**Time–Frequency Extraction Model Based on Variational Mode Decomposition and Hilbert–Huang Transform for Offshore Oil Platforms Using MIMU Data**

**Jian Wang 1,2,\*, Xu Liu 1,2, Wen Li 1,2, Fei Liu 2 and Craig Hancock 3**


**Abstract:** Time–frequency extraction is a key issue to understand structural symmetry of dynamic responses of offshore oil platforms for early warning during drilling operations. Current popular methods for signal characteristics extraction can only obtain the attributes with a single dimension or poor precision. To solve this, a combined Hilbert–Huang transform (HHT) and variational mode decomposition (VMD) method is proposed to extract multidimensional dynamic response characteristics of time, frequency, and energy of offshore oil platforms. Based on the extracted time– frequency–energy information, the frequency-domain integration approach (FDIA) can be applied to calculate the displacement using accelerometer in the micro inertial measurement unit (MIMU). A complementary filtering algorithm was designed to measure the torsion angle of platforms using six degrees of freedom data from the MIMU to obtain the torsion angle information. The performance of the proposed method was validated using a series of simulation shaking-table tests and a field test conducted on an offshore oil platform at Dongying City, Shandong Province, China. During the field test, seven out of eight collisions were detected in the frequency range 5 Hz to 12 Hz. The intensity of the fifth collision was the highest, and the maximum displacement obtained by the accelerometer was 6 mm. In addition, the results show a correlation between the axes of the accelerometer and gyroscope, and their combination can measure a torsion angle up to 1.1◦.

**Keywords:** time–frequency extraction; micro inertial measurement unit (MIMU); variational mode decomposition (VMD); Hilbert–Huang transform (HHT); frequency-domain integration approach (FDIA); torsion angle calculation; offshore oil platform
