# The CIPCA-BPNN Failure Prediction Method Based on Interval Data Compression and Dimension Reduction
## 5 Results
### Fault Prediction  
We randomly selected two-thirds of the data to train the model and used the remaining data as the test set to verify the predictive ability of the model. We selected accuracy, precision, recall, \(F_{1}\) score, and AUC(Area Under Curve) as the evaluation indicators of the model's predictive ability and conducted 500 repeated experiments to obtain the average value of each indicator. Taking the hidden layer of BP neural network with 30 neurons as an example, the modeling time (500 repeated experiments) of CIPCA-BPNN and PCA-BPNN was 599.76 min and 301.86 min, respectively. As can be seen from Figure 7a, CIPCA-BPNN could predict failures well. Its accuracy could reach more than 95% and precision was more than 90%; although the value of recall changed greatly, when the number of hidden neurons was more than 20, it could also reach 90%. In addition, the ensemble classifier effect of CIPCA-BPNN was better than the two base classifiers, indicating that the ensemble classifier used more data features, reflecting the advantages of CIPCA-BPNN. Finally, the model effect got better and better with the increase in the number of hidden neurons and tended to stabilize after the number of hidden neurons reached 30. In practical applications, more than 30 hidden neurons can be used to build a model, and a good prediction effect can be obtained. We also constructed a PCA-BPNN prediction model and compared it with CIPCA-BPNN under the same circumstances. It can be seen from Figure 7b that the accuracy and precision of PCA-BPNN was slightly lower than that of CIPCA-BPNN and was much lower than CIPCA-BPNN in recall. In fault prediction, recall is more important than accuracy and precision because recall refers to the probability that a fault can be accurately predicted when it actually occurs. The AUC curve in Figure 7c also shows that the prediction effect of CIPCA-BPNN was better than that of PCA-BPNN. The details of each evaluation index of the model's prediction ability are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Number of** \\ **Components** \\ \end{tabular} } & \multicolumn{2}{c}{**CIPCA**} & \multicolumn{2}{c}{**PCA**} \\ \cline{2-5}  & **Proportion** & **Cumulative** & **Cr**u** & **Cr**u** & **Cr**u** \\  & **Explained** & **Explained** & **Explained** & **Explained** \\ \hline
1 & 0.367 & 0.367 & 0.107 & 0.107 \\
2 & 0.206 & 0.573 & 0.074 & 0.181 \\
3 & 0.163 & 0.736 & 0.064 & 0.245 \\
4 & 0.056 & 0.792 & 0.060 & 0.305 \\
5 & 0.051 & 0.843 & 0.059 & 0.364 \\
6 & 0.042 & 0.885 & 0.058 & 0.423 \\
7 & 0.027 & 0.912 & 0.053 & 0.475 \\
8 & 0.019 & 0.931 & 0.050 & 0.526 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Flight data variance explained by CIPCA and PCA. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Number of** \\ **Hidden Neurons** \\ \end{tabular}  } & \multicolumn{6}{c}{**CIPCA-BPNN**} & \multicolumn{6}{c}{**PCA-BPNN**} \\ \cline{2-11}  & **Accuracy** & **Precision** & **Recall** & **\(F_{1}\)-Score** & **AUC** & **Accuracy** & **Precision** & **Recall** & **\(F_{1}\)-Score** & **AUC** \\ \hline
10 & 0.973 & 0.922 & 0.743 & 0.823 & 0.986 & 0.958 & 0.850 & 0.617 & 0.715 & 0.960 \\
15 & 0.982 & 0.932 & 0.854 & 0.891 & 0.993 & 0.969 & 0.884 & 0.725 & 0.797 & 0.977 \\
20 & 0.986 & 0.940 & 0.895 & 0.917 In practice, if the fault can be accurately predicted before the fault occurs, it can help us avoid the fault or take measures to reduce the loss that the fault may cause. In order to achieve this goal, we calculated the CIIPCA-BPNN test set prediction results at different times before the failure. Our experiment divided the flight data into 0.1 s intervals, but in practice, it is difficult to respond effectively to a fault with only a 0.1 s warning. Therefore, we summarized the prediction results within 1 s and observed the prediction effect of the model.