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From: Aws Abu-Khudhair on 30 Mar 2010 19:44
Hi,
I am currently trying to model a road profile from a given PSD value. It is my understanding that I should be able to obtain time signal amplitude and frequency information from the PSD value (but not phase information). I have been reading a number of papers and journals that deal with this in one way or another, My understanding of how you go about doing this is:
generate the amplitudes+ frequency from the PSD
generate a uniformly distributed phase angle
use that information to generate the various sin waves
Combine the various sin waves into a single signal.

My problem is for some reason the final sin wave does not look random at all (can still see a sin wave pattern) bellow is the code I am using to accomplish this. Any help in the matter will be greatly appreciated.

Aws

(main reference http://jvc.sagepub.com/cgi/content/abstract/10/2/215)
d=1;
count=1;
A=4e-6; %ISO PSD Coefficient
v=20; %vehicle speed

t=[0:0.05:40];
for k=0.5:d:150 %generate a 150 amplitudes and frequencies
f1=k;
f2=k+d;
f(count)=(f1+f2)/2; %generate the frequency
sf(count)=A*f(count)^(-2.5);
amp(count)=sqrt(4*sf(count)*d) %generate the amplitude
count=count+1;
end

angle=2*pi*rand(1,length(f));%generate the phase
Xg=zeros(150,length(t));
for x=1:150
Xg(x,:)=amp(x)*sin(f(x)*t+angle(x));%generate the various sin waves
end
FullWave=zeros(1,length(Xg));
for col=1:length(Xg)
for row=1:150
FullWave(1,col)=FullWave(1,col)+Xg(row,col); %combine the sine waves into one
end
end
From: bee on 2 Apr 2010 10:51
hi, i am also doing on this minor road input, and i have no idea how to create it...
the final result that we getting should be in the amplitude vs time, is it?
the phase angle is uniformly distributed?
as i know, the phase angle is not uniformly distributed (maybe i am wrong)...
and i found that, some values are wrong in the formulation, the A=4.47e-5 and the amp(count)=sqrt(2* it should be is 2 and not 4...(u try to check first, as i scare i doing the mistake)
and, if u have found the correct way to do it, can u show it to me?
From: Aws Abu-Khudhair on 4 Apr 2010 14:50
bee <bee_bee9118(a)hotmail.com> wrote in message <1203221966.492557.1270234339586.JavaMail.root(a)gallium.mathforum.org>...
> hi, i am also doing on this minor road input, and i have no idea how to create it...
> the final result that we getting should be in the amplitude vs time, is it?
> the phase angle is uniformly distributed?
> as i know, the phase angle is not uniformly distributed (maybe i am wrong)...
> and i found that, some values are wrong in the formulation, the A=4.47e-5 and the amp(count)=sqrt(2* it should be is 2 and not 4...(u try to check first, as i scare i doing the mistake)
> and, if u have found the correct way to do it, can u show it to me?

Hi, the final result should be in road amplitude (road variation) VS. time, the road profile data has to be generated using a uniformly distributed phase angle (see the reference I had in the original post), also the ISO PSD values are in the rage of e-6 not e-5 as you are indicating.

In regards to the formula used to calculate the amplitude I have found numerous references with different formulas some of them are using
amp(count)=sqrt(2*...
some using
amp(count)=sqrt(4*...
and some without the 2 and 4 constants, at this point I am not sure which is the correct equation. Any help in the matter would be greatly appreciated.

Aws.
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