Calculating Intensity/Strenght of Vibration with 3DOF
I want to calculate the intensity/strength of vibration at a given location. I have measured the acceleration at this location, using an accelerometer. So my measures look for example like:
t1 - x:-3.81 y:-10.13 z:5.82
t2 - x:-5.81 y:-9.13 z:3.82
t3 - ...
These are measures along the x,y,z axis in m/s^2. My assumption is that the actual strength of the vibration at t1 can be calculated by calculating the distance in 3d space from (0,0,0). I calculate the distance using the Pythagorean theorem for 3 dimensional space. To get the average intensity I just take a lot (e.g. 1.000 .000) measurements and calculate the average of the distances in 3d space of these measures.
Is this correct/valid? Are there better ways to do this?
Would it be better to use the Jerk? If I use the Jerk, how would I calculate it? Using the distance in 3D seems to be wrong, since the distance is always positive and is not associated with any direction. So I am not sure if it would be correct.
Edit As I was asked in the comments about my usecase: I want to measure the vibration intensity of a vehicle at different positions of the vehicle. In the end, I want to find the sweet spot of the vehicle, where the least vibration occurs. For example I would want to mount a vibration sensitive device there or add a driver seat to that position to reduce the vibration for the driver.
Edit2 This is a plot of approx 1400 samples. I added the 3 axis and the distance in 3d space. The distance is green, z is yellow, y is orange, x is blue.
Edit3 Ok so I just created an FFT analysis of the above data. 563
Attached are 2 different plots. One for the 3d distance (left) and one for only the x-axis (right). Essentially the results tell me that the strongest acceleration occurs in the low frequencies, right? I should definitely get finer grained data.
BTW: I used the following function in R plot.frequency.spectrum(fft(accMeasures$x0), xlimits=c(0,1500)) the function itself can be found here.
Edit4
This is the normalized FFT Plot of the sample magnitude (left) and the x-axis (right) of my actual samples here:
So I tested my accelerometer by hanging it to a rubber band and let it bounce. I sampled with ~100Hz. You can see two spike at 20Hz and 100Hz using the FFT analysis. When I "subtract from every value the calculated average" (I will use the word normalize for that - I hope that is correct). When I compare the non-normalized magnitude (3d distance) to the normalized magnitude, the frequency spikes change from 20 and 100Hz to 40 and 80Hz. This seems to be weird, since the spikes for every axis on its' own are at 20 and 100Hz. This plot shows the x-axis (the axis the main movement of the rubber band occured). On the left you can see the non-normalized FFT and on the right you can see the normalized FFT. This looks like what I would expect from normalizing the values.
This plot shows the magnitude, left is non-normalized, right is normalized. The change of frequency spikes is weird IMHO. 441