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Proceedings Paper

Fast estimation of bifurcation conditions using noisy response data
Author(s): Nicholas Miller; Chris Burgner; Mark Dykman; Steven Shaw; Kimberly Turner
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Paper Abstract

In this work we consider the effects of noise on system behavior during parameter sweeps through bifurcations that induce sharp jumps in response amplitudes. These problems arise in a variety of applications, including the use of bifurcation amplification in micro-sensors. Due to inherent system noise, the observed bifurcation events are stochastic in nature and one must estimate parameter values from a distribution. A stochastic dynamical systems analysis allows one to distill the problem to a one-dimensional, one-parameter Fokker-Planck equation, where the parameter is the ratio of the noise intensity to sweep rate. Approximate closed form solutions for the distributions are obtained in the limits of slow and fast parameter sweep rates, and a numeric solution captures the intermediate sweep range that bridges these two approximations. These results are essential for quantifying errors in bifurcation amplifiers and for optimizing bifurcation detection schemes, as used in sensing applications. Preliminary experimental results for a parametrically excited microdevice show good qualitative agreement with the theory.

Paper Details

Date Published: 31 March 2010
PDF: 12 pages
Proc. SPIE 7647, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2010, 76470O (31 March 2010); doi: 10.1117/12.847585
Show Author Affiliations
Nicholas Miller, Michigan State Univ. (United States)
Chris Burgner, Univ. of California, Santa Barbara (United States)
Mark Dykman, Michigan State Univ. (United States)
Steven Shaw, Michigan State Univ. (United States)
Kimberly Turner, Univ. of California, Santa Barbara (United States)

Published in SPIE Proceedings Vol. 7647:
Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2010
Masayoshi Tomizuka, Editor(s)

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