# Monitoring of Preload Variation of Linear Guide Positioning Stage Using Artificial Neural Network
## 4 Prediction of Linear Guide Preload--ANN Modeling
### Evaluation of ANN Model  
Previously, predictive ANN models were successfully established based on a dataset that was assessed from motion experiments for stages with specific preload conditions. Subsequently, the ANN predictive models were validated by employing another dataset as the input variable to predict rigidity. The dataset for validation was collected from experiments conducted on stages with different combinations of linear guides with different preloads. Details of the preload setting of the stages for the motion tests are described in the following cases. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & \multicolumn{3}{c}{**Training Dataset**} & \multicolumn{3}{c}{**Testing Dataset**} & \multicolumn{3}{c}{**Validation Dataset**} \\ \hline
**ANN Model** & **R** & **RMSE** & **MAPE** & **R** & **RMSE** & **MAPE** & **R** & **RMSE** & **MAPE** \\ \hline MLP 8-16-1 & 0.975 & 69.4 & 2.19\% & 0.959 & 88.2 & 2.95\% & 0.971 & 77.4 & 2.65\% \\ MLP 8-18-1 & 0.967 & 78.5 & 2.74\% & 0.964 & 82.8 & 2.68\% & 0.962 & 86.3 & 2.95\% \\ MLP 8-28-1 & 0.981 & 59.5 & 2.38\% & 0.959 & 87.4 & 3.40\% & 0.970 & 76.2 & 3.50\% \\ MLP 8-30-1 & 0.971 & 74.3 & 2.56\% & 0.967 & 78.9 & 2.64\% & 0.964 & 90.0 & 2.91\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical values of neural network models. Figure 15: Comparisons of the stage rigidity between rated values and ANN predictions: (**a**) MLP 8-16-1; (**b**) MLP 8-18-1; (**c**) MLP 8-26-1; (**d**) MLP 8-30-1. 1. Case IV: Stage with three high preload and one low preload sliding blocks. This condition simulated one of the linear guide blocks subjected to severe wear at the rolling interfaces, and hence the preload decreased owing to the reduction of interference. This was also regarded as a moderate abnormal state, and the overall rigidity of the stage was 1809 N/\(\upmu\)m, which was reduced by approximately 10% from an initially high preloaded stage. 2. Case V: Stage with two high preload and two low preload sliding blocks. This condition simulated two linear guides in a severe failure state with uneven wear at the rolling interface, which greatly reduced the preload of the two carriages from high to low values. In this severely abnormal state, the overall rigidity of the stage was 1598 N/\(\upmu\)m, which was reduced by approximately 21%, from an initially high preloaded stage. 3. Case VI: Stage with three sliding blocks at medium preload and one low preload. This was intended to simulate the failure of the linear guide blocks subjected to severe wear at the rolling interfaces, yielding a preload loss of approximately 10%. In this case, in a moderately abnormal state, the overall rigidity of the stage was 1566 N/\(\upmu\)m, which was reduced by approximately 10% from an initially medium preloaded stage. Again, there were 38 records of vibration signals obtained from the tests conducted at a feed rate of 2000-8000 mm/min. The dataset was fed into the selected ANN models with a better performance. The statistical values of the ANN models are listed in Table 8. For cases (IV) and (VI), the average percentage prediction error of the stage rigidity was approximately 5.96-8.6%. The prediction error for case (V) was approximately 15-17%. The average prediction accuracy of the stage rigidity for the three evaluation cases was approximately 8.54-11.23%. It was found that the prediction performance of the selected ANN models in the model evaluation phase was slightly inferior to those demonstrated in the model training phase. In the training phase, all the data were measured from the stage with a specific preload. However, each stage was assembled with sliding blocks rated at the same preload level, which enabled all rolling interfaces in sliding blocks with consistent characteristics. This ensured that the stage vibrated at a consistent level, with less fluctuation.