Determining the duration of a frequency and the magnitude

Question

I am working with a system in which I am getting data from a sensor (gyro) at 1KHz.

What I am trying to do is determine when the system is vibrating so that I can turn down the PID gains on the output.
What I currently have is a high pass filter on the incoming values. I then have set the alpha value to 1/64, which I believe should be filtering for about a 10KHz frequency. I then take this value and then integrate if it is individual above a threshold. When my integrated value passes another threshold, I then assume that the system is vibrating. I also reset the integrated value every half second to ensure that it does simply grow towards the threshold.
What I am trying to do with this system is make sure that it is really vibrating and not seeing a jolt. I have tried to do this with a upper limit to how much will be added to the integrated value, but this is not really appearing to work.

What I am looking for is any better way to go about detecting that the system is vibrating, and not being effected by a jolt, my primary issue is that that I do not miss detect a jolt for a vibration because then that will cause the values on the PID to be lowered unnecessarily.

Answer 1

FFT. It will separate out the "jolts" from the vibrations, because jolts will register across all frequencies and vibrations will spike around a particular frequency.

Answer 2

I agree with the above. There are many free algorithms for the Fast Fourier Transform avalible online. If you are not familiar with the FFT it is an operation that defines a relationship between a function in the time domain and its representation in the frequency domain, enabling analysis of the original function’s frequency content. This will enable you to determine if there is any noise or oscillatory behavior in your signal or time-series.

Another method your could use to establish whether your time-series has underlying periodicity is that of the Structure Function (Structure Function Analysis). Structure function analysis provides a method of quantifying time variability in a signal without the problem of aliasing, or windowing, that are encountered using the traditional FFT technique. Potentially it is able to provide information on the nature of the process that causes variability. The method is mainly concerned with the categorization of underlying noise processes and the identification of correlation time-scales. This is a fairly simple algorithm that you could probably write yourself.

Going one step further and being more "snazzy" would be to use a Wavelet Transform. Fourier analysis is a very powerful tool for detecting and quantifying periodic oscillations in time-series; that is signals of truly constant period, phase, and amplitude. However, real systems almost never exhibit such consistent behavior; periodic oscillations often arising intermittently as transient phenomenon. Although Fourier analysis can, to some extent detect and quantify such transient behavior, it is far from ideal for such purposes. Wavelet analysis has been developed to overcome these difficulties. See http://atoc.colorado.edu/research/wavelets/software.html for some source code and more information about wavelets.