Method of Determining Thermophysical Properties of Soil Based on the Solution of Invers Heat Conduction Problems

The article addresses the problem of determining the thermophysical characteristics (TPC) of soil based on results from a thermal-physics experiment involving temperature measurements for the rational design of heat pump (HP) systems. The approach relies on achieving a stable solution to the coefficient inverse problems of heat conduction (IPHC) using Tikhonov regularization principles with an effective algorithm for determining the regularization parameter. The functional minimization is carried out iteratively, where at each step, the minimum of a quadratic functional is sought. This functional is constructed through linearization of the functional dependence of computed temperature on the sought characteristic, represented as two additional terms of the Taylor series. The proposed approach has proven effective for both individual thermal-physical characteristics of the medium and for solving combined IPHC while simultaneously identifying soil TPC. The article emphasizes the independence of the convergence of the iterative parameter mathematical model search process from their initial approximation. At the same time, it should be noted that the accuracy of recovering the TPC of soil depends on the number of temperature measurement points: reducing their number decreases the precision of identification. Another factor affecting the accuracy of identification is the measurement error of temperatures at the thermometry points, which is modeled in the study as a random variable with zero mean and unit variance. Thus, numerical experiments have shown that the accuracy of identification decreases as the thermometry error increases.