# Latent Monotonic Feature Discovery for Structural Health Monitoring

## TL;DR

This paper introduces a new method to detect subtle structural degradation in infrastructure using sensor data by finding monotonic patterns that indicate long-term health changes.

## Contribution

The novel contribution is the Latent Monotonic Feature Discovery (LMFD) method, which identifies monotonic sensor combinations to detect structural degradation.

## Key findings

- Sensor subgroups with elevated monotonicity can serve as robust proxies for structural health.
- LMFD successfully constructs monotonic features from non-monotonic sensors in real-world monitoring data.
- The approach uncovers latent degradation trends in civil infrastructure using interpretable indicators.

## Abstract

Quantifying the health of civil infrastructure using sensor data remains challenging, as degradation-related signals are typically weak and obscured by dominant environmental and operational effects. In structural health monitoring (SHM), this often results in sensor measurements that are highly periodic or intermittent, while long-term degradation manifests only as subtle drift. This study addresses the problem of extracting meaningful proxies for structural health from such data. We propose monotonicity as a guiding principle, operationalized through absolute Spearman’s rank correlation between sensor values and time. Two complementary methods are introduced. First, subgroup discovery is employed to identify structurally coherent groups of sensors that exhibit significantly elevated monotonicity, enabling the construction of robust health proxies through aggregation. Second, we present Latent Monotonic Feature Discovery (LMFD), a data-driven method inspired by equation discovery, which searches for arithmetic combinations of sensors that yield monotonic behaviour even when individual sensors are predominantly non-monotonic. The methods are evaluated on a two-year monitoring dataset from a Dutch concrete highway bridge comprising strain gauges, geophones, and temperature sensors. Results show that meaningful monotonic proxies can be derived both from naturally monotonic sensor subgroups and from composite features constructed from periodic signals. The proposed approach provides indirect yet interpretable indicators of structural health and offers a principled way to uncover latent degradation trends in long-term SHM data.