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

• Autores: Melike Sirlanci, Susan E. Luczak, Catharine E. Fairbairn, Dahyeon Kang, Ruoxi Pan-, Xin Yu, Gary Rosen
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 106, 2019, págs. 101-109
• Idioma: inglés
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• Resumen

  • 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.