1. Why Pipeline Positioning Is Hard: GNSS-Denied Dead Reckoning and a Diverging Azimuth
A satellite navigation system can, in most application scenarios, provide a carrier with real-time position and velocity of a certain accuracy. But for a pipeline inspection gauge (PIG) moving inside a pipeline, the satellite signal is affected by soil and the pipe wall, so it cannot provide the SINS used for in-pipe positioning with continuous, real-time position and velocity correction information.
At present, in order to reduce the error of a MEMS IMU SINS-aided pipeline inspection and positioning system, on one hand odometers mounted around the tail of the PIG measure its axial velocity, and at the same time, combined with the non-holonomic constraints of the PIG inside the pipeline, the lateral and vertical velocities of the PIG are constrained to zero, so the PIG pipeline inspection and positioning system has a continuous 3D velocity measurement update inside the pipeline. On the other hand, before pipeline inspection, magnetic signal transmitters are installed at AGMs spaced at a certain interval along the pipeline, with their positions accurately provided by DGPS. When the PIG passes the AGM where a magnetic signal transmitter is located, the signal receiver on the PIG records the corresponding time and position information, providing the MEMS SINS-aided pipeline inspection and positioning system with a discrete 3D position update. However, the azimuth error of the MEMS SINS-aided pipeline inspection and positioning system has a diverging character, while the PIG inspection and positioning system has no measurement update value at all; the azimuth error of the MEMS SINS causes the north and east components of the PIG’s horizontal acceleration measurement to carry cumulative error during long-duration pipeline inspection and positioning, which in turn produces a positioning error in the PIG pipeline inspection and positioning system that accumulates over time. Providing an azimuth measurement update for the MEMS SINS-aided pipeline inspection and positioning system is therefore an important way to guarantee the accuracy of the PIG inspection and positioning system.
Considering the diameter of the pipeline to be inspected and the cost, a navigation-grade or tactical-grade IMU can no longer meet the inspection and positioning task requirements of the large number of small-diameter pipelines (such as urban underground water pipes, liquefied natural gas pipes, and water-heating and heating supply pipes). A low-cost, small-volume MEMS IMU has become the inertial sensor of choice to replace navigation-grade or tactical-grade IMUs. However, MEMS inertial sensors are much lower than tactical-grade or navigation-grade IMUs in their accuracy specifications, which greatly degrades the accuracy specification of a MEMS-inertial-aided pipeline inspection and positioning system over long-duration pipeline inspection and positioning tasks.
For ordinary marine or land inertial navigation systems, geomagnetic azimuth sensors and visual images have already been successfully applied to correct the azimuth divergence error of the SINS. But for an inertial-aided pipeline inspection and positioning system used for in-pipe inspection, the material of the pipeline laid underground and the complex surrounding environment greatly reduce the measurement accuracy of these auxiliary azimuth sensors. These existing azimuth auxiliary sensors cannot be used to correct the azimuth measurement error of the MEMS SINS inside the pipeline.
2. Three Kinds of Aiding Measurements: Position, Velocity and Attitude
2.1 Continuous Velocity Update: Odometer and Non-Holonomic Constraints
When performing inspection and positioning inside a pipeline, in addition to correcting the PIG’s axial velocity continuously, the non-holonomic constraints that exist in the PIG’s longitudinal and lateral directions can also be used for correction. Because the PIG is designed as a cylinder or torpedo shape according to the characteristics of the pipeline, it has only axial velocity when moving inside the pipeline, and its longitudinal and lateral velocities are zero in the PIG coordinate system. This characteristic can therefore be used to provide zero-velocity update (ZUPT) information for the pipeline-inspection SINS in those two directions. Together with the axial velocity information the odometer provides for the PIG, this achieves a continuous 3D correction of the SINS velocity inside the pipeline.
2.2 Attitude Correction: Pitch and Roll Are Observable, Azimuth Is Not
Inside a pipeline, in addition to the continuous 3D correction of the velocity and the discrete 3D correction of the position of the pipeline-measurement MEMS SINS, the attitude angles of the SINS (pitch, roll and azimuth) also need to be corrected. In navigation applications near the Earth’s surface, the SINS pitch error and roll error have a strongly coupled relationship with the system’s north velocity error and east velocity error respectively. That is: when the north velocity and east velocity of the PIG pipeline inertial positioning system are observable, the system’s pitch and roll are also observable, meaning that the pitch and roll errors do not accumulate and diverge over time. In an inertial-aided pipeline inspection and positioning system, when the PIG is measuring inside the pipeline, the non-holonomic constraints make the measured velocities in its longitudinal and lateral directions zero, and the axial velocity correction information from the odometer velocity sensor provides the PIG with observable north and east velocity measurements. However, there is no strongly coupled relationship between the azimuth and the velocity of the PIG pipeline inertial positioning system, so a new measurement update for the system’s azimuth is usually required to suppress the divergence over time that characterizes azimuth error accumulation.
