# fractional-order filter for wave force on platform

Hi,

For control purposes, I have to model the wave force acting on platform by white noise w(t) with amplitude less than or equal to one, passing through a low pass filter having the frequency response of the power spectrum. Are there anyone to know the appropriate transfer function that could obviate such a kinds of needs?

Please recommend a convenient one for OC3-Hywind with known coefficients.

Regards,
Mehdi

Dear Mehdi,

I’m not really sure I understand your question, but according to linear wave theory, the wave-excitation force is linearly proportional to the amplitude of the wave in the frequency domain e.g.

F_Wave(t) = RE{ SUM( n=1,N, A(omega_n)*X(omega_n)*EXP( SQRT( -1 )omega_nt ) ) }

where,
t - Time
omega_n - Wave frequency of the wave component n
N - Number of wave components
F_Wave(t) - Time-dependent wave-excitation load
A(omega_n) - Frequency-dependent wave amplitude (complex, including amplitude and phase)
X(omega_n) - Frequency-dependent wave-excitation load normalized by wave amplitude

X(omega_n) is an output from WAMIT, as supplied with FAST model of the OC3-Hywind system.

Best regards,

Dear Jason,

Please see attached picture. As you see, I am looking forward of a_n,a_n-1,…,a_0 and b_m,b_m-1,…,b_0. In fact a transfer function between hydrodynamic wave force and wave elevation (fluctuation according to unit white noise).

Mehdi,

Dear Mehdi,

Effectively, X(omega_n) in my previous post is a frequency-response function. You should be able to convert this to a transfer-function form. The only problem I see is that you know X(omega_n) numerically instead of analytically. So, you’ll likely need to do curve fitting. I’m sure you can find some papers related to that.

Best regards,

I am a little amazed, if is it possible give some information about how to get X(omega_n) from OC3-fast to calculate F/A.

Dear Mehdi,

The spar.3 file in the CertTest/5MW_Baseline/HydroData folder of the FAST archive is a WAMIT output file containing the first-order wave excitation loads (3 forces, 3 moments) per unit wave amplitude as a function of wave frequency and direction for the OC3-Hywind model. The wave-excitation load in the spar.3 file is normalized by densitygravity(wave amplitude). (The normalization also includes length scales; however, this WAMIT model is based on a length scale of unity (L = 1 m).) So for a fixed wave direction, X(omega_n) = (data in spar.3)densitygravity. While the spar.3 file contains both the magnitude/phase and real/imaginary components of the first-order wave-excitation loads, only the latter are used by HydroDyn. More details can be found in Chapter 4 of the WAMIT User’s Manual: wamit.com/manual6.4/Chap4.pdf.

Best regards,