## 4 Experimental Validation and Analysis
### Experiment Comparison and Analysis  
There is a certain mapping relationship between the performance degradation state of each aircraft engine and its remaining life cycle. In order to explore and analyze the relationship between the engine life cycle, 81, 32, 76, and 56 randomly selected aerospace engines from the FD001 to FD004 datasets were used to predict the entire life cycle. To better evaluate the accuracy of this paper's method in predicting engine RUL, ridge regression [35], lasso regression [36], and light gradient boosting machine (LGBM) [37] methods were compared with the method proposed. As shown in Figure 11, the predicted RUL values of the aircraft engines using the method proposed are closer to the true values compared to other methods, and the predicted results are within the 95% confidence interval.  
In order to further evaluate the performance of the proposed method in terms of the prediction error, four different models constructed as mentioned above were compared. The boxplots of the prediction errors are shown in Figure 12. The orange solid line in each box represents the expected value of the predicted RUL of the engine. The size of the box in the boxplot can measure the uncertainty of RUL prediction. The RUL prediction error boxplots for datasets FD002 and FD004 are relatively large compared to other test sets. This is because the data in these datasets were collected in a complex environment with multiple operating conditions, indicating that there are more uncertainty factors in the multi-operational mode. In the verification sets of FD001 and FD004 under single-operational and multi-operational conditions, engine 32 and engine 56 were randomly selected, respectively, and the probability density curves of RUL prediction values at different cycle periods are shown in Figure 13. As the cycle period increases, the RUL prediction value becomes closer to the true value.  
To objectively evaluate and verify the RUL prediction results under different operating conditions, we constructed the three methods mentioned above and selected four prediction methods from the literature, including K-Neighbors Regressor (KNR) [38], to compare and analyze them with proposed method. The evaluation metrics of the RMSE and  
Figure 10: Validation set RMSE of MLP with different parameter values.  
values of the aviation engine RUL prediction results were compared. The comparison results are shown in Figure 14. The evaluation metric RMSE for the test sets FD001 and FD003 is considerably smaller than that for FD002 and FD004 under multiple operating conditions, and the \(R^{2}\) value is also closer to 1. Moreover, compared with the evaluation results of other methods, the RUL prediction results of our proposed method for aviation engines have mostly smaller evaluation metrics. This effectively shows that our proposed RUL prediction method has a better prediction accuracy and performance, and that the predicted RUL values of the engine are closer to the actual values.  
Figure 11: Comparing the RUL prediction results of different methods on different engines.  
Figure 12: Box plots depicting prediction errors of various models on different datasets.