## 5 Results
### Laser Shock Peening Parameter Optimization  
The DNN model was trained to predict the extended RUL of bearings after LSP remanufacturing, using input parameters such as laser power density, overlapping rate, spot diameter, and the current RUL. The model provided accurate predictions of extended RUL, which were utilized as the fitness function in various optimization algorithms to find the optimal LSP parameters that maximize bearing life. Table 3 shows the effectiveness of different optimization algorithms for determining the optimal LSP parameters. The fruit fly optimization (FFO) algorithm performed better than other methods; a fitness value of 0.97 with a convergence in 23 iterations was achieved, and there was a 29.33% improvement in fitness over the fitness without optimization. FFO algorithm showed efficient optimization performance for maximizing extended RUL of remanufactured bearing.  
Ant colony optimization (ACO), multi-objective particle swarm optimization (MOPSO), quantum particle swarm optimization (QPSO), simulated annealing (SA), whale optimization algorithm (WOA), grey wolf optimizer (GWO), nondominated sorting genetic algorithm II (NSGA-II), and genetic algorithm (GA) also showed improvements in fitness values ranging from 0.89 to 0.96; the improvements were between 18.67% and 28.00%. However, the algorithms converged at a slightly slower pace or achieved lower fitness values compared to FFO. Therefore, the FFO algorithm was deemed most suitable for balancing convergence speed and maximizing the improvement in bearing life through optimal LSP parameter selection (See Figure 8).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & **Parameters Settings** & **RMSE** & **Validation Accuracy** & **Training Accuracy** \\ \hline
1 & heads = 2, lr = 0.001 & 1.213 & 0.912 & 0.944 \\
2 & heads = 4, lr = 0.001 & 1.152 & 0.921 & 0.954 \\
3 & heads = 8, lr = 0.001 & 1.134 & 0.925 & 0.957 \\
4 & heads = 16, lr = 0.001 & 1.112 & 0.935 & 0.962 \\
5 & heads = 4, lr = 0.01 & 1.135 & 0.928 & 0.955 \\
6 & heads = 4, lr = 0.05 & 1.124 & 0.929 & 0.958 \\
7 & heads = 8, lr = 0.0008 & 1.109 & 0.937 & 0.963 \\
8 & heads = 8, lr = 0.005 & 1.204 & 0.916 & 0.947 \\
9 & heads = 8, lr = 0.01 & 1.098 & 0.946 & 0.968 \\
10 & heads = 16, lr = 0.005 & 1.073 & 0.956 & 0.974 \\
11 & **heads = 8, lr = 0.002** & **0.989** & **0.963** & **0.982** \\
12 & heads = 4, lr = 0.0008 & 1.105 & 0.932 & 0.961 \\
13 & heads = 4, lr = 0.005 & 1.198 & 0.919 & 0.948 \\
14 & heads = 2, lr = 0.002 & 1.125 & 0.925 & 0.955 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The training and validation accuracy under different parameter settings.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Fitness (0-1)** & **Convergence Iterations** & **Improvement in Fitness (\%)** \\ \hline Without Optimization & 0.75 & - & - \\ FFO Algorithm & 0.97 & 23 & 29.33 \\ ACO Optimization & 0.92 & 25 & 22.67 \\ MOPSO Optimization & 0.95 & 26 & 26.67 \\ QPSO Optimization & 0.90 & 31 & 20.00 \\ SA Optimization & 0.91 & 18 & 21.33 \\ WOA Optimization & 0.96 & 21 & 28.00 \\ GWO Optimization & 0.94 & 32 & 25.33 \\ NSGA-II Optimization & 0.89 & 27 & 18.67 \\ GA Optimization & 0.93 & 30 & 24.00 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of different optimization algorithms for LSP parameters.