Research Papers

Multiscale Uncertainty Quantification Based on a Generalized Hidden Markov Model

[+] Author and Article Information
Yan Wang

Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405yan.wang@me.gatech.edu

J. Mech. Des 133(3), 031004 (Mar 01, 2011) (10 pages) doi:10.1115/1.4003537 History: Received April 27, 2010; Revised January 23, 2011; Published March 01, 2011; Online March 01, 2011

Variability is the inherent randomness in systems, whereas incertitude is due to lack of knowledge. In this paper, a generalized hidden Markov model (GHMM) is proposed to quantify aleatory and epistemic uncertainties simultaneously in multiscale system analysis. The GHMM is based on a new imprecise probability theory that has the form of generalized interval. The new interval probability resembles the precise probability and has a similar calculus structure. The proposed GHMM allows us to quantify cross-scale dependency and information loss between scales. Based on a generalized interval Bayes’ rule, three cross-scale information assimilation approaches that incorporate uncertainty propagation are also developed.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

The generalized hidden Markov model for multiscale systems to capture spatial and scale dependency

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Figure 2

The illustration of cross-scale information assimilation based on GIBR

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Figure 3

CNT composites in design of biomimetic actuator (50)

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Figure 4

Empirical c.d.f.’s and the distributions of data from Ref. 51

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Figure 5

Empirical c.d.f. of composites conductivity with 1.0 wt % of CNT from Ref. 53



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