Calculation of relative velocity change of coherent waves using improved stretching technique

The stretching cross-correlation technique is widely used in ultrasonic signal analysis to estimate relative wave velocity changes (dv/v₀) for nondestructive testing and structural health monitoring. It enables high-resolution velocity measurements in the time domain without requiring extremely high sampling rates. In strongly scattering heterogeneous materials such as concrete and rock, dv/v₀ is often used to detect temporal changes or damage. Acoustoelastic testing in metals relies on accurate dv/v₀ measurement from coherent waves, where the applicability and accuracy of the stretching technique remain uncertain and insufficiently addressed in the literature. This study theoretically investigates the sources of error in the stretching method when applied to coherent waves and introduces a modified algorithm based on stretching the reference signal. Simulations show that the accuracy of dv/v₀ estimation depends on multiple parameters, including the stretching window, wave transit time, and signal frequency. These factors are systematically analyzed in this study. The proposed method is validated through numerical simulations and experimental measurements of thermally induced velocity changes in a nylon specimen subjected to temperature variations.