Synthesizing Nonstationary, Non-Gaussian Random Vibrations

摘要

This paper presents a novel technique by which non-Gaussian vibrations are synthesized by generating a sequence of random Gaussian processes of varying root mean square (rms) levels and durations. The technique makes use of previous research by the authors which shows that non-Gaussian vibrations can be decomposed into a sequence of Gaussian processes. Synthesis is achieved by first computing a modulation function which is produced from the rms and the segment length distribution functions, both of which were developed in previous research. This is achieved by first generating a sequence of uniformly distributed random numbers scaled to the range of segment length, which itself is a function of the desired total duration of the synthesized process. In order to transform a uniformly distributed random variable into any arbitrary non-uniform distribution, the cumulative distribution function is established and used as a transfer function applied to the uniformly distributed random variable. This modulation function is applied to a Gaussian random signal itself generated by a standard laboratory random vibration controller (RVC) by means of a purposed-designed variable gain amplifier system. In order to counteract the feedback function of the RVC, a second variable gain amplifier is introduced into the system in order to attenuate the feedback signal in inverse proportion to the gain applied to the command signal. This result is a nonstationary, non-Gaussian random signal that statistically conforms to the desired PSD as well as the RMS distribution function.