Novel Study on Strain Modes‐Based Interval Damage Identification Methodology Utilizing Orthogonal Polynomials and Collocation Theories

ABSTRACT The sensitivity of strain modes to local stiffness changes within a structure underscores their potential as robust indicators of damage, enhancing the efficacy of damage identification processes. This study establishes sensitivity matrices of natural frequencies and strain modes to damage parameters, laying the groundwork for a novel fusion index that integrates both metrics to assess structural damage extent. In order to quantify the impact of uncertainty information on the results of damage identification processes, a non‐probabilistic structural damage identification method rooted in the collocation methodology is proposed in this study. In consideration of computational efficiency, a two‐step damage identification strategy encompassing localization and quantification is proposed. Initially, damage localization is achieved through the dynamic fingerprints, followed by the quantification of the uncertainty of damage extent. The proposed methodology is validated through a detailed numerical example, illustrating that the fusion index outperforms individual indices in terms of accuracy and computational efficiency. The non‐probabilistic structural damage identification method based on collocation methodology can identify the damage extent and uncertainty interval even under the influence of uncertain factors.