## 3 Case Study
### Vibration Signal Analysis  
Figures 7-9, respectively, present the time-domain, power spectral density, and time-frequency spectrograms of a segment of \(R_{i}\), measured over \(\Delta t\), in states A, B, C, and D.  
In state A, the vibration signal deviated noticeably from the vibration neutral axis, despite the relatively small amplitude and overall smooth changes. This deviation can be attributed to the asynchronous drive cylinder expansion and contraction, which makes the main stress platform of the HBM tilt at a certain angle. Furthermore, during the climb, the HBM frame may encounter localized wall protrusions, generating relatively large vibrations or shocks. These shocks occasionally peak at more than 2 gal and occur at relatively large intervals. The power spectrum value of the vibration signal was relatively small, and the time-frequency spectrogram showed a certain frequency distribution.  
In state B, the amplitude of the vibration signal was relatively large, with a power spectrum that was more evenly distributed and with larger power spectrum values compared to the climbing state. This can be attributed to the impact, friction, and vibration generated during the workers' knocking operation, the movement of the tower crane and construction hoist, and other ancillary equipment during the normal working conditions of the HBM, resulting in the production of the vibration signal. During the operating state, the activities of people and mechanical equipment on the HBM are more frequent, so the peak-to-peak intervals of such signals are smaller.  
In state C, the amplitude of the vibration signal exceeded 20 gals, and there was a clear pulse waveform. The power spectrum value of the vibration signal was the highest among the four states, and a clear pulse signal was evident in the time spectrum diagram. This can be attributed to the rigid or semi-rigid connection between the HBM and the placing boom. As a result, the vibration signals from the concrete transfer pump during concrete pumping are transmitted to the main load-bearing platform of the HBM. This transmission occurs via the base of the placing boom or the pump pipe. The accelerometer is mounted on the steel beams of the platform and is sensitive to the vibration of the placing boom.  
In state D, the amplitude of the vibration signal typically did not exceed 0.5 gals. Additionally, the power spectrum of the signal was evenly distributed across all frequency bands, with relatively low power spectrum values. The time-frequency spectrogram exhibited relatively smooth temporal variation without any significant frequency changes. This is because, in a no-load state, the various components of the HBM remain unchanged, resulting in minimal vibration or shock. The vibration signal is mainly affected by the wind load, environmental noise, and accelerometer noise. Thus, the frequency distribution of the vibration signal remained relatively uniform and changed smoothly.  
Figure 6: Accelerometer deployment in the HBM of Shanghai Xujiahui Center (SXC).  
Figure 8: Power spectral density plots of acceleration signals for four states: (**a**) state A, (**b**) state B, (**c**) state C, and (**d**) state D.  
Figure 7: Typical acceleration time-domain curves for four states: (**a**) state A, (**b**) state B, (**c**) state C, and (**d**) state D.  
In summary, the main characteristics of the HBM vibration signals include spectrum, noise, and multimodal mixing. The signal manifests differently in different situations. These differences may be attributed to variations in the motion state of the HBM, pressure changes in the hydraulic system, and other influencing factors. Among the four states, the peak and frequency characteristics of the vibration signals in states C and D were more apparent, while the differences in the vibration signals in states A and B were relatively small. Therefore, the difficulty in real-time recognition of the HBM's working state through the triaxial accelerometer sensor lies in distinguishing between states A and B.