Unsupervised anomaly detection via local standard distance metric-aided exponential slow feature analysis under changing environments

Modal frequencies are widely used as damage-sensitive features in vibration-based unsupervised anomaly detection for full-scale civil structures. However, environmental variations introduce nonlinear and non-Gaussian behaviors in modal frequencies, characterized by multicentricity and substantial variance differences. These behaviors inevitably mask damage-induced frequency shifts, leading to increased false-detection rates and degraded real-time performance. To address this, this paper presents a novel unsupervised framework for early-stage anomaly detection that integrates exponential slow feature analysis (SFA) with just-in-time learning-aided standard K -nearest neighbor metrics. First, nonlinear modal features with minimum temporal variation are extracted from modal frequencies via exponential SFA for dimensionality reduction. Afterward, under the standard measurement criteria, the Euclidean squared distances between each sample in the entire training set and its nearest neighbors are computed. The standard distance for each neighbor is then modeled, with the number of neighbors automatically selected through Bayesian optimization and cross-validation. The primary purpose of this step is to ensure that the nearest neighbor distances between samples under different environmental conditions and damage conditions including abrupt anomalies or gradual degradations, are measured on a consistent scale, thereby minimizing environmental variability. After that, a robust detection indicator is derived from the mean of squared nearest neighbor distances and combined with kernel density estimation to determine an online detection threshold for outliers. The results indicate the proposed method effectively mitigates strong environmental variability without prior environmental measurements and accurately identifies anomalies in bridge modal frequencies with negligible false-positive and false-negative errors.