Over the past decades, Vibration-Based Methods (VBMs) have consistently exhibited exceptional effectiveness in the field of Structural Health Monitoring when it comes to assessing structural damage in both civil and mechanical structures. Recently, the progress made in data-driven strategies for localizing structural damage through the VBMs has resulted in substantial benefits. These advanced strategies not only enable an efficient decision-making process but also provide precise identification of repair locations for monitored structures. Importantly, they achieve this without the inherent complexity and computational burden typically associated with traditional model-based methods. In this study, an innovative data-driven method for localizing and quantifying structural damage is proposed. The method is developed on the basis of the principles of Linear Discriminant Analysis (LDA) and a newly devised modeling strategy that utilizes the power cepstral coefficients extracted from the structural acceleration response. The developed LDA model is able to highlight the local structural characteristics (i.e., mode shape-related information) embedded in the cepstral coefficients in the LDA latent space. Based on the highlighted local characteristics of the cepstral coefficients, a statistical pattern recognition strategy is proposed to effectively conduct the quantification and localization of structural damage. The proposed damage localization method is designed to function in a completely unsupervised-learning manner, which eliminates the requirement for the model to have access to any prior knowledge or information regarding structural damage during the training phase. The proposed method has been validated by both numerical simulations and experimental data.
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