Anomaly detection by Mahalanobis-squared distance (MSD) is a popular unsupervised learning approach to structural health monitoring (SHM). Despite the popularity and high applicability of the MSD-based anomaly detection method, some major challenging issues and limitations such as environmental variability, determination of an inappropriate threshold limit, estimation of an inaccurate covariance matrix, and non-Gaussianity of training data may lead to false alarms and erroneous results of damage detection. The main objective of this article is to propose a novel anomaly detection method based on adaptive Mahalanobis-squared distance and one-class kNN rule called AMSD-kNN for SHM under varying environmental conditions. The central idea behind the proposed method is to find sufficient nearest neighbors of training and testing datasets in a two-stage procedure for removing the environmental variability conditions and estimate local covariance matrices. An effective approach based on a multivariate normality hypothesis test is proposed to find sufficient nearest neighbors that guarantee the estimate of well-conditioned local covariance matrices. The great novelty of the proposed AMSD-kNN method is to create a novel unsupervised learning strategy for SHM by a new multivariate distance measure and one-class kNN rule. Generalized extreme value distribution modeling by the block maxima (BM) method is presented to determine an accurate threshold limit. Due to the importance of choosing adequate blocks in the BM method, a goodness-of-fit measure via the Kolmogorov-Smirnov hypothesis test is applied to select an optimal block number. The performance and effectiveness of the proposed methods are verified by two well-known benchmark structures. Several comparative studies are also conducted to demonstrate the superiority of the proposed methods over some state-of-the-art techniques. Results show that the proposed AMSD-kNN and BM methods highly succeed in detecting damage under environmental variability conditions.

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