The figure below shows the difference in amplitude distributions of the tests. Amplitude distribution can be measured with histograms. It can be seen that the tails extend out much farther with the higher Kurtosis. The controller changes this amplitude distribution by adjusting the phase of the randomly generated drive signal. Since only the phase is changed, there is no effect on the frequency content of the vibration.

# Kurtosis Control

Kurtosis control in the Spider Random test mode controls the amplitude distribution of the random vibration. With Kurtosis control, more realistic tests can be conducted that better simulate real-world environments.

In the real world many kinds of vibration environments are characterized by signals that have high kurtosis value (relative to Gaussian random).  The fatigue and damage potential for these vibrations are higher than for a pure Gaussian replication of the environment.  Hence using the traditional Gaussian random signal as the test signal will actually under test the product for its service environment.

Kurtosis can be expressed as a normalized value “K” by dividing the fourth statistical moment divided by the square of the second statistical moment. The equation below shows the K calculation for N samples.

Without kurtosis control, the output distribution of the random controller is Gaussian. This means that large peaks are relatively rare; the random waveform will be less than 4 times its RMS value 98% of the time. Real-world vibration, such as the vibration in a car driving over rough pavement, often has peaks 5 to 10 times the RMS level. Kurtosis is a measure of this "peakedness” and is related to the amplitude distribution. A random vibration with higher kurtosis will contain more “outlier” peaks in the extremes of the distribution. A pure Gaussian distribution always has a Kurtosis of 3, while real-world vibration may have a kurtosis of 5 to 8.

By increasing the kurtosis of the random vibration to match the kurtosis of anticipated real-world vibration, the vibration test will more closely match the actual environment.

The figures below show the vibration measured from two tests, each using the same RMS level and frequency distribution. However, the vibration waveform shown in the lower figure has a kurtosis of 7, while the vibration waveform in the upper figure has a Gaussian distribution.