Estimation of time-dependent reaction coefficient with extended Kalman filter approach

Sin Kim; Kyung-Youn Kim; Cheng-Hung Huang

Journal of Industrial and Engineering Chemistry, Vol.18, No.1, 349-354, January, 2012

DOI10.1016/j.jiec.2011.11.093 Export Citation

Estimation of time-dependent reaction coefficient with extended Kalman filter approach

Sin Kim^{1, 2, †}, Kyung-Youn Kim³, and Cheng-Hung Huang⁴

¹Department of Nuclear and Energy Engineering, Jeju National University, Jeju 690-756, Republic of Korea
²Applied Radiological Science Research Institute, Jeju National University, Jeju 690-756, Republic of Korea
³Department of Electronic Engineering, Jeju National University, Jeju 690-756, Republic of Korea
⁴Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC

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This work introduces an extended Kalman filter (EKF) to the estimation of the unknown time-dependent reaction coefficient based on the concentration measurement data. An autocatalytic reaction pathway is chosen as a model problem. This inverse estimation algorithm does not assume any functional form of the reaction coefficient. The performance of the proposed algorithm is verified through the numerical experiments with the exact and the contaminated concentration measurement data.

Keywords:Inverse problem;Reaction coefficient estimation;Function estimation;Extended Kalman filter;Autocatalytic reaction pathway

[References]

Storozhev VB, J. Aerosol Sci., 26(8), 1179 (1995)
Harrison RM, Collins GM, J. Autom. Chem., 30, 397 (1998)
Cartry G, Magne L, Cernogora G, J. Phys. D-Appl. Phys., 33, 1303 (2000)
Alifanov OM, Artyukhin EA, Rumyantsev SV, Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems, Begell House, Inc., New York (1995)
Huang CH, Wu PY, Kim S, Inverse Probl., 26, 065009 (2010)
Chen WL, Yang YC, Energy Conv. Manag., 50(12), 3096 (2009)
Huang CH, Shih CC, Kim S, Appl. Math. Model., 33, 2683 (2009)
Orlande HRB, O¨ zis¸ ik MN, J. Heat Trans. -T. ASME., 116, 1041 (1994)
Huang CH, Kim S, Chem. Eng. Sci., 60(2), 447 (2005)
Kalman RE, J. Basic Eng. -T. ASME., 82, 35 (1960)
Watzenig D, Brandner M, Steiner G, Meas. Sci. Technol., 18, 30 (2007)
Ijaz UZ, Chung SI, Khambampati AK, Kim KY, Kim S, Meas. Sci. Technol., 19, 065501 (2008)
Vashaee D, Tayebi L, Luxat J, Ann. Nucl. Energy., 35, 228 (2008)
Engelhardt M, Stavroulakis GE, Antes H, Comput. Mech., 37, 249 (2006)
Park HM, Sung MC, Comput. Meth. Appl. Mech. Eng., 192, 3689 (2003)
Muhammada NM, Kim KY, Huang CH, Kim S, J. Ind. Eng. Chem., 16(1), 106 (2010)
Robertson AH, in: Walsh J (Ed.), Numerical Analysis, vol. 26, Thomas Brook Co.,Washington, 1179 (1967)

[1] Storozhev VB, J. Aerosol Sci., 26(8), 1179 (1995)

[2] Harrison RM, Collins GM, J. Autom. Chem., 30, 397 (1998)

[3] Cartry G, Magne L, Cernogora G, J. Phys. D-Appl. Phys., 33, 1303 (2000)

[4] Alifanov OM, Artyukhin EA, Rumyantsev SV, Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems, Begell House, Inc., New York (1995)

[5] Huang CH, Wu PY, Kim S, Inverse Probl., 26, 065009 (2010)

[6] Chen WL, Yang YC, Energy Conv. Manag., 50(12), 3096 (2009)

[7] Huang CH, Shih CC, Kim S, Appl. Math. Model., 33, 2683 (2009)

[8] Orlande HRB, O¨ zis¸ ik MN, J. Heat Trans. -T. ASME., 116, 1041 (1994)

[9] Huang CH, Kim S, Chem. Eng. Sci., 60(2), 447 (2005)

[10] Kalman RE, J. Basic Eng. -T. ASME., 82, 35 (1960)

[11] Watzenig D, Brandner M, Steiner G, Meas. Sci. Technol., 18, 30 (2007)

[12] Ijaz UZ, Chung SI, Khambampati AK, Kim KY, Kim S, Meas. Sci. Technol., 19, 065501 (2008)

[13] Vashaee D, Tayebi L, Luxat J, Ann. Nucl. Energy., 35, 228 (2008)

[14] Engelhardt M, Stavroulakis GE, Antes H, Comput. Mech., 37, 249 (2006)

[15] Park HM, Sung MC, Comput. Meth. Appl. Mech. Eng., 192, 3689 (2003)

[16] Muhammada NM, Kim KY, Huang CH, Kim S, J. Ind. Eng. Chem., 16(1), 106 (2010)

[17] Robertson AH, in: Walsh J (Ed.), Numerical Analysis, vol. 26, Thomas Brook Co.,Washington, 1179 (1967)