Baseline-Free Damage Localization for Layered Composites Based on Nonlinear Damage Coefficient and Whale Optimization Algorithm

Layered carbon fiber composite materials are widely employed in key load-bearing components such as aircraft wings and fuselages in the aerospace industry owing to their high strength-to-weight ratio. However, they are prone to hidden internal damage including delamination and debonding during service, which poses a severe threat to the operational safety and structural integrity of aircraft structures. Traditional probabilistic imaging algorithms for ultrasonic guided wave inspection of layered composites depend on intact baseline signals. Tiny damage features are easily masked by noise, which results in weak imaging convergence and unsatisfactory localization accuracy. This paper proposes a baseline-free damage localization method based on the Nonlinear Damage Coefficient (NDC). The energy-normalized NDC is constructed from the nonlinear scattering responses under dual-amplitude excitations, and a power adjustment factor is introduced to distinguish damage signatures from background noise, thus improving imaging contrast. To resolve the subjectivity of manual parameter selection, the Whale Optimization Algorithm (WOA) is applied to realize joint adaptive optimization of the NDC power exponent $\lambda$ and probabilistic imaging shape factors $\sigma$ and $\beta$. Numerical simulations and physical experiments are conducted on carbon fiber-reinforced polymer (CFRP) laminates with central single damage, offset single damage and double damage to validate the proposed method. The experimental results demonstrate that single and multiple damage sites can be identified without baseline signals. After WOA optimization, remarkable localization-error reduction is observed in numerical simulation cases, and imaging artifacts were effectively suppressed. Especially for offset and double damage cases, the relative localization error was maintained below 0.5%. Validated under well-controlled laboratory experimental conditions, the proposed method achieves high localization precision and provides feasible technical support for non-destructive testing and structural health monitoring of layered composite structures.