This work deals with numerical simulation of a hyperthermia treatment of skin cancer as a state estimation problem, where uncertainties in the evolution and measurement models, as well as in the measured data, are accounted for. A reduced model is adopted, based on a coarse mesh for the solution of the partial differential equations that describe the physical problem, in order to expedite the solution of the state estimation problem with a particle filter algorithm within the Bayesian framework of statistics. The so-called approximation error model (AEM) is used in order to statistically compensate for model reduction effects. The Liu and West algorithm of the particle filter, together with the AEM, is shown to provide accurate estimates for the temperature and model parameters in a multilayered region containing a tumor loaded with nanoparticles. Simulated transient temperature measurements from one sensor are used in the analysis.
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Particle Filter and Approximation Error Model for State Estimation in Hyperthermia
Bernard Lamien,
Bernard Lamien
Department of Mechanical Engineering,
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: lamienbernard@hotmail.com
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: lamienbernard@hotmail.com
Search for other works by this author on:
Helcio Rangel Barreto Orlande,
Helcio Rangel Barreto Orlande
Department of Mechanical Engineering,
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: helcio@mecanica.coppe.ufrj.br
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: helcio@mecanica.coppe.ufrj.br
Search for other works by this author on:
Guillermo Enrique Eliçabe
Guillermo Enrique Eliçabe
Institute of Materials Science and Technology
(INTEMA),
University of Mar del Plata and National
Research Council (CONICET),
J. B. Justo 4302,
Mar del Plata 7600, Argentina
e-mail: elicabe@fi.mdp.edu.ar
(INTEMA),
University of Mar del Plata and National
Research Council (CONICET),
J. B. Justo 4302,
Mar del Plata 7600, Argentina
e-mail: elicabe@fi.mdp.edu.ar
Search for other works by this author on:
Bernard Lamien
Department of Mechanical Engineering,
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: lamienbernard@hotmail.com
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: lamienbernard@hotmail.com
Helcio Rangel Barreto Orlande
Department of Mechanical Engineering,
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: helcio@mecanica.coppe.ufrj.br
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: helcio@mecanica.coppe.ufrj.br
Guillermo Enrique Eliçabe
Institute of Materials Science and Technology
(INTEMA),
University of Mar del Plata and National
Research Council (CONICET),
J. B. Justo 4302,
Mar del Plata 7600, Argentina
e-mail: elicabe@fi.mdp.edu.ar
(INTEMA),
University of Mar del Plata and National
Research Council (CONICET),
J. B. Justo 4302,
Mar del Plata 7600, Argentina
e-mail: elicabe@fi.mdp.edu.ar
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 18, 2016; final manuscript received June 25, 2016; published online September 8, 2016. Editor: Dr. Portonovo S. Ayyaswamy.
J. Heat Transfer. Jan 2017, 139(1): 012001 (12 pages)
Published Online: September 8, 2016
Article history
Received:
February 18, 2016
Revised:
June 25, 2016
Citation
Lamien, B., Barreto Orlande, H. R., and Enrique Eliçabe, G. (September 8, 2016). "Particle Filter and Approximation Error Model for State Estimation in Hyperthermia." ASME. J. Heat Transfer. January 2017; 139(1): 012001. https://doi.org/10.1115/1.4034064
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