Diagnosis of nonlinear systems using time series analysis

Hunter, Jr, N F

Title: Diagnosis of nonlinear systems using time series analysis

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Abstract

Diagnosis and analysis techniques for linear systems have been developed and refined to a high degree of precision. In contrast, techniques for the analysis of data from nonlinear systems are in the early stages of development. This paper describes a time series technique for the analysis of data from nonlinear systems. The input and response time series resulting from excitation of the nonlinear system are embedded in a state space. The form of the embedding is optimized using local canonical variate analysis and singular value decomposition techniques. From the state space model, future system responses are estimated. The expected degree of predictability of the system is investigated using the state transition matrix. The degree of nonlinearity present is quantified using the geometry of the transfer function poles in the z plane. Examples of application to a linear single-degree-of-freedom system, a single-degree-of-freedom Duffing Oscillator, and linear and nonlinear three degree of freedom oscillators are presented. 11 refs., 9 figs.

Authors:: Hunter, Jr, N F

Publication Date:: Tue Jan 01 00:00:00 EST 1991

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE; USDOE, Washington, DC (United States)

OSTI Identifier:: 5242934

Report Number(s):: LA-UR-91-2283; CONF-911241-2
ON: DE91016041

DOE Contract Number:: W-7405-ENG-36

Resource Type:: Conference

Resource Relation:: Conference: 3. international machinery monitoring and diagnostic conference, Las Vegas, NV (United States), 9-12 Dec 1991

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; NONLINEAR PROBLEMS; OSCILLATORS; FREQUENCY ANALYSIS; ALGORITHMS; DATA ANALYSIS; DEGREES OF FREEDOM; ITERATIVE METHODS; ELECTRONIC EQUIPMENT; EQUIPMENT; MATHEMATICAL LOGIC; 657000* - Theoretical & Mathematical Physics; 990200 - Mathematics & Computers

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                    Hunter, Jr, N F. Diagnosis of nonlinear systems using time series analysis.  United States: N. p., 1991. 
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                    Hunter, Jr, N F. Diagnosis of nonlinear systems using time series analysis.  United States.

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                    Hunter, Jr, N F. 1991.  
        "Diagnosis of nonlinear systems using time series analysis".  United States.  https://www.osti.gov/servlets/purl/5242934.

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@article{osti_5242934,

  title        = {Diagnosis of nonlinear systems using time series analysis},

  author       = {Hunter, Jr, N F},

  abstractNote = {Diagnosis and analysis techniques for linear systems have been developed and refined to a high degree of precision. In contrast, techniques for the analysis of data from nonlinear systems are in the early stages of development. This paper describes a time series technique for the analysis of data from nonlinear systems. The input and response time series resulting from excitation of the nonlinear system are embedded in a state space. The form of the embedding is optimized using local canonical variate analysis and singular value decomposition techniques. From the state space model, future system responses are estimated. The expected degree of predictability of the system is investigated using the state transition matrix. The degree of nonlinearity present is quantified using the geometry of the transfer function poles in the z plane. Examples of application to a linear single-degree-of-freedom system, a single-degree-of-freedom Duffing Oscillator, and linear and nonlinear three degree of freedom oscillators are presented. 11 refs., 9 figs.},

  doi          = {},

  url          = {https://www.osti.gov/biblio/5242934},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Tue Jan 01 00:00:00 EST 1991},

  month        = {Tue Jan 01 00:00:00 EST 1991}

}

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