# Digital Twin-Based Vibration Monitoring of Plant Factory Transplanting Machine
## 3 Results and Discussion
### Analyzing Different Sensor Solutions for the Deployment of AD Applications
The duration of the lateral movement of the horizontal slider is approximately 2 s.  
According to Figure 8, the vibration amplitude above the transplanting manipulator remains below 3 m/s\({}^{2}\). The vibration cloud in the \(X\)-axis orientation has a shape resembling a rugby ball, exhibiting a small amplitude of vibration and a uniform vibration signal in the \(X\)-axis direction. From Figure 7b,c, the fitted vibration clouds in the Y and Z directions are dumbbell-shaped. The comparison of the clouds reveals that the vibration trend is more noticeable in the \(Z\) and \(X\) axes above the transplanting manipulator compared to the \(Y\)-axis. However, these observations only consider the effect of the amplitude of the vibration and a frequency domain analysis should be carried out to obtain more information on the vibration characteristics. Figure 7: Fitting cloud of transplanter vibration during horizontal sliding. (**a**) Vibration cloud fitting in the \(X\)-axis direction. (**b**) Vibration cloud fitting in the \(Y\)-axis direction. (**c**) Cloud fitting vibration along the \(Z\)-axis direction. (**d**) Comparing clouds for vibration fitting in the direction of the \(XYZ\)-axis. Comparison of the Power Spectral Density of Modal Vibrations When Using Different Operating Conditions for Transplanting Equipment  
To examine the probability distribution of vibration energy in different frequency domains and time periods, we utilize power spectral density (PSD) analysis. PSD analysis represents the distribution of the mean square value of statistical parameters in the frequency domain of the stochastic process. By analyzing the power spectral density, we can determine the average concentration of vibration energy in a vibration excitation with varying intrinsic frequencies. This information helps us prevent or enhance vibration excitation to minimize vibration damage. For solving the power spectral density, we employ spectral analysis using rectangular as the type of window, 100 spectral lines, a resolution of 10,000 Hz, and an interval of 0.2 Hz. Linear averaging is employed for this analysis. In Figure 8 below, you can observe the power spectral density waterfall in the XYZ orientation  
Figure 8: Waterfall of power spectral density. (**a**) PSD waterfall clouds in the \(XYZ\)-axis under working condition one. (**b**) PSD waterfall cloud in the \(XYZ\)-axis under working condition two. (**c**) PSD waterfall clouds in \(XYZ\)-axis direction under working condition three. (**d**) PSD waterfall clouds in the \(XYZ\)-axis direction under working condition four. for various operational circumstances. Figure 8 displays a waterfall diagram that allows for the visualization of the average density of vibration energy present in the vibration excitation at various inherent frequencies through the analysis of the power spectrum density. Figure 8a illustrates that the initial vibration magnitude in the \(XYZ\)-axis direction is negligible when subjected to working condition one. Following the equipment's initiation, a surge arises in the low-frequency vibration range, aligning with the findings from the prior FFT analysis. Under condition two, the \(Y\)-axis vibration amplitude experiences a substantial increase, exhibiting multiple peaks in the mid-frequency range along the \(Z\)-axis direction, as depicted in Figure 8b. The findings align with the outcomes of the prior analysis; however, the peaks display variability and could potentially be attributed to the robot's significant impact on vibration solely during the clamping of transplants and the release of seedlings. Significant amplitude enhancement in the \(Z\)-axis direction is observed for working condition three (Figure 8c). The amplitude in the \(X\)-axis direction is higher than in the other two directions within the 0-80 Hz low-frequency range. In condition four, the power spectral density exhibits increased turbulent peaks in the X and Y directions. The highest vibration amplitude is 12.03 Hz, which means that there may be more parts resonating.