SYNTHESIZING NONSTATIONARY,
NON-GAUSSIAN WHEELED VEHICLE
VIBRATIONS
Vincent Rouillard & Michael A. Sek
Victoria University, Australia
Introduction & objective
  Vehicle vibrations can damage consignment / on-board equipment
o  Estimated that, in Asia, 1/3 of produce is thrown out due to
damage - much of it caused by the rigours of handling & transport
o  Demand for protective packaging is high and increasing
  Products & protective packaging systems need to be engineered and
optimized
  This requires that vertical vibrations be accurately simulated
Introduction & objective
  Aim of research:
  Develop better method for synthesizing vehicle vibrations
  Presentation outline:
  Overview of current vehicle vibration simulation method
  Discuss statistical nature of vehicle vibrations
  Present novel method for synthesizing realistic vibrations
  Present and discuss preliminary results
Current approach for simulating vehicle vibrations
  Simulating vehicle vibrations (current approach):
o  Vibrations are generated using (large) vibration tables
o  Vibrations are assumed to be random, stationary and Gaussian
o  Random vibration synthesized from a Power Spectral Density (PSD)
function (estimated from measured data)
o  This produces a stationary (constant rms) Gaussian random signal.
Current approach for simulating vehicle vibrations
Average PSD
Vibration response
Current approach for simulating vehicle vibrations
Average PSD
Test sample
Vibration table
Generate synthetic signal
from spectral model
(IFFT)
Hydraulic
Power Unit
Current approach for simulating vehicle vibrations
Average PSD
Kurtosis = 3.0
Statistical nature of vehicle vibrations
  Nonstationary - Vibration intensity (rms) varies
o Kurtosis
Mainly
due to variations in pavementKurtosis
roughness
and vehicle speed
= 14.7
= 14.7
  Non-Gaussian - As a direct consequence of nonstationarity
Statistical nature of vehicle vibrations
  Current simulation method does not reproduce the fluctuations in
vibration intensity (rms) that are so typical of real vehicle vibrations:
Original measured vibrations
Overall rms: 15 m/s2
Stationary vibrations produced by current method
Overall rms: 15 m/s2
Statistical nature of vehicle vibrations
  Research has shown that road vehicle vibrations can be treated as a
sequence of Gaussian segments with varying rms levels and duration:
Change-points
Stationary (Gaussian)
segments
Statistical nature of vehicle vibrations
  In such cases non-Gaussianity is a consequence of nonstationarity.
  When a sequence of Gaussian processes each with a proportional
duration, Di , and an rms level, σi , exists, the overall distribution is
non-Gaussian. Example:
Overall kurtosis = 7.5
σ3
Acceleration [-]
σ1
σ2
D2
D1
Elapsed time [s]
D3
Statistical nature of vehicle vibrations
  Non-Gaussianity is a consequence of nonstationarity.
  When a sequence of Gaussian processes each with a proportional
duration, Di , and an rms level, σi , exists, the overall distribution is
non-Gaussian. Example:
P(x)
Overall signal (non-Gaussian)
Gaussian segment # 2
Gaussian segment # 1
Gaussian segment # 3
Normalised acceleration, x [rms]
Statistical nature of vehicle vibrations
  Non-Gaussianity is a consequence of nonstationarity.
  When a sequence of Gaussian processes each with a proportional
duration, Di , and an rms level, σi , exists, the overall distribution is
non-Gaussian. Example:
Overall signal (non-Gaussian)
Gaussian segment # 2
Gaussian segment # 1
Ln {p(x)}
Gaussian segment # 3
|x|x
Synthesizing nonstationary vehicle vibrations
  If vehicle vibrations can (as has been shown) be modelled as a
sequence of Gaussian events, nonstationary vibrations can be produced
by modulating a Gaussian random signal
  The creation of the modulation function needs to represent reality:
  The rms modulation level is random
  The rms modulation level needs to conforms to the rms distribution
  The length (duration) of (Gaussian) segments is random
  The length (duration) of (Gaussian) segments needs to conform to a
statistical distribution.
Synthesizing nonstationary vehicle vibrations
  Statistical distribution of (Gaussian) segment lengths
Synthesizing nonstationary vehicle vibrations
RMS distribution
Average PSD
Gaussian random signal
×
=
Modulation function
Nonstationary, non-Gaussian random signal
Synthesizing nonstationary vehicle vibrations
Random Vibration Controller
Test sample
Vibration table
Feedback
Accelerometer
Measured PSD
Servo
valve
Target PSD
Drive
(output)
Feedback
(input)
SVS
Statistical Vibration Synthesizer
RVC Adaptor Module
Servo-hydraulic
Actuator
Servo
amplifier
Charge
Amplifier
Synthesizing nonstationary vehicle vibrations
Video demonstration
Synthesizing nonstationary vehicle vibrations - Results
Nonstationary synthesized vibrations produced with the SVS system
Overall rms: 15 m/s2
Stationary vibrations produced by current method
Overall rms: 15 m/s2
Original measured vibrations
Overall rms: 15 m/s2
Synthesizing nonstationary vehicle vibrations - Results
16(a)
Synthesizing nonstationary vehicle vibrations - Results
16(b)
Synthesizing nonstationary vehicle vibrations - Results
16(b)
Conclusions
  Shown that current method for simulating vehicle vibrations has
significant limitations
o  Does not account for nonstationarity (hence non-Gaussianity) of
wheeled vehicle vibrations
  The treatment of nonstationary vibrations as a sequence of Gaussian
segments has been discussed
  New approach based on the generation of a random modulation
function has been introduced
  Results confirm that the synthesized nonstationary vibrations do
produce the desired non-Gaussian effect and conform to both the
spectral and statistical character of vehicle vibrations.
  Future work needs to determine whether this method yields better
correlation with damage rates in the field.
SYNTHESIZING NONSTATIONARY,
NON-GAUSSIAN WHEELED VEHICLE
VIBRATIONS
Vincent Rouillard & Michael A. Sek
Victoria University, Australia
Synthesizing nonstationary vehicle vibrations
Synthesizing nonstationary vehicle vibrations
Synthesizing nonstationary vehicle vibrations
Synthesizing nonstationary vehicle vibrations
Synthesizing nonstationary vehicle vibrations
Synthesizing nonstationary vehicle vibrations