# Machine Learning Based Design of Railway Prestressed Concrete Sleepers
## 4 Results and Discussion
### Discussion  
From Figure 6, both the experimental data and the data from the hand calculation of some cross-sections of sleepers are different, but most of them are similar. The reasons these differences exist may be the following points. * First, the design strength of the materials may be different from the actual material characteristics. In the test, the actual strength of materials of the sleepers, such as concrete and prestressed reinforcement, is not necessarily the same as the design data for which were recorded. However, most of the input data are calculated using the recorded design data. This may cause a discrepancy. * Second, the loss of prestressing, in reality, can be different from the design estimation of loss. In the hand design calculation, according to the requirements of the code, the unified use of 40 years of loss of prestress is adopted. Around 25% of the total loss of prestress is commonly used in the design. * Third, there are some discrepancies in the calculation. In various parts of the open literature, some key design data have not been given or tested directly, such as eccentricity and cross-section modulus. They need to be estimated through the design data. Therefore, many approximations are used in obtaining the values of these data sets. Through computational verification, this effect has relatively little impact on the calculation results, but some error still exists. * Fourth, the measurement instruments and measurement conditions in the laboratory can cause an error. For example, there is a small deviation between the loading position and the recorded position, which directly affects the obtained bending moment data. Another example is that the effect of temperature is not considered in the calculation (assumed to be 20 \({}^{\circ}\)C). However, in the test, the temperature could cause the deformation of the prestressed concrete sleepers, affecting the experimental data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline Bayesian ridge & 2.52 & 1.59 & 1.14 & 0.95 \\ Random forest & 0.54 & 0.74 & 0.25 & 0.99 \\ Deep learning & 31.73 & 5.63 & 4.52 & \(-\)0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of models’ prediction accuracy. Figure 6: Comparison between experimental data and hand-calculated data. Due to these effects, data sets with very similar data will be selected for subsequent computation and machine learning. However, due to the potential causes of the error, some improvement measures are proposed. First, it is critical to search for more options and collect and find more design data (especially to obtain more laboratory data). Second, temperature and other factors could be included in hand calculation to increase the accuracy of the calculation and make the design data from hand calculation closer to the actual performance (obtained from experimental tests). The purpose of this study is to apply machine learning to the design of the railway prestressed concrete sleepers and to determine the most suitable machine learning technique among the three algorithms that have been developed. There are four indicators and parameters to measure the quality of the algorithms including mean squared error (MSE), root-mean-square error (RMSE), mean absolute error (MAE), and coefficient of determination (R\({}^{2}\)). MSE (mean squared error) is an important indicator to measure the quality of different prediction algorithms, and it measures the deviation between the data of prediction and the true value. MSE is more sensitive to the outliers in the database, and it is ideal for ensuring that the model which has been trained does not have outlier predictions with large errors [37]. When the predicted data agrees exactly with the true data, the value of the MSE is equal to 0 [38]. Table 1 shows that the random forest algorithm is optimal, as the value of the MSE is only 0.54. The value of the MSE of the Bayesian ridge algorithm is 2.52.