Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model

Krzysztof Oprzędkiewicz, Maciej Rosół and Wojciech Mitkowski
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Krzysztof Oprzędkiewicz: Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, Poland
Maciej Rosół: Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, Poland
Wojciech Mitkowski: Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, Poland

Energies, 2022, vol. 15, issue 6, 1-13

Abstract: In the paper, the problem of modeling of thermal traces is addressed. The proposed model allows prediction of the behaviour of a thermal mark left by a warm body on cooler ground. In the model, a fractional order (FO) approach is employed. This allows consideration of an inital function (not only a condition in one, initial time instant). The proposed model uses a scalar FO differential equation approximated with the use of Continuous Fraction Expansion (CFE) approximation. This allows maintenance of a relatively small size of the model with good accuracy in the sense of a Mean Square Error (MSE) cost function. Experimental verification confirms good accuracy of the proposed model in modeling of thermal traces.

Keywords: non integer order systems; 2D heat transfer; fractional order state equation; initial problem; CFE approximation; thermal camera; thermal trace (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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