Extreme Value Statistics for Alarm Threshold Setting in Data-Driven Damage Detection

Damage detection in data-driven Structural Health Monitoring of civil structures is commonly performed using novelty detection methods. The availability of techniques to distinguish data referring to the healthy state of the structure, even under varying environmental and operational conditions, from data corresponding to a damaged state and appropriate threshold setting primarily affect the performance of data-driven SHM. The selection of the alarm level according to a Gaussian distribution of data in normal conditions involves a gross assumption on the tails of the distribution, where the outliers corresponding to damaged condition observations lie. Optimizing threshold setting with respect to type I and type II errors requires a more refined modeling of the tails of distribution. This paper analyzes the use of Extreme Value Statistics for threshold setting. First, a novelty index is defined in terms of Mahalanobis Squared Distance. Then, extreme values are selected and analyzed according to an extreme value distribution. This step involves the selection of the appropriate limit distribution and the estimation of its parameters. The fitted model has been finally used to set the threshold for outliers analysis. The proposed method is applied to the benchmark data of the Z24 bridge, with its first four natural frequencies as damage sensitive features, comparing its anomaly detection performance with those obtained when the threshold is defined under the assumption of normal distribution of data.