## 4 Validation of MD Calculation Scheme for Lifter Operation
### Time-Series Simulation of MD\({}^{2}\) Based on Long-Term Operation  
We simulated the transition of the MD\({}^{2}\) values based on the measured vibration data collected from the continuous operation of the lifter over a period of two years, assuming that the mechanical condition of the guide wheel will change from the normal state to the anomaly state when damaged to the same extent as described in the previous section over this period. First of all, we have two kinds of vibration data in the normal and damaged conditions that does not include the intermediate transition data in the period between the normal and anomaly terms. Therefore, the transition data were simply simulated assuming that the energy level in each frequency band linearly decays. The required time for the value of MD\({}^{2}\) to exceed the anomaly threshold value was estimated based on the simulated transition. In this case study, we sought to validate that high-pass filtering can remove the short-term periodic trend but can preserve the long-term transition of the MD\({}^{2}\) that appears as a gradual increase in the estimated values over several years. As reported earlier, the short-term periodic components that result in the unnecessary trend observed in the vibration time-series data were removed by high-pass filtering; however, we wanted to validate its usefulness in a practical case involving the long-term continuous observation of MD\({}^{2}\). Figures 19a and 23 show the time-series energy levels in each frequency band under normal and anomaly (guide wheel damage) conditions, respectively. Here, the transition of the energy levels from the normal condition (Figure 19a) to the anomaly condition involving damage to the guide wheel (Figure 23) was simulated to linearly change from one state to the other when operating the lifter continuously for 780 days. Note that, for the time-series data in the normal condition, 90 days were added before the 780 days of operation to verify that the MD\({}^{2}\) value in the normal condition was constant at around 1.0. The transition of the time-series energy levels during the simulated 780 days was generated as follows. First, the data for the normal condition for the eight days that were described in Section 4.3.1 were combined repeatedly. The steady-state time-series data for 780 days was then linearly decreased to smoothly connect to the energy levels under the condition of a damaged guide wheel. As an example, the data for the 1378 Hz band are shown in Figure 24. In these data, the energy level decreases monotonically by approximately 5 dB over the 780-day period. Then, as shown in Figure 25, by using the time-series data of the first five days (50,460 data values), the unit space was generated. Next, the 50,460 values of MD\({}^{2}\) for the five days beginning on the second day were calculated and the average value, \(\overline{\text{MD}}_{1}{}^{2}\), was treated as the first MD\({}^{2}\) data value. This operation was performed in the same manner for all of the data simulated over 870 days, each time advancing the five-day range by one day. The resulting \(\overline{\text{MD}}_{1}{}^{2}\) (\(1\leq i\leq 866\)) values are given in Figure 26a. As shown in the figure,  
Figure 23: Vibration time-series data under the damaged-bearing condition: In this simulation study, the transition of the energy levels from the normal condition (Figure 19a) to this anomaly condition is simulated to linearly change from one state to the other when operating the lifter continuously for 780 days. the value of \(\overline{\text{MD}}^{2}\) changes as the energy level changes from the normal state to the anomaly state. The \(\overline{\text{MD}}^{2}\) for the first 200 days is shown in Figure 26b. The threshold value of 3.3 is also shown.