Vibration-based damage detection of beams using Hybrid Genetic Algorithm with combined l0 and l1 regularization

Vibration-based damage detection is an effective way of identifying beam damages before they become severe and potentially catastrophic. This paper introduces a novel and robust method for detecting multiple cracks in beams using a Hybrid Genetic Algorithm (HGA). The objective function of the proposed method, based on dynamic properties, can be employed with partial modal information and is enhanced by including the initial residuals between numerical and experimental models along with combined l0 and l1 regularization. This enhancement mitigates the impact of limited modal data, experimental noise, and modeling inaccuracies. Additionally, a method of selecting an appropriate regularization parameter by analyzing residual and solution norm curves is presented. The performance of the proposed method is evaluated and verified using both numerical simulations and experimental studies on a steel cantilever beam under four damage scenarios. In the experimental study, natural frequencies and mode shapes were determined under ambient vibration conditions using Enhanced Frequency Domain Decomposition (EFDD) and the Stochastic Subspace Identification (SSI) method. Finite element models of the beam were developed in ABAQUS software for numerical analysis, and a comparative study of numerical and experimental data was conducted. The proposed approach successfully identifies, locates and quantifies single and multiple damages in the beam, demonstrating its reliability and effectiveness, particularly in scenarios with limited modal data and significant experimental noise.