Time–Frequency Extraction Model Based on Variational Mode Decomposition and Hilbert–Huang Transform for Offshore Oil Platforms Using MIMU Data
Abstract
:1. Introduction
2. A VMD–HHT Approach for Extracting Time–Frequency–Energy Characteristics of Dynamic Responses
2.1. Hilbert–Huang Transform
2.2. Variational Mode Decomposition
2.3. VMD–HHT Model
3. Dynamic Responses Monitored by MIMU
3.1. Accelerometer-Derived Displacement Reconstruction
3.2. Gyro-Derived Torsion Reconstruction
- (1)
- The accelerometer is normalized to a single vector .
- (2)
- The acceleration data in the geographical coordinate system are converted to the carrier coordinate system, and the estimation in the carrier coordinate system is given by
- (3)
- The deviation between the acceleration estimation and the measurements by accelerometer is the error item between the integrated torsion angle of the gyroscope and the torsion angle measured by the accelerometer. The value can be expressed by the cross product.
- (4)
- The corrected torsion angle can be obtained based on a PI controller using the results from the previous step,
- (5)
- The quaternion differential equation can be solved by using the corrected torsion angle (See Formula (8)), and the quaternion can be updated to calculate the theoretical estimation of the accelerometer (transfer to Equation (2)).
3.3. The Schematic to Monitor Dynamic Responses Based on VMD–HHT Characteristic Extraction Model
4. Simulation Shaking-Table Tests
4.1. Simulation Shaking Table
4.2. Data Collection
4.3. Comparison of PSD, HHT, and VMD–HHT
4.4. Reconstruction of Dynamic Displacement Using FDIA Based on the VMD–HHT Model and GPS
5. Trial Analysis of CB4A Offshore Oil Platform
5.1. Equipment for Monitoring Dynamic Responses
5.2. Data Acquisition
5.3. Dynamic Responses Time–Frequency Extraction
5.4. Reconstruction of Dynamic Displacement Based on VMD–HHT Using Accelerometer
5.5. Evaluation of the Torsion Angle Based on Mahony Complementary Filter Using MIMU
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Equipment | Performance | |
---|---|---|
GNSS | Signal Tracking | BDS: B1/B2; GPS:L1/L2 GLONASS: L1/L2; GALILEO:E1/E5b |
RTK (RMS) | Horizontal: 8 mm + 1 ppm Vertical: 15 mm + 1 ppm | |
Updating Frequency | 5 Hz | |
Accelerometer | Dynamic Range | |
Bias Stability | ||
Noise Density | ||
Updating Frequency | 100 Hz |
Index Item | Gyroscope | Accelerom |
---|---|---|
Standard full range | ±450 °/s | ±20 g |
Initial bias error (one year) | 0.2 °/s | 5 mg |
In-run bias stability | 10 °/h | 15 µg |
Bandwidth (−3 dB) | 415 Hz | 375 Hz |
Noise density | 0.01 °/s/√Hz | 60 µg/√Hz |
g-sensitivity (calibrated) | 0.003 °/s/g | N/A |
Nonorthogonality | 0.05 deg | 0.05 deg |
Nonlinearity | 0.01% | 0.1% |
Tracking Signal | BDS B1/B2/B3 |
GPS L1/L2/L5 | |
GLONASS /L1/L2 | |
GALILEO E1/E5a/E5b | |
QZSS L1/L5 | |
SBAS L1 | |
Single(RMS) | Plane: 1.5 m; Altitude: 3 m |
DGPS(RMS) | Plane: 0.4 m; Altitude: 0.8 m |
RTK(RMS) | Plane: 8 mm + 1 ppm Altitude: 15 mm + 1 ppm |
Sampling rate | 5 Hz |
Collision | First | Second | Third | Fourth | Fifth | Sixth | Seventh | Eighth |
---|---|---|---|---|---|---|---|---|
Time | 15:34:37 | 15:35:28 | 15:36:00 | 15:36:58 | 15:37:30 | 15:37:51 | 15:38:17 | 15:38:46 |
GPS Period | 200094.6 | 200145.6 | 200177.6 | 200235.6 | 200267.6 | 200290.8 | 200314.6 | 200343.8 |
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Wang, J.; Liu, X.; Li, W.; Liu, F.; Hancock, C. Time–Frequency Extraction Model Based on Variational Mode Decomposition and Hilbert–Huang Transform for Offshore Oil Platforms Using MIMU Data. Symmetry 2021, 13, 1443. https://doi.org/10.3390/sym13081443
Wang J, Liu X, Li W, Liu F, Hancock C. Time–Frequency Extraction Model Based on Variational Mode Decomposition and Hilbert–Huang Transform for Offshore Oil Platforms Using MIMU Data. Symmetry. 2021; 13(8):1443. https://doi.org/10.3390/sym13081443
Chicago/Turabian StyleWang, Jian, Xu Liu, Wen Li, Fei Liu, and Craig Hancock. 2021. "Time–Frequency Extraction Model Based on Variational Mode Decomposition and Hilbert–Huang Transform for Offshore Oil Platforms Using MIMU Data" Symmetry 13, no. 8: 1443. https://doi.org/10.3390/sym13081443
APA StyleWang, J., Liu, X., Li, W., Liu, F., & Hancock, C. (2021). Time–Frequency Extraction Model Based on Variational Mode Decomposition and Hilbert–Huang Transform for Offshore Oil Platforms Using MIMU Data. Symmetry, 13(8), 1443. https://doi.org/10.3390/sym13081443