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Research Papers: Offshore Technology

Utilizing the Ensemble Kalman Filter and Ensemble Kalman Smoother for Combined State and Parameter Estimation of a Three-Dimensional Towed Underwater Cable Model

[+] Author and Article Information
Jan Vidar Grindheim

Geograf AS,
Strandgata 5,
Sandnes NO-4307, Norway;
Faculty of Science and Technology (IMT),
Norwegian University of Life Sciences (NMBU),
P. O. 5003,
Ås NO-1432, Norway;
Laboratório de Ondas e Correntes (LOC),
UFRJ/COPPE,
Rio de Janeiro 21941-450, Brazil
e-mail: jg@geograf.no

Inge Revhaug

Professor
Faculty of Science and Technology (IMT),
Norwegian University of Life Sciences (NMBU),
P. O. 5003,
Ås NO-1432, Norway

Egil Pedersen

Professor
Department of Engineering Science and Safety,
The Arctic University of Norway (UiT),
Hansine Hansens veg 18,
Tromsø NO-9037, Norway

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received July 30, 2015; final manuscript received June 16, 2017; published online August 8, 2017. Assoc. Editor: Robert Seah.

J. Offshore Mech. Arct. Eng 139(6), 061303 (Aug 08, 2017) (8 pages) Paper No: OMAE-15-1076; doi: 10.1115/1.4037173 History: Received July 30, 2015; Revised June 16, 2017

A finite difference method (FDM) solving the coupled partial differential equations governing three-dimensional (3D) motions of a towed underwater cable has been implemented in a combined ensemble Kalman filter (EnKF) and ensemble Kalman smoother (EnKS), as a new approach to combined state and parameter estimation for towed underwater cables. A simulation study of the method applied to a seismic streamer has been performed. Cable state variables as well as model parameters are estimated. Parameters estimated are crossline ocean current varying with time as well as cable tangential drag coefficient. The presented results indicate that the method is able to estimate state as well as parameters for seismic streamers.

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References

Figures

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Fig. 1

3D marine seismic surveys involve an acoustic source and an array of receivers. (Courtesy of Petroleum Geo-Services.)

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Fig. 2

Orientation of local (t, n, b) and absolute (x, y, z) coordinate systems, and angles θ and φ. Axis x, y, and b are in the horizontal (level) plane, whereas z is perpendicular to the horizontal (level) plane. φ is in the vertical plane, and θ is in the horizontal plane. Positive directions of rotation are indicated.

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Fig. 3

Coordinate plot of the validation simulation at time 301 s, also showing node A and node B, and the next to last element (Fig. 4; Table 2). Recall that front node is origin.

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Fig. 4

Depth of node A and node B (Fig. 6; Table 2): present results compared to the results of Ablow and Schechter [7] and Milinazzo et al. [8]

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Fig. 5

Crossline position estimation results: time-averaged difference between estimated and true position, for each node, as well as filter estimated standard deviations (ref. plot legend). Results for both EnKF and EnKS are presented. Results are average of 100 simulations. Note the similar patterns of differences and estimated standard deviations, although standard deviations are somewhat underestimated. Absolute difference between measured and true positions is shown by the circles.

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Fig. 6

Depth position estimation results: time-averaged difference between estimated and true position, for each node, as well as filter estimated standard deviations (ref. plot legend). Results for both EnKF and EnKS are presented. Results are average of 100 simulations. Note the similar patterns of differences and estimated standard deviations, although standard deviations are somewhat underestimated. Absolute difference between measured and true positions is shown by the circles.

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Fig. 7

Estimated crossline current Ucrossline: actual absolute deviations from true values, and estimated standard deviations, showing results for both EnKF and EnKS (ref. plot legend). The results presented are average of 100 simulation runs. For EnKF, actual deviations are lowest when the current is at its peak values, hence the sinelike shape. Recall that Ucrossline varies with time according to a sine curve with peak amplitude of 0.4 m/s and wavelength 502 s.

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Fig. 8

Tangential drag coefficient Ct: actual absolute deviations from true values, and estimated standard deviations, showing results for both EnKF and EnKS (ref. plot legend). The results presented are average of 100 simulation runs. Values are in percent of Ct0 (nominal Ct). Note: the initial values at time = 0 s is not included in this plot; hence, the large reduction in deviation at initial measurement update does not show.

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Fig. 9

Front tension T: actual absolute deviations from true values, and estimated standard deviations, showing results for both EnKF and EnKS (ref. plot legend). The results presented are average of 100 simulation runs. Front tension measurement standard deviation is 100 N (black circles).

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