Error analysis of IMU pipeline bending strain detection based on full-scale test

The strain identification technology based on inertial mapping unit (IMU) internal detectors is currently a widely used internal detection technology for identifying pipeline bending strain both domestically and internationally. It calculates the bending strain of the entire pipeline through the detected centerline coordinate data. However, there are issues such as abnormal vibration and noise during the actual operation of the inertial navigation internal detector, as well as trajectory deviation during the detector’s operation. This issue leads to a certain deviation between the strain detected by IMU and the actual strain of the pipeline. This article utilizes a self-designed full size pipeline bending strain loading device to conduct full size pipeline bending strain tensile tests. Compare the internal detection data obtained from the experiment with the actual bending strain data of the pipeline and conduct error analysis. The research conclusion indicates that as the bending strain increases, the error between the IMU detection strain and the actual strain of the pipeline increases. When there is vibration noise, the maximum error is 0.077% for 0.33% true strain, and the maximum error rate for larger strain segments is 27.1%. The comparison between noise reduction detection data and true strain shows that when the true strain is 0.12%, 0.21%, and 0.33%, the average error is 0.0285%, 0.0315%, and 0.0555%, respectively. The research conclusion provides technical support and guidance for obtaining true strain of pipelines based on IMU internal detection in the future.


Introduction
Pipeline is currently the most efficient and common tool for transporting oil and natural gas [1] , and is an important part of ensuring energy stability in China.Oil and gas pipelines pass through complex areas, and when settlement or surrounding soil collapse occurs, rock pressure and other factors can cause local deformation and displacement of the pipeline, resulting in bending strain [2] [3] .When the strain exceeds the limit of the pipeline material, defects such as cracks and depressions will occur.In severe cases, it can lead to pipeline failure and fracture [4] resulting in pipeline leakage, causing casualties [5] and economic losses.
At present, inertial navigation technology is gradually maturing for internal detection of pipeline bending strain.IMU measures the three-dimensional coordinates of the pipeline and obtains the centerline of the pipeline [6] , thereby obtaining the strain situation at each position of the pipeline.China Petroleum Pipeline Company [7] independently developed a high-precision IMU inertial navigation surveying and mapping system to calculate pipeline bending strain.However, due to the complexity of the IMU inertial navigation system during the detection process, there are certain differences between the results and the actual results [8] .Li Rui et al. [9] used the IMU inertial navigation system for pipeline detection in permafrost regions, proposed a method based on IMU data for bending strain and displacement, and corrected the problem of displacement divergence.Feng Qingshan et al. [10] used GPS and mileage wheel data to correct the pipeline position and improve detection accuracy.
In summary, current domestic and foreign researchers have revised and optimized the IMU detection data [11][12] , but have not conducted precise error analysis between the IMU detection data and the true strain of the pipeline.The relationship between the measured value of pipeline bending strain and the actual value cannot be determined.To this end, tensile tests were conducted on IMU internal detectors under different bending strain loading conditions for full-scale pipelines, and the error between the IMU internal detection data and the true strain data was ultimately obtained.

Bending strain calculation based on center line coordinates
The bending curvature of the pipeline can be calculated from the projection of the centerline of the pipeline on the horizontal plane and the projection on the vertical plane, respectively.Its total curvature, horizontal component curvature and vertical component curvature [13] have the following relationship: In the formula˖ k is the total curvature of the pipeline; kv is the curvature of the pipeline in the horizontal plane; kh is the curvature of the vertical plane of the pipe.
Let the equation of the pipeline center line curve be˖ y=f (x), and f (x) has a second derivative.The curvature kv and kh of this point are calculated according to the first derivative y' horizontal, y' vertical and the second derivative y " , y " vertical, respectively.The specific calculation method is as follows: kv and kh are calculated, and the total strain k is calculated by the formula, and then the bending strain of the pipeline is calculated by the following formula.

D k H (3)
In the formula˖ D is the outer diameter of the pipeline, mm; İ is the bending strain of the pipe, %.

Bending strain solution based on IMU attitude data
Based on the above analytical calculation method for pipeline bending strain, it can be seen that within the elastic deformation range, the bending strain of the pipeline is directly proportional to the change in curvature.Therefore, when calculating pipeline bending strain, the curvature of the pipeline should be calculated first.Among them, the pitch change of the internal detector represents the change in inclination angle of the pipeline relative to the horizontal plane in a fixed observation pipeline, and the heading represents the angle between the direction along the pipeline and the due north direction [14] , as follows: Where: kv is the curvature of the pipeline in the horizontal plane; kh is the curvature of the vertical plane of the pipeline; ĳ is the pitch Angle of the inertial measurement device along the vertical tangent direction of the pipe, (°); ǻs is the length of the fixed pipe section, m; ǻĮ is the angular change of the inertial measurement device along the horizontal tangent direction of the pipe, (°).
The curvature kv of the horizontal plane of the pipeline and the curvature kh of the vertical plane of the pipeline are obtained and the total strain k is obtained by equation (1).The bending strain İ of the pipeline can be obtained by bringing it into equation (3).The bending strain of the pipeline is related to the pitch Angle of the inertial measurement device along the vertical tangent direction of the pipeline and the Angle along the horizontal tangent direction of the pipeline as follows:

