## 5 Conclusions  
In this work, the pressure sensitivity is predicted quickly and accurately through the thickness and roughness of the paint based on an ANN. After applying the data augmentation method, its prediction error MAPE is reduced from 9.2730% on the original data set to 8.8186%. In order to prevent over-fitting in the training stage, the discarding method was adopted, and its MAPE was reduced to 6.5088%. Through the PSP pressure measurement experiment, it is further verified that the two methods can improve prediction accuracy. In terms of characterization research, this method can quickly obtain the relationship between pressure sensitivity and paint thickness and roughness. After inputting paint thickness and roughness, pressure sensitivity can be obtained. By inputting multiple sets of paint thickness and roughness into the trained ANN, and then screening the pressure sensitivity obtained from the ANN, the paint thickness and roughness required for the target pressure sensitivity can be obtained. When studying the relationship between multiple influencing factors and paint characterizations, the time cost and economic cost of calibration experiments can be reduced to a certain extent. In the PSP pressure measurement tests, in order to avoid the pressure measurement error due to the difference in paint thickness and roughness between the model surface and the sample, we propose a new ANN-based method to measure the pressure: we use the ANN to predict coefficients A and B in the Stern-Volmer equation. We use the neural network N\({}_{1}\) to predict the pressure sensitivity through the paint thickness and the roughness of the model. The pressure sensitivity is approximately equal to B, so we use the pressure  
Figure 15: The distribution of pressure measured by electronic-scanned pressure sensor, the in situ method, the method in this paper-M\({}_{0}\), the method in this paper-M\({}_{50}\), and the sample calibration experiment. \begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **RMSE (Pa)** \\ \hline In situ & 47.4431 \\ Method in this paper-M\({}_{0}\) & 63.4736 \\ Method in this paper-M\({}_{50}\) & 139.6155 \\ Sample calibration experiment & 73.0223 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: RMSE of pressure calculated by the in situ method, the method in this paper-M\({}_{0}\), the method in this paper-M\({}_{50}\), and the sample calibration experiment. sensitivity to predict coefficient A through N\({}_{2}\). The MAPE of prediction coefficient A is 2.1315%. According to the Stern-Volmer equation, the delta wing pressure was calculated and compared with the in situ method and the sample calibration experiment. In the delta wing pressure measurement test, the RMSE of the in situ calibration, the method in this paper, and the pressure measured by the calibration experiment are 47.4431 Pa, 63.4736 Pa, and 73.0223 Pa, respectively. The RMSE of the method in this paper is greater than the in situ method, but smaller than the sample calibration experiment, so the ANN-based method to measure pressure in the PSP pressure measurement experiment deserves attention. Conceptualization, C.W. and L.L. ; data curation, H.J. ; funding acquisition, X.L. and C.W. ; methodology, X.L., C.Z., Z.G. and Z.L. ; writing--original draft, X.L. ; writing--review and editing, L.L. and Z.L. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Key R&D Program of China (Grant No. 2020 YFA0405700), the National Natural Science Foundation of China (NSFC No. 12202476), and supported by the Innovation Fund of Postgraduate, Xihua University (Grant Number: YCJJ2021033). Not applicable. * _[PERSON] et al. (2006)_ [PERSON]; [PERSON]; [PERSON] Aircraft Ice Accretion Prediction Based on Neural Networks. _J. Aircr._**2006**, _43_, 233-240. [CrossRef]
* [PERSON] et al. (2014) [PERSON]; [PERSON]; [PERSON] [PERSON] Prediction of Aircraft Failure Times Using Artificial Neural Networks and Genetic Algorithms. _J.