Statistical Tests of System Linearity Based on the Method of Surrogate Data

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When dealing with measured data from dynamic systems we often make the tacit assumption that the data are generated by linear dynamics. While some systematic tests for linearity and determinism are available - for example the coherence fimction, the probability density fimction, and the bispectrum - fi,u-ther tests that quanti$ the existence and the degree of nonlinearity are clearly needed. In this paper we demonstrate a statistical test for the nonlinearity exhibited by a dynamic system excited by Gaussian random noise. We perform the usual division of the input and response time series data into blocks as required by the ... continued below

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Hunter, N.; Paez, T. & Red-Horse, J. November 4, 1998.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Laboratories, Albuquerque, NM, and Livermore, CA
    Place of Publication: Albuquerque, New Mexico

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Description

When dealing with measured data from dynamic systems we often make the tacit assumption that the data are generated by linear dynamics. While some systematic tests for linearity and determinism are available - for example the coherence fimction, the probability density fimction, and the bispectrum - fi,u-ther tests that quanti$ the existence and the degree of nonlinearity are clearly needed. In this paper we demonstrate a statistical test for the nonlinearity exhibited by a dynamic system excited by Gaussian random noise. We perform the usual division of the input and response time series data into blocks as required by the Welch method of spectrum estimation and search for significant relationships between a given input fkequency and response at harmonics of the selected input frequency. We argue that systematic tests based on the recently developed statistical method of surrogate data readily detect significant nonlinear relationships. The paper elucidates the method of surrogate data. Typical results are illustrated for a linear single degree-of-freedom system and for a system with polynomial stiffness nonlinearity.

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  • International Modal Analysis Conference; Orlando, FL; 02/08-11/1999

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  • Other: DE00001557
  • Report No.: SAND98-2466C
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 1557
  • Archival Resource Key: ark:/67531/metadc618877

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  • November 4, 1998

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  • June 16, 2015, 7:43 a.m.

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  • Dec. 8, 2016, 11:14 p.m.

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Hunter, N.; Paez, T. & Red-Horse, J. Statistical Tests of System Linearity Based on the Method of Surrogate Data, article, November 4, 1998; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc618877/: accessed November 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.