Sparse Damage Identification for Beam-Like Structures Using Multiple-Metric Fusion and Nuclear Norm Regularization

The increasing complexity of modern bridge structures necessitates more accurate and robust methods for structural health monitoring, particularly during both construction and service phases. In this paper, a novel model-based structural damage identification (SDI) framework integrating multiple-metric fusion with nuclear norm regularization is proposed, which aims to improve the SDI accuracy and robustness for beam-like structures against uncertainties such as measurement noise. The proposed multimetric fusion strategy combines a high-order cosine similarity indicator (HCSI) and a Chebyshev distance indicator (CDI). HCSI is calculated based on mode shapes and amplifies sensitivity to subtle modal variations. And CDI is designed to capture critical deviations in the frequency sequence. To further promote sparsity in SDI results for improved robustness under uncertain conditions, nuclear norm regularization is embedded into the objective function via a structured matrix transformation of the damage factor vector. The resulting optimization problem is solved using a multirole collaborative swarm optimization algorithm, which provides an effective balance between global exploration and local exploitation. The proposed method is validated through two numerical structures and an experimental test. Results demonstrate its superior performance in terms of accuracy, sparsity, and robustness, highlighting its potential for practical applications in bridge health monitoring.