# Transfer Learning-Based Fault Diagnosis under Data Deficiency
## 3 Application  
### Linear Motion Guide Dataset  
A linear motion (LM) guide is a frequently used mechanical part in the manufacturing field because it moves heavy workpieces while maintaining precision at high speeds. The LM guide in the experiment is a ball guide type with a rectangular LM block whose height and width are 24 mm and 34 mm. Only one LM block is installed in a single rail. The seal type of the LM block is an end seal for dust prevention. The workpiece is fixed to the surface of the LM block, which travels along a linear rail with dozens of balls circulating inside of the block as shown in Figure 2. Since the balls move along the track in the LM block, flaking may occur due to the rolling contact fatigue loads. Four LM guides are prepared, and test rigs are made, which consist of the motor and belt drive (not shown here), rail, workpiece, and LM guides as shown in Figure 3a. The LM block reciprocates along a 450 mm-long rail with a sequence of acceleration for 0.23 s, a constant speed of 1.667 m/s for 0.04 s, and deceleration for 0.23 s, which is shown in Figure 4a. A three-axis accelerometer with a sampling rate of 10.2 kHz is installed at the LM block as shown in Figure 3b. The vibration signal is measured intermittently at the 0, 20 k, 50 k, and 100 k'th cycles for the early period, and at every 100 k cycle for the subsequent period. At each recording cycle, the signal is recorded twice with different speeds: first at the original 1.667 m/s (high) and next at 0.1 m/s (low). This is to simulate the on-line operation during the production and the off-line inspection operation during the maintenance, respectively. The speed profile for the latter case is shown in Figure 4b. In the recording cycle, the measurement is repeated nine or ten times at random under each speed. The experiment is terminated when one of the LM guides encounters the flaking appearance during the inspection, which has taken about two months. As a result, the total number of datasets is given by 680 and 723 for the high and low speeds, respectively, where a dataset refers to the measured data for a single trip. Figure 5a shows the plot of the vibration signal under the low speed over the whole period acquired for one of the LM guides. Figure 5b is its three-dimensional spectrogram, which is the stack of the frequency spectrum made by fast Fourier transform at each cycle. The figure shows that the amplitudes at around 3 kHz increase from a certain time period, which is about the last 25% of the whole cycle. The same phenomena are found in the other LM guides. The authors believe that this represents the fault progression of LM guides, eventually leading to the flaking failure. Since the data can be easily acquired during the maintenance, the latter is defined as the source domain, whereas the former being the target domain. Then the imbalance condition is considered where the fault data in the target domain are much less available than those in the source domain due to the infrequent occurrence in the real operation. Among the datasets in the source domain (low speed), those in the first six. Note that 25% and the last 25% of the whole period are chosen as the normal and fault at our convenience to make the number of datasets in each class the same. The results are 152 datasets in common for the normal and fault conditions. Then, the NN is trained using the all the datasets (152 normal samples and 152 fault samples) in the source domain. In the target domain (high speed), the datasets of the normal and fault conditions are chosen in the same way, and the results are 160 datasets in common. Then, the datasets are divided into the training and test, with the number being 100 and 60, respectively. The training datasets are used to train the NN which is pre-trained and transferred from the source domain. The test datasets are used to examine the accuracy of the trained NN.