SYNTHESIZING NONSTATIONARY, NON-GAUSSIAN WHEELED VEHICLE VIBRATIONS. Vincent Rouillard & Michael A. Sek Victoria University, Australia

Transcription

1 SYNTHESIZING NONSTATIONARY, NON-GAUSSIAN WHEELED VEHICLE VIBRATIONS Vincent Rouillard & Michael A. Sek Victoria University, Australia

2 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

3 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

4 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.

5 Current approach for simulating vehicle vibrations Average PSD Vibration response

6 Current approach for simulating vehicle vibrations Average PSD Test sample Vibration table Generate synthetic signal from spectral model (IFFT) Hydraulic Power Unit

7 Current approach for simulating vehicle vibrations Average PSD Kurtosis = 3.0

8 Statistical nature of vehicle vibrations Nonstationary - Vibration intensity (rms) varies o Mainly due to variations in pavement roughness and vehicle speed Kurtosis = 14.7 Kurtosis = 14.7 Non-Gaussian - As a direct consequence of nonstationarity

9 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/s 2 Stationary vibrations produced by current method Overall rms: 15 m/s 2

10 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

11 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, D i, and an rms level, σ i, exists, the overall distribution is non-gaussian. Example: Overall kurtosis = 7.5 σ 1 σ 2 σ 3 Acceleration [-] D 1 D 2 D 3 Elapsed time [s]

12 Statistical nature of vehicle vibrations Non-Gaussianity is a consequence of nonstationarity. When a sequence of Gaussian processes each with a proportional duration, D i, and an rms level, σ i, exists, the overall distribution is non-gaussian. Example: Overall signal (non-gaussian) P(x) Gaussian segment # 2 Gaussian segment # 1 Gaussian segment # 3 Normalised acceleration, x [rms]

13 Statistical nature of vehicle vibrations Non-Gaussianity is a consequence of nonstationarity. When a sequence of Gaussian processes each with a proportional duration, D i, and an rms level, σ i, exists, the overall distribution is non-gaussian. Example: Overall signal (non-gaussian) Ln {p(x)} Gaussian segment # 2 Gaussian segment # 1 Gaussian segment # 3 x x

14 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.

15 Synthesizing nonstationary vehicle vibrations Statistical distribution of (Gaussian) segment lengths

16 Synthesizing nonstationary vehicle vibrations Average PSD RMS distribution Gaussian random signal Modulation function = Nonstationary, non-gaussian random signal

17 Synthesizing nonstationary vehicle vibrations Random Vibration Controller Test sample Vibration table Feedback Accelerometer Measured PSD Target PSD Servo valve Drive (output) Feedback (input) Servo-hydraulic Actuator SVS Statistical Vibration Synthesizer RVC Adaptor Module Servo amplifier Charge Amplifier

18 Synthesizing nonstationary vehicle vibrations Video demonstration

19 Synthesizing nonstationary vehicle vibrations - Results Nonstationary synthesized vibrations produced with the SVS system Overall rms: 15 m/s 2 Stationary vibrations produced by current method Overall rms: 15 m/s 2 Original measured vibrations Overall rms: 15 m/s 2

20 Synthesizing nonstationary vehicle vibrations - Results 16(a)

21 Synthesizing nonstationary vehicle vibrations - Results 16(b)

22 Synthesizing nonstationary vehicle vibrations - Results 16(b)

23 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.

24 SYNTHESIZING NONSTATIONARY, NON-GAUSSIAN WHEELED VEHICLE VIBRATIONS Vincent Rouillard & Michael A. Sek Victoria University, Australia

25 Synthesizing nonstationary vehicle vibrations

26 Synthesizing nonstationary vehicle vibrations

27 Synthesizing nonstationary vehicle vibrations

28 Synthesizing nonstationary vehicle vibrations

29 Synthesizing nonstationary vehicle vibrations

30 Synthesizing nonstationary vehicle vibrations