## 2 Materials and Methods
### Experimental Framework for Acoustic Properties Assessment  
To assess the influence of robotic EAM toolpath planning factors on the acoustic properties of the designed acoustic panels, a rigorous experimental framework has been developed. This framework adopts the Taguchi method for the design of experiments (DOE), a statistical approach that utilizes a set of orthogonal arrays to examine numerous factors with as few experiments as possible. The goal of this framework is to identify how three key toolpath planning factors, including the infill percentage of the toolpath referring to the spacing between adjacent beads of material, the toolpath design pattern, which defines the geometric arrangement of deposition toolpath, and the ratio of geometric discretization of the panels, which determines the division of the panels into planar and non-planar slicing regions. The L9 Taguchi orthogonal array is being used in this study (Table 3), which accommodates four factors, each tested at three levels. This configuration provides a comprehensive evaluation of the toolpath planning factors while reducing the total number of experiments to nine different configurations. Four factors being assessed in this experiment include the following:  
1. The infill percentage of the non-planar layers, referring to the density of the deposited material in the region that is being sliced non-planarly;
2. The infill percentage of the planar layers, referring to the density of the deposited material in the region that is being sliced planarly;
3. The infill pattern used in the planar layers, including Differential Growth Curve (DGC), Parallel, and 3D Honeycomb. Planar layers here represent the region in the panels that will be sliced planar;
4. The ratio between the number of layers in planar and non-planar regions of the panel. Figure 6: The test scenario highlights stair-stepping in planar slicing (**a**), layer height variability in non-planar slicing (**b**), and the improved accuracy of the hybrid slicing strategy (**c**) [23]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factor** & **F1:** & **F2:** & **F3:** & **F4:** \\
**Level** & **Infill \%** & **Infill \%** & **Infill Pattern** & **Layer Ratio** \\  & **(Non-Planar)** & **(Planar)** & **(Planar)** & **(Non-Planar–Planar)** \\ \hline L1 & 90\% & 90\% &
\begin{tabular}{c} Differential Growth \\ Curve (DGC) \\ Parallel \\ \end{tabular} & 1.7 \\ L2 & 75\% & 75\% & Parallel & 2.6 \\ L3 & 60\% & 60\% & 3D Honeycomb & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental factors and their corresponding levels used in the L9 Taguchi orthogonal array design. The Differential Growth Curve (DGC) is being used as an infill pattern for all non-planar layers to maintain the geodesic distance between adjacent material beads. Table 3 shows the different levels of each factor being used in this experimental framework, and Table 4 outlines the experimental matrix, where each row represents a specific combination of factor levels corresponding to the design of experiments. The ASTM E1050-19 standard outlines a method for measuring the sound absorption coefficient and acoustic impedance of the material using an impedance tube [32]. In this study, the two-microphone transfer-function method is used as defined in ASTM E1050-19. This study uses two tube sizes, 100 mm and 29 mm in diameter, to assess low- and high-frequency ranges, respectively. The 100 mm tube is calibrated for frequencies between 50 Hz and 1600 Hz, while the 29 mm tube covers a range from 505 Hz to 6400 Hz. Cylindrical acoustic samples are fabricated to match the inner dimensions of the impedance tubes for proper sealing and accurate measurements, and each sample is 38 mm in thickness. For statistical reliability, three replicates are fabricated for each of the samples defined in Table 4. Each replicate was measured three times for the repeatability and reliability of the measurement.