A challenging issue in data-driven methods is the limitation of applying high-dimensional damage-sensitive features (HD-DSFs) to localize and quantify structural damage. This is because the use of such data causes a time-consuming process for feature classification. Low damage detectability is another important challenge that may cause unreliable and erroneous results. The main objective of this study is to deal with these challenging issues by proposing hybrid distance methods as combinations of a distance-based indicator called residual relative error (RRE) and Kullback–Leibler divergence (KLD) with the well-known Mahalanobis distance. Autoregressive modeling is used to model vibration responses and extract the residual samples from normal and damaged conditions as HD-DSFs. The major contribution of this article is to propose two hybrid distance-based methods in unsupervised learning manners for locating and quantifying damage using low-dimensional feature samples obtained from the RRE index and KLD. The great advantage of these methods is that they not only reduce the size of HD-DSFs and behave as dimensionality reduction tools but also can increase damage detectability by the low-dimensional feature samples that are distance quantities. For this reason, both the RRE and KLD are individually capable of detecting early damage. An ability to locate and quantify damage under varying environmental and operational conditions is the other advantage of these methods. To validate the proposed methods, experimental vibration datasets of two benchmark laboratory structures are utilized. Results demonstrate that the proposed methods are practical and reliable tools to accurately localize and quantitatively quantify damage by addressing the limitation of using HD-DSFs.

数据驱动方法中的一个挑战性问题是应用高维损伤敏感特征（HD-DSF）来定位和量化结构损伤的局限性。这是因为使用此类数据会导致耗时的特征分类过程。损坏检测能力低是另一个重要挑战，可能会导致结果不可靠和错误。这项研究的主要目的是通过提出混合距离方法，将基于距离的指标（称为残差相对误差（RRE）和Kullback-Leibler散度（KLD））与著名的马哈拉诺比斯距离相结合，来解决这些难题。自回归建模用于对振动响应进行建模，并从正常和受损条件下提取剩余样本作为HD-DSF。本文的主要贡献是，提出了两种无监督学习方式的基于距离的混合方法，用于使用从RRE指数和KLD获得的低维特征样本来定位和量化损伤。这些方法的最大优点是，它们不仅可以减小HD-DSF的尺寸并充当降维工具，而且可以通过作为距离量的低维特征样本来提高损伤检测能力。因此，RRE和KLD都可以分别检测早期损坏。这些方法的另一个优点是能够在变化的环境和操作条件下定位和量化损坏。为了验证所提出的方法，利用了两个基准实验室结构的实验振动数据集。