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Synthesizing nonstationary, non‐Gaussian random vibrations
Author(s) -
Rouillard V.,
Sek M. A.
Publication year - 2010
Publication title -
packaging technology and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 50
eISSN - 1099-1522
pISSN - 0894-3214
DOI - 10.1002/pts.907
Subject(s) - gaussian , random variable , mathematics , gaussian function , control theory (sociology) , random vibration , cumulative distribution function , probability density function , vibration , computer science , statistics , physics , acoustics , control (management) , quantum mechanics , artificial intelligence
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. Copyright © 2010 John Wiley & Sons, Ltd.