15 juni 2005
This manual is combination of all manuals made for different Matlab scripts.
The setup may differ per script. An overview of the usage has been given in
Usage.doc.
Table of Contents
Manual Matlab scripts Laboratory of Fluid Mechanics
Asc2wav, Converting Ascii files and using the
DELFT-AUKE program Waves.
Decomp, Separate spectrum of irregular wave in incident
and reflected part.
Calculate distance of wave gauges needed
How to handle if a file cannot be read
Refreg, calculation of the reflection of a regular
wave
Short description of the program Refreg:
Additional program points in the future
Refreg and Spect, remarks about spectra
De header in the ASCII-file produced
by Decomp is 11 lines long.
==============================================================
REMARK:
the scale factor from measurement to meters is:
1 if the output of Decomp is used as
input in waves,
depending on the settings of the
wave gauges if the measurement file is input to waves.
==============================================================
Copy *.dat, *.seq, and the
.pcf-file to a folder where you want to store the results; make a file
Waves.bat with line
waves.exe in=name1.pcf ou=name2.out
er=waves.err
name1 is the name of the .pcf-file:
waves.pcf if you confirmed to overwrite the file, otherwise: the name of the
.dat-file,
name2 is a name chosen by yourself,
e.g. the name of the .dat-file.
exceedance,perc=...
27
April 2005
Decomp, Separate spectrum
of irregular wave in incident and reflected part.
18 April 2005
To be able to separate the waves into incident and reflected
wave, 2 or 3 wave gauges are needed (3 is preferable). The signals from the
wave gauges lead to a system of equations, which will enable the calculation of
incident and reflected wave. If the distance is a multiple of the wavelength,
the system of equations will be singular.
If three wave gauges are used, distances of 0.3 m between
gauge 1 and gauge 2, and 0.4 m between gauge 2 and gauge 3 will do in most
cases, where gauges 1 is supposed to be nearest to the wave board. This will
work if the peek period is between 1 to 3 seconds.
If two wave gauges are used, the program Distance of WL |
Delft Hydraulics can be used:
DelftAUKE,
program Distance (DOS), 2 wave gauges.
Input to
Distance:
Tp peak period
h water depth
Output:
fmin - fmax frequency range of valid solution
Lmin –
Lmax wave lengths according to
frequencies at given water depth
dxlow
- dxhigh range of distances between which a valid
solution is possible.
The minimum
distance of the wave gauges specified in the manual is 0.2 m. If this distance
is not in the range found by the program Distance, specify 0.2 m as input to
the program Distance. In that case Distance calculates the frequncy range of
valid solution if the distace is 0.2 m.
Measurements -> Dasylab file
Input parameters to Decomp (input from .txt-file):
About measurements:
parameter |
description |
dt
(s) |
time step used in data file |
Tp
(s) |
approximated peak period (only used to calculate the
frequency resolution in the variance spectra to be calculated) |
fres |
desired frequency resolution of spectrum/peak frequency |
fmin
- fmax (Hz) |
frequency range where the spectrum of incident and
reflected wave must be calculated (fmax=-1
to calculate this interval automatically from the distances in case of two
gauges, and takes the default 0 – 2.5 Hz in case of 3 gauges). Some times, fmax=-1
will select a part that doesn’t cover the whole Jonswap spectrum. Decomp will
show a message box on the screen in that case. |
thresh |
threshold to determine the part of the variance spectrum
where the decomposition is valid, E>=thresh • Emax. Most of the times, the frequency range of an ideal Jonswap
spectrum with the same threshold will extend this part, caused by noise in
the calculated spectrum. The program will print both ranges in the output
file. |
col_t |
column number in the data file where the time has been
registrated(0 if not registrated); col_t
is used by the input function only; it will not be used by this program, but
it is needed to locate the colum numbers of the wave gauges correctly. |
about channels to be analysed:
column number
position of gauge (m)
scale from registered data value to meters
about the water depth as a function of the position:
x (m), h (m) position
and water depth in at least P+1
points, where P is the number of wave
gauges
Method: based
on method of Zelt en Skjelbreia (1992)
Matlab version: Henk
Jan Bakkenes (2002)
Suppose N points, measured at time t=n∆t, n=1,2,…N. In this case a wave can be described by N spectral terms.
