Amplitude Probability Distribution

The vibration signature of a machine always has some random variation, i.e., its instantaneous value is not predictable. Nevertheless, the probability of a given value falling within a certain amplitude range is predictable in a statistical sense. For example, consider a short sample of the vibration velocity signal from an operating machine. The vibration velocity V at any instant can vary in a random manner about some mean value. Suppose the velocity scale is divided into a series of small divisions DV. Then, the statistical probability that the signal will be in any given division can be measured by noting the time the signal spends in each division divided by the total time the signal is monitored. The probability density is a measure of the distance away from the mean value the amplitude will be, plotted against the amplitude.

The most familiar probability density curve is the famous "normal", or Gaussian, distribution, also popularly known as the "bell-shaped curve".

The RMS value of a signal with a Gaussian distribution is equal to the Standard Deviation of the signal, and is abbreviated with the Greek letter s (sigma). A random vibration signal will produce a Gaussian distribution, and experience shows that healthy machines also produce Gaussian distributions. As faults develop in machines, the amplitude distribution curve changes shape; for instance, a small bearing fault will introduce "spikes" in the vibration wave form, and this will increase the level of the "tails" of the distribution curve, as shown below. The U.S. Navy has studied the use of the amplitude distribution in machine monitoring for some time, but it has not been generally adopted by industry.