Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Stochastic Modeling of Nonlinear Random Vibrations Using Heavy-tailed Mixture Distribution
Katsutoshi YoshidaYoshikazu Yamanaka
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JOURNALS OPEN ACCESS

2020 Volume 33 Issue 1 Pages 9-15

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Abstract

In this study, we propose a simple probability density function (PDF) model of Gaussian-Laplacian mixture (GLM) type, which provides a concise parameterization of heavy-tailed data. We construct our model as convex combination of Gaussian and Laplacian PDFs to obtain a minimal parameterization of heavy-tailed data. We then conduct least-squares fitting of our model to a heavy-tailed data generated by a random Duffing oscillator and obtain over 94% of residual sum of squares (RSS) fitness. The resulting model is applied to predicting transient moment responses and achieves over 90% of RSS fitness to Monte–Carlo simulation results of the original system.

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© 2020 The Institute of Systems, Control and Information Engineers
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