Uncertainty-Based Scale Identification and Process–Topography Interaction Analysis via Bootstrap: Application to Grit Blasting

Finding the relevant scale to observe the influence of a process is one of the most important purposes of multiscale surface characterization. This study investigates various methods to determine a pertinent scale for evaluating the relationship between the relative area and grit blasting pressure. Several media types were tested alongside two different methods for calculating the relative area and three bootstrapping approaches for scale determination through regression. Comparison with the existing literature highlights innovations in roughness parameter characterization, particularly the advantages of relative area over traditional parameters like Sa. This study also discusses the relevance of different media types in influencing surface topography. Additionally, insights from a similar study on the multiscale Sdq parameter and blasting pressure correlation are integrated, emphasizing a scale relevance akin to our Sdr method’s 120 µm cut-off length. Overall, our findings suggest a pertinent scale of 10,000 µm² for the Patchwork method and a 120 µm cut-off length for the Sdr method, derived from bootstrapping on residual regression across all media. At the relevant scale, every value of R² inferior to 0.83 is not significant with the threshold of 5% for the two methods of calculation of the relative area. This study enhances the understanding of how media types and blasting pressures impact surface topography, offering insights for refining material processing and surface treatment strategies.