Blind Deconvolution for Two-Thermocouple Sensor Characterization

[+] Author and Article Information
Peter C. Hung, Robert J. Kee, George W. Irwin

Virtual Engineering Centre, Queen’s University Belfast, Belfast BT9 5HN, Northern Ireland

Seán F. McLoone1

Department of Electronic Engineering, National University of Ireland, Maynooth, Maynooth, Co. Kildare, Irelands.mcloone@ieee.org


Corresponding author.

J. Dyn. Sys., Meas., Control 129(2), 194-202 (Jun 10, 2006) (9 pages) doi:10.1115/1.2431814 History: Received January 05, 2006; Revised June 10, 2006

Thermocouples are one of the most popular devices for temperature measurement due to their robustness, ease of manufacture and installation, and low cost. However, when used in the harsh environment found in combustion systems and automotive engine exhausts, large wire diameters are required and consequently the measurement bandwidth is reduced. This paper describes two new algorithmic compensation techniques based on blind deconvolution to address this loss of high-frequency signal components using the measurements from two thermocouples. In particular, a continuous-time approach is proposed, combined with a cross-relation blind deconvolution for parameter estimation. A feature of this approach is that no a priori assumption is made about the time constant ratio of the two thermocouples. The advantages, including small estimation variance and limitations of the method, are highlighted using results from simulation and test rig studies.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Two-thermocouple cross-relation characterization

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Figure 2

(a) Three-dimensional plot of log(J2) and (b) contour plot of J2 (cross shows the local minimum)

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Figure 3

Trajectories of the minimum value of J2 with respect to τ̂1 and τ̂2, respectively (as a function of the other time constant), projected on (a) the τ̂1 axis; (b) the τ̂2 axis. In each case, the trajectories intersect at the local minimum value of J2.

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Figure 4

A portion of Fig. 2 in the vicinity of the local minimum reproduced at a higher resolution, showing the two superimposed trajectories intersecting at the local minimum

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Figure 5

Typical cost function obtained with 1D cross-relation characterization: (a) 1D cost function plot; (b) projection of the 1D cost function onto the 2D J2 contour map

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Figure 6

Block diagram representation of the simulated two-thermocouple measurement system

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Figure 7

(a) Means and (b) standard deviations (SD) of percentage errors in thermocouple parameter estimate τ̂1 at low noise levels Le averaged over 100 runs

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Figure 8

Cost function J1 at different noise levels Le at search interval of 1ms

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Figure 9

Cost function J1 at large noise level Le=6% with mean and 95% confidence intervals of τ̂2 from 20 Monte Carlo runs

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Figure 10

Modified cost functions J1* at large noise level Le=6% with mean and 95% confidence intervals from 20 Monte Carlo runs. The search interval is 1ms.

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Figure 11

Schematic illustration of the test rig

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Figure 12

Experimental test rig outputs Tref, T1, and T2 from the fine wire thermocouples with diameters 12.5, 25, and 50μm, respectively

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Figure 13

Contour plots of cost function J2 from test rig thermocouple data. The search interval is 0.1ms.




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