# Runway Pavement Structural Analysis Using Remote Laser Doppler Vibrometers
## 3 Compensation Methods
### Angle Compensation  
Deflection refers to the vertical displacement experienced by the pavement due to the weight exerted by vehicles or aircraft. The vibrational data gathered using RLDV represents the velocity component of this vertical pavement vibration, measured in the direction of the respective angle. Consequently, the equation below (Equation (1)) demonstrates the conversion relationship between the pavement's vertical vibrational velocity and the monitoring data collected by RLDV.  
\[v=v^{\prime}/\sin\theta \tag{1}\]  
where \(v\) and \(v^{\prime}\), respectively, represent pavement vibration velocity and values measured by RLDV in the direction of laser incidence angle \(\theta\).  
This research carried out indoor validation experiments focused on the angle compensation methodology. The experimental setup was arranged as follows: RLDV was positioned at a height of 1 m to capture vibration data from a standard shaker located at distances of 15 m, 25 m, and 35 m from the laser. The vertical vibrational speed of the shaker was set at 40 mm/s, and the frequency at 80 Hz. Figure 3 illustrates the vibration data collection experiments using RLDV under three distinct operational conditions. The  
Figure 2: Runway deflection detection scheme based on RLDV.  
measurement point was identified as the green area illuminated by the laser on the shaker, as confirmed by high-definition images captured by the camera.  
Figure 4 and Table 1, respectively, display the vibration data acquired by RLDV under three distinct operational conditions. The initial vibration velocities recorded were 2.57 mm/s, 1.57 mm/s, and 1.08 mm/s. Following angular compensation utilizing Equation (1), the resultant values were 38.45 mm/s, 39.20 mm/s, and 37.95 mm/s. The experimental discrepancies for the three operational conditions were calculated as 3.88%, 2.00%, and 5.13%, respectively. Another condition was carried out in the validation experiment of angular compensation. A reflector was placed above the shaker, which served to change the direction of the obliquely incident measurement beam to the vertical direction. Figure 4d shows the vibration data collected at a measuring distance of 35 m with a reflector, with the result of 39.97 mm/s and an error of 0.08%.  
Upon analyzing these outcomes, it was observed that the measured values across all three experimental sets were marginally lower than the standard value. Moreover, the error under the reflector condition is only 0.08%. In contrast to vertical incidence, tilted incidence of the measuring beam results in part of the laser light reflecting off the measuring surface and being difficult to be received by the photodetector, which reduces the signal strength and results in measuring errors. Thus, this deviation can be attributed to energy loss during small-angle measurement. However, the compensatory impact of the formula proved to be highly effective, with the maximal error being 5.13%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Conditions(m)** & **Preliminary Results (mm/s)** & **Processing Results (mm/s)** & **Error (\%)** \\ \hline
15 & 2.57 & 38.45 & 3.88 \\
25 & 1.57 & 39.20 & 2.00 \\
35 & 1.08 & 37.95 & 5.13 \\
35 (reflector) & 39.97 & - & 0.08 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Analysis of angle compensation experimental results.  
Figure 3: Angle compensation verification experiment.  
Figure 4: _Cont_.