prediction. A two-stage federated feature extraction algorithm—federated dominant subspace identification and federated MFPC-scores computation—enables joint learning without sharing raw data, while a federated LLS regression estimates model parameters. Extensive simulations and a NASA turbofan case study show the Federated Model achieves the same predictive accuracy as a centralized approach and outperforms models built by individual users, especially when local data are limited. The work demonstrates that privacy-preserving, distributed prognostics with incomplete multi-sensor signals can attain centralized-level performance and scale to many participants in industrial settings.

Abstract

Most prognostic methods require a decent amount of data for model training. In reality, however, the amount of historical data owned by a single organization might be small or not large enough to train a reliable prognostic model. To address this challenge, this article proposes a federated prognostic model that allows multiple users to jointly construct a failure time prediction model using their multi-stream, high-dimensional, and incomplete data while keeping each user's data local and confidential. The prognostic model first employs multivariate functional principal component analysis to fuse the multi-stream degradation signals. Then, the fused features coupled with the times-to-failure are utilized to build a (log)-location-scale regression model for failure prediction. To estimate parameters using distributed datasets and keep the data privacy of all participants, we propose a new federated algorithm for feature extraction. Numerical studies indicate that the performance of the proposed model is the same as that of classic non-federated prognostic models and is better than that of the models constructed by each user itself.
Paper Structure (23 sections, 1 theorem, 12 equations, 14 figures, 2 algorithms)

This paper contains 23 sections, 1 theorem, 12 equations, 14 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. The Prognostic Model and Parameter Estimation
  3. The Federated Feature Extraction Algorithm
  4. Feature Extraction Using Centralized Data
  5. Federated Feature Extraction Using Decentralized Data
  6. Federated Dominant Subspace Identification
  7. Federated Algorithm for MFPC-scores Computation
  8. Prognostic Model Training and Time-To-Failure Prediction
  9. Simulation Study I
  10. Data Generation and Benchmarking Models
  11. Results and Analysis
  12. Simulation Study II
  13. Stragglers Effect
  14. Large Scale Applications
  15. Computational Time
  16. ...and 8 more sections

Key Result

Proposition 1

Given an uncentered matrix $\boldsymbol{X}\in\mathbb{R}^{N\times J}$ and $\boldsymbol{U}_{new}\in\mathbb{R}^{N\times K}$ whose orthonormal columns span the $K$-dimensional dominant subspace of $\boldsymbol{X}$, the MFPC-scores discussed in Section sec: sub: para_center can be computed from $\boldsym

Figures (14)

  • Figure 1: Overview of proposed federated feature extraction method
  • Figure 2: The prediction errors of federated and non-federated models.
  • Figure 3: The prediction errors of federated model and individual model (User 1)
  • Figure 4: The prediction errors of federated model and individual model (User 2)
  • Figure 5: The prediction errors of federated model and individual model (User 3)
  • ...and 9 more figures

Theorems & Definitions (1)

  • Proposition 1