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Research Papers

Simulation of Wide-Sense Stationary Random Time-Series With Specified Spectral Densities

[+] Author and Article Information
Ana-Maria Mitu

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141, Romania
e-mail: anamariamitu@yahoo.com

Tudor Sireteanu

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141, Romania
e-mail: siret@imsar.bu.edu.ro

Marius Giuclea

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141 Romania;
Department of Mathematics,
Bucharest Academy of Economic Studies,
6 Romana Square,
Bucharest 010374, Romania
e-mail: marius.giuclea@csie.ase.ro

Ovidiu Solomon

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141 Romania;
Department of Mathematics,
Bucharest Academy of Economic Studies,
6 Romana Square,
Bucharest 010374, Romania
e-mail: ovidiu.solomon@csie.ase.ro

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 5, 2015; final manuscript received February 2, 2016; published online April 13, 2016. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 138(3), 031011 (Apr 13, 2016) (12 pages) Paper No: VIB-15-1153; doi: 10.1115/1.4032899 History: Received May 05, 2015; Revised February 02, 2016

In this paper, an effective approach to the simulation of wide-sense stationary random time-series, defined by its power spectral density (PSD) is presented. This approach is based on approximating the sample paths of target random process by finite series of sample functions of random processes, obtained as the outputs of suitably chosen set of second-order linear filters to independent limited band Gaussian white noise inputs. Thus, the Gaussian distribution of simulated time-series is obtained without applying the central limit theorem. Also, the Fourier spectra of the simulated sample paths are not discrete functions, as in the case of the multisine random time-series representation used by most classical simulation methods. The method can be applied to any analytical or nonparametric representation of the specified PSD. The proposed approach is applied to simulation of road input sample paths, compatible with PSDs described by analytical forms that can or cannot be derived by linear shape filters. The method is validated by comparison of spectral response of a half-car model to the input induced by a measured road profile with that obtained for the simulated road input. This input is derived from the nonparametric PSD, determined by third-octave filtering of the measured profile. The advantages of the proposed approach are highlighted by its comparison with a conventional method, based on the representation of simulated road input by a sum of harmonics with random phases.

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References

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Figures

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Fig. 1

The first seven amplification factors of filters for independent white noise signals

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Fig. 2

The target spectral density and the values used in simulation

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Fig. 3

Target and predicted PSD of road input for different traversing speeds

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Fig. 4

Simulated sample paths of road profile for different traversing speeds

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Fig. 5

Target and predicted PSDs obtained by the proposed method and by filtering of white noise

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Fig. 6

Road input simulated samples: linear filtering method; proposed method

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Fig. 7

Simulated road input

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Fig. 8

Target and simulated road input PSDs

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Fig. 9

Target and simulated road inputs

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Fig. 10

PSD of the road input

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Fig. 11

Cumulative distribution functions of target and simulated road inputs

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Fig. 12

Schematic of half-car model

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Fig. 13

PSD front absolute acceleration

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Fig. 14

PSD rear absolute acceleration

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Fig. 15

PSD front contact force

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Fig. 16

PSD rear contact force

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Fig. 17

PSD front rattle space

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Fig. 18

PSD rear rattle space

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Fig. 19

Target and simulated road inputs by proposed and standard methods

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Fig. 20

PSD of target and simulated road inputs by proposed and standard methods

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Fig. 21

Amplitude spectrum of target road input

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Fig. 22

Amplitude spectrum of simulated road input by proposed method

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Fig. 23

Amplitude spectrum of simulated road input by standard method

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