Simultaneous estimation of temperature-dependent volumetric heat capacity and thermal conductivity functions via neural networks

Abstract

An artificial neural network based solution of the inverse heat conduction problem of simultaneous identification of the temperature-dependent volumetric heat capacity and thermal conductivity function of a solid material is presented in this paper. The inverse problem was defined according to the evaluation of the BICOND thermophysical property measurement method. The volumetric heat capacity and thermal conductivity vs. temperature functions are to be determined using the measured transient temperature histories of two sensors. In this study noiseless and noisy artificial measurements were generated by the numerical solution of the corresponding direct heat conduction problem. The inverse problem was solved by multi-layer feed-forward neural network trained by back-propagation algorithm (BP) and radial basis function (RBF) type neural network applying the whole history mapping approach. As suggested by Czél et al. [1], a novel (time vs. temperature) representation of the input data was applied. Numerical tests were performed to analyze the accuracy of the two network types with noiseless and noisy inputs. Moreover, it is not necessary to retrain the network when the temperature range of the measurement is changed. Based on the presented results it can be stated that feed-forward neural networks are powerful tools in non-iterative solution of function estimation inverse heat conduction problems and they are likely to be very effective in evaluation of real measured temperature histories to simultaneously determine the volumetric heat capacity and thermal conductivity as an arbitrary function of temperature.