# Monitoring of Preload Variation of Linear Guide Positioning Stage Using Artificial Neural Network
## 4 Prediction of Linear Guide Preload--ANN Modeling
### ANN Predictive Models  
In the ANN modeling, input data were collected from the dynamic motion tests of the stage with high, medium, and low preloads. All 242 records were divided into three groups, of which 75% were randomly selected for neural network training, 15% for testing, and the remaining 15% for validation. Several sample data for the ANN modeling are listed in Table 5.  
The architecture of the neural network included one input layer, one hidden layer, and one output layer. The ANN modeling was conducted using multilayered perception (MLP) through Statistica Neural Networks software [43]. After many attempts, four different ANN models were selected based on the prediction performance and correlation coefficients. Each ANN model was labeled with a specific number, including the number of neurons in each layer, and the number of neurons in the hidden layer was optimized. For example, MLP 8-16-1 had 8 and 16 neurons in the input and hidden layers, respectively, and one neuron in the output layer. The models MLP 8-18-1 and MLP 8-30-1 were optimized with 28 and 30 neurons in the hidden layer, respectively.  
Table 6 shows the sensitivity level of the constructed ANN input parameters. A larger value has less influence on the output parameter; conversely, the smaller the value, the greater the influence. It was found that in these models, the sensitivity values of all the input neurons had no significant differences, which means that the selected variables were suitable for input neurons. In addition, the initial preload state did not serve as the input neuron, but it could be employed as a reference to evaluate the degradation of the linear guide preload when compared with the output target, that is, stage rigidity predicted from the ANN model.  
The statistical values for the selected ANN models, such as the correlation coefficient (R), RMSE, and MAPE, were used as the basis for determining the performance of the neural network modeling solutions, as summarized in Table 7. The value of R represents the extent of agreement between the predicted and measured values. The values of R for all the ANN models within all datasets were in the range of 0.958-0.980. Figure 15 shows a  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**ANN** & **X-** & **Y-** & **Z-** & **XYZ** & **Pitching** & **Rolling** & **Yawing** & **Feed** \\
**Model** & **RMS** & **RMS** & **RMS** & **-RMS** & **RMS** & **RMS** & **RMS** & **Rate** \\ \hline MLP 8-16-1 & 3.975 & 6.674 & 4.272 & 2.988 & 2.703 & 3.584 & 4.015 & 2.456 \\ MLP 8-18-1 & 3.425 & 2.482 & 5.324 & 2.976 & 2.875 & 1.802 & 1.976 & 1.422 \\ MLP 8-28-1 & 3.113 & 9.626 & 6.590 & 8.392 & 2.737 & 5.653 & 5.212 & 2.73 comparison of the measured and predicted values of the stage rigidity for all data, which indicates that a high agreement of the prediction results with a correlation coefficient is achieved by neural network models.  
In addition, the RMSE values for prediction were less than 3.50%, which indicates that the average percentage prediction accuracy of all datasets was approximately 96.5%. This implies that the rigidity of the stage can be accurately predicted from the measured vibration signals based on the proposed ANN models. In addition, the root mean square error between the predicted stage rigidity and actual stage rigidity ranged from 59 to 90 N/\(\upmu\)m, which means that the error of the ANN model for predicting preload failure was approximately 3.0-5.0% when compared with the initial rigidity value of 2020 N/\(\upmu\)m.