## 4 Conclusions  
This paper used the Taguchi orthogonal experiment design, investigated the influence of laser power, scanning speed, gas flow, and SiC powder ratio on the micro-hardness and wear volume in the cladding layer. Based on the signal to noise ratio conversion, this study applied grey relational analysis to achieve the optimization on multiple objectives simultaneously. The predicted processing parameters set was verified through experimental validation. Conclusions are addressed as follows:  
1. The analysis on the micro-hardness alone indicates it was primarily affected by the SiC powder ratio, while other processing parameters were shown to be statistically insignificant. The micro-hardness of cladding layer was improved with the increasing SiC powder ratio.
2. The analysis on the wear volume by itself also shows the primarily influence from the SiC powder ratio, while other processing parameters were statistically insignificant. The wear volume of cladding layer was reduced with the increasing SiC powder ratio.
3. The contribution of SiC powder ratio on the micro-hardness and wear volume in their corresponding ANOVA was 92.08% and 79.39%, respectively. This indicates that the micro-hardness and wear volume were primarily affected by SiC powder ratio and other processing parameters had a negligible impact.
4. Grey relational analysis was applied to achieve the objective of maximizing micro-hardness while minimizing wear volume simultaneously. The processing parameters set fulfilling this target was 1800 W laser power, 6 mm/s scanning speed, 110 L/h gas flow, and 30% SiC powder ratio.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variables/Responses** & **Input/Output** & **6 th Run in L\({}_{\text{1g}}\) Design** & **Optimal Set Prediction** & **Validation** \\ \hline \multirow{4}{*}{Processing Parameters} & Laser Power (W) & 1400 & 1800 & 1800 \\  & Scanning Speed (mm/s) & 7 & 6 & 6 \\ \cline{1-1}  & Gas Flow (L/h) & 1500 & 1100 & 1100 \\ \cline{1-1}  & SiC Powder Ratio (\%) & 30 & 30 & 30 \\ \hline \multirow{4}{*}{Outcomes} & Micro-Hardness (HRC) & 66.3 & - & 68.9 \\  & Wear Volume (mm\({}^{3}\)) & 0.0003904 & - & 0.0003121 \\ \cline{1-1}  & GRG & 0.931034 & 1 & 0.949887 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Experimental validation result and comparison.  
The grey relational grade was predicted and then experimentally validated in the multi-objectives grey relational analysis. The error rate was 5.3% between predicted value and actual value. It validates the applicability of applying grey relational analysis on multi-objectives optimization.  
Methodology, G.L. and C.Z.; experiment, C.Z.; analysis, G.L., C.Z., Y.Z., M.F., and J.J.; writing--original draft preparation, G.L. and C.Z.; writing--review and editing, G.L. and Y.Z.; supervision, G.L. and Y.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 51575110), and the Fujian Provincial Education and Research Program for Young and Middle-Aged Teachers (Grant No. JAT190407).  
The authors gratefully acknowledge the support from the Public Service Platform for Technical Innovation of Machine Tool Industry in Fujian Province at Fujian University of Technology.  
The authors declare no conflicts of interest.