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Research Papers

Identification of Time-Varying Time Constants of Thermocouple Sensors and Its Application to Temperature Measurement

[+] Author and Article Information
Kenneth Kar, Robert Raine

Department of Mechanical Engineering, The University of Auckland, Private Bag-92019, Auckland Mail Center, Auckland-1142, New Zealand

Akshya K. Swain

Department of Electrical and Computer Engineering, The University of Auckland, Private Bag-92019, Auckland Mail Center, Auckland-1142, New Zealand

J. Dyn. Sys., Meas., Control 131(1), 011005 (Dec 05, 2008) (10 pages) doi:10.1115/1.3023111 History: Received June 24, 2007; Revised September 07, 2008; Published December 05, 2008

The present study addresses the problem of estimating time-varying time constants associated with thermocouple sensors by a set of basis functions. By expanding each time-varying time constant onto a finite set of basis sequences, the time-varying identification problem reduces to a parameter estimation problem of a time-invariant system. The proposed algorithm, to be called as orthogonal least-squares with basis function expansion algorithm, combines the orthogonal least-squares algorithm with an error reduction ratio test to include significant basis functions into the model, which results in a parsimonious model structure. The performance of the method was compared with a linear Kalman filter. Simulations on engine data have demonstrated that the proposed method performs satisfactorily and is better than the Kalman filter. The new technique has been applied in a Stirling cycle compressor. The sinusoidal variations in time constant are tracked properly using the new technique, but the linear Kalman filter fails to do so. Both model validation and thermodynamic laws confirm that the new technique gives unbiased estimates and that the assumed thermocouple model is adequate.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Time-varying time constants

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Figure 2

True temperature and thermocouple temperatures

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Figure 3

Comparison of time-varying time constants using different model structures; (a) results for θ1 and (b) results for θ2

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Figure 4

Estimates of time-varying parameters using Model 1

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Figure 5

Comparison of parameter estimates using the OLS-BFE method and KF

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Figure 6

Schematics of the practical system

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Figure 7

Pictures of the thermocouple probe

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Figure 8

Parameter estimates from the measured temperatures using OLS-BFE algorithm and linear KF

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Figure 9

Estimated time constants of 25 μm and 50 μm thermocouples using the OLS-BFE algorithm and linear KF

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Figure 10

Comparison of the measured and reconstructed gas temperatures using the OLS-BFE algorithm and linear KF

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Figure 11

Results of model validation test. The horizontal dotted lines indicate the 95% confidence interval.

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Figure 12

Logarithmic of the gas pressure and temperature. Reconstructed temperature points are crosses; uncompensated temperature points are dots.

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