Test scheme and device
The IMU full size pipeline pulling test was carried out using 508×10mm full size pipeline, full size pipeline bending strain loading device and IMU internal inertial navigation detector.The full-size pipe bending strain loading device was designed and used to load the load to the preset working condition.
The IMU inertial navigation detection data collected by the IMU detector was obtained by the traction device, and then the error analysis between the full-size pipe IMU test detection data and the real pipe strain data was carried out.The length of the stretch test pipe is 100m, and the length of the bending deformation section pipe is 20m.The bending strain loading device of the pipeline comprises the structure of support plate, end plate, column and so on.The output load of a single hydraulic jack of 508mm full-size pipeline bending strain loading device is 500kN.During the bending test loading, two hydraulic jacks above starting can realize vertical upward bending of the pipeline.The overall length of the device is 3m, and the load of the reaction frame is 2000kN.The main technical parameters of the device are shown in table 1, and the assembly drawing of the full-scale axial loading device is shown in Figure 1.
A total of 4 groups of different bending strain conditions of the pipeline were set up in the test.First, the basic working conditions were tested when the pipeline was in a straight line.The design strains of the pipeline strain section from the second to the fourth times were 0.1%, 0.2% and 0.3%, respectively.Considering the errors of the actual field test process and device loading, the actual offset of the field pipeline was determined as the basis for the comparison between the strain detected by IMU and the true strain.The actual offset of the pipeline in each group of field test conditions was 124mm and 180mm.The design bending strain and actual offset under different working conditions are shown in table 2

Test result
For each group of strain conditions, the drawing speed of 1m/s is pulled twice.The bending strain of the pipeline was calculated using the attitude information measured by IMU, and the data collected by the IMU in-inertial navigation detector at the same drawing speed and bending strain of the pipeline were analyzed.When using IMU to calculate the bending strain, the position coordinates of the center line of the pipeline are calculated by using the combined inertial navigation algorithm.After obtaining the exact coordinates of the whole line of the pipeline and the attitude information such as pitch Angle and azimuth Angle, the bending strain is further calculated.Select condition one as the basic condition.The aligned data is denoised using wavelet to reduce the interference of fluctuating sawtooth noise in the detection results.Based on the results of the tensile test, it can be seen that the bending strain detected by the inertial navigation detector is basically the same under the same working condition of the strain deformation section.The data before and after noise reduction in IMU for the two groups of IMU pull test under condition 2 are shown in Figure 2-3.The strain results detected in IMU under different test conditions are shown in table 3.

True strain calculation
According to the bending strain calculation method based on center line coordinates, the true strain value of pipeline under different test offset conditions is calculated.The center line data of IMU pipeline without interference and error under different working conditions and the true bending strain of the pipeline under different working conditions are shown in 4-5.The true strain data of the pipeline under different pipeline migration are 0.12%, 0.21% and 0.33% respectively.

Inclusion noise error
Error calculation was carried out based on test data under different working conditions and pipeline true strain data, and error results were shown in Figure 6.The error calculation results show that the error increases gradually with the increase of strain.When the true strain is 0.33%, the maximum error reaches 0.0772%.The error rate of IMU detection data and true strain data was calculated (Figure 6-7).It was found that the error rate of the section with large strain, that is, the middle deformation area, was higher, reaching 27.1%, nearly twice that of the two sides.In this paper, the mapping research is carried out for the large strain section, that is, the 5m-15m part of the deformation section of the whole pipeline.

Error after noise reduction
The attitude data obtained by the detector in IMU was calculated for pipe bending strain.Working condition 1 was selected as the basic working condition, interference of relevant objective factors was excluded, and wavelet noise reduction algorithm was selected for data noise reduction, and the data after noise reduction was obtained.The errors of noise reduction data and true strain data after tests under different working conditions are calculated, and the error results are shown in table 4. When the true strain is 0.33%, the average error reaches 0.0555%.It can be seen from the calculation results that after the abnormal noise such as vibration is removed, there is still a certain error between the strain detected by the detector in IMU and the true bending strain of the pipeline due to the deviation of the inner detector's running track line and other reasons.

Conclusion
In this paper, a full-size pipe bending strain loading device is designed and a 508mm diameter pipe is used to carry out the pull test of IMU in-inertial navigation detector.Four groups of operating conditions were carried out, with a total of eight pulling tests twice in each group.Through the error analysis of the strain detected by the detector in IMU and the true strain value of the pipeline, it can be seen that the detection error of the detector in IMU comes from two factors, such as abnormal vibration noise and the track deviation caused by the detector size.The research conclusions are as follows: (1) In this paper, the full-scale pipeline detector pull test is carried out respectively.When the actual pipeline offset of each group of working conditions is 68mm, 124mm and 180mm in the field test, the detected strain is 0.091% and 0.092%; 0.181%, 0.183%; 0.276%, 0.273%.
(2) As the bending strain of the pipeline gradually increases, the error between the noisy data detected by the detector in IMU and the real data gradually increases.When the true strain is 0.33%, the error reaches 0.077%, and the error rate between the actual strain and the true strain is detected by IMU.
(3) As the bending strain of the pipeline gradually increases, the error caused by the trajectory deviation of the detector in the IMU gradually increases.When the true strain is 0.12%, 0.21% and 0.33%, the average error is 0.0285%, 0.0315% and 0.0555%, respectively.

Figure 1 .
Figure 1.Full size axial loading device assembly drawing.

Figure 2 .
Figure 2. Data before and after noise reduction of the first pull IMU detection in the second working condition.

Figure 3 .
Figure 3. Data before and after noise reduction of the second pull IMU detection in the second working condition.

Figure 4 .
Figure 4. IMU reconstructed model to obtain pipeline center line data with different working conditions.

Figure 5 .
Figure 5. Bending strain of pipeline under different working conditions.

Figure 6 .
Figure 6.The detector in IMU detects strain data and true.

Figure 7 .
Figure 7.The detector in the IMU detects the strain data and the true strain error rate.

Table 1 .
Full size loading device main technical parameters table.

Table 2 .
. Pull test different preset conditions and actual offset.

Table 3 .
Strain measured in IMU under different test conditions.

Table 4 .
Detection of noise reduction data and true strain error by IMU under different test conditions.