**6. Conclusions**

In this paper, a model combined by HHT and VMD is proposed to extract multidimensional dynamic responses characteristics of time, frequency, and energy of offshore oil platforms. A series of shaking-table tests and field tests in an offshore oil platform in Shengli Oilfield at Dongying City were performed using a single GPS receiver and a single accelerometer. By comparing analysis results between PSD and VMD–HHT, we found that dynamic response characteristics of ship collisions cannot be extracted entirely relying only on PSD. In contrast, VMD–HHT could effectively extract the characteristics of time, frequency, and energy simultaneously. Based on the analysis results of VMD–HHT, the dynamic displacements were reconstructed using the accelerometer in the MIMU, and the maximum displacement calculated by VMD–HHT based FDIA was 6 mm. Moreover, acceleration and angular rate obtained by MIMU had a high similarity and clear axial correlation, and such integration could also be used to calculate the torsion angle of offshore oil platforms; the maximum torsion angle is up to 1.1◦.

This novel proposed method could aid in the avoidance of collisions of offshore oil platforms and be further applied in oil exploitation and platform maintenance and monitoring. However, VMD–HHT model will not be able to effectively extract feature information when the noise frequency is close to the frequency of dynamic response events.

**Author Contributions:** Conceptualization, J.W. and X.L.; methodology, J.W.; validation, J.W., X.L. and W.L.; investigation, J.W.; resources, J.W. and C.H.; data curation, F.L.; writing—original draft preparation, X.L.; writing—review and editing, J.W., X.L., W.L., F.L. and C.H.; funding acquisition, J.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by The National Natural Science Foundation of China, Grant Number 41874029, and The National Key Research and Development Program of China, Grant Number 2020YFD1100201.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
