Finding amplitude from PSD data? Part 2

[midsidenode]

reference closed thread384-197452....

My problem is similar to that in the referenced thread. Nevertheless, I have 5 frequencies present. Can I integrate to obtain the Grms and do something similar? For example, my frequencies and PSD values are:
1. 10 Hz, .12 G^2/Hz
2. 25 Hz, .18 G^2/Hz
3. 100 Hz, .21 G^2/Hz
4. 1000 Hz, .04 G^2/Hz
5. 2000 Hz, .025 G^2/Hz
I come up with a cumulative Grms value of 10.77 when I take the area under the curve. Can I use this to come up with a peak displacement?

Thanks,
msn

 

[GregLocock]

As you know, information is lost when going from time history data to a PSD, so you cannot accurately reproduce a time history from its PSD.

You can't use the Grms value to get back to a displacement because the relationship between G and displacement involves frequency, and you have averaged teh G acrioss all teh frequencies.

That may sound like wrist-slitting time. However, it is a fair punt that the frequency components are uncorrelated (no fixed phase relationship) and the the crest factor (peak amplitude/RMS) is 5 (that's just a general observation about real signals that provide usable test sequences)

So you can either back synthesise a time history from a spectrum that consists of your psd and random phase for each bin, and checking the crest factor, or you can read up on Tom's excellent advice here

http://vibrationdata.wordpress.com/...-history-to-satisfy-a-power-spectral-density/

Cheers

Greg Locock


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[amanuensis]

Hi,

I find a GRMS equals to 12.72g instead of your indicated value.

You can also get a mean frequency from your DSP.
f=SQRT(Integral(f²*DSP(f)df)/Integral(DSP(f)df))

Under these circumstances, the mean frequency is 27Hz.

Regards,
Amanuensis

 

[amanuensis]

You also can determine the irregularity factor, which characterises the frequency width band of your signal.
The irregularity factor of your signal is equal to 0.67.

If the irregularity factor is near from zero then your signal is broadband, otherwise if irregularity factor is close to 1, then your signal is narrow band.

Your signal is quite narrow band.

Regards,
Amanuensis

 

[midsidenode]

thanks to both of you for your replies.
This curve is oviously reasonably flat and well defined. As a result, I'm assuming that's why you can calculate and assume a good frequency mean - right? So would it also be fair to say that the mean frequency (if so calculated) is where the majority of the energy resides?

 

[amanuensis]

To know the mean frequency can be useful if you want to estimate the the peak value of a random signal.
Suppose that in addition to the Grms and the mean frequency, you also know the duration time T of your signal. Then you can estimate the maximum value of your signal by using the following formula:
Gmax=Grms*sqrt(ln(f*T)).
With a probability of 50%, the peak acceleration of your signal should be Gmax.

 

[midsidenode]

in addition to getting a different value for GRMS, i'm having problems getting the same answer (as you) for mean frequency. i get around 23 Hz. can you explain how you use the curve to get the mean frequency. I get the area unde the curve as 163.10 G^2.