3. Extracting Azimuth from the Straight Pipe: Pipeline Junction Detection
A pipeline junction is an important device for connecting various straight pipeline sections and for pipeline branch laying. For the motion of a PIG inside a pipeline, a pipeline junction not only guides the PIG toward a different pipeline branch, but also changes the attitude angles of the inertial-aided pipeline inspection and positioning system running inside the pipeline, mainly in azimuth and pitch. Therefore, in a single straight pipeline section the azimuth and pitch of the inspection device are unchanging, whereas the roll is irregularly varying, affected by the pressure difference on both sides of the PIG and the resistance of the medium transported inside the pipeline.
3.1 Straight Sections and Junction Sections Have Completely Different Spectra
When a strapdown-IMU-based pipeline inspection and positioning system is applied to actual pipeline inspection, the measurement data of the inertial measurement sensors exhibits different spectral characteristics in different pipeline stages, that is, in the two main parts: the straight pipeline and the pipeline junction. Under normal circumstances, the inertial measurement data in a straight pipeline mainly contains the low-frequency spectrum of the PIG’s motion inside the pipeline and the low-frequency noise spectrum of the inertial sensors, which on the whole is a very steady process. In the pipeline junction section, however, the inertial measurement data contains not only the low-frequency spectrum of the inspection device’s motion and the low-frequency noise spectrum of the sensors, but also the abrupt spectral components from the PIG suddenly turning or touching the junction at this stage. The inertial sensor measurement data of the straight pipeline section is therefore clearly different from that of the pipeline junction section.
When building an IMU of the same type, an accelerometer is usually better than a gyroscope in both the stability and the accuracy of its measurement data. Similarly, in comparable applications such as bridge monitoring, pipeline deformation measurement and structural health monitoring, the measurement data of accelerometers is generally used and analyzed rather than that of gyroscopes. Pipeline junction detection therefore likewise uses accelerometer measurement data for processing and analysis.
3.2 Two Detection Algorithms: Complex Continuous Wavelet Transform and Fast Orthogonal Search
Both the denoised accelerometer measurement data and the raw accelerometer measurement data can identify the pipeline junction sections by means of a complex Gaussian continuous wavelet transform. The pipeline junction results identified from the two signals are then the same, meaning that when the complex continuous wavelet transform method is used for pipeline junction detection, the result is independent of the measurement accuracy of the inertial measurement sensor used.
FOS can correctly identify the pipeline junction sections and the straight pipeline sections from the raw pipeline measurement signals of a low-cost MEMS accelerometer. However, when FOS is applied to pipeline junction signal detection, the algorithm suffers from a long computation time and a large memory requirement.
3.3 How to Use the Detection Result: One Fixed Azimuth and Pitch per Straight Section
In general, when the PIG moves inside the pipeline and there is no blockage, the time the PIG takes to pass through a pipeline junction is within a few seconds or even shorter, and the azimuth error and pitch error produced in that time are within an acceptable range. The azimuth and pitch that the PIG inertial positioning system first computes with the SINS for each straight pipeline section can therefore be taken as the azimuth and pitch measurement updates for the corresponding straight pipeline section, correcting the azimuth error and pitch error of the SINS over the whole straight pipeline section.
In this way, the inertial sensor measurement data is not only used for the SINS solution but is analyzed and reused to detect the pipeline junctions and provide azimuth and pitch correction information for the SINS in the straight pipeline stages. The ultimate purpose is to suppress the divergence of the SINS azimuth error and improve the output accuracy of the inertial-aided pipeline inspection and positioning system, and this method carries no additional system hardware cost whatsoever.
4. A Welcome Surprise: Roll Motion and IMU Selection
A PIG is a torpedo-like pipeline robot designed according to the internal diameter of the pipeline to be inspected. Given the PIG’s shape, in addition to the forward linear motion driven by the pressure difference across its two ends, an irregular pressure difference also drives a tangential force on it, so that it additionally has a rotational motion about its forward axis. The whole PIG therefore gradually completes the inspection of the entire pipeline by moving through it in a helical motion.
