Study of the amplitude modulation method for kurtosis control purposes

Abstract

The amplitude modulation method is used to create non-stationary and non-Gaussian signals with desired kurtosis values, which act as non-stationary excitations for shaker-table fatigue tests. However, the non-stationary signals produced by the method have been proved to possess a relatively narrow band of kurtosis values, thus limiting its potential in accelerated life test. To solve the problem, the kurtosis model of a non-stationary signals produced by the amplitude modulation method is investigated. It is found that the feature of the beta distribution imposes restrictions on the kurtosis range. Based on the finding, two types of updates are put forward in this article. The first one is to utilize the gamma-distributed random numbers to scale the amplitudes of the modulating waves. The second update is to employ stationary non-Gaussian signals, instead of the stationary Gaussian signals, to synthesize the non-stationary and non-Gaussian signals. The two alternatives are all verified with numerical and experimental examples. The results demonstrate that both methods can widen the band of kurtosis. But the non-stationary excitations produced by the second method turn out to have different kurtosis transferring rates in a linear time-invariant dynamical system. Especially, the excitations created with sub-Gaussian signals have larger kurtosis transferring rates than the excitations made by the original amplitude modulation method do, making them suitable to be applied in an accelerated fatigue test.