## 4 The Accurate and Stable MDTF Fault Identification Framework and Its Experimental Evaluation
### The gearbox Testbed and Data Acquisition  
A gearbox testbed, self-developed at the Ulsan Industrial Artificial Intelligence laboratory, for acquiring vibration data is shown in Figure 7. The testbed can be explained as follows: an AC motor is directly connected to the pinion wheel through the drive shaft (DS), whereas the gear wheel is fixed with a non-drive shaft (NDS) and the adjustable blades (the load). The pinion wheel with 25 teeth, whose length is 9 mm, and the gear wheel (38 teeth) are engaged with each other and housed in the gearbox, creating a gear reduction ratio of 1:1.52. The rotation movement (torque) of the load is provided by the motion of the AC motor through the gearbox. Therefore, the rotational speed of the pinion wheel is equal to the rotational speed of AC motors, and the gear frequency is calculated by the pinion frequency and the gear ratio. The vibration sensor (the accelerometer) is placed at the end of the NDS, 72.5 mm from the gear wheel. The rotational speed of the DS (a pinion frequency) is measured by the displacement transducer, which is mounted for tracking the hole in DS once per revolution. The data acquisition system, which is the PCI-2 data acquisition board, is connected to the accelerometer (622B01) to measure and digitize vibration signals, and to store digital vibration samples. The specifications of the accelerometer, speed sensor, and data acquisition system are given in Table 1.  
The MDTF gearbox was created by cutting one tooth, mounted on the gear wheel, to different degrees. Figure 8 shows the degrees of cut teeth and the vibration signals obtained under each condition for all observed defect types in this study, including a normal or perfect condition gear (PC), 6.6% degree of tooth defect (DT1), 10% degree of tooth defect (DT2), 20% degree of tooth defect (DT3), 30% degree of tooth defect (DT4), 40% degree of tooth defect (DT5), and 50% degree of tooth defect (DT6). These multiple degree tooth faults were seeded for simulation of the same behavior of the gear defects caused by long-term operation of a gearbox system (e.g., tooth spalling, tooth cracking, worn tooth, etc.). The vibration characteristic for fault states of a gearbox was analyzed in detail in Section 2. Figure 6: Block diagram of the proposed accurate and stable MDTF gear fault identification framework. Figure 7: Gearbox experimental testbed. Table 2 demonstrates the configuration of the dataset used in this paper. The data acquisition system converts the analog vibration signal to a digital vibration signal with a sampling frequency of 65,536 Hz. Each sample is one second long, termed a one-sec sample. A total of 200 samples were collected under each defect condition with variable rotating speed (four shaft rotational speeds are evaluated in this study). Therefore, there are 800 samples for each defect condition, and a total of 5600 samples are extracted from this testbed. LADT Performance for Effective Noise Removal of Vibration Signals of a MDTF Gearbox under Variable Speed Conditions  
The raw vibration signals were digitized at a high sampling frequency of 65,536 Hz in order to gather rich discrete vibration samples, and to capture the extent of feasible defect-related components in each one-sec vibration signal. The vibration data collected from the gearbox contain fault-related information and interference noise. By sampling the vibration signal at a frequency of 65,536 Hz, the frequency spectrum of a discrete vibration sample is from 0 Hz to 32,768 Hz (according to the Nyquist-Shannon sampling theorem). However, the accelerometer is capable of sensing the vibration oscillations in the frequency range of 0.42-10,000 Hz (Table 1). Thus, the fault-related information is in the frequency range of 0.42-10,000 Hz. Therefore, rather than providing the raw vibration signal to LADT, the vibration signal is pre-processed by performing down-sampling using a low-pass filter to avoid aliasing [22].