# Diagnosis of the Hollow Ball Screw Preload Classification Using Machine Learning
## 3 Experiment Set-Up and Results
### Vibration Signal  
Accelerometer sensors are widely used for diagnosing machine health status in rolling element bearings [14]. Various localized defects and loading conditions with a range of rotation speeds were used to analyze the behavior of vibration signals for the classification of bearing faults. The least-squares SVM model with two root-mean-square (RMS) input features and kurtosis was used to classify the types of bearing faults according to the defect size. Another data-driven approach was presented by the authors of [15] for detecting the precursor of power-electronics converter failures in power-conversion systems. Several statistical features were extracted followed by feature selection. It must be determined whether only one accelerometer feature signal can be used to diagnose the preload status. Figure 7 represents the plots of the vibration signals acquired from Figure 1b. The linear SVM kernel function and nonlinear RBF SVM kernel function (Figures 5 and 6) were deployed in Figure 8. Classification rates of 74% and 78% were obtained for the testing and training data, respectively, based on the 25 forward and backward signals of the maximum peak value under a rotation speed of 300 rpm, pretension of 10 \(\mu\), and operation time of 5 min. Figure 6: 100% classification rate results for the 2% and 4% ball-nut preloads based on the current and linear scale signals without oil-cooling circulation with the (**a**) linear SVM kernel function, (**b**) radial kernel function, (**c**) linear SVM kernel function with an additional pretension of 5 \(\mu\), and (**d**) radial kernel function with an additional pretension of 5 \(\mu\). The aim of this study was to produce a classifier or a machine-learning method that could be suitably used for various ball-nut preloads. Figure 9 represents the flow chart of the prognostic diagnosis based on feature extraction and the GA/KNN classifier model. Figure 8: Training and classified results for the (**a**) linear SVM kernel function, and (**b**) nonlinear radius-based function (RBF) SVM kernel function of the vibration signals for the 2% and 4% ball-nut preloads with a pretension of 10 \(\upmu\). Figure 7: Sampled vibration signals. Raw data of 1,620,992 vibration signals were acquired and then filtered using the Kalman filter, since the Kalman filter is the Bayesian optimal solution to the problem of sequentially estimating the states of a dynamical system in which the state evolution and measurement processes are both linear and Gaussian [19]. The Kalman-filtering algorithm has low computation complexity, and can be implemented in digital signal-processing hardware for a real-time system. A satisfactory classification rate could not be obtained with the SVM for the data-acquisition region around the peak signal. The constant speed profile was redirected for the duration of machine learning when the commanded ball-screw motion stage was cruising with a constant speed. As displayed in Figure 10, the smooth vibration signals were divided into 338 segments after filtering. Each segment was labeled as one  
Figure 9: Flow chart of prognostic diagnosis based on feature extraction and the genetic algorithm/k-nearest neighbor (GA/KNN) classifier model. cell with its own feature vector. Each feature vector contained six feature elements, namely the RMS, kurtosis, variance, crest factor, standard deviation, and skewness of the vibration signals. The feature vectors included an additional 30 elements based on the fast Fourier transform of the vibration signal. The frequency spectrum from 1 kHz to 2.56 kHz was divided into 30 segments. The average frequency amplitude of each frequency segment (covering a range of 85.3 Hz) was calculated based on all the frequencies associated with the segment. Finally, the power spectral density of the vibration signal based on the amplitude and shape of the frequency segments' average, standard deviation, skewness, and kurtosis were all augmented with an additional eight features.