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Estimating the distribution of random parameters in a diffusion equation forward model for a transdermal alcohol biosensor

Sirlanci, Melike and Luczak, Susan E. and Fairbairn, Catharine E. and Kang, Dahyeon and Pan, Ruoxi and Yu, Xin and Rosen, I. Gary (2019) Estimating the distribution of random parameters in a diffusion equation forward model for a transdermal alcohol biosensor. Automatica, 106 . pp. 101-109. ISSN 0005-1098. doi:10.1016/j.automatica.2019.04.026.

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We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol. The underlying model is a diffusion equation with input: blood alcohol concentration and output: transdermal alcohol concentration. We reformulate the dynamical system so that the random parameters are treated as additional space variables. When the distribution to be estimated is absolutely continuous with a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation. Well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject.

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Additional Information:© 2019 Elsevier Ltd. Received 27 October 2017, Revised 31 December 2018, Accepted 31 March 2019, Available online 16 May 2019. This research was supported by grants from the National Institute on Alcohol Abuse and Alcoholism (NIAAA) (R21AA17711, R01AA026368-01 S.E.L./I.G.R.), and (R01AA025969, C.E.F.). The material in this paper was partially presented at the SIAM Conference on Uncertainty Quantification, April 16–19, 2018, Garden Grove, California, USA. This paper was recommended for publication in revised form by Associate Editor Martin Enqvist under the direction of Editor Torsten Söderström.
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National Institute on Alcohol Abuse and AlcoholismUNSPECIFIED
Record Number:CaltechAUTHORS:20190520-141811771
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95612
Deposited By: Tony Diaz
Deposited On:20 May 2019 22:58
Last Modified:16 Nov 2021 17:14

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