Structural Damage Detection in Reinforced Concrete Frames Using a Novel Objective Function and a Hybrid Manta–Secretary Algorithm: Five-Algorithm Comparison

Structural damage detection is vital for ensuring the safety, integrity, and serviceability of reinforced concrete (RC) structures, which are inherently susceptible to progressive deterioration over time. This study presents an advanced model updating framework enhanced with metaheuristic optimization algorithms for accurate and robust identification of structural damage. A novel objective function was formulated by integrating three critical dynamic features: natural frequencies, mode shapes, and modal strain energy. To validate the effectiveness and robustness of the proposed approach, five metaheuristic algorithms—GOA, WOA, MRFO, SBOA, and AOA—were employed and their performance evaluated across two predefined damage scenarios under three levels of simulated noise (0%, 3%, and 10%). Comparative results indicated that while MRFO and SBOA achieved higher accuracy and noise resistance, GOA demonstrated faster convergence rates. To overcome limitations observed in individual algorithms, a novel hybrid optimization algorithm, MSOA, was developed. MSOA effectively balanced exploration and exploitation tendencies, improved convergence behavior, and reduced the risk of premature convergence, particularly under noisy conditions. The error between simulated and estimated results, averaged over twenty runs for each damage scenario, was less than 4 percent. The results demonstrate that the proposed model updating framework, which integrates a novel objective function with the MSOA algorithm, provides high accuracy and robustness for structural damage detection in RC frames, even under conditions of measurement uncertainty.