# An Analysis of Rock Bolt Dynamic Responses to Evaluate the Anchoring Degree of Fixation
## 2 Materials and Methods
### Data Processing  
A vibration analysis estimates vibration levels and investigates patterns in vibration signals. It is commonly conducted directly on the time waveforms of the vibration signal as well as on the frequency spectrum, which is obtained by applying the Fourier transform to the time waveform. We primarily focused on the analysis of the amplitude spectrum to detect the resonance frequencies of the system.  
The preliminary data processing involved the time-windowing of shot events to extract the useful part of the signal, a frequency analysis of each single windowed event, and the analysis and detection of the main frequencies of resonance.  
The data acquisition was performed by collecting at least five shots for each rock bolt. All the responses were collected in the same recording, which lasted 2 s. The data processing involved splitting the record into several sub-records (windowing) of the same length (1024 samples), where each sub-record contained the separate response to a single shot. Consequently, several responses for each rock bolt were available for the subsequent frequency domain analysis, in which the records had the same number of samples.  
One must note the following:  
* Time-windowing was necessary because we collected the data without any trigger during a window of 10 s and we recorded several excitations in this window; during the post processing, we extracted several sub-windows from the signal for each of 1024 samples, and we performed a frequency analysis on those signals.
* The application of a detrend filter was necessary to remove some of the drift of the signal because of electromagnetic effects on the sensors and cable. Specifically, these refer to the value of a static or slowly varying signal that can be both positive and negative. This value is usually almost constant within a specific time window. The detrend filter recognizes this constant value and removes it within the time window.  
The mean or a best fit line (in the least squares sense) were subtracted from the original data before the windowing was performed. Removing the trend from the data enabled us to focus the analysis on the fluctuations in the data of the trend. In a specific case, a systematic shift was noticed as the result of sensor drift, probably because of the sensitivity  
Figure 8: The rugged PC used for the field test and the NI-DAQ card used for the data acquisition. The compactness of the instrumentation is evident for easy handling.  
of the devices (sensor sand cables) to external electromagnetic noise. This shift did not impact on the final quality of the recorded vibration because it was coherently removed using detrend filtering.  
A spectral analysis of vibration is the process of transforming a signal from one in the time domain to one in the frequency domain. We performed a spectral analysis using a fast Fourier transform (FFT) to calculate a spectrum from the time waveform. A FFT converts a signal from the time domain into the frequency domain, where the calculation can break down a signal into all its frequencies. The signal is then analyzed to determine any substantial frequencies originating from each single record. A peak in the frequency signal is associated with the likely mode of vibration.