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Dielectric elastomers are employed for a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many cases a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. Accurate estimation of the elastomer’s viscoelastic behavior to quantify parameter uncertainty motivates the use of Markov Chain Monte Carlo (MCMC) methods. Since MCMC is a sampling based method, requiring many model evaluations, efficient estimation of the fractional derivative operator is crucial. In this paper, we demonstrate the effectiveness of using quadrature techniques to approximate the Riemann–Liouville definition for fractional derivatives in the context of estimating the uncertainty of a nonlinear viscoelastic model. We also demonstrate the use of parameter subset selection techniques to isolate parameters that are identifiable in the sense that they are uniquely determined by measured data. For those identifiable parameters, we employ Bayesian inference to compute posterior distributions for parameters. Finally, we propagate parameter uncertainties through the models to compute prediction intervals for quantities of interest.
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A Symmetric Neural Network to Compute Fractional Derivatives by Training with Integer Derivatives
Fractional calculus is an increasingly recognized important tool for modeling complicated dynamics in modern engineering systems. While, in some ways, fractional derivatives are a straight-forward generalization of integer-order derivatives that are ubiquitous in engineering modeling, in other ways the use of them requires quite a bit of mathematical expertise and familiarity with some mathematical concepts that are not in everyday use across the broad spectrum of engineering disciplines. In more colloquial terms, the learning curve is steep. While the authors recognize the need for fundamental competence in tools used in engineering, a computational tool that can provide an alternative means to compute fractional derivatives does have a useful role in engineering modeling. This paper presents the use of a symmetric neural network that is trained entirely on integer-order derivatives to provide a means to compute fractional derivatives. The training data does not contain any fractional-order derivatives at all, and is composed of only integer-order derivatives. The means by which a fractional derivative can be obtained is by requiring the neural network to be symmetric, that is, it is the composition of two identical sets of layers trained on integer-order derivatives. From that, the information contained in the nodes between the two sets of layers contains half-order derivative information
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- Award ID(s):
- 1826079
- PAR ID:
- 10328631
- Date Published:
- Journal Name:
- 2022 IEEE/SICE International Symposium on System Integration (SII)
- Page Range / eLocation ID:
- 291 to 296
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/SII52469.2022.9708840
