Abstract. The use of the Kalman digital filter algorithm for parametric identification of differential-difference models of heat transfer in body systems by solving inverse problems of thermal conductivity is considered. The Kalman filter allows to estimate the uncertainty of recovery of the required parameters by minimizing the discrepancy between the measured and model values of the parameters, in particular, the unsteady heat flow. An analysis of the Kalman filter by parameters is given, its advantages and disadvantages are specified. An extended Kalman filter allowing to reduce significantly the volume of calculations of a matrix of sensitivity functions and to exclude completely need of a task of often unknown initial temperature distribution in object of research is proposed. The proposed method of recovery of non-stationary heat flow using the extended Kalman filter is implemented by the software complex "Heat Identification" and implemented in the practice of non-stationary thermometry. The results of model and full-scale experimental studies are presented.

Keywords: Kalman filter, heat flux, heat flux transducer, differential-difference models

References:

1. Pilipenko N.V. Journal of Instrument Engineering, 2017, no. 7(60), pp. 664–671. (in Russ.)
2. Pilipenko N. Heat Transfer Research, 2008, no. 4(39), pp. 318–315.
3. Sivakov J.A., Pilipenko N.V. Measurement Techniques, 2011, no. 3(54), pp. 318–323.
4. Pilipenko N.V., Gladskih D.A. Measurement Techniques, 2014, no. 2(57), pp. 181–186.
5. Pilipenko N.V. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2009, no. 3(61), pp. 52–58.
6. Derusso P.M., Roy R.J., Close Ch.M. State Variables for Engineers, Wiley, 1965.
7. Beck J.V., Blackwell V., Clair C.R. Inverse Heat Conduction, Ill-Posed Problems, 1989, 312 p.
8. Pilipenko N.V. Metody parametricheskoy identifikatsii v nestatsionarnoy teplometrii (Parametric Identification Methods in Non-Stationary Calorimetry), St. Petersburg, 2016, 79 р. (in Russ.)
9. Pilipenko N.V., Sivakov I.A. MEASUREMENT TECHNIQUES, 2011, no. 3(54), pp. 318–323.
10. Pilipenko N.V. Primeneniye fil'tra Kalmana v nestatsionarnoy teplometrii (Using Kalman Filter in Non-Stationary Calorific Value), St. Petersburg, 2017, 34 р. (in Russ.)
11. Pilipenko N.V. Pribory i metody nestatsionarnoy teplometrii (The Devices and Methods of Non-Stationary Thermometry), St. Petersburg, 2016, 82 р. (in Russ.)
12. Meditch J.S. Stochastic optimal linear estimation and control, NY, McGraw-Hill Book Co., 1969, 394 p
13. 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.)
14. Kirillov K.V., Pilipenko N.V. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2010, no. 5(69), pp. 106–109. (in Russ.)
15. Lykov A.V. Teoriya teploprovodnosti (Heat Conduction Theory), Moscow, 1966, 591 р. (in Russ.)