Present-day methods of random testing assume a Gaussian mode of distribution of random data. Modern controllers run random vibration tests with the majority of the RMS values near the mean RMS level, thus vibrating the product only for a short time at peak RMS values. In fact, a Gaussian waveform will instantaneously exceed three times the RMS level only 0.27% of the time. When measuring field data, the situation can be considerably different, with amplitudes exceeding three times the RMS level as much as 1.5% of the time. This difference can be significant, since it has also been reported that most fatigue damage is
generated by accelerations in the range of two to four times the RMS level (ref. 1). Significantly reducing the amount of time spent near these peak values by using a Gaussian distribution can therefore result in significantly reducing the amount of fatigue damage caused by the test relative to what the product will experience in the real world. Gaussian distribution, therefore, is not
very realistic.
This Gaussian distribution has been in use since the infancy of random vibration testing and continues to be used in present-day industry for several reasons. First, linear filtering of one Gaussian distribution will result in another Gaussian distribution. So spectrum shaping and the shaker frequency response function do not change the amplitude distribution. This linear transformation property also means that Gaussian data in the time domain transformed through a Fourier Fast Transform (FFT) (as is done in digital random control systems) will result in Gaussian distributions in the frequency domain. Secondly, a Gaussian distribution can be completely determined by two parameters – the mean and standard deviation. In a random vibration context the mean (the average acceleration) is always zero. Therefore, the Gaussian distribution of a standard random vibration test can be completely defined using a single
parameter – the standard deviation (the RMS acceleration). Gaussian distribution is used, therefore, because of its simplicity.