# Intelligent Prediction of Aeroengine Wear Based on the SVR Optimized by GMPSO
## 4 Aeroengine Wear Prediction Case  
The wear situation of a certain civil aviation engine can be reflected by the Fe element in the oil, and the content of the Fe element in the oil can be obtained periodically through spectroscopic analysis. Figure 2 demonstrates the change in the Fe content with the increasing of the flight cycle. There are total 88 data; in this paper, the last five data were selected as the test data to verify the optimized SVR. To improve the prediction accuracy and convergence speed, reducing the difference between the data, the data in Figure 2 can be scaled using Equation (7):  
\[s_{i}=(1+\exp(-q_{i}/q_{1})) \tag{7}\]  
where \(q_{i}\) denotes the \(i\)th original data in the Fe data series, and \(s_{i}\) denotes the \(i\)th scaled data. Assume that \(p_{i}\) denotes the \(i\)th prediction data, which can be restored using Equation (8):  
\[q_{i}=-\lg(-1/p_{i}-1)\cdot q_{1} \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Function** & **SRPSO** & **ALCFSO** & **SLPSO** & **IWPSO** & **SFPSO** & **DNPSO** & **SAPSO** & **MAPSO** & **GMPSO** \\ \hline \(\mathrm{f_{Sph}}\) & 0.00025 & 8.4617 & 4174.53 & 474.278 & 1956.71 & 0.1176 & 132.214 & 0.0042 & \(3.98\times 10^{-48}\) \\ \hline \(\mathrm{f_{Sch}}\) & 0.4481 & 0.4548 & 0.4928 & 0.4451 & 0.4886 & 0.4995 & 0.4455 & 0.3816 & \(6.67\times 10^{-11}\) \\ \hline \(\mathrm{f_{Cri}}\) & 0.0055 & 0.3550 & 2.0718 & 1.1099 & 1.4751 & 0.0105 & 0.9869 & 0.0041 & 0 \\ \hline \(\mathrm{f_{Ack}}\) & 21.1626 & 19.2621 & 18.6374 & 19.7884 & 20.6655 & 20.0057 & 19.4486 & 18.8497 & 0 \\ \hline \(\mathrm{f_{Ras}}\) & 193.353 & 950.846 & 4564.84 & 1124.34 & 2613.14 & 471.213 & 1176.23 & 204.646 & 0 \\ \hline \(\mathrm{f_{Ras}}\) & 155.083 & 5219.32 & 8819.17 & 5891.12 & 2059.34 & 168.554 & 2634.42 & 148.853 & 47.3102 \\ \hline \(\mathrm{f_{SDPF}}\) & \(3.15\times 10^{8}\) & \(1.22\times 10^{24}\) & \(6.12\times 10^{52}\) & \(1.48\times 10^{38}\) & \(1.43\times 10^{39}\) & 0.1566 & \(9.66\times 10^{35}\) & \(7.84\times 10^{7}\) & \(1.77\times 10^{-101}\) \\ \hline \(\mathrm{f_{RhEF}}\) & 917.416 & 1033.42 & 9612.11 & 10436.4 & 6855.24 & 675.486 & 2506.73 & 1258.76 & \(4.37\times 10^{-56}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the optimization results of PSO variants. Figure 2: The time sequence of Fe in the oil. The fitness function outputs the measurement value of the PSO's optimization effect. In order to improve the prediction performance, \(k\)-fold cross validation (\(k\)-CV) is used to design the fitness function. Generally, \(k\)-CV is used to determine the model parameters, so that the generalization performance of the model is better. The principle of \(k\)-CV is that the original data are divided into \(k\) groups, each group is taken as the test data successively, and then the rest of the groups are taken as the training data, so there are \(k\) test results, and the mean of \(k\) results will be the output of the fitness function. For example, a known data set is divided into \(k\) groups. First, group 1 is selected as the test data, group 2 to \(k\) are used to train the algorithm. The trained algorithm will be tested using group 1 and output a test result for group 1. Then, group 2 is selected as the test data and groups 1 and 3 to \(k\) are used to train the algorithm, then output a test result for group 2. Successively, we can obtain \(k\) test results; the mean of \(k\) test results is the output of the fitness function, the suitable parameters can be found through cross training. Obviously, the advantage of the fitness function based on \(k\)-CV is the maintenance of the ergodicity of the data due to non-repeated sampling. On the other hand, [19] discusses the organizational form of time series data; therefore, we will organize the time series data according to [19]. Furthermore, the embedding dimension \(D\) of the training samples is a key parameter in organizing the data.