Accurate modeling of thermal systems depends upon the determination of the material properties and the surface heat transfer coefficients. These parameters are frequently estimated from temperatures measured within the system or on the surface or from measured surface heat fluxes. Because of sensor errors or lack of sensitivity, the measurements may lead to erroneous estimates of the parameters. These errors can be ameliorated if the sensors are placed at points of maximum sensitivity. This paper describes two methods to optimize sensor locations: one to account for signal error, the other to consider interacting parameters. The methods are based upon variants of the normalized Fisher information matrix and are shown to be equivalent in some cases, but to predict differing sensor locations under other conditions, usually transient.

1.
Artyukhin
E. A.
,
1985
, “
Experimental Design of Measurement of the Solution of Coefficient-Type Inverse Heat Conduction Problem
,”
Journal of Engineering Physics
, Vol.
48
, No.
3
, pp.
372
376
.
2.
Artyukhin
E. A.
, and
Nenarokomov
A. V.
,
1988
, “
Optimal Experimental Design for Determining the Total Emissivity of Materials
,”
High Temperatures
, Vol.
26
, No.
5
, pp.
761
767
.
3.
Beck, J. V., and Arnold, K. J., 1977, Parameter Estimation in Engineering and Science, Wiley, New York.
4.
Beck, J. V., et al., 1992, “Joint American-Russian NSF Workshop on Inverse Problems in Heat Transfer,” Michigan State University.
5.
Cruse, T. A., 1989, “Probabilistic Structural Analysis Methods (PSAM) for Select Space Propulsion Components,” manuscript prepared under SwRI Project No. 06-8338, NASA Contract NAS3-24389.
6.
Ditlevesen, O., 1981, Uncertainty Modeling—With Application to Multidimensional Civil Engineering Systems, McGraw-Hill.
7.
Emery, A., and Fadale, T. D., 1990, “The Sensitivity of the Temperature Histories in the Shuttle Thermal Protection System to Radiation Heat Transfer,” ASME HTD-Vol. 137, pp. 81–88.
8.
Fadale, T. D., 1993, “Uncertainty Analysis Using Stochastic Finite Elements,” Ph.D. Dissertation, University of Washington, Seattle, WA.
9.
Fadale
T. D.
, and
Emery
A. F.
,
1994
, “
Transient Effects of Uncertainties on the Sensitivities of Temperatures and Heat Fluxes Using Stochastic Finite Elements
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
116
, pp.
808
814
.
10.
Fedorov, V. V., 1972, Theory of Optimal Experiment, Academic Press, New York.
11.
Ghanem, R. G., and Spanos, P. D., 1988, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York.
12.
Gill, P. E., et al., 1986, “User’s Guide for NPSOL—A Fortran Package for Nonlinear Programming,” Department of Operations Research, Stanford University, Palo Alto, CA.
13.
Goodwin
G. E.
,
Zarrop
M. B.
, and
Payne
R. L.
,
1974
, “
Coupled Design of Test Signals, Sampling Intervals and Filters for System Identification
,”
IEEE Transactions of Automatic Control
, Vol.
AC-19
, No.
6
, pp.
784
752
.
14.
Goodwin, G. E., and Payne, R. L., 1977, Dynamic System Identification. Experiment Design and Data Analysis, Academic Press, New York.
15.
Gorton, M. P., and Shideler, J. L., 1988, “Measured and Calculated Temperatures of a Superalloy Honeycomb Thermal Protection System Panel,” Proc. Workshop on Correlation of Hot Structures Test Data With Analysis, NASA Ames Dryden Flight Research Center.
16.
Haftka, R. T., and Kamat, M. P., 1985, Elements of Structural Optimization, Martinus Nijhoff Publishers.
17.
Kubrusly, C. S., and Malebranche, H., 1982, “A Survey on Optimal Sensors and Controllers Locations in DPS,” IFAC 3rd Symposium, Control of Distributed Parameter Systems, pp. 59–73.
18.
Lin, Y. K., 1967, Probabilistic Theory of Structural Dynamics, McGraw-Hill, New York.
19.
Liu, W. K., Besterfield, G., and Belytschko, T., 1988, “Transient Probabilistic Systems,” Computer Methods in Applied Mechanics and Engineering, Vol. 67.
20.
Musylev
N. V.
,
1980
, “
Uniqueness Theorems for Certain Inverse Heat Conduction Problems
,”
Zh. Vychisl. Mat. Fiz.
, Vol.
20
, No.
2
, pp.
388
400
.
21.
Polis, M. P., 1982, “The Distributed System Parameter Identification Problem: A Survey of Recent Results,” IFAC 3rd Symposium, Control of Distributed Parameter Systems, pp. 45–58.
22.
Seber, G. A. F., and Wild, C. J., 1989, Nonlinear Regression, Wiley-Interscience, New York.
23.
Sorenson, H. W., 1980, Parameter Estimation: Principles and Problems, Marcel Dekker, Inc., New York.
24.
Vanmarcke, E., 1977, “Probabilistic Modeling of Soil Profiles,” Journal of the Geotechnical Engineering Division, Vol. 103, GT11.
25.
Walter
E.
, and
Pronzato
L.
,
1990
, “
Qualitative and Quantitative Experiment Design for Phenomenological Model—A Survey
,”
Automatica
, Vol.
26
, No.
2
, pp.
195
213
.
This content is only available via PDF.
You do not currently have access to this content.