Research Papers

Joint State and Input Estimation for One-Dimensional Heat Conduction

[+] Author and Article Information
Sangeeta Nundy

Department of Electrical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India
e-mail: sangeeta2007@gmail.com

Siddhartha Mukhopadhyay

Department of Electrical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India
e-mail: smukh@ee.iitkgp.ernet.in

Alok Kanti Deb

Associate Professor
Department of Electrical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India
e-mail: alokkanti@ee.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 31, 2014; final manuscript received June 16, 2015; published online August 11, 2015. Assoc. Editor: P. K. Das.

J. Heat Transfer 137(12), 121014 (Aug 11, 2015) (10 pages) Paper No: HT-14-1372; doi: 10.1115/1.4030962 History: Received May 31, 2014

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.

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Fig. 1

Geometry of the heat-conducting body

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Fig. 2

Comparison of the frequency response between actual TF and the approximated TF

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Fig. 3

Comparison of FDM and OCM with analytical solution at location x = xs

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Fig. 4

Analytical solution of temperature at x = 0 and x = xs for constant heat flux input and delay analysis

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Fig. 5

Estimated heat flux without and with compensation for sinusoidal input heat flux

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Fig. 6

Estimated heat flux without and with compensation for square input signal

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Fig. 7

Estimated heat flux without and with compensation for triangular signal

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Fig. 8

Estimated states compared with actual states at two spatial locations for triangular signal

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Fig. 9

Estimated heat flux for sinusoidal signal with process uncertainty 5% and measurement uncertainty 10%

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Fig. 10

Estimated heat flux for sinusoidal signal with process uncertainty 5% and measurement uncertainty 5%

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Fig. 11

Estimated input temperature with actual for process uncertainty 0.5% and measurement uncertainty 10%



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