## 4 Validation of MD Calculation Scheme for Lifter Operation
### Effect of Each Type of Damage on MD\({}^{2}\)  
#### 4.3.1 Calculation of MD\({}^{2}\) Under Normal Condition  
To calculate MD\({}^{2}\) under the normal condition, the unloaded lifter was continuously operated in the normal state for nine days. A unit space was generated based on the fragment data (10,046 waveforms) obtained from measurements on the first day; the MD\({}^{2}\) of the fragment data for the remaining eight days (80,368 waveforms) in the generated unit space was then produced using the method described in Section 2.  
From the frequency characteristics of the vibration data obtained from R1 during normal operation (Figure 18), the energy levels in the 1/12 octave band around the four prominent peak frequencies at 724 Hz, 1020 Hz, 1378 Hz, and 1744 Hz were obtained and used for the calculation of MD\({}^{2}\). Note that the frequency components around the lowest peak at 340 Hz were excluded from the calculation since the level fluctuation in each operation was quite large. Figure 19 shows the time series of the energy levels in each of the four selected frequency bands. Since some trends in the time series of the energy levels were apparent, the periodic components of these series were checked using the results of FFT processing at the sampling frequency of 10,046 Hz. The frequency component of 724 Hz that included the largest trend component is shown in Figure 20. Since long-term periodic components were dominant in the quite low-frequency range, a high-pass filter with a cutoff frequency of 4.16 Hz in the sampling frequency of 10,046 Hz was applied to the time-series data in each band and the effects of the fluctuations were cut off. The filtered time-series data of the energy levels and the MD\({}^{2}\) values obtained from these data are shown in Figures 19b and 21, respectively. The trends were removed by the filtering, and the MD\({}^{2}\) values during the nine days of normal operation appear to be relatively constant around an average value of 0.94.  
Figure 17: Comparison of the frequency characteristics of the vibration in the normal condition and when operating with a damaged bearing: This result shows that the characteristic difference in the peak-dip tendencies received at R1 shown in Figure 15 is not observed; however, in the damaged-bearing condition, the energy level is approximately 5 dB lower than under the normal condition over the entire frequency range.  
Figure 19: Time-series data of the vibration in the normal conditions (**a**) without high-pass filtering and (**b**) with high-pass filtering: Since some trends in the time series of these energy levels in the respective bands were apparent, the periodic components of these series were investigated using the results of FFT processing, and will be removed by filtering.  
Figure 18: Selection method using frequency bands to calculate the MD\({}^{2}\) of the lifter: From these frequency characteristics of the vibration data obtained from R1 during normal operation, the energy levels in the 1/12 octave band around the four prominent peak frequencies at 724 Hz, 1020 Hz, 1378 Hz, and 1744 Hz were obtained and used for the calculation of MD\({}^{2}\).  
Figure 20: Frequency component of the fluctuation in the time-series data of vibration of the lifter under the normal condition.