## 4 Conclusions  
In this study, a grating-based laser ultrasonic technique was proposed for the non-contact evaluation of porosity in metal AM components. This method relies on the relationship between SAW velocity and material porosity, as established through theoretical modeling that accounts for changes in the effective elastic modulus and density due to void defects. By generating narrowband SAWs using a pulsed laser grating and detecting the wave signals with a laser interferometer, this fully non-contact excitation and detection configuration makes the technique well suited for online monitoring during the AM process. Moreover, this method enables the accurate calculation of the SAW velocity based solely on local frequency and wavelength information, independent of source-detector distance.  
Numerical simulations on aluminum alloy models with varying porosity levels demonstrated that increased porosity leads to signal attenuation, waveform distortion, and a leftward shift in the frequency spectrum. These changes are consistent with the theoretical prediction that porosity reduces wave speed and increases scattering. Simulated  
Figure 9: Experimental comparison of SAW signals for specimens with different porosity levels.  
SAW velocities and actual porosity values exhibited excellent agreement with the theoretical velocity-porosity relationship, and the inverse estimation of porosity achieved high accuracy (\(R^{2}\) = 0.9426, MAE = 0.7919%).  
To further verify the feasibility of the method, experiments were conducted on two WAAM-fabricated aluminum alloy specimens with distinctly different porosity levels--one with low porosity (near-zero) and the other with high porosity (in the range of 1-2%). The experimental results exhibited waveform features and spectral trends consistent with the simulation, including the appearance of reflected waves and moderate shifts in spectral content. Although quantitative porosity estimation was not performed due to the lack of precise material property data (e.g., elastic modulus and density), the observed responses confirmed the sensitivity of SAW signals to internal porosity. This experimental validation reinforces the potential of the proposed approach for detecting porosity in additively manufactured materials.  
Future work will focus on extending this method toward experimental quantitative evaluation by incorporating reliable material parameters. Additionally, while stable SAW signals can be obtained on as-built rough surfaces, further investigation is needed to quantify the influence of surface roughness on evaluation accuracy.  
Conceptualization, J.Y. and C.P.; Methodology, J.Y. and C.P.; Software, Y.L. and Q.G.; Validation, H.L. and Z.G.; Formal analysis, H.L., Q.G. and Z.G.; Investigation, H.L. and Z.G.; Resources, Y.L. and Q.G.; Data curation, H.L., Y.L. and Z.G.; Writing--original draft, H.L. and J.Y.; Writing--review & editing, C.P.; Visualization, H.L., J.Y. and Q.G.; Supervision, Y.L. and C.P.; Project administration, C.P.; Funding acquisition, Y.L. and C.P. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Natural Science Basic Research Program of Shaanxi [No. 2024]C-YBQN-0545], Key Science and Technology Projects for Basic and Prospective Research of CNPC [No. 2023 ZZ11], Shaanxi Province Key Research and Development Project [No. 2024 PT-ZCK-48], and National Natural Science Foundation [No. 92366301].  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by PetroChina Changqing Oilfield Company. Author [PERSON] was employed by Huanqing Oil Production Plant of Yumen Oilfield. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.