Statistical identification of local heat-transfer parameters

Abstract

This article examines an external inverse heat,conduction problem on determining thermal parameters which are variable over time and along a boundary.Since mathematical models are generally inadequate for fully describing thermal processes, identification of the parameters of a thermal system (parametric identification) usually entails simultaneous solution of a problem of structural identification (refinement of the mathematical model itself).Naturally, the structural identification is the more complicated task. Thus, to reduce its importance in the overall problem, when constructing the model it is necessary to account as fully as possible for all internal relationships, thermophysical characteristics and external effects.In particular, in solving the internal inverse heatconduction problem, it is best to determine not the mean values of the characteristics but values dependent onthe space and time coordinates.The latter instance more accurately reflects processes actually occurring in objects with distributed parameters. Such processes are usually described by an imprecise structural model [i] which, in the most general formulation, is nonlinear and requires linearization --since it is necessary to construct transfer matrices to describe a nonsteady thermal process in the form of a dynamic recursion system. When methods of statistical identification are used, it is expedient to also employ statistical linearization, entailing the best probability approximation of nonlinear relations by relations linearized on the basis of normalization of the laws of the distribution of random processes [2]. A simple and adequate course of action here is to replace the nonlinear Px, ~) U(~),where fo is a vectorial statistical characteristic of nonlinearity, i.e., a function of the probability moments of the variables X.. The norm of the vector fo --Am X is sufficiently l small.The components of the matrices A and B and the vector fo can be found from the criterion of the minimum of the mean square error [3]. In the formulation being considered, the vector of state will include the desired local heat-transfer parameters, which vary along the boundary.It should be noted that, in identifying local parameters (such as heat-~rans-fer coefficients variable over the contour of the investigated region), we deal with individual closed contour loops which are joined together into a single multiple-connected automatic control system.The number of loops, meanwhile, is determined by the number of sections of the surface being investigated within which the heat-transfer parameters are taken as constant. In other words, since determining the local boundary conditions requires making allowance for the correlations between all of the control loops, it is best to include characteristic temperatures of each of the investigated local regions in the measurement vector.Thus, the object function, which has to be constructed, should include all of the sought parameters and the results of temperature measurements.Since the problem being examined is ...

Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution

“…However, because the experimental temperature data are inevitably affected by uncertainties, the stopping criterion can be defined by adopting the approach called the discrepancy principle, originally formulated by Morozov [39] and later on implemented for filtering technique and applied by many authors [5,40,41]. According to this principle, the inverse problem solution is regarded to be sufficiently accurate when the difference between the estimated and measured temperatures is close to the standard deviation of the measurements.…”

“…With regard to this and other similar problems, the iterative procedures described in [4,5,26] have proven to be very effective. According to the approach followed in [26], the temperature distribution on a thin wall obtained by numerically solving the corresponding direct problem is forced to match the experimental noisy data acquired by means of infrared thermography by tuning the local value of the heat transfer coefficient under the constraint given by the sensitivity of the adopted experimental facility.…”

“…The desired information is then suitably restored from either the steady or the unsteady local energy balance in the wall by solving the corresponding steady or unsteady inverse heat conduction problem (also referred to, respectively, as SIHCP and UIHCP) with the temperature distribution as input data [1][2][3]. More precisely, because the unknown quantity is a boundary surface function, this problem is often referred to as a boundary inverse heat transfer problem [4][5][6].…”