Abstract 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.

中文翻译：

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基于自适应马氏平方距离和一类kNN规则的环境影响下结构健康监测异常检测新方法

摘要 通过马氏平方距离（MSD）进行异常检测是一种流行的结构健康监测（SHM）无监督学习方法。尽管基于 MSD 的异常检测方法流行且适用性高，但一些主要的挑战性问题和局限性，例如环境可变性、确定不适当的阈值限制、估计不准确的协方差矩阵以及训练数据的非高斯性可能会导致误报和损坏检测的错误结果。本文的主要目的是提出一种基于自适应马氏平方距离和一类 kNN 规则的新异常检测方法，称为 AMSD-kNN，用于在不同环境条件下进行 SHM。所提出的方法背后的中心思想是在两阶段过程中找到足够的训练和测试数据集的最近邻居，以消除环境变化条件并估计局部协方差矩阵。提出了一种基于多元正态性假设检验的有效方法，以找到足够的最近邻，以保证条件良好的局部协方差矩阵的估计。所提出的 AMSD-kNN 方法的巨大新颖之处在于通过新的多元距离度量和一类 kNN 规则为 SHM 创建了一种新的无监督学习策略。提出了通过块最大值 (BM) 方法进行的广义极值分布建模，以确定准确的阈值限制。由于在 BM 方法中选择足够的块的重要性，应用通过 Kolmogorov-Smirnov 假设检验的拟合优度度量来选择最佳块数。所提出方法的性能和有效性通过两个众所周知的基准结构进行了验证。还进行了几项比较研究，以证明所提出的方法优于一些最先进的技术。结果表明，所提出的 AMSD-kNN 和 BM 方法在检测环境变化条件下的损伤方面非常成功。