# Health Index Estimation Through Integration of General Knowledge with Unsupervised Learning

arXiv: https://arxiv.org/abs/2405.04990 · HTML: https://mlsanity.com/paper/2405.04990/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 74 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 7 of 7)

- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Fusing Physics-based and Deep Learning Models for Prognostics](https://mlsanity.com/paper/2003.00732/) (2020)
- [Machine learning pipeline for battery state of health estimation](https://mlsanity.com/paper/2102.00837/) (2021)
- [Multi-Sensor Prognostics using an Unsupervised Health Index based on LSTM Encoder-Decoder](https://mlsanity.com/paper/1608.06154/) (2016)
- [Domain Adaptation via Alignment of Operation Profile for Remaining Useful Lifetime Prediction](https://mlsanity.com/paper/2302.01704/) (2023)
- [A Comparison of Residual-based Methods on Fault Detection](https://mlsanity.com/paper/2309.02274/) (2023)

## Built on by (most cited first, 3 of 3)

- [Disentangling Slow and Fast Temporal Dynamics in Degradation Inference with Hierarchical Differential Models](https://mlsanity.com/paper/2509.00639/) (2025)
- [Improving Anomaly Detection in Industrial Time Series: The Role of Segmentation and Heterogeneous Ensemble](https://mlsanity.com/paper/2510.09079/) (2025)
- [Physics-Informed Machine Learning in Prognostics and Health Management: A Systematic Literature Review](https://mlsanity.com/paper/2608.10047/) (2026)

## Abstract (arXiv)

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.