This paper presents a joint state and input estimation algorithm for the one-dimensional heat-conduction problem. A computationally efficient method is proposed in this work to solve the inverse heat-conduction problem (IHCP) using orthogonal collocation method (OCM). A Kalman filter (KF) algorithm is used in conjunction with a recursive-weighted least-square (RWLS)-based method to simultaneously estimate the input boundary condition and the temperature field over the heat-conducting element. A comparison study of the algorithm is shown with explicit finite-difference method (FDM) of approximation and analytical solution of the forward problem, which clearly reveals the high accuracy with lower-dimensional modeling. The estimation results show that the performance of the estimator is robust to noise sensitivity up to a certain level, which is practically acceptable.
Issue Section:
Research Papers
Keywords:
Conduction
References
1.
Haberman
, R.
, 1987
, Elementary Applied Partial Differential Equations
, Prentice-Hall
, Englewood Cliffs, NJ
.2.
Faghri
, A.
, Zhang
, Y.
, and Howell
, J. R.
, 2010
, Advanced Heat and Mass Transfer
, Global Digital Press
, Columbia, MO
.3.
Villadsen
, J.
, and Stewart
, W.
, 1967
, “Solution of Boundary-Value Problems by Orthogonal Collocation
,” Chem. Eng. Sci.
, 22
(11
), pp. 1483
–1501
.4.
Bar-Shalom
, Y.
, and Li
, X.-R.
, 1993
, Estimation and Tracking: Principles, Techniques, and Software
, Artech House
, Boston.5.
Simon
, D.
, 2006
, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
, Wiley-Interscience
, New York.6.
Zhou
, J.
, Zhang
, Y.
, Chen
, J. K.
, and Feng
, Z. C.
, 2011
, “Inverse Estimation of Surface Heating Condition in a Finite Slab With Temperature-Dependent Thermophysical Properties
,” Heat Transfer Eng.
, 32
(10
), pp. 861
–875
.7.
Chen
, T.-C.
, and Liu
, C.-C.
, 2008
, “Inverse Estimation of Heat Flux and Temperature on Nozzle Throat-Insert Inner Contour
,” Int. J. Heat Mass Transfer
, 51
(13–14
), pp. 3571
–3581
.8.
Molavi
, H.
, Rahmani
, R. K.
, Pourshaghaghy
, A.
, Tashnizi
, E. S.
, and Hakkaki-Fard
, A.
, 2010
, “Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary
,” ASME J. Heat Transfer
, 132
(8
), p. 081301
.9.
Tadrari
, O.
, and Lacroix
, M.
, 2006
, “Prediction of Protective Banks in High Temperature Smelting Furnaces by Inverse Heat Transfer
,” Int. J. Heat Mass Transfer
, 49
(13–14
), pp. 2180
–2189
.10.
Wei
, C. C.
, Chen
, J. J. J.
, Welch
, B. J.
, and Voller
, V. R.
, 1997
, “Modelling of Dynamic Ledge Heat Transfer
,” Light Metals: Proceedings of Sessions, TMS Annual Meeting
, Minerals, Metals & Materials Society (TMS), TMS, Orlando, FL, pp. 309
–316
.11.
Ozisik
, M. N.
, and Orlande
, H. R. B.
, 2000
, Inverse Heat Transfer: Fundamentals and Applications
, Taylor & Francis
, New York
.12.
Feng
, Z.
, Chen
, J.
, Zhang
, Y.
, and Griggs
, J. L.
, 2011
, “Estimation of Front Surface Temperature and Heat Flux of a Locally Heated Plate From Distributed Sensor Data on the Back Surface
,” Int. J. Heat Mass Transfer
, 54
(15–16
), pp. 3431
–3439
.13.
Soti
, V.
, Ahmadizadeh
, Y.
, Pourgholi
, R.
, and Ebrahimi
, M.
, 2007
, “Estimation of Heat Flux in One-Dimensional Inverse Heat Conduction Problem
,” Int. Math. Forum
, 2
(10
), pp. 455
–464
.14.
Ji
, C.-C.
, Tuan
, P.-C.
, and Jang
, H.-Y.
, 1997
, “A Recursive Least-Squares Algorithm for On-Line 1-D Inverse Heat Conduction Estimation
,” Int. J. Heat Mass Transfer
, 40
(9
), pp. 2081
–2096
.15.
Chan
, Y.
, Hu
, A.
, and Plant
, J.
, 1979
, “A Kalman Filter Based Tracking Scheme With Input Estimation
,” IEEE Trans. Aerosp. Electron. Syst.
, AES-15
(2
), pp. 237
–244
.16.
Chen
, T.-C.
, and Hsu
, S.-J.
, 2007
, “Input Estimation Method in the Use of Electronic Device Temperature Prediction and Heat Flux Inverse Estimation
,” Numer. Heat Transfer, Part A
, 52
(9
), pp. 795
–815
.17.
Lu
, T.
, Liu
, B.
, Jiang
, P.
, Zhang
, Y.
, and Li
, H.
, 2010
, “A Two-Dimensional Inverse Heat Conduction Problem in Estimating the Fluid Temperature in a Pipeline
,” Appl. Therm. Eng.
, 30
(13
), pp. 1574
–1579
.18.
Beck
, J. V.
, Blackwell
, B.
, and St. Clair
, C. R.
, 1985
, Inverse Heat Conduction: Ill-Posed Problems
, Wiley
, New York
.19.
Woodbury
, K. A.
, Beck
, J. V.
, and Najafi
, H.
, 2014
, “Filter Solution of Inverse Heat Conduction Problem Using Measured Temperature History as Remote Boundary Condition
,” Int. J. Heat Mass Transfer
, 72
, pp. 139
–147
.20.
Feng
, Z.
, Chen
, J.
, Zhang
, Y.
, and Montgomery-Smith
, S.
, 2010
, “Temperature and Heat Flux Estimation From Sampled Transient Sensor Measurements
,” Int. J. Therm. Sci.
, 49
(12
), pp. 2385
–2390
.21.
Chen
, T.-C.
, and Tuan
, P.-C.
, 2005
, “Input Estimation Method Including Finite-Element Scheme for Solving Inverse Heat Conduction Problems
,” Numer. Heat Transfer, Part B
, 47
(3
), pp. 277
–290
.Copyright © 2015 by ASME
You do not currently have access to this content.
