ISO 8608: get the time history from PSD of road roughness?

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serbring
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Hi all,

I have a vehicle multibody model and I want to excite it in different conditions. So I'm thinking to use the PSD or road roughness as reported in the ISO 8608. What I don't understand is, how can I get an equivalent time history of the vertical road displacement from the PSD?

thanks
 
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Think how you would get the PSD from the time history (using an FFT). Then do the inverse operation.

That won't give you a unique answer, because the PSD only contains the amplitude information from the FFT, not the phase information. So you can choose any values for the phases when you do the inverse.

If you set all the phases = 0, you will probably get a big "spike" in the time history at one point, which may or may not be realistic depending on what you are simulating. Either choose random phases for each Fourier component, or do some research into how to select the phases to control the "crest factor", i.e. the peak displacement / RMS displacement (or acceleration if that is more interesting) in the time domain. For example http://www.stanford.edu/~boyd/papers/pdf/multitone_low_crest.pdf
 
AlephZero said:
Think how you would get the PSD from the time history (using an FFT). Then do the inverse operation.

That won't give you a unique answer, because the PSD only contains the amplitude information from the FFT, not the phase information. So you can choose any values for the phases when you do the inverse.

If you set all the phases = 0, you will probably get a big "spike" in the time history at one point, which may or may not be realistic depending on what you are simulating. Either choose random phases for each Fourier component, or do some research into how to select the phases to control the "crest factor", i.e. the peak displacement / RMS displacement (or acceleration if that is more interesting) in the time domain. For example http://www.stanford.edu/~boyd/papers/pdf/multitone_low_crest.pdf

Many thanks for your help I'll take a look at the linked document