## 5 Dependence of RUL Prediction on Working Time  
In order to further analyze the prediction effect of the life prediction model on different working times of the concrete piston, life prediction was performed at a step size of 5% of the actual working life, with a typical result of on \(\alpha\) and RUL prediction shown in Table 4. In Table 4, \(M_{a}\) is the actual RUL of the concrete piston.  
Figure 8: RFR model.  
Figure 9: Comparison diagram of RMSE value of each model.  
Three concrete pistons with an actual working life of 210, 240 and 270 h, respectively, were selected to analyze the prediction effect of the model, and all the data are calculated to draw the RMSE curve of the prediction results, as shown in Figure 10. From Figure 10a-c, it can be seen that the prediction effect is best when the actual working life reaches approximately 80%. The RUL of 325 concrete pistons is predicted using the proposed method, where the estimation error is less than 4.73%. Figure 10d shows the averaged RMSE value on the predicted RUL at different working times. It can be seen that, in the early-life stage of the concrete piston, the prediction has a large error due to less condition monitoring data. However, the prediction accuracy improves as the working time increases until the working time is at 80% of the actual working life. Then, the prediction accuracy becomes worse as the working time increases.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **0** & **5\%** & **10\%** & **15\%** & \(\dots\) & **85\%** & **90\%** & **95\%** & **100\%** \\ \hline \(M_{0}\) & 0 & 12.62 & 25.25 & 37.87 & \(\dots\) & 214.60 & 227.22 & 239.85 & 252.47 \\ \(M_{a}\) & 252.47 & 239.85 & 227.22 & 214.60 & \(\dots\) & 37.87 & 25.25 & 12.62 & 0 \\ \(\alpha\) & 1 & 1.0021 & 1.0082 & 1.0089 & \(\dots\) & 1.0479 & 1.0596 & 1.0778 & 1.1026 \\ \(M_{r}\) & 239.63 & 227.51 & 216.34 & 203.89 & \(\dots\) & 36.50 & 26.69 & 18.41 & 11.74 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Data of a concrete piston at different life prediction points.  
Figure 10: Prediction results. (**a**) Actual working life of 210 h; (**b**) Actual working life of 240 h; (**c**) Actual working life of 270 h; (**d**) RMSE curve.  
At present, the concrete pistons of the concrete pump trucks are not replaced preventively due to the lack of supportive approaches. They are usually replaced after wearing until failure, which often leads to the unplanned downtime of the concrete pump truck, causing unnecessary economic losses and even affecting the project's progress. To achieve preventive replacement, it is very important to choose an appropriate replacement time. Replacing too early will lead to increased costs, and replacing too late may lead to unplanned downtime. Therefore, it is necessary to develop a replacement plan when the working time is close to the actual working life and the prediction error is small. Through the research of this work, it is found that the RUL prediction model of the concrete piston based on probability statistics and data-driven methods has the best prediction effect when the concrete piston working life reaches 80% of the predicted RUL; this result can be used for the formulation of preventive replacement plans. It can be set as a replacement warning point, which can be used as the main basis for maintenance according to the situation, and a reasonable maintenance replacement and inventory management plan can be developed to reduce costs and economic losses.