# Diagnosis of the Hollow Ball Screw Preload Classification Using Machine Learning
## 3 Experiment Set-Up and Results
### Vibration Signal
Thus, 44 features constituted the feature vector for the 338 cells. Before feature extraction from the 338 cells using the 44 features in each cell's feature vector, outliers (extreme values) were removed from the cells by using the Z-score technique [20]. The criterion for Z-score computation was set at three times the standard deviation. Point A was treated as an outlier after Z-score computation (Figure 11). Therefore, nine cells were removed from the original 338 cells. The remaining 329 cells were used to extract the representative ball-screw quantitative values, which reflected the ball-nut preload behavior. Figure 11: The Z-score technique for removing the outliers (**red**) among the acquisitioned data (**blue**). Figure 10: Partial view of the original vibration signal (**blue**) and signal profile after Kalman filtering (**red**). [PERSON]'s criteria were used to select the significant features from the 44 features that could distinguish between the 2% preload loss and the 4% preload (normal preload) or 6% preload (extra preload). Using all the extracted features for assessing the prognostic-diagnosis health model is unfeasible and inefficient. Some extracted features have a low contribution in classification models. Therefore, the [PERSON] criterion score (Equation (1)) was selected to determine significant features from the 44 feature vectors. Each feature had its own score, which was calculated as follows:  
\[\text{Fisher score }=\frac{\mu_{1}-\mu_{2}}{\sigma_{1}^{2}+\sigma_{2}^{2}}, \tag{1}\]  
where \(\mu\) and \(\sigma\) indicate the mean and standard deviation, respectively, of the same class, and 1 and 2 represent classes 1 and 2, respectively. The selection of the remaining 14 features that could distinguish between the various ball-nut preloads or ball-screw pretensions is illustrated in Figure 12. The orange line in Figure 12 denotes the average score of the 44 features. For the 329 cells, 329 \(\times\) 14 arrays were constituted. Each cell contained 14 column features, including the 2% and 4% preloads. The N(\(\mu\), \(\sigma^{2}\)) distribution of the 329 \(\times\) 14 arrays was executed into a value between [0,1]. The formula as shown in Equation (2) for the new value of each cell feature was as follows:  
\[X_{ij}=\frac{x_{ij}-x_{min}}{x_{max}-x_{min}},\text{where }i=1,\;2,\;\ldots,\;329 \text{ and }j=1,\;2,\ldots,\;14. \tag{2}\]  
This normalization process was preserved as a new 329 \(\times\) 14 array. The new normalized array could then be used in the GA/KNN classifier model. The KNN data-mining algorithm was used to classify the normalized dataset of the 329 \(\times\) 14 array for the 2% and 4% preloads. The KNN algorithm was selected because this algorithm is the most commonly used method for datasets of discrete series [21]. The KNN classifier is a simple but effective algorithm that classifies a testing sample based on its similarity to the labeled training samples. For a new testing feature, the five nearest neighbors from the training set are first identified according to  
Figure 6:0 Selection of 14 of the 44 features based on the Fisher criterion. Euclidean distance. Secondly, a voting mechanism assigns the class label with the largest vote to the testing sample. The voting mechanism may encounter a dilemma when the distance calculation is vague. This may cause the aggregation of two different classes when a new feature is identified. In the genetic algorithm, a weighting coefficient was added to the distance calculation for the 14 features (Equation (3)). The number of genes was 50, with a mutation rate of 0.08 and a crossover rate of 0.6 for the computation of 100 generations. Figure 6:1  
Figure 13 displays the classification rate for the C0 and C1 classes. The training set had 229 cells, and the test set comprised 100 cells. As displayed in the left image of Figure 13, when the tested data for the 4% preload was close to the trained set, the C0 class was denoted.