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Parameter identification and sensitivity analysis to a thermal diffusivity inverse problem

Leventhal, Brian and Fu, Xiaojing and Fowler, Kathleen and Eslinger, Owen (2015) Parameter identification and sensitivity analysis to a thermal diffusivity inverse problem. Involve, a Journal of Mathematics, 8 (3). pp. 385-400. ISSN 1944-4184. doi:10.2140/involve.2015.8.385.

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The solution to inverse problems is an application shared by mathematicians, scientists, and engineers. For this work, a set of shallow soil temperatures measured at eight depths between 0 and 30 cm and sampled every five minutes over 24 hours is used to determine the diffusivity of the soil. Thermal diffusivity is a modeling parameter that impacts how heat flows through soil. In particular, it is not known in advance if the subsurface region is homogeneous or heterogeneous, which means the thermal diffusivity may or may not depend on depth. To this end, it is not clear which assumptions may apply to represent the physical system embedded within the parameter estimation problem. Analytic methods and a simulation based least-squares approach to approximate the diffusivity are compared to fit the temperature profiles to different heat flow models. The simulation is based on a spatially dependent, nonsteady-state discretization to a partial differential equation. To complete the work, a statistical sensitivity study using analysis of variance is used to understand how errors that arise in the modeling phase impact the final model. We show that for the analytic methods, errors in the initial fitting of the temperature data to sinusoidal boundary conditions can have a strong impact on the thermal diffusivity values. Our proposed framework shows that this soil sample is heterogeneous and that modeling depends significantly on data used as top and bottom boundary conditions. This work offers a protocol to determine the soil type and model sensitivities using analytic, numerical, and statistical approaches and is applicable to modifications of the classic heat equation found across disciplines.

Item Type:Article
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Fu, Xiaojing0000-0001-7120-704X
Additional Information:© 2015 Mathematical Sciences Publishers. Received: 28 April 2011; Revised: 11 November 2013; Accepted: 20 December 2013; First available in Project Euclid: 22 November 2017.
Subject Keywords:inverse problems, subsurface flow, sensitivity analysis
Issue or Number:3
Classification Code:MSC 2010: primary 35K05, 49N45, 62J10; secondary 35Q93
Record Number:CaltechAUTHORS:20200903-152905682
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Official Citation:Leventhal, Brian; Fu, Xiaojing; Fowler, Kathleen; Eslinger, Owen. Parameter identification and sensitivity analysis to a thermal diffusivity inverse problem. Involve 8 (2015), no. 3, 385-400. doi:10.2140/involve.2015.8.385.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105253
Deposited By: Tony Diaz
Deposited On:08 Sep 2020 18:20
Last Modified:16 Nov 2021 18:41

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