Generation of time histories with a specified auto spectral density and probability density function

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It is recognized that some dynamic and noise environments are characterized by time histories which are not Gaussian. An example is high intensity acoustic noise. Another example is some transportation vibration. A better simulation of these environments can be generated if a zero mean non-Gaussian time history can be reproduced with a specified auto (or power) spectral density (ASD or PSD) and a specified probability density function (pdf). After the required time history is synthesized, the waveform can be used for simulation purposes. For example, modem waveform reproduction techniques can be used to reproduce the waveform on electrodynamic or electrohydraulic ... continued below

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6 p.

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Smallwood, D.O. August 1, 1996.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

It is recognized that some dynamic and noise environments are characterized by time histories which are not Gaussian. An example is high intensity acoustic noise. Another example is some transportation vibration. A better simulation of these environments can be generated if a zero mean non-Gaussian time history can be reproduced with a specified auto (or power) spectral density (ASD or PSD) and a specified probability density function (pdf). After the required time history is synthesized, the waveform can be used for simulation purposes. For example, modem waveform reproduction techniques can be used to reproduce the waveform on electrodynamic or electrohydraulic shakers. Or the waveforms can be used in digital simulations. A method is presented for the generation of realizations of zero mean non-Gaussian random time histories with a specified ASD, and pdf. First a Gaussian time history with the specified auto (or power) spectral density (ASD) is generated. A monotonic nonlinear function relating the Gaussian waveform to the desired realization is then established based on the Cumulative Distribution Function (CDF) of the desired waveform and the known CDF of a Gaussian waveform. The established function is used to transform the Gaussian waveform to a realization of the desired waveform. Since the transformation preserves the zero-crossings and peaks of the original Gaussian waveform, and does not introduce any substantial discontinuities, the ASD is not substantially changed. Several methods are available to generate a realization of a Gaussian distributed waveform with a known ASD. The method of Smallwood and Paez (1993) is an example. However, the generation of random noise with a specified ASD but with a non-Gaussian distribution is less well known.

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6 p.

Notes

OSTI as DE96011844

Source

  • NOISE-CON `96: engineering professional programs, Seattle, WA (United States), 29 Sep - 2 Oct 1996

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  • Other: DE96011844
  • Report No.: SAND--96-1385C
  • Report No.: CONF-9609155--1
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 266910
  • Archival Resource Key: ark:/67531/metadc671940

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  • August 1, 1996

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

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  • April 14, 2016, 7:45 p.m.

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Smallwood, D.O. Generation of time histories with a specified auto spectral density and probability density function, article, August 1, 1996; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc671940/: accessed August 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.