[scilab-Users] vibration test analysis

[Charlie Warner]

Several versions of Scilab ago, there was an excellent Signal Processing document in *.pdf.  Does this document still exist in the system?  Not only is it an excellent reference, it is tied to the Scliab function libraries...

Charlie

From: ray at aarden.us
To: users at lists.scilab.org
Date: Sun, 10 Oct 2010 18:18:58 -0700
Subject: RE: [scilab-Users] vibration test analysis

Paul,
 
Basically, FFT then find the peak.  
 
The difficulties with any digital system (sampled data) which is always what we have when we are performing an analysis on a digital computer (these could be bypassed if we used an analog recording and computers).  
 
Sampling data from a system produces what is called the Gibbs phenomena.  Analytically, when we jump into a data steam and take a dataset, we are convolving a square window with the input data.  There is no getting around it - that is a sampled data system.  
 
To get an idea of what this does, take a signal that is constant, say a value of 1 all the way through the sample time.  FFT this data.  We will see a function the peaks at zero (constant value) but the extends out and drops to zero, passing through zero, bottoms out, goes back up and wiggles up and down with less and less amplitude.  In fact, it is the function sin(x)/x.  
 
This is most disruptive if the frequency content of the signal is low enough and our sample window (duration) is short enough.  An additional sample conditioning process can be applied  which is called windowing.  This is a window to help suppress some of the 'wiggles' experienced with the rectangular window of standard sampling.  Rather than the 'square edge' or rapid rise of the standard sample process, a window is designed to smooth the transition.  There are many window designs such as the raised cosine and Hamming window.  See Richard Hamming's book 'Digital Signals' for specific details.  
http://www.amazon.com/Digital-Filters-Richard-W-Hamming/dp/048665088X
 
The frequency resolution depends upon the number of samples taken.  The larger number can be real signal or you can pad the signal with zeros or some 'windowed' solution.  
 
The Nyquist’s samping theory says that the sampling rate must be at least 2 times the highest frequency contained in the signal.  This does not mean the highest frequency you are interested in but the highest frequency contained.  So if your vibration process has as its highest frequency 50 kHz, you must sample at 100 kHz or higher.  If there is a noise source, say an inductive heater operating at 100 kHz and that noise gets into your measurement circuit, that becomes signal content.  This noise signal will be aliased by the digital system and appear as many signals inside the desired signal band.  This aliased signal can not be filtered by a filter algorithm.  The only thing to do is to put an analog filter in front of the sampling system to make sure the higher frequency noise does not get into the sample.
 
So the key is to define everything you are going to do to be doing with the data, the entire analysis system and understand what will be required by each step.  Then work up the sampling systems and processes.
 
Ray Joseph, PE
832 586-5854
ray at aarden.us
 
 

-------- Original Message --------
Subject: [scilab-Users] vibration test analysis
From: "Paul CARRICO" <paul.carrico at free.fr>
Date: Sun, October 10, 2010 3:02 pm
To: <users at lists.scilab.org>





All,
 
Does somebody has ever wrote/coded (under Scilab but not necessary) a program that analyses the vibration tests results (i.e. automatically find the natural frequencies) ? 
 
I do it manually but studying the transmissibility’s and the phase changes but I would like to code it under Scilab and of course there won’t be any human appreciation/analysis
 
The purpose of this email is not to have this code but to have advices/information’s on the method / algorithm and so on !
 
In any way It’s a good challenge for me
 
 
Thanks for any help
 
Paul 		 	   		  
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20101010/e0f1e626/attachment.htm>