## 4 Conclusions  
The surface roughness of Inconel 718 work-piece was accurately predicted in the milling process through the signal feature extraction techniques as well as the Elman neural network in this research. The well-trained surface roughness prediction model was utilized to optimize the cutting parameters through the PSO algorithm based on the scenario that the feed rate is maximized in case of different constraints of surface roughness requirements. The experiment results show that the surface roughness of Inconel 718 work-piece can be accurately predicted in the milling process by using the selected signal features as well as the cutting parameters. The Ra prediction was achieved through the Elman neural network model with the MAPE value of 13.48%. Meanwhile, the optimized cutting parameters were validated experimentally to demonstrate that the proposed method is feasible to accelerate the milling process under the different requirements of surface quality. With the optimal \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Expected Ra** & **Cutting Speed** & **Feed Per Tooth** & **Cutting Depth** & **Clamping Force of** & **Feed Rate** & **Predicted Ra** \\
**(\(\mu\)m)** & **(m/min)** & **(mm/tooth)** & **(mm)** & **Vise (N)** & **(mm/min)** & **(\(\mu\)m)** \\ \hline \multirow{4}{*}{1.0} & 45.00 & 0.25 & 1.32 & 9807 & 447.62 & 1.00 \\  & 45.00 & 0.25 & 0.87 & 9807 & 447.62 & 1.00 \\  & 45.00 & 0.25 & 0.75 & 9807 & 447.62 & 1.00 \\ \hline \multirow{4}{*}{0.8} & 45.00 & 0.25 & 0.50 & 26,479 & 447.62 & 0.75 \\  & 45.00 & 0.25 & 1.29 & 62,765 & 447.62 & 0.75 \\  & 45.00 & 0.25 & 1.50 & 45,112 & 447.62 & 0.74 \\ \hline \multirow{4}{*}{0.6} & 44.76 & 0.22 & 1.47 & 62,765 & 384.68 & 0.58 \\  & 45.00 & 0.22 & 1.33 & 45,112 & 393.91 & 0.60 \\  & 45.00 & 0.23 & 1.50 & 45,112 & 409.04 & 0.60 \\ \hline \multirow{4}{*}{0.4} & 30.00 & 0.05 & 0.50 & 9807 & 59.68 & 0.39 \\  & 33.83 & 0.07 & 1.10 & 62,765 & 93.72 & 0.31 \\ \cline{1-1}  & 30.00 & 0.09 & 0.50 & 62,765 & 108.71 & 0.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimal cutting parameter combinations from particle swarm optimization (PSO) algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Expected Ra (\(\mu\)m)** & **Feed Rate (mm/min)** & **Predicted Ra (\(\mu\)m)** & **Measured Ra (\(\mu\)m)** & **Error (\%)** \\ \hline \multirow{4}{*}{1} & 447.62 & 1.00 & 0.93 & \(-\)7.00 \\  & 447.62 & 1.00 & 1.19 & 19.00 \\  & 447.62 & 1.00 & 1.05 & 5.00 \\ \hline \multirow{4}{*}{0.8} & 447.62 & 0.75 & 0.78 & 3.45 \\  & 447.62 & 0.75 & 0.73 & \(-\)2.67 \\  & 447.62 & 0.74 & 0.73 & \(-\)1.35 \\ \hline \multirow{4}{*}{0.6} & 384.68 & 0.58 & 0.55 & \(-\)5.17 \\  & 393.91 & 0.60 & 0.63 & 5.00 \\  & 409.04 & 0.60 & 0.64 & 6.67 \\ \hline \multirow{4}{*}{0.4} & 59.68 & 0.39 & 0.34 & \(-\)13.49 \\  & 93.72 & 0.31 & 0.39 & 25.00 \\ \cline{1-1}  & 108.71 & 0.28 & 0.37 & 30.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Experiment results by using the selected optimal combinations of cutting parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Expected Ra (\(\mu\)m)** & **Maximum Feed Rate in Experiment (mm/min)** \\ \hline \multirow{4}{*}{1} & 447.62 \\  & 447.62 \\  & 447.62 \\  & 437.89 \\  & 143.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Verification of experimental result for feed rate maximization. cutting parameter combinations, the measured Ra values are closed to the required Ra values with the overall accurate MAPE value of 10.38%. The required Ra values of 1, 0.8 and 0.6 \(\upmu\)m can be achieved by the maximized feed rates that have the errors of less than 1%. The required Ra values of 0.4 \(\upmu\)m can be achieved by the feed rate of 24% more speed. [PERSON] was in charge of the supervision in this research, including initiating the research project, conducting the experiment setup, advising the data analysis methods and final manuscript writing. [PERSON] was in charge of the experiment implementation, vibration signal acquisition, signal analysis and parameters optimization.