Abstract
A method is obtained for the parameter identification of one-dimensional heat conduction systems with unknown boundary conditions. The boundary conditions are assumed to be known up to constant parameters. The identification problem is formulated as the simultaneous estimation of unknown parameters and input functions based on the overspecified boundary data. Applyinig the concept of elementary solutions, an integral representation is introduced so as to give the explicit expression for the measured data in terms of unknown parameters and estimated input functions. The least square method is applied for the identification of distributed and boundary parameters. The input functions are estimated by solving a second-kind Volterra's integral equation. The methodology is applied for the modeling of the dynamic behavior of ambient temperature based on the observations at the surface of the earth. The simulation results are compared with measured data to prove that the mathematical model proposed in this paper can describe the diurnal variation of ambient temperature caused by solar radiation.