4.1 The Selection Conclusion: The Axis Parallel to the PIG’s Own Axis Needs the Best Specs
As for the gyroscope bias error, analysis of the inertial sensor error model under PIG roll rotation shows that this irregular roll rotation of the PIG can effectively modulate the gyroscope bias errors of the X axis and the Z axis, making them exhibit error characteristics in the form of sinusoidal oscillation. For the Y-axis gyroscope bias error, however, PIG roll rotation has no effect at all. Therefore, when selecting a gyroscope for pipeline inspection, and in order to achieve the optimal accuracy combination, the Y-axis gyroscope bias error should be relatively smaller than the X-axis and Z-axis gyroscope bias errors, that is, the Y-axis gyroscope accuracy must be higher than that of the X-axis and Z-axis gyroscopes.
As for the Y-axis accelerometer bias error, PIG roll rotation has no effect on it at all, and the PIG positioning error it causes still propagates according to the original error characteristics, so the Y-axis accelerometer bias error selected should be relatively smaller than the X-axis and Z-axis accelerometer bias errors.
In short, when selecting gyroscopes and accelerometers dedicated to pipeline inspection, the performance specifications of the inertial sensor that coincides with or is parallel to the PIG axis should be better than those of the other two directions perpendicular to it. The Y-axis inertial sensor bias error and scale factor error should both be as small as possible, so as to reduce the positioning error of the pipeline inertial positioning system of the whole PIG during pipeline inspection, and to achieve the best result with the optimal cost input.
5. Bringing the Measurements Together: EKF and Post-Processing Smoothing
The Kalman filter is a classic estimation tool in the fields of control, navigation and multi-sensor fusion, and this filter is hailed as the most reliable estimator in modern digital technology. Fixed-point and fixed-lag smoothers are near-real-time estimation methods, whereas the fixed-interval smoother can only be implemented in post-processing applications. Because measurement is a typical post-processing task that requires computing the information of all measurement points, the fixed-interval smoother has already found wide application in fields such as pipeline inspection, geodesy and subsea surveying and mapping.
6. Measured Results: How Much Did the Error Drop with the Corrections
During the initial period of PIG pipeline inspection, the azimuth error, horizontal position error and altitude error are all within a very small range, meeting the accuracy requirements that pipeline inspection imposes on these specifications. However, as the distance the PIG travels inside the pipeline grows longer, all the error specifications of the SINS-aided pipeline inspection and positioning system show a diverging trend and gradually increase. In a 90-minute pipeline inspection task, the azimuth error of the SINS-aided pipeline inspection and positioning system reached a maximum of 8.770º, and the maximum horizontal position error and altitude error were 252,844 metres and 342.054 metres respectively. The root-mean-square errors of the azimuth error, horizontal position error and altitude error measurements were 3.322º, 127,362 metres and 162.42 metres respectively, far exceeding the accuracy specification requirements for pipeline inspection and positioning (which generally require the RMS error of the azimuth measurement error of a pipeline inspection and positioning system to be within 0.5º, and the RMS error of the horizontal or altitude position error to be at the metre level).
After the pipeline junction detection provides azimuth and pitch error corrections, the maximum azimuth error of the PIG inspection and positioning system dropped from 2.175° to 0.725°, an improvement of 66.67%; the maximum horizontal position error of the system dropped from 121.10 metres to 49.28 metres, an improvement of 59.31%; and the maximum altitude error of the system dropped from 5.405 metres to 2.350 metres, an improvement of 56.52%.
After RTSS is applied, the overall positioning error of the system is reduced, and the mean error of the PIG inspection and positioning system at 8 reference points dropped from 10.86 metres to 3.73 metres, an improvement in positioning accuracy of 65.65%. After the azimuth and pitch error corrections that the pipeline junction detection results provide in the straight pipeline are added, the mean position error at the 8 marker points drops further, from 3.73 metres to 1.70 metres. As the pipeline junction detection results and the offline smoothing technique RTSS are added, the accuracy of the PIG inspection and positioning system becomes higher and higher, essentially meeting the requirements on pipeline defect positioning accuracy in pipeline inspection and maintenance.
7. Summary: How Far Down Does This System Push the Error
Aiming at the present situation in which accurate positioning of defect inspection in small-diameter pipelines is difficult, an inertial-aided pipeline inspection and positioning system based on a MEMS IMU was designed and implemented, using SINS/AGM/odometer/pipeline junction. The experimental results show that a pipeline inspection and positioning system using a low-accuracy MEMS IMU, once the pipeline junction detection results provide azimuth and pitch error corrections for the system in the straight pipeline, can improve the positioning accuracy of the entire system by up to 54.33%, and can effectively reduce the inspection time and cost of raising the overall system accuracy by using a large number of AGMs, making long-distance inspection and positioning of small-diameter pipelines possible.
