In this paper, the interaction of a broadband Rayleigh wave generated by a laser and an artificial rectangular notch is analyzed theoretically and experimentally. For the theoretical analysis, a Gaussian function is adopted to analyze the modulation of notch depth on the frequency spectrum via reflection and transmission coefficients. By the finite element method, the Rayleigh wave generated by pulsed laser beam irradiation and its scattering waves at cracks are calculated. A curve with a slope close to 4 fitted by crack depth and critical wavelength of the threshold phenomenon is obtained by the wavelet transform and Parseval’s theorem according to simulated and experimental results. Based on this relationship, the critical frequency at which the threshold phenomenon happens due to energy transformation of transmission/reflection Rayleigh waves is adopted to determine the size of sub-wavelength surface crack. The experimental results of artificial notch depth estimation on aluminum alloy specimens consistent with theoretical analysis validates the usefulness of the critical frequency method based on a broadband Rayleigh wave generated by laser ultrasonic.

The laser ultrasonic method using the characteristics of transmitted Rayleigh waves in the frequency domain to determine micro-crack depth is proposed. A low-pass filter model based on the interaction between Rayleigh waves and surface cracks is built and shows that the stop band, called the sensitive frequency range, is sensitive to the depth of surface cracks. The sum of transmission coefficients in the sensitive frequency range is defined as an evaluated parameter to determine crack depth. Moreover, the effects of the sensitive frequency range and measured distance on the evaluated results are analyzed by the finite-element method to validate the robustness of this depth-evaluating method. The estimated results of surface cracks with depths ranging from 0.08 mm to ~0.5 mm on the FEM models and aluminum-alloy samples demonstrate that the laser ultrasounds using the characteristics of Rayleigh waves in the frequency domain do work for quantitative crack depth.

To measure the angles of oblique surface cracks on a specimen, the method of using the time difference between the reflected and scattered waves generated by the interaction of the surface waves and the crack is proposed. Based on the reflection and scattering waves’ paths at the surface crack, an analytical equation that involves the crack depth, width, and inclined angle is developed. On the basis of establishing the ratio of width to depth, ∆t-φ curves and estimated error images without the width term can be analyzed in detail. The finite element simulation and experimental results for aluminum alloy samples show that a crack’s angle can be detected using the time difference method. The effects of the width term in the analytical equation on the estimated angles of the surface cracks are also verified. Measurement of the quantitative angle of inclined surface cracks is first regarded as a multiparameter inversion problem. The simulation and the experimental discussion of the interrelation between the depth, width, and angle of the inclined surface crack in this work are very meaningful for quantitative determination using laser ultrasound.

In this work, a two-parameter inversion problem is analyzed, related to surface crack widths for measuring depths of normal surface notches, based on a laser-based ultrasonic measurement method in the time domain. In determining the depth measurement formulas, the main technique is the time delay between reflected and scattered waves. Scattered waves are generated by two reflections along the bottom and three mode transformations at the surface of the crack tips. Moreover, the scattering angle of the mode-conversion waves is 30°. These two key factors lead to corrected item “2wβ” in the depth measurement formula. A laser-based ultrasonic experimental platform is built to generate and receive surface waves in a non-contact manner on aluminum and steel specimens with surface cracks. The depth measurement method proposed in this paper has been validated through theoretical, simulation, and experimental methods. Finally, in this paper, an effective approach for quantitatively measuring crack depths, based on laser ultrasound, using the time-domain properties of surface wave propagation is provided.

Installation eccentricity of an in-pipe ring array changes the water-layer propagation path and degrades time-of-flight (TOF) extraction in small-diameter thin-walled tubes. This study proposes an array-level physics-informed neural network (PINN) that jointly processes an azimuth-ordered 16 × M echo matrix. A shared temporal encoder and circular-topology feature-fusion module exploit periodic inter-element correlations, while an analytical eccentric-geometry prior and a coordinate-conditioned acoustic-wave-equation residual constrain the solution. A two-dimensional water–pipe-wall finite-element model in COMSOL 6.3 generates 16-channel echo sets under multiple eccentricities and directions. For the representative +x channel and eccentricities from 0.00 to 0.90 mm, the proposed method achieves a TOF mean absolute error (MAE) of 2.33 ns, a root-mean-square error (RMSE) of 2.37 ns, and a maximum absolute error of 3.03 ns. Under the two added noise levels (20 and 10 dB), its TOF MAEs are 1.62 and 1.53 ns, respectively. Within the two-dimensional simulation assumptions and investigated eccentricity range, the corresponding wall-thickness MAE is approximately 0.007 mm and the maximum absolute error is approximately 0.0095 mm. These values quantify algorithmic error under the modeled eccentric propagation and waveform distortion only; they do not represent the total uncertainty of a practical measurement system.