Last updated on Aug 22, 2025.

netsse.analys.dsa.polynom_DSA#

netsse.analys.dsa.polynom_DSA(tau, om0m, weighting='uniform', nu23=1 + 2**1 / 2 / 2, full_output=False)#

Computes the polynomial approximation of the Doppler Shift.

Note

This implementation uses the derivations presented in Mounet et al. (2025a,b).

Parameters:

  • tau (array_like of shape (Ntau,)) – Array of Doppler shift intensities.

  • om0m (float) – Cut-off frequency of the DSA.

  • weighting ({'uniform','tripvalpb','lowfreq'}, optional) –

    Weighting method to use:

    • ’uniform’ :

      Equal weight is given to all frequencies in the range [0,om0m] in the cost function. This is the default option. It is introduced in Mounet et al. (2025a).

    • ’tripvalpb’ :

      Same as 'uniform' weighting, but the om0m is set to a value of \((1+\sqrt{2})/(2\tau)\) when \(\nu>\nu_{23}\). This ensures the DSA features an optimal accuracy in the range of frequencies where the triple-value problem occurs. This idea is introduced in Mounet et al. (2025b).

    • ’lowfreq’ :

      A decreasing (affine) weighting function is applied in the range [0,om0m], such that low frequencies are given more importance in the cost function. This option is not recommended for general use.

  • nu23 (float, optional) – Threshold value of nu for switching between the concave and convex forms of the approximation. Default is \((1+\sqrt{2})/2\).

  • full_output (bool, optional) – If True, the function returns nu``and ``kappa as additional outputs. Default is False.

Returns:

  • rho_p (array_like of shape (Ntau,)) – Computed rho_p values.

  • nu_p (array_like of shape (Ntau,)) – Computed nu_p values.

  • nu (array_like of shape (Ntau,)) – Computed nu values.

  • kappa (array_like of shape (Ntau,)) – Computed kappa values.

See also

trans_2Dmat_DSA

Computes the matrices for applying the Doppler shift approximation (DSA).

References

  1. Mounet, R.E.G., Nielsen, U.D., and Takami, T. (2025a). “Doppler Shift Approximation in Seakeeping Problems: A New Formulation for Ships Advancing at Any Forward Speed.” In: Proceedings of the 16th International Symposium on Practical Design of Ships and Other Floating Structures (PRADS 2025), Ann Arbor, MI, USA. (Accepted).

  2. Mounet, R.E.G., Nielsen, U.D., and Takami, T. (2025b). “Approximating the Doppler Shift in Sea-Wave Spectra Observed from an Advancing Floating Platform.” Applied Mathematical Modelling. (Submitted).

Example

>>> rho_p, nu_p = polynom_DSA(tau, om0m, weighting='tripvalpb', full_output=False)