The data registered by wave gauge p can be represented by a sum of incident and reflected wave:
(1)
where ai,j
and ar,j are complex (i.e. containing
the phase shift of the incident and reflected wave respectively). The mean
value of η is zero, so j=0
disappears.
Furthermore, ωj=2π/T, whereT=N∆t.
Standard Fourier analysis of η(xp,t ) gives:
(2)
Combination of (1) and (2) -> system of P linear equations and two unknown
complex values (ai,j and ar,j )
for each spectral component j (P :
number of gauges).
A least-squares solution can be calculated using a standard
Matlab operation.
Equations must be well conditioned: it is not allowed to put
wave gauges in points of equal phase.
To calculate the distances needed, a DOS program Distance is
available (from the Delft Hydraulics package DELFT-AUKE).
Steps of Decomp:
(1) Ask which output the user desires (see list on p.5).
(2) Read data file, parameter file, and file containing profile of water depth.
(3) If asked by user: calculate frequency range of valid decomposition according to the distances of the wave gauges. Otherwise, use the values supplied by the user.
(4) Ask part of input data to be analysed (begin and end point).
(5) Calculate phase shift at positions of the wave gauges, and if needed, calculate the change of the amplitude caused by changes in water depth.
(6) For each wave gauge, calculate FFT A , variance spectrum E, and averaged spectrum Es, averaged over frequency bands of length specified by input.
Points (7) through (9) describe parameter calculations per wave gauge. The parameters are chosen according to a program Reflecmf from the DELFT-AUKE package (manual July 2000).
(7) From averaged variance spectrum: peak period Tp , period TpD in middle of connected part of the spectrum where Es >= 0.8 Esmax , and the frequency range of a connected part of the spectrum where Es >= thresh • Emax . This frequency range will be used to calculate the parameters in points (8) and (9).
(8) From "raw" variance spectrum in frequency range Es >= thresh • Emax : spectral moments (m0, m2, and m4).
(9) From spectral moments: mean period between successive zero crossings and between successive maxima, and correlation between successive wave heights.
Continuation of program Decomp:
As a valid frequency range, the frequencies must be valid for the used distances (point (3)), and the spectrum must be above the threshold (point (7)), otherwise the equations will be of the type
0.x = 0.
Most of the times, an ideal Jonswap spectrum will have a wider frequency range above the threshold. This range will be given in the output as well. Compare the range used by Decomp with the frequecy range of an ideal Jonswap spectrum to evaluate the results.
In the figures, more frequencies than the above range are shown. This will help the user to inspect if the valid frequency range contains a good representation of the signal. Vertical lines with arrows are used to show which part of the spectrum is valid.
If the coefficient matrix of the equations is nearly singular, the program will stop, and show an error message. Sometimes the conditions in the equations are reasonable, but the spectrum will show an unexpected peak. If this peak is in the valid part of the spectrum, the distances may be chosen incorrectly. Check if the values are in accordance with this program.
More information about distances: DELFT-AUKE Process Document (2000).
(10) Calculate amplitude spectra of incident and reflected wave from FFT-values A for each spectral component.
(11) Variance spectrum and spectrum averaged over frequency bands of incident and reflected wave in specified frequency range.
(12) Spectral parameters from "raw" variance spectra of incident and reflected wave: moment m0, significant wave height, and mean factor of reflection.
(13) Reconstruction of the incident and reflected wave as a time series by inverse FFT. Only the "valid" part of the spectrum will be used for this computation.
Parameters calculated in steps (8) and (9):
parameter |
description |
|
spectral moments |
T0,1 = m0/m1 |
average period |
|
average period between two zero crossings |
|
average period between two successive local maximum values |
|
narrowness parameter |
|
broadness parameter |
κ |
correlation value, defined in DELFT-AUKE manual (2000), p.4-6 |
γ |
coefficient of linear correlation, defined in DELFT-AUKE manual (2000), p.4-7 as ρHH |
Hm0 = 4√m0 |
significant wave height |
N.B.: This program uses dialog boxes. In Matlab 7, dialog boxes will not be deleted immediately after clicking OK, but the program will continue; please don’t click OK again.
Input files:
· data file (Dasylab file),
· parameter file: .txt file
Contents of parameter file:
time step used in data file
0.02
Tp (s), f-resol/Tp fmin (Hz), fmax (Hz), thresh
1.27, 0.025, 0.25, 1.65, 0.005
column with time (0 if none)
1
columno gauge, pos (m), scale fact to m
2, 0, 0.025
3, 0.25, 0.025
Line number
1, 3, 5, and 7 are text lines; the other lines are data lines; if more values
are stored in one line, the values must be separated by commas. The values are
examples, and have to be replaced by the user. If fmax = -1, fmin and fmax will
be calculated by the program (2 gauges), or replaced by 0.02 and 2.5
respectively (3 or more gauges).
