Optimized Sensor Layout and Monte Carlo-Based dMSE Damage Detection in Truss Structures Using Modal Expansion

초록

This study proposes an integrated framework for optimal sensor layout, data expansion, and damage detection in truss structures. Mode shapes used for sensor optimization are reconstructed from sparse measurements via pseudoinverse-based modal expansion. Based on these expanded mode shapes, optimal sensor layouts are determined using effective independence (EI), QR decomposition, and a genetic algorithm guided by the Modal Assurance Criterion (GA-MAC). Damage localization is achieved through the computation of modal strain energy (MSE) and its relative deviation (dMSE) at the element level. A planar 19-node truss model serves as the numerical benchmark for evaluating the proposed methodology. Monte Carlo simulations with sensor noise are conducted to establish statistical thresholds for robust damage identification. The results demonstrate that the GA-MAC approach outperforms conventional methods in both response reconstruction accuracy and damage detection reliability, achieving high true positive rates while maintaining low false positive rates (FPRs). This study contributes to advancing practical strategies for structural health monitoring (SHM) of truss systems by enhancing detection accuracy, noise robustness, and scalability. The study's integrated pipeline includes the following: GA-MAC-based sensor layout, modal expansion for response reconstruction, and dMSE-based damage detection with Monte Carlo thresholding. In particular, under the multiple-damage scenario, the GA-MAC configuration achieved a true-positive rate (TPR) of 100% and a FPR of 0%, which represents approximately an 8% improvement in TPR and a 5% reduction in FPR compared to the EI method.

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