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Non-linear threshold autoregressive models for non-linear random vibrations

Published online by Cambridge University Press:  14 July 2016

Tohru Ozaki
Tohru Ozaki*
Affiliation:
The Institute of Statistical Mathematics
*
∗Postal address: The Institute of Statistical Mathematics, 4–6–7 Minami Azabu, Minato-ku, Tokyo, Japan — 106.
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Abstract

Time series models for non-linear random vibrations are discussed from the viewpoint of the specification of the dynamics of the damping and restoring force of vibrations, and a non-linear threshold autoregressive model is introduced. Typical non-linear phenomena of vibrations are demonstrated using the models. Stationarity conditions and some structural aspects of the model are briefly discussed. Applications of the model in the statistical analysis of real data are also shown with numerical results.

Keywords

NON-LINEAR TIME SERIES MODELAUTOREGRESSIVE MODELTHRESHOLD MODELNON-LINEAR VIBRATIONSLIMIT CYCLEAMPLITUDE-DEPENDENT FREQUENCYDUFFING EQUATIONVAN DER POL EQUATIONSINGULAR POINTSTATIONARITYJUMP PHENOMENA
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 443 - 451
Copyright
Copyright © Applied Probability Trust 

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