·
profile of depth
Contents of
file containing profile of depth:
pos (m), depth (m)
0.0 0.6
0.125 0.6
0.25 0.6
0.5 0.6
Line 1
contains text; the other lines contain data, separated by blanks or tabs. The
values are examples.
If P gauges are used, at least P+1 data lines are needed (this
restriction has not yet been checked).
N.B.: In the file containing the depth profile, spaces or tabs ar allowed as a separation. In the parameter file, commas are allowed only, since the data are read in a different way. The program will send a message if a comma is missing.
Usage:
·
Open Matlab and go to the folder where
Decomp and subfolder .\Functions are stored.
Type Decomp.
Remark: the user must make the parameter file and
the file containing the profile of depth in advance. The contents are described
above.
·
Desired output:
The program
shows a list of possible outputs:
plot of raw
variance spectrum of original time signal
plot of
averaged variance spectrum of original time signal
plot of
averaged variance spectrum of incident and reflected wave
plot of
reflection factor
file of
statistical results (spectral moments, refl. coeff)
file of
variance spectra of inc. and refl. waves
file of time
signal of inc. and refl. wave
For each item
of the list, fill in 1 for yes or 0 for no.
·
The input files are asked from dialog
boxes.
·
The time interval to be used in the
calculations is asked by the program. A plot of the measurements will be put on
the screen, which will help the user to select suitable data.
The begin
time and end time in seconds must be given in a dialog box.
Close the
figure to start the calculation.
· If the frequency range selected in the input file covers less than 90% of the frequency range of an ideal Jonswap spectrum with peak period TpD (mean value of all wave gauges), a message box will be shown on the screen.
The frequency
range of an ideal Jonswap spectrum will be printed to the output file of
statistical results. The algorithme to calculated this ideal Jonswap spectrum
has been copied from
·
The desired figures will be produced,
and dialog boxes will ask the names of the desired output files. If the spectra
of incident and reflected waves show peeks, the equations probably have a
singularity at those frequencies.
The incident and reflected wave as time series are
calculated using the inverse FFT of the spectra of incident and reflected wave.
Only frequencies for which the spectrum has been detected as "valid"
will be used for the reconstruction. If the output file of time series of
incident and reflected wave is asked by the user (see "Desired
Output"), these series can be used as input for the DELFT-AUKE program
Waves, which determines special wave parameters. A special Matlab script
Asc2wav has to be run to make the files readable by Waves (and other DELFT-AUKE
programs). Information from the programmer of Stevin III, room 0.07, tel.
85974.
The
next errors may occur:
Number of colums in line -- of ASCII file ... must be the same as the previous line.
In such a case, remove all spaces, signs, or numbers
from the first position of each header line.
If the number of header lines specified is more than
the actual number, no message will occur, but less data lines will be read.
where nchan is the number of channels used. If more data are needed, change the value of maxnum in \Functions\FN_indata7, line 86, or read the file in parts, using different sample numbers. Sample numbers to be read can be specified via the dialog box:
read
all samples?
Specify No in this case.
In
a Dasylab file, it is preferable to store the time in decimal format. The time
format with a ':' in Dasylab is not read as a time in Matlab.
March 16, 2005
The Matlab function Lvmview has been developed to view
ASCII files containing measurement data. If times are recorded, the recommended
format is decimal. The ":"-format may differ from the Matlab time
format (e.g. Dasylab files have a different time format).
Specifications to be fulfilled by the ASCII files are
given in Help, General, or in the document Usage.doc. Some incidental occuring
error message are discussed at the end of this manual.
The data can be viewed directly in the program Lvmview. After
closing Lvmview, the data are kept in the workspace, and commands as mean(A) and
plot(A(:,2)) can be given.
The use of Lvmview will be explained here.
1. Start Matlab.
2. Go to folder D:\Matlab_progs\Labprogs.
3. Type: Lvmview.
4. In the menu bar, click on File, followed by Open.
5. The box Input File is shown; find the file to be viewed, and select it.
6. The box Read all data? will be shown. In most cases, yes is the best choice. Choose no in case of a file of 10 MB or more only.
