3.2.3. Experimental result and discussion

Due to the rolling motion of PIG, the X-axis accelerometer in IMU is used for the data analysis, which is shown in Figure 4. The blue curve shows the raw X-axis accelerometer measurement

Figure 4. Raw accelerometer data (blue curve), wavelet denoised data (yellow curve), and FOS denoised data (red curve).

data that is contaminated by high Gaussian white noise (GWN). Hence, it is necessary to conduct data denoising before the PJ detection. The "db" family of wavelet was certificated to be a useful selection for the denoising of MEMS inertial sensors data [19]. Here, "db8" wavelet with four level of decomposition (LOD) is used for denoising on the accelerometer measurement data, and the result is demonstrated by yellow curve in Figure 4. In addition, FOS has shown superior performance in the denoising of low-cost MEMS inertial sensors in some applications [20], and the FOS denoised accelerometer data are represented by red curve in Figure 4. Both methods could provide robust MEMS accelerometer data denoising by reducing the random GWN level and maintaining the dynamic characteristic of the PIG. Moreover, FOS has shown significant improvement in the elimination of low-frequency noises, which could not be eliminated by wavelet denoising technology. Therefore, FOS is more suitable for low-cost MEMS inertial sensors for PJ detection application.

The upper panel in Figure 5 reveals the raw measurement data of X-axis accelerometer. The jumps or spikes are the singular signals that expected to be identified accurately to provide azimuth and pitch updates in SPS. The lower panel of Figure 5 also displays the amplitude that is calculated by FOS after the raw measurement data of accelerometer are denoised by FOS. The amplitude and the epochs indicate the singular signals of the raw measurement data of accelerometer.

Figure 5. Raw X-axis accelerometer data (upper panel) and FOS amplitude (lower panel).

Figure 6 displays the PJ identification result by FOS on denoised measurement data of X-axis accelerometer. Specifically, the PIG passing through a PJ part is represented by the spike intervals in the red curve. These spikes are calculated by the preset threshold on the FOS amplitude. That is to say, when the FOS amplitude is bigger than the threshold, the intervals are detected as the PJs, while the other intervals are detected as SPSs. Furthermore, a magnified view of the second and third PJs in the Figure 6 is also demonstrated to make the PJ detection result to be more intuitive. Specifically, a pitch angle variation of the PIG is shown by the second PJ, while an azimuth angle variation of the PIG is revealed by the third PJ. Therefore, the PJ could be detected correctly by FOS even with the raw accelerometer data in GWN-contaminated environment. After that, the accurate PJ detection results can be used for azimuth and pitch updates at the SPS in SINS.

The Figures 4–6 shows the FOS-based PJ detection method on accelerometer measurement data for PIG navigation. The accelerometer measurement data are logged by using 2103HT table to simulate the azimuth and pitch changes of PIG in the pipeline. Moreover, the detection capability and precision of FOS are also verified with the FOS technology on accelerometer measurement data. The final results demonstrated that the FOS could detect the PJ correctly even when the accelerometer data contaminated with high GWN. Therefore, the proposed FOS can detect the PJ by measurement of the low-cost inertial sensors even in noised pipeline operational environments.

Figure 6. PJ recognition result by FOS.
