Session 9b: Vehicle design and technology 1
Synthesizing nonstationary, non-Gaussian wheeled vehicle
vibrations
Vincent Rouillard, Victoria University, Australia, Vincent.Rouillard@vu.edu.au
Michael A. Sek, Victoria University, Victoria, Michael.Sek@vu.edu.au
The current, widely adopted, technique for laboratory simulation of transport vibrations
assumes that the vibrations produced by wheeled vehicles can be approximated by a zeromean, normally-distributed (Gaussian) random process. By ignoring the nonstationary
character of random vehicle vibrations (caused in the main by variations in pavement
roughness and vehicle speed|) such systems fail to reproduce the random fluctuations in rms
level that naturally occur when wheeled vehicles travel over roads with irregular surfaces.
The proposed method considers the nonstationary character of vehicle vibrations as the main
cause of its overall non-Gaussian nature. The proposed vibration synthesis is based on
previous research that shows that wheeled vehicle vibrations can be represented as a
sequence of Gaussian segments of arbitrary length and rms levels. This approach has been
found to be accurate as it accounts for the inherent nonstationarities that are characteristic to
random vehicle vibrations. Previous research by the authors has also shown that, since the
process can be modelled statistically as a sequence of Gaussian segments with varying
standard deviations, there exists identifiable boundaries (change-points) at which the
transition from one segment to another occurs. The identification of such change-points
makes it possible to determine the segment lengths as well as their statistical characteristics.
This resulted in a mathematical model that was found capable of describing the statistical
distribution of stationary vibration segment lengths.
Synthesis of nonstationary, non-Gaussian vibrations by modulating a normally-distributed
random Gaussian signal itself produced for a spectral function that characterises the vehicle
vibration response. The modulation function is produced from the statistical distribution of
the rms level and the segment length distribution function. This modulation function then is
applied to a Gaussian signal and results in a nonstationary, non-Gaussian random signal that
statistically conforms to the desired Power Spectral Density and RMS distribution functions.
This signal is used as a target vibration to be reproduced by a suitable vibration actuator.
This is achieved by a specially-designed software tool that uses an adaptive Impulse
Response Function algorithm to compensate for the dynamic characteristics (transfer
function) of the vibration actuator and associated hardware. Results show that the adaptive
algorithm, which uses a Least-Mean-Squared (LMS) method, is very effective at controlling
the motion of the vibration actuator. The effectiveness of the technique was evaluated by
comparing the Probability Density Estimates and the overall kurtosis values of the target and
synthesized vibrations. Results show that the technique offers significant advantages by
enabling the synthesis of more realistic random vibrations that conforms to a desired PSD as
well as the statistical distributions of the process.