## 3 Results and Discussion
### The Effect of Process Parameters on the Micro-Hardness of the Coating  
The effect of the process parameters on the coating's micro-hardness was evaluated with the _S/N_ ratio and the results are shown in Table 4. The rank of the influence of each factor on the micro-hardness is \((S\times V)>D>(L\times S)>(D\times S)>L>S>V\). The analysis results of ANOVA are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Sample No.**} & \multirow{2}{*}{**\(\mathbf{L}\)**} & \multirow{2}{*}{**\(\mathbf{D}\)**} & \multirow{2}{*}{**S**} & \multirow{2}{*}{**\(\mathbf{V}\)**} & \multicolumn{6}{c}{**Micro-Hardness (HV\({}_{0.2}\))**} \\ \cline{5-10}  & & & & & & & & **ExperimentBPNN** & **BPNN-PSO** & **BPNN-QPSO** \\ \hline \multicolumn{10}{c}{Training group} \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 3: The micro-hardness of the coatings from experiments and models.  
Figure 6: Cross-section of Ti(C, N) ceramic coating.  
(\(L\times S\)) and (\(S\times V\)) were highly significant factors, while \(D\) and (\(D\times S\)) were significant factors. Figure 7 shows the main effect diagram that analyzed the influence of factors on micro-hardness. According to Figure 7a, the process parameters that are beneficial to improve the micro-hardness of the coating are selected. \(L_{1}\) and \(L_{2}\) were selected for laser power, \(D_{1}\) for the spot diameter, \(S_{1}\) and \(S_{3}\) for the overlapping ratio, and \(V_{2}\) for the scanning velocity. When there was a significant interaction between the two factors, the optimal level of the factor was selected from the interaction of the factors, regardless of whether the effect of the factor itself was significant [25]. Because (\(L\times S\)), (\(S\times V\)), and (\(D\times S\)) were significant factors, the optimal process parameter combination was confirmed from the interaction of factors. According to Figure 7b-d, the combinations of factors were confirmed successively are \(L_{2}S_{1}\), \(D_{1}S_{1}\), and \(S_{1}V_{2}\). Therefore, the optimal combination of process parameters was \(L_{2}D_{1}S_{1}V_{2}\), i.e., laser power \(L_{2}\) = 450 W, spot diameter \(D_{1}\) = 1 mm, overlapping ratio \(S_{1}\) = 20%, and scanning velocity \(V_{2}\) = 7 mm/s.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Level** & \(L\) & \(D\) & **(\(S\times V\))** & \(S\) & **(\(L\times S\))** & \(V\) & **(\(D\times S\))** \\ \hline
1 & 59.54 & 59.71 & 59.28 & 59.51 & 59.22 & 59.4 & 59.53 \\
2 & 59.55 & 59.42 & 59.64 & 59.32 & 59.67 & 59.55 & 59.27 \\
3 & 59.24 & 59.2 & 59.41 & 59.5 & 59.44 & 59.37 & 59.54 \\ Delta & 0.31 & 0.51 & 0.58 & 0.19 & 0.48 & 0.17 & 0.43 \\ Rank & 5 & 2 & 1 & 6 & 3 & 7 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Effect of laser cladding process parameters on the micro-hardness of the coatings (\(S/N\) ratio).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **DoF** & **Adj SS** & **Adj MS** & **\(F\)-Value** & **\(p\)-Value** & **Significance** \\ \hline \(L\) & 2 & 7092 & 3546 & 2.45 & 0.166 & \\ \(D\) & 2 & 14604 & 7302 & 5.05 & 0.052 & S \\ \(S\) & 2 & 2676 & 1338 & 0.93 & 0.446 & \\ \(V\) & 2 & 2169 & 1085 & 0.75 & 0.512 & \\ \(L\times S\) & 4 & 30172 & 7543 & 5.22 & 0.037 & HS \\ \(D\times S\) & 4 & 22013 & 5503 & 3.81 & 0.071 & S \\ \(S\times V\) & 4 & 54765 & 13691 & 9.47 & 0.009 & HS \\ Error & 6 & 8672 & 1445 & & & \\ \hline Total & 26 & 142163 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANOVA of the micro-hardness of the coatings.  
Figure 7: Effect of laser cladding parameters on micro-hardness of coatings: (**a**) the influence of single factors; (**b**) the interaction of \(S\) and \(L\); (**c**) the interaction of \(S\) and \(D\); (**d**) the interaction of \(V\) and \(S\).