Generating Non-Gaussian Vibration for Testing Purposes

Abstract

There is increasing interest in simulating vibration environments that are non-Gaussian, particularly in the transportation arena. A method is presented here for generating time histories that are realizations of a zero mean, non-Gaussian random process with a specified spectrum, skewness, and kurtosis. A zero-memory nonlinear (ZMNL) monotonic function y = f(x) is generated to convert a zero mean Gaussian realization x with a specified autospectral density (ASD) into a non-Gaussian waveform y. The transformation is generated using the density method. The zero crossings are preserved in the transformation, which preserves most of the spectral information. The nonlinear transformation does introduce some harmonic distortion of the spectrum that can be reduced in an iterative process. The method does not preserve the phase structure between frequencies and is unable to match higherorder spectra. The resulting time history can then be used in a simulation or reproduced on a shaker using commercially available waveform reproduction software. The generation of non-Gaussian noise has had a renewed interest in the defense industry for two reasons. The first is the realization that many surface transportation and wave environments are non-Gaussian. The second is the development of shaker control systems that could replicate long time histories that are non-Gaussian. The original, and many current shaker control systems, for generating random vibration tests generate only Gaussian random noise. However, waveform replication techniques now allow the reproduction of any waveform whose characteristics are within the bounds of a shaker. Many articles have been written on the subject of generating non-Gaussian waveforms. This article uses the method of a zero-memory nonlinear (ZMNL) function. This method was proposed as far back as 1967. 1,2 At that time, analog circuits were used to implement the methods. The basic method relies on the equation: 3