netsse.analys.sawb.specres

netsse.analys.sawb.specres(Rxy, TRF, freq, beta, opt=None)

Computes an estimate of the sea state using the spectral-residual method from Brodtkorb et al. (2017) and Nielsen et al. (2018).

The heave, roll, and pitch response cross-spectra are used as input. Using the motion transfer functions of the vessel, the wave spectrum is estimated through iteration.

Warning

Long-crested wave conditions are assumed in this sea state estimation method.

Note

This Python code is based on a MATLAB/Simulink implementation by Astrid H. Brodtkorb.

Parameters:

• Rxy (array_like of shape (Nfreq,6)) – The complex-valued response spectra, given as in: Rxy = [heaveheave, rollroll, pitchpitch, heaveroll, heavepitch, rollpitch].

• TRF (array_like of shape (Nfreq,3*Nbeta)) –

  The transfer functions of the ship, in heave, roll, and pitch, concatenated along the second axis as in: TRF = [heave_TF,roll_TF,pitch_TF]

  Note

  The phase of the complex transfer functions is not important in this implementation, and the amplitude alone can be provided without this affecting the estimation results.

• freq (array_like of shape (Nfreq,)) – The frequencies of the response spectra and the transfer functions (should match).

• beta (array_like of shape (Nbeta,)) –

  The discretized heading angles [deg] at which the transfer functions are known.

  Tip

  For a port-starboard symmetric ship, directions from 0 deg to 180 deg only can be considered to lower the computational cost.

• hij (array_like of shape (6,)) – The iteration gains of the algorithm.

• opt (dict, optional) –

  Optional parameters controlling the SSE calculation. Available options are:

  • ’maxiter’int, or array_like of shape (6,)

    Maximum number of iterations (default: 50).

  • ’tolCoef’float, or array_like of shape (6,)

    Tolerance coefficient (default: 0.1).

  • ’gainFact’float, or array_like of shape (6,)

    Gain factor, as a fraction of the maximum gain value (default: 0.5).

  • ’weights’float, or array_like of shape (6,)

    Weights given to each response in the calculation of the final spectrum estimate (default: equal weight for each response, i.e. wij = 1/6).

  Note

  array_like entries of the dictionary can be input for a response-specific option. In such case, the array elements must be provided in the same order as for the response spectra.

Returns:

• S_wave (array_like of shape (Nfreq,)) – The estimated 1-D wave spectrum.

• beta_est (float) – The estimated relative wave heading [degrees].

• num_it (array_like of shape (6,)) – The average number of iterations used per heading angle, for the individual response pairs organised as: num_it = [it3, it4, it5, it34, it35, it45].

References

1. Brodtkorb, A. H., Nielsen, U. D., & Sørensen, A. J. (2018). Online wave estimation using vessel motion measurements. IFAC-PapersOnLine, 51(29), 244–249. https://doi.org/10.1016/j.ifacol.2018.09.510

2. Brodtkorb, A. H., Nielsen, U. D., & Sørensen, A. J. (2018). Sea state estimation using vessel response in dynamic positioning. Applied Ocean Research, 70, 76–86. https://doi.org/10.1016/j.apor.2017.09.005

3. Nielsen, U. D., Brodtkorb, A. H., & Sørensen, A. J. (2018). A brute-force spectral approach for wave estimation using measured vessel motions. Marine Structures, 60, 101–121. https://doi.org/10.1016/j.marstruc.2018.03.011

4. Brodtkorb, A. H., & Nielsen, U. D. (2023). Automatic sea state estimation with online trust measure based on ship response measurements. Control Engineering Practice, 130. https://doi.org/10.1016/j.conengprac.2022.105375

Example

>>> S_wave, beta_est, num_it = specres(Rxy, TRF, freq, beta, opt=None)