Abstract. A method is proposed for assessment of uncertainty in recovering non-stationary heat flux by parametric identification of differential-difference models of heat transfer in the system of bodies. The requirements imposed upon the structure of non-stationary heat flux transducers, mathematical models of heat transfer in the body system, and the nature of heat flux change and the used recovery methods are formulated. A Kalman filter with required parameters is employed to minimize the discrepancy between measured values and the model parameters. Mathematical expressions derived for the sensitivity functions describes the effects of all relevant factors of non-stationary thermometry including type and parameters of heat transfer in the heat flux transducers (HFT), number and location of temperature measuring points or drops, the quality of recording channels of measured quantities, specific of input actions. Obtained dependences determining the Gram matrix (the Fisher information matrix) for system of vectors of sensitivity functions allow to calculate the confidential region for measurement of the desired parameters. The proposed method of uncertainty estimation for heat flux recovery makes it possible to determine the boundaries of the method applicability with the account for permissible uncertainty, to formulate requirements for the used HFT, select the type and structure of HFT that meets the requirements, create HFT with desired characteristics. An example of confidence region determination for non-stationary flux measurement using battery HFT is presented.

Keywords: uncertainty of non-stationary heat flux measurement, parametric identification of differential-difference models, Kalman filter, Gram matrix

References:

1. Pilipenko N.V. Journal of Instrument Engineering, 2003, no. 10(46), рp. 67–71. (in Russ.)
2. Simbirskiy D.F. Temperaturnaya diagnostika dvigateley (Temperature diagnostics of engines), Kiev, 1976, 208 p. (in Russ.)
3. Pilipenko N. Heat Transfer Research, 2008, no. 4(39), рp. 311–315. (in Russ.)
4. Alifanov O.M., Vabishchevich P.N., Mikhaylov V.V. et al. Osnovy identifikatsii i proektirovaniya teplovykh protsessov i sistem (Bases of Identification and Design of Thermal Processes and Systems), 2001, 400 р. (in Russ.)
5. Alifanov O.M. Identifikatsiya protsessov teploobmena letatel'nykh apparatov. Vvedenie v teoriyu obratnykh zadach teploobmena (Identification of Processes of Heat Exchange of Aircraft. Introduction to the Theory of the Return Problems of Heat Exchange), Moscow, 1979, 216 p. (in Russ.)
6. Beck J.V., Blackwell V., Clair C.R. Inverse Heat Conduction, Ill-Posed Problems, 1989, 312 p.
7. Artyukhin E.A. Journal of Engineering Physics and Thermophysics, 1989, no. 3(56), рp. 378–382. (in Russ.)
8. Yaryshev N.A. Teoreticheskie osnovy izmereniya nestatsionarnykh temperatur (Theoretical Bases of Measurement of Non-Stationary Temperatures), Leningrad, 1990, 256 р. (in Russ.)
9. Yaryshev N.A. Nauchnaya shkola i shkola zhizni (Scientific School and the School of Life), St. Petersburg, 2010, 296 р. (in Russ.)
10. Simbirskiy E.F., Gol'tsov A.S., But E.N. Teplofizika i teplotekhnika, 1977, no. 33, рp. 92–96. (in Russ.)
11. Simbirskiy D.F., Oleynik A.V., Makarenko G.V. Planirovanie i otsenka pogreshnosti kosvennykh izmereniy (Planning and Assessment of an Error of Indirect Measurements), Leningrad, 1989, рр. 47–49. (in Russ.)
12. Simbirskiy D.F. Мeasurement Techniques, 1983, no. 1, pp. 12–14. (in Russ.)
13. Pilipenko N.V. Мeasurement Techniques, 2007, no. 8, pp. 54–59.
14.  Hudson D.J. Lectures on Elementary Statistics and Probability, Geneva, 1964.
15.  Himmelblau D.M. Process Analysis by Statistical Methods, NY, John Wiley & Sons, Inc., 1970.
16. Pilipenko N.V., Kirillov K.V. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2010, no. 5(69), рp. 106–109. (in Russ.)
17. Pilipenko N.V., Kazartsev Ya.V. Journal of Instrument Engineering, 2011, no. 5(54), рp. 88–93. (in Russ.)