Health Index Estimation Through Integration of General Knowledge with Unsupervised Learning

TL;DR

This work addresses HI estimation from condition monitoring data under limited labeled data by introducing an unsupervised hybrid method that encodes general degradation knowledge within a causally informed convolutional autoencoder. It combines an inductive bias (structure reflecting causal X, W, Z relations) with learning biases (soft cycle-based constraints) to produce HI directly from latent representations. The method is validated on turbofan engine and Li-ion battery case studies, showing consistent improvements over residual HI approaches and competitive performance with supervised models across in-distribution and out-of-distribution scenarios, with the functional constraint often yielding the best HI and RUL prognostic gains. The results highlight the value of integrating generalized degradation knowledge into neural architectures for robust HI estimation and practical PHM impact, while also outlining limitations and avenues for broader applicability.

Abstract

Accurately estimating a Health Index (HI) from condition monitoring data (CM) is essential for reliable and interpretable prognostics and health management (PHM) in complex systems. In most scenarios, complex systems operate under varying operating conditions and can exhibit different fault modes, making unsupervised inference of an HI from CM data a significant challenge. Hybrid models combining prior knowledge about degradation with deep learning models have been proposed to overcome this challenge. However, previously suggested hybrid models for HI estimation usually rely heavily on system-specific information, limiting their transferability to other systems. In this work, we propose an unsupervised hybrid method for HI estimation that integrates general knowledge about degradation into the convolutional autoencoder's model architecture and learning algorithm, enhancing its applicability across various systems. The effectiveness of the proposed method is demonstrated in two case studies from different domains: turbofan engines and lithium batteries. The results show that the proposed method outperforms other competitive alternatives, including residual-based methods, in terms of HI quality and their utility for Remaining Useful Life (RUL) predictions. The case studies also highlight the comparable performance of our proposed method with a supervised model trained with HI labels.

Figures (12)

• Figure 1: Overview of the unsupervised hybrid method for HI estimation that relies primarily on general knowledge about degradation.
• Figure 2: Possible shapes for univariate health degradation curves (adapted from meeker2022statistical)
• Figure 3: Overview of different HI estimation methods.
• Figure 4: Overview of the proposed unsupervised hybrid method. The proposed method utilizes an AutoEncoder whose architecture is informed by prior knowledge regarding the structure of the HI estimation problem. The encoder processes sensor readings (X) to estimate degradation (Z), while the decoder reconstructs (X) using operating conditions (W) and estimated degradation (Z). The loss function incorporates an additional constraint derived from prior knowledge about degradation's temporal evolution. Finally, the HI is derived from degradation through subsequent post-processing steps.
• Figure 5: Causal representation of variables in a degrading system. $X$ denote the sensor readings, $W$ the operating conditions and $Z$ the degradation. Observable variables are depicted by solid lines, while dashed lines illustrate hidden variables.