## 5 Experimental Verification and Discussion
### Validation of Roundness Error Evaluation Method  
The roundness error of the connecting rod journal was evaluated according to the filtered profile data. The initial particle swarm was selected as the random coordinates in the region around the \(O_{L}\) according to the position of the center of the least squares. The parameters of PSO were selected as follows: particle swarm size \(n=50\), iteration number \(T=100\), learning factor \(c_{1}=c_{2}=1.49\), maximum inertia weight \(\omega_{max}=0.9\) and minimum inertia weight \(\omega_{min}=0.4\), maximum velocity \(V_{max}=0.001\) and minimum velocity \(V_{min}=-0.001\), population boundary = [\(-0.2\),\(0.2\)].  
The genetic algorithm (GA), particle swarm optimization (PSO) and improved particle swarm optimization (IPSO) were used to calculate the roundness of crankshaft connecting rod journal P4. The convergence of the algorithms is shown in Figure 10.  
The same method was used to perform five independent calculations on the measurement section, and the results are shown in Table 1.  
Improved particle swarm optimization (IPSO) was used to calculate the connecting rod journal P4 independently five times. The calculated positions of the center of the circle are close, and the deviation of the diameter is less than \(0.1\upmu\)m. The general population of \(20/30\) generations can evolve into the optimal population, and the convergence speed is fast and stable. The results of various numerical calculations are basically the same, which shows that the particle swarm optimization algorithm has high accuracy.  
Several evaluation methods were used to calculate the connecting rod journal P4 of the crankshaft sample, the results were compared, as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Center of Circle (\(10^{-3}\) mm)** & **Evolutionary Generations** & **Inscribed Point** & **External Point** & **Diameter/mm** & **Roundness/\(\upmu\)m** \\ \hline
1 & (0.020, \(-0.049\)) & 21 & 242 & 383 & 39.9876 & 1.87 \\
2 & (0.051, \(-0.016\)) & 19 & 438 & 383 & 39.9877 & 1.85 \\
3 & (0.061, \(-0.016\)) & 32 & 438 & 383 & 39.9877 & 1.87 \\
4 & (0.050, \(-0.026\)) & 27 & 438 & 383 & 39.9877 & 1.84 \\
5 & (0.062, \(-0.057\)) & 31 & 438 & 383 & 39.9876 & 1.86 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of 5 independent calculations on the measured data of crankshaft sample P4 using improved PSO.  
Figure 10: Convergence process of calculating P4 measuring section of the crankshaft sample.  
Through comparison, it is found that the calculation error of diameter is small and the calculation error of roundness is large in the results of the least-squares method. It shows that the diameter value calculated by the least-squares method can ensure certain accuracy in the case of more sampling points, but there is still a certain error in the results of roundness.  
By comparing the calculated results of two intelligent algorithms, it is found that the calculated center position error is small and all of them are around the center of the least square circle, which verifies the feasibility of the least-squares center as the starting point of the optimization algorithm. The positions of the minimum inscribed point and the maximum external point calculated by the genetic algorithm and particle swarm algorithm are basically the same, and the errors of diameter are small, which verifies the feasibility of the intelligent optimization algorithm. The global search performance of the genetic algorithm is better, while the local search performance of the particle swarm algorithm is better. After determining the optimal solution around the least-squares center, the inertia weight of the particle swarm algorithm is improved to find the optimal solution faster.