7.
The number of header lines will
be asked. Specify 0 if the input file has been created by Dasylab, because the
program detects the end of the header of Dasylab files.
If no is specified in pint 6, begin sample, end sample, and step size are asked as well. Lvmview will send a warning if there are too many data to be read in once.
8. The parameter screen appears. Fill in the values asked by the screen:
· time step in the data file (this is not read from the header, because all types of ASCII files can be read),
· number of the column where the time has been stored (0 if no times are written to the data file, or if ":" is present in the time format).
9. The window channels appears. Select the channels to be plotted by clicking the mouse and holding the <control> key.
10. A plot of all samples of the first and the last channel will be shown, combined with a dialog box asking the time interval to be plotted on the screen. The times can be read from the horizontal axes. Fill in the desired interval, and click on OK. The samples chosen are displayed on the next screen. Close the figure to continue.
11. Click on Plot on the menu bar. Choose one of the next possibilities:
· plot channels separated in subplots, 3 channels per figure,
· plot all channels in one figure,
· choose other samples,
· choose other channels.
12.
If one of the plot options has
been chosen, one or more figures appear. The figures can be edited (see the
manual "Using Matlab Graphics"), and/or printed. If wanted, the
figure can be saved by clicking File, save as on the
menu bar of the figure, and afterwards the figure can be opened by clicking File,
Open on the menu bar of Lvmview.
If another time interval must be viewed, close the figures and press Plot, option samples on the menu bar.
13. After closing the figures, File, Open can be used to open a new file. This can be a figure (.fig), or an ASCII file. A .fig file always will be opened as a picture, and all other files will be opened as a data file. The old file will be kept in the workspace as long as no new file has been read, even after closing Lvmview. At the next restart of Lvmview, the file last read can be plotted again without reopening it.
To close Lvmview, always click the upper right cross, or click on File, Exit. Before closing Lvmview, check if all figures are closed (the figures are not closed automatically).
The
next errors may occur:
Number of colums in line -- of ASCII file ... must be the same as the previous line.
In such a case, remove all spaces, signs, or numbers
from the first position of each header line.
If the number of header lines specified is more than
the actual number, no message will occur, but less data lines will be read.
where nchan is the number of channels used. If more data are needed, change the value of maxnum in \Functions\FN_indata7, line 86, or read the file in parts, using different sample numbers. Sample numbers to be read can be specified via the dialog box:
read all
samples?
Specify No in this case.
April 02
Feb 03
June 05
To calculate the reflection of a regular wave, a Matlab program Refreg has been written in the Laboratory of Fluid Mechanics. The method used has been described by Goda and Suzuki (1976), see Goda (1985). In this method two wave gauges are used at a distance of about one fourth of the wave length.
Basic equations in the case of a regular
wave with wave gauges at positions x=x1 en x=x2 are:
(1a)
(1b)
where
η the water-surface elevation relative to the mean water level,
t the time,
ai,n , ar,n the amplitude of the n-th harmonic of the incoming and the reflected wave,
kn the wave number of the n-th harmonic,
ωn the angular wave frequency of the n-th harmonic,
φi,n ,φr,n the phase of the n-th harmonic of the incoming and the reflected wave.
In the Refreg program, the first harmonic is used only. Higher harmonic components and free or bound harmonics are not taken into account.
Equations (1a) and (1b) for the first harmonic are
(2a)
(2b)
(2a) can be written as
or
(3a)
In the same way, (2b) can be written as
(3b)
where
(4a)
(4b)
(4c)
(4d)
(4a) through
4(d) lead to the complex equations:
(5a)
, (5b)
where i=√-1.
(5a) and (5b) can be written as matrices:
(6)
The A and B in the right hand side of (6) can be found from a harmonic analysis of η(x1,t) and η(x2,t) in (3a) and (3b), e.g. by using a Fast Fourier Transform (FFT). In the program Refreg two zero crossings with the same sign, one at the begin and one at the end of the first data series, are used to determine the length of the series to be analysed. In that case the data series can be regarded as cyclic. The only error is a cut off error if the wave period does not fit on the time step. The FFT of Matlab is used on the two data series from the wave gauges under consideration, where the number of points used fits to the time between the zero crossings as meant above. The period with the maximum modulus of the FFT-coefficients is used as the base period.
