# Intelligent Prediction of Aeroengine Wear Based on the SVR Optimized by GMPSO
## 3 Improved PSO Algorithm
### PSO Performance Verification  
In order to verify the performance of the improved PSO, some typical test functions can be used to compare the different well-known PSO variants. The typical test functions are listed in Table 1. In Table 1, \(x_{i}\) and \(d\) represent an element and the number of elements in each function, respectively.  
The follow PSO variants were improved based on different strategies, so they were used for the comparison discussed in this paper. PSO variants include SRPSO (self-regulating PSO) [12], ALCPSO (aging leader and challengers PSO) [13], SLPSO (social learning PSO) [14], IWPSO (inertia weights PSO) [11], SFPSO (shrinkage factor PSO) [15], DNPSO (dynamic neighborhood PSO) [16], SAPSO (simulated annealing PSO) [17], and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Function** & **Search Range** & **Dimension** & **Optimal Solution** & **Optimal Extremum** \\ \hline Sphere: \(\text{f}_{\text{Sph}}=\sum\limits_{i=1}^{d}x_{i}^{2}\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \hline [PERSON]: \(\text{f}_{\text{Sch}}=0.5+\dfrac{\left(\sin\sqrt{\frac{d}{\varepsilon_{1}}}x_{ i}^{2}\right)^{2}-0.5}{\left[1+0.001\left(\frac{d}{\varepsilon_{1}}x_{i}^{2} \right)\right]^{2}}\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \hline [PERSON]: \(\text{f}_{\text{Gri}}=\sum\limits_{i=1}^{d}\dfrac{x_{i}^{2}}{4000}-\sum\limits _{i=1}^{d}\cos\left(\frac{x_{i}}{\sqrt{i}}\right)+1\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \hline [PERSON]: \(\text{f}_{\text{Ack}}=\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \(-20\cdot e^{-\left(2\sqrt{\frac{1}{\varepsilon_{1}}}\frac{d}{\varepsilon_{1}}x_ {i}^{2}\right)}-e^{\frac{1}{\varepsilon_{1}}\sum\limits_{i=1}^{d}\cos\left(2 \pi x_{i}\right)}+20+e\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \hline Rastrigin: \(\text{f}_{\text{Ras}}=\sum\limits_{i=1}^{d}\left[x_{i}^{2}-10\cdot\cos(2\pi x _{i})+10\right]\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \hline Rosenbrock: \(\text{f}_{\text{Ross}}=\sum\limits_{i=1}^{d}\left[100\left(x_{i}^{2}-x_{i+1} \right)^{2}+(x_{i}-1)^{2}\right]\) & \([-100,\,100]\) & 50 & \((1,\,1,\,\ldots,1)50\) & 0 \\ \hline SDPF: \(\text{f}_{\text{SDPF}}=\sum\limits_{i=1}^{d}\left|x_{i}\right|^{i+1}\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \hline RHEF: \(\text{f}_{\text{RHEF}}=\sum\limits_{i=1}^{d}\left(\sum\limits_{i=1}^{i}x_{i} \right)^{2}\) & \([-100,\,100]\) & 50 & \((0,\,0,\,\ldots,\,0)50\) & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters for radio communication.  
Figure 1: The procedure of the guided mutation strategy.  
MAPSO (multiple agents PSO) [18]. Furthermore, the population size was 60, and the total iteration number was 400, and all the algorithms were operated in the same computational environment. Furthermore, the calculations of each PSO variant were repeated 100 times to obtain the mean of the fitness values. Table 2 shows the mean changes, which can prove the global optimal performance of PSO variants. Table 2 proves the advantage of GMPSO (guided mutation strategy PSO). Obviously, it was able to solve all of the test functions in Table 1, and its better global optimization performance is conducive to engineering applications.