# Dynamic Deformation Monitoring of Offshore Oil Platforms with Integrated GNSS and Accelerometer

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. CEEMD–Chebyshev Hybrid Filtering

#### 2.1.1. Complementary Ensemble Empirical Mode Decomposition Algorithms

- (1)
- Introduce n sets of complementary and independently and identically distributed white noise N(t) to the original signal F(t), thus obtaining two new sequences A1, A2 with superimposed white noise, the total number of sequences being 2n.

- (2)
- Decompose the obtained sequences A1, and A2 respectively to obtain m IMF components, and denote c
_{ij}(t) as the jth IMF obtained from the ith decomposition, where i = 1,…, n; j = 1,…, m. - (3)
- The value of the jth IMF is obtained by averaging c
_{ij}for each set of IMF components as follows:

- (4)
- The original sequence F(t) eventually decomposes into:$$F\left(t\right)={\sum}_{j=1}^{m}IM{F}_{j}\left(t\right)+r\left(t\right)$$

#### 2.1.2. Chebyshev Filtering

_{0}is the desired cutoff frequency, ε denotes the passband ripple size and is a positive number less than 1, and$\text{}\frac{\omega}{{\omega}_{0}}$is the passband width at a certain attenuation decibel of the filter.

#### 2.2. Frequency Domain Integration

#### 2.3. Overview of Offshore Oil Platforms

## 3. Results and Discussions

#### 3.1. Overall Displacement Reconfiguration Process

#### 3.2. Data Processing

#### 3.2.1. Introduction to the Raw Data

#### 3.2.2. Processing and Analysis of GNSS Data

#### 3.2.3. Processing and Analysis of Acceleration Data

#### 3.2.4. Overall Displacement Reconfiguration

## 4. Conclusions

- (1)
- Based on the selection principles of the t-test and correlation coefficients, the CEEMD–Chebyshev hybrid filter was capable of removing the high-frequency component of the GNSS signal and reducing the noisy part of the low-frequency component, achieving effective extraction of the low-frequency displacement. The maximum displacement amplitude was reduced from 26.79 to 21.22 mm, and the correlation after denoising was 0.8860, with a high degree of correlation.
- (2)
- The integrated displacement of the accelerometer coincided with the high-frequency displacement monitored by GNSS, and the feasibility study indicated that the accelerometer can monitor the high-frequency vibration information of the platform. In addition, the method of frequency domain integration can avoid the influence of the integration trend term to obtain the partial displacement information of the platform.
- (3)
- The hybrid filter was also suitable for the processing of acceleration data when combined with power spectrum identification to filter the appropriate components to reconstruct the acceleration data and frequency domain integration to obtain the high-frequency dynamic displacement of the platform to millimeter precision.
- (4)
- Integrating low-frequency components from GNSS with high-frequency components from accelerometers yielded the global dynamic displacement. The correlation coefficient with the original GNSS monitoring data was 0.8576, and the signal correlation after denoising and refactoring was greater than 85%, retaining important information components and providing a significant foundation for structural health monitoring of offshore oil platforms. The integrated GNSS and accelerometer monitoring technique has certain practicality and reliability in monitoring the dynamic displacement of offshore oil platforms.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**An hour (GPS time of 36,000–39,600 s) of monitoring acceleration raw data in the north direction.

**Figure 6.**The autocorrelation normalization function of each IMF component in the reconstructed signal.

**Figure 7.**Comparison of the low-frequency displacement amplitude of GNSS data after the first refactoring and the second refactoring.

**Figure 9.**Comparison of GNSS high-frequency displacements with the displacement for integration of the original acceleration.

**Figure 10.**(

**a**) CEEMD decomposition results of acceleration data and (

**b**) the corresponding power spectral density functions for each order of IMF components.

**Figure 11.**High-frequency displacement amplitude of platform vibration after integration of denoising acceleration.

Index | P1 | Index | P1 |
---|---|---|---|

index 1 | 0.6461 | index 8 | 0.0001 |

index 2 | 0.8844 | index 9 | 2.00 × 10^{−6} |

index 3 | 0.8377 | index 10 | 5.94 × 10^{−16} |

index 4 | 0.6491 | index 11 | 0 |

index 5 | 0.9306 | index 12 | 0 |

index 6 | 0.4012 | index 13 | 0 |

index 7 | 0.0006 | index 14 | 0 |

IMF Component | R1 | IMF Component | R1 |
---|---|---|---|

IMF1 | 0.3847 | IMF8 | 0.5049 |

IMF2 | 0.2330 | IMF9 | 0.7003 |

IMF3 | 0.1598 | IMF10 | 0.4714 |

IMF4 | 0.1185 | IMF11 | 0.3383 |

IMF5 | 0.0940 | IMF12 | 0.3470 |

IMF6 | 0.1339 | IMF13 | 0.3446 |

IMF7 | 0.2764 | IMF14 | 0.2485 |

Index | P2 | Index | P2 |
---|---|---|---|

index 1 | 0.8528 | index 10 | 0.0009 |

index 2 | 0.9599 | index 11 | 1.03 × 10^{−77} |

index 3 | 0.8528 | index 12 | 1.29 × 10^{−6} |

index 4 | 0.9364 | index 13 | 1.81 × 10^{−72} |

index 5 | 0.9196 | index 14 | 0.0002 |

index 6 | 0.7604 | index 15 | 3.14 × 10^{−6} |

index 7 | 0.7089 | index 16 | 0 |

index 8 | 0.2409 | index 17 | 0 |

index 9 | 0.0001 | index 18 | 0 |

IMF Component | R2 | IMF Component | R2 |
---|---|---|---|

IMF1 | 0.7790 | IMF10 | 0.0018 |

IMF2 | 0.4726 | IMF11 | 0.0019 |

IMF3 | 0.3157 | IMF12 | 0.0015 |

IMF4 | 0.2461 | IMF13 | 0.0010 |

IMF5 | 0.1775 | IMF14 | 0.0012 |

IMF6 | 0.2029 | IMF15 | 0.0013 |

IMF7 | 0.1639 | IMF16 | 0.0011 |

IMF8 | 0.0844 | IMF17 | 0.0021 |

IMF9 | 0.0032 | IMF18 | 0.0022 |

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**MDPI and ACS Style**

Yang, S.; Xu, C.; Mi, J.; Gu, S.
Dynamic Deformation Monitoring of Offshore Oil Platforms with Integrated GNSS and Accelerometer. *Sustainability* **2022**, *14*, 10521.
https://doi.org/10.3390/su141710521

**AMA Style**

Yang S, Xu C, Mi J, Gu S.
Dynamic Deformation Monitoring of Offshore Oil Platforms with Integrated GNSS and Accelerometer. *Sustainability*. 2022; 14(17):10521.
https://doi.org/10.3390/su141710521

**Chicago/Turabian Style**

Yang, Songliangzi, Changhui Xu, Jinzhong Mi, and Shouzhou Gu.
2022. "Dynamic Deformation Monitoring of Offshore Oil Platforms with Integrated GNSS and Accelerometer" *Sustainability* 14, no. 17: 10521.
https://doi.org/10.3390/su141710521