N.B.: This program uses dialog boxes. In Matlab 7, dialog boxes will not be deleted immediately after clicking OK, but the program will continue; please don’t click OK again.
N.B. After closing a
(sub)menu, allways check the number of Matlab Windows (see Matlab icon in lower
bar of monitor), and close all windows left open (except Labmenu, and the main
program being in use).
Don’t forget to jump
back to a dialog box if help is consulted, and the box is left open.
Remarks:
· 1. Input parameters
Parameters to be typed via dialog boxes :
read all samples? choose yes (no only in case of files of 10 Mb or more),
number of header lines 0 in case of a Dasylab file (prog. determines length of header); otherwise: the number of header lines,
At this point an error message may occur, see
point 7.
time step in original data file,
number of harmonic components to be printed,
average water depth in m.
For each of the two wave gauges:
column number of the wave gauge series in the file,
position of the wave gauge in m,
scale factor of measurements from volts to meters.
Next, a graph of the read samples will appear, together with a dialog box to choose a suitable time interval. The graph can be helpful to choose this interval.
After making your choise, click on OK; a new graph will be displayed, showing the time interval chosen; close this graph to start the calculation.
Next an output file must be chosen. Choose a file, and click on OK, or click on Cancel to stop.
The output file will be opened after the calculation, and the user can view the results.
· 2. Subtraction of mean value
In Refreg, the mean value of the time signal is substracted. In Refreg19 (folder Lab_process\Extra_s), a moving average over the length of the basic period is substracted. The step used in the moving average is the time step in the data file.
· 3. Determination of the length of the signal
In the input
part of the program, the user specified the part of the data that can be used
in the calculation. From the begin and endpoint of this part, two zero
crossings with equal sign are searched. This is done for the first wave gauge.
The length of the series between the two zero crossings enables the program to
find the correct base period from the FFT.
· 4. Checking the time step
Generally, a period does not contain an integer number of samples. To reduce the error caused by this fact, the Matlab function Resample is used if there less than 20 points per period are present. Note that the phase may be inaccurate in that case.
· 5. Calculating the first harmonic using the FFT of Matlab
The frequency having the maximum C-coefficient will be taken, where C = √(A2 + B2).
To coeffficients are determined by the Matlab function fft, and multiplied by 2/N as a scaling factor, where N is the number of points used in the FFT (see "using Matlab, v. 6, p. 6-32).
· 6. Calculating the amplitude and the phase of the incoming and the reflected wave
Equation (6) has the form La = b, where a and b are vectors and L is a matrix. This equation system can be solved in Matlab directly.
The wave number k is determined by the dispersion relation in case of free gravitation surface waves is used:
,
where ω is the angular frequency and g
the gravitational acceleration constant.
The calculation is performed by the Matlab-function Disper, written by Gert
Klopman.
· 7. How to handle if a file cannot be read
The
next errors may occur:
Number of colums in line -- of ASCII file ... must be the same as the previous line.
In such a case, remove all spaces, signs, or numbers
from the first position of each header line.
If the number of header lines specified is more than
the actual number, no message will occur, but less data lines will be read.
where nchan is the number of channels used. If more data are needed, change the value of maxnum in \Functions\FN_indata7, line 86, or read the file in parts, using different sample numbers. Sample numbers to be read can be specified via the dialog box:
read all
samples?
Specify No in this case.
In a Dasylab file, it is preferable to store the
time in decimal format. The time format with a ':' in Dasylab is not read as a
time in Matlab.
To test Refreg, a program ‘testsig’ has been written. In this program, an incoming and a reflected wave with one frequency are generated. The user must specify the following parameters:
name of the output file,
number of wave periods to be generated,
time step,
wave period,
water depth,
distance between water gauges,
reflection coefficient,
phase of the incoming wave,
phase of the reflected wave,
amplitude of normally distributed random noise.
The program has been tested with an amplitude of 1 for the incoming wave (To get an answer in meters, in the program Refreg a scaling factor may be used).
The random noise has been used only to investigate the influence of noise on the frequency of the first harmonic found. If the time step is small, this kind of noise can influence the frequency found, since the zero crossings with equal sign can be shifted by half a period if the frequency of the noise has the order of half the sampling frequency. This kind of noise will normally not be found in waves. It is better to use another kind of disturbance if testing the program. It may be useful to add higher harmonic components to the test signals in the future.
1.
