The kurtosis parameter shifts the distribution smoothly over the full range from Gaussian through high kurtosis levels. A feedback control loop can be implemented in the controller to achieve the desired kurtosis level in the acceleration waveform. It is important to implement feedback control on the acceleration measurements, because the kurtosis level at the controller output will typically be different from that in the acceleration waveform. Without the feedback control, you could set the kurtosis of the controller output signal, but this would not achieve the desired kurtosis on your shaker.
For example, a Gaussian distribution (kurtosis = 3) spends only 0.27% of the time above three times the RMS level. Increasing the kurtosis to four will increase this time to 0.83%, while increasing the kurtosis to seven increases this time to 1.5%. This may not sound like much, but consider that during a 1-hour test, the test article will be approaching a full minute at levels
above three sigma, rather than below three sigma. This statistic can translate to significant
product stresses. These stresses will not occur with a traditional Gaussian distribution but do occur in a real environment.
To illustrate this point, we divide each vertical amplitude in Figure 5 by the amplitude for
k = 3 (the Gaussian case) to get the relative time above absolute value versus three sigma for
each value of k. This is plotted in Figure 6, where we can clearly see that with increased kurtosis,
the relative amount of time spent at the higher levels is increased many times over the Gaussian case.
The kurtosis parameter shifts the distribution smoothly over the full range from Gaussian through high kurtosis levels. A feedback control loop can be implemented in the controller to achieve the desired kurtosis level in the acceleration waveform. It is important to implement feedback control on the acceleration measurements, because the kurtosis level at the controller output will typically be different from that in the acceleration waveform. Without the feedback control, you could set the kurtosis of the controller output signal, but this would not achieve the desired kurtosis on your shaker.For example, a Gaussian distribution (kurtosis = 3) spends only 0.27% of the time above three times the RMS level. Increasing the kurtosis to four will increase this time to 0.83%, while increasing the kurtosis to seven increases this time to 1.5%. This may not sound like much, but consider that during a 1-hour test, the test article will be approaching a full minute at levelsabove three sigma, rather than below three sigma. This statistic can translate to significantproduct stresses. These stresses will not occur with a traditional Gaussian distribution but do occur in a real environment.To illustrate this point, we divide each vertical amplitude in Figure 5 by the amplitude fork = 3 (the Gaussian case) to get the relative time above absolute value versus three sigma foreach value of k. This is plotted in Figure 6, where we can clearly see that with increased kurtosis,the relative amount of time spent at the higher levels is increased many times over the Gaussian case.
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