Guided waves in plates with complex thickness variations: comparison of statistical modeling approaches

• The study introduces a Chebyshev-based method to more accurately model thickness variations in corroded plates. • The results demonstrate that traditional normal distribution and constant-thickness approximations can lead to significant errors in wave velocity estimation. • The paper verifies theoretical and numerical findings with controlled experiments on plates featuring sinusoidal thickness variations. • The insights for improving non-destructive testing and structural health monitoring of corroded metal structures are provided. Guided wave-based techniques are particularly effective for corrosion assessment due to their sensitivity to geometric variations and ability to propagate over long distances. However, most existing approaches rely on simplifying assumptions about thickness distribution, which can introduce inaccuracies in real-world applications, e.g., the thickness reduction due to the corrosion degradation. This study investigates the impact of thickness variability on guided wave propagation in plate-like structures with non-uniform geometry, specifically sinusoidal thickness variations. A combined experimental, numerical, and theoretical approach is employed to analyze wave velocity changes under different statistical assumptions about thickness distribution. The study compares constant-thickness approximations, normal distribution models, and a novel application of Chebyshev’s theorem, which provides a more generalized representation of thickness variability. Experimental validation is performed using CNC-fabricated plates with controlled thickness variations, and numerical simulations are conducted using finite element modeling. The results demonstrate that standard assumptions, particularly normal distribution approximations, can introduce significant errors in velocity estimation, whereas the Chebyshev-based approach offers a more accurate and flexible method for modeling non-uniform thickness distributions. These findings provide valuable insights into the development of improved guided wave-based methodologies for corrosion assessment and structural health monitoring.