## 5 Experimental Validation
### Measurement Texperiment of Two Horizontal Parallel Surfaces
#### 5.1.2 Results and Analysis  
The measurements of laser displacement sensor are shown in Figures 16 and 17. When the contact line \(A\) is located at the starting position, computer begins to record the data. After the contact line \(A\) reached the end position, where it necessary to save the data, the measurement mechanism is in a static state, and the measurements of this process represent a straight line approaching the level. It is known that the measurements between starting position and end position is defined as valid measurements. Therefore, the suspended time series waveforms need to be separated and the effective measurements were obtained. Figure 16: The measurements when \(PB\) is the measured surface (**a**) measurements 1 (**b**) measurements 2 (**c**) measurements 3 (**d**) measurements 4. Figure 15: Measurement system of two horizontal parallel surfaces. (**a**) \(PB\) is the measured surface. (**b**) \(PA\) is the measured surface. When the effective measurements and \(X_{0}\) were obtained, the combined projection waveforms were calculated according to Equations (1) and (2). Figure 18 shows the combined projection waveforms. It can be seen that the waveforms change with sampling time, and the measurement time is different, which has greater randomness. The measurements in Figure 18 are sequenced according to the measurement time from short to long. Then, FFT is carried out to obtain the amplitude frequency characteristics, as shown in Figure 19. It can be seen from the analysis of the amplitude of the low-frequency band that the amplitudes of the spectrum graphs corresponding to different waveforms are basically identical. Further, the peak mainly occurs near 0 Hz and there is no frequency doubling relationship in the amplitude frequency characteristics. This is because the measurements changes with the shape of the measured plane and is not affected by other factors. When 2-28 Hz is amplified, it is found that the amplitude does not increase or decrease monotonously with the increase of measurement time. It shows that the measurement time has no effect on the amplitude frequency characteristics of the measurements. It can also be understood that when four waveforms are converted into spatial sequences, the overall shape of the waveforms does not change significantly. Figure 17: The measurements when \(PA\) is the measured surface (**a**) measurements 1 (**b**) measurements 2 (**c**) measurements 3 (**d**) measurements 4. Figure 18: Combined projection waveforms. (**a**) \(PB\) is the measured surface (**b**) \(PA\) is the measured surface. Extracting the amplitude corresponding to the 2 Hz, 4 Hz, 6 Hz, 8 Hz, as shown in Figure 20, it can be seen that the amplitude corresponding to the same frequency has little difference with varying measurement time, indicating that different driving speed has little impact on the attribute of measurements. Therefore, the average velocity can be used as the calculation parameter. Then the waveforms in Figure 18 are processed by the time-space conversion algorithm. The converted spatial sequence waveforms are shown in Figure 21. Because the positional relation curve is macro geometric, therefore, the trend curves of the waveforms in Figure 21 are extracted, which are called the combined projection curves, as shown in Figure 22. It can be seen from Figures 21 and 22, when the measurement mechanism detects the identical surface, \(A\), \(B\), and \(C\) always pass the shape contours of the identical surfaces. Although the characteristic measurements at the same position are not exactly the same, but the overall shape of the waveform trend curve is constant, the combined projection curves on the identical measured surfaces are close to coincidence. This shows that the detection mechanism has good repeatability and stability, and the time-space conversion algorithm successfully converts the waveforms of time-deviation into the position-deviation. Figure 19: Amplitude frequency characteristics of measurements.