Health Indicator Eval

---
name: health-indicator-eval
description: Evaluates the ability of unsupervised contrastive learning models to extract robust, degradation-sensitive health indicators from sensor data. It probes how well the learned features correlate with actual wear or track operational degradation over time, while remaining invariant to noise and operating condition shifts. Use when the user wants to benchmark on Milling Machine Wear Dataset, Railway Wheel Dataset, or asks about evaluating this task. Reports correlation value to the wear.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2208.13288
  bibtex_key: rombach2022learning
  confidence: high
---

# health-indicator-eval

> Learning Informative Health Indicators Through Unsupervised Contrastive Learning — Rombach et al. (2022) (arXiv:2208.13288, 2022)

## What this evaluates

Evaluates the ability of unsupervised contrastive learning models to extract robust, degradation-sensitive health indicators from sensor data. It probes how well the learned features correlate with actual wear or track operational degradation over time, while remaining invariant to noise and operating condition shifts.

## Datasets

- **Milling Machine Wear Dataset** — total ?; splits: train (-1), val (-1), test (-1)
- **Railway Wheel Dataset** — total ?; splits: train (-1), test (-1)

## Metrics

- `correlation value to the wear` **(primary)** — range: [-1, 1]
  - Pearson correlation coefficient between the predicted health index trajectory and the ground truth wear measurements. Values closer to 1 indicate a stronger monotonic relationship between the learned indicator and actual degradation.

## Input / output format

**Input**: Time-series sensor data (e.g., vibration/acceleration) from milling machines or railway wheels, formatted as sequential measurements over operational cycles or months.

**Output**: A scalar health index per time step, calculated as the distance to the decision boundary of an OC-SVM trained on the contrastive features.

## Scoring recipe

```python
def compute_metric(predictions, gold):
    # predictions: health index trajectory
    # gold: ground truth wear measurements
    n = len(predictions)
    mean_p = sum(predictions) / n
    mean_g = sum(gold) / n
    cov = sum((p - mean_p) * (g - mean_g) for p, g in zip(predictions, gold)) / n
    std_p = (sum((p - mean_p)**2 for p in predictions) / n) ** 0.5
    std_g = (sum((g - mean_g)**2 for g in gold) / n) ** 0.5
    return cov / (std_p * std_g) if std_p * std_g > 0 else 0.0
```

## Common pitfalls

- The health index is an arbitrary distance to an OC-SVM boundary, not a direct wear prediction; higher values indicate degradation but lack a fixed physical scale.
- Positive pairs for contrastive learning are defined by operational time (cycles or months), which can mix samples of different degradation levels if the time window is too wide.
- The railway dataset lacks ground truth wear labels, so evaluation relies on trajectory analysis rather than direct correlation, making cross-dataset metric comparison difficult.

## Evidence (verbatim from paper)

> The architecture is chosen based on the performance of the health indicator based on the correlation value to the wear in the validation dataset (c4).

## Citation

```bibtex
@misc{rombach2022learning,
  title={Learning Informative Health Indicators Through Unsupervised Contrastive Learning},
  author={Rombach et al. (2022)},
  year={2022},
  note={arXiv:2208.13288}
}
```

- arXiv: 2208.13288