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UNCERTAINTY OF NON-STATIONARY HEAT FLUX RECOVERY BY PARAMETRIC IDENTIFICATION OF DIFFERENTIAL-DIFFERENCE MODEL OF HEAT TRANSMISSION

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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.

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