18 April 2005
Separate spectrum of irregular wave in incident and
reflected part.
1.
Calculate distance of wave gauges
needed
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.
2.
Measurements -> Dasylab file
3.
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
4.
Program Decomp
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 |
Usage of the program:
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.
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. (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 Incident and Reflected Wave Fields Using an Arbitrary Number
of Wave Gauges, Proc. 23rd Int. Conf. Coastal Eng., ASCE, pp.
777-789.