Generation of non-Gaussian stationary random excitations with specified cross-power spectral densities using zero memory non-linear transformation for fatigue test purposes

Abstract

Zero-memory non-linear (ZMNL) methods have long been a type of very useful tools in creating super-Gaussian random excitations for fatigue test. The major drawback of this method is that the magnitude distortion can be seen in both auto-power spectral density (ASD) and cross power-spectral density (CSD) of the excitation if the dynamic range of the target power spectral density (PSD) is large. To study the problem, we introduced Fourier series of a Gaussian signal into a cubic system, which is a common mathematical model shared by most of the ZMNL functions. We found that the cubic system produces a component leading to the distortion of both ASD and CSD. Meanwhile, if the shape of the reference ASD is flat in a frequency band, the distortion will not happen in the band. Based on this findings, a novel method is proposed in this article. It employs a pseudo reference PSD with flat ASDs to generate non-Gaussian signals in order to avoid the PSD distortions. Designed FIR filters are then applied to rescale the ASDs of the generated signals. After, iterative processes are introduced to recover the kurtoses of these filtered signals. The method is applied on a two-input and two-output numerical model, the feasibility and the availability of the method is verified. Finally, two control schemes based on the proposed pseudo reference PSD method are provided for a shaker table test. Test results show that both control schemes can eliminate the mismatch between the target PSD and the measured PSD of a shaker table.