A Bayesian Low-Rank Prior Framework for Structural Damage Identification under Noisy Conditions

Structural damage identification (SDI) is a key part of structural health monitoring (SHM) and is essential for ensuring the safety and reliability of civil engineering structures. However, measurement noise and other uncertainties often reduce identification accuracy. To address this issue, this study introduces nuclear norm regularization as a special and effective low-rank structural prior into the modeling of the damage factor matrix within a Bayesian multi-sample framework. This naturally constrains the sparsity of damage patterns and the correlations among elements during maximum a posteriori estimation, enhancing the stability and physical interpretability of damage identification under noisy conditions. To efficiently solve the optimization problem, this study develops a multi-role collaborative hybrid optimization algorithm called SCSOA-INM. This algorithm combines the global exploration ability of the Sine–Cosine Seagull Optimization Algorithm (SCSOA) with the local refinement capability of the improved Nelder–Mead (INM) method, achieving better convergence and accuracy through information sharing and dynamic role switching. Numerical results verify that the proposed method can accurately identify both the locations and severities of structural damage, maintaining strong robustness and reliability under noise interference.