The influence of the time step, the duration of the measurements, and
the wave period on the results.
2. A method to detect the wave period from the
measurements, e.g. a regression method.
3.
The influence of perturbations, e.g. due to the equipment or caused by
undesired objects in the measurement
system.
4.
A sensitivity analysis of the results. If some noise of a period of
about two times the time step is present, an error may be found in the first
harmonic component found from the zero crossings. This kind of noise is not
expected in surface waves. On the other hand a small shift of the wave gauges
can change the results.
A sensitivity analysis can be done by cross correlation methods.
1.
Te water velocity as a parameter (now: velocity 0).
2.
Adding more (higher) harmonics to the calculation, and splitting into
bounded and free components. To be able to find the reflection of more
harmonics, more than two wave gauges are needed.
June, 2002
Determination of the amplitude spectrum of a regular wave from measurements
1. Sample time: at least 20 points per period are needed.
2. Duration: at least 20 periods are needed, starting from a point where the signal is stationary.
3. After the data has been stored, start the computation. First of all, subtract the mean value from the measurements to avoid a high value in the spectrum at frequency zero.
4. The harmonic components of the signal can be found from a Fast Fourier Transform (FFT)-spectrum. The dominating component in the spectrum is the basic wave period. The frequencies in the spectrum are at discrete values k * 1/T for k = 0,1,…,N/2, where T is the record time and N the total number of samples. As a concequence, having the basic wave period as a spectral component, the part of the signal used in the calculation of the FFT must be an integer number of periods.
This can be obtained as follows:
Method 1:
Determine a zero-crossing at the begin and at the end of the stationary part of the data. The two zero-crossings must have the same sign:
Use the points nearest to the begin and the end of the stationary part of the measured data as begin and end point of the analyses.
Method 2:
If the basic wave period is known beforehand, the multiple of the number of samples per period nearest to the total number of samples can be calculated:
The number of samples per period is
Np = floor (Tw / ∆t),
where
floor( ): a function returning the nearest integer <= the argument,
Tw: the wave period,
∆t: the time step in the measurements,
Np: the rounded-off number of periods.
The number of periods in the used part of the signal is:
Nc = floor (Ns / Np),
where
Ns: the total number of samples in the analysed part of the signal (= stationary part),
Nc: the rounded-off number of periods in the analysed part of the signal.
The number of points to be used in the FFT is
Nfft = Nc * Np (1)
If Nfft > Ns , use (Nc-1) * Np points.
The methods 1 and 2 described above give an integer number of periods. Generally, method 1 gives a better result than method 2.
In some applications, the number of points in the FFT must be a power of two. In that case other methods are needed to find the basic wave period.
5. Calculate the FFT, using the number of points calculated as described above.
6. Determine the maximum absolute value in the FFT-spectrum.
The FFT of a time signal x(n∆t), 0 ≤ n ≤ N-1
can be written as
where i = √-1 and N must be replaced by Nfft as found from eqation (1).
X(k) can be written as
X(k) = A(k) + i B(k),
and the absolute value of X(k) is
Find the maximum of |X(k)|.
If k1 is the index of the first maximum, the basic harmonic is at frequency k1 / Nfft∆t.
The second harmonic component can be found at k2 ≈ 2k1. Since the round-off error in the basic frequency found is about 0.5 times the frequency step, search between the indices 2k1-1 and 2k1+1 for a lokal maximum of |X(k)|.
The same method can be used to find more harmonic components (at 3k1, 4k1, …). Because of the round-off error mentioned above, search in the interval [round(i*(k1-1)), round(i*(k2-1))].
contact person:
Bakkenes, Henk Jan (2002), Observation and separation of bound and free low-frequency waves in the nearshore zone, MSc-Thesis, Delft University of Technology, Faculty of Civil Engineering and Geosciences, Fluidmechanics section, June 2002.
Battjes,J.A., Windgolven. Collegehandleiding
b78, uitgave 1984, 5e herdruk 1992 (Dutch version).
Goda, Y. en Y. Suzuki (1976). "Estimation of Incident and Reflected Waves in Random Wave
Experiments". Proc. 15th Int Conf. Coastal Engrg.,
pp. 828-845.
Goda, Y. (1985). Random seas and design of maritime structures. Univ.
WL Delft Hydraulics (2000), Delft-Auke Process Description, July 2000.
Zelt,
J.A. en J.E. Skjelbreia (1992), Estimating
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