Some Strategy for Handling Measurement Biases in Inverse Problems with Application to Thermophysical Properties Identification

The influence of measurement biases on the estimation of thermophysical properties in transient experiments by means of inverse technique is analyzed. The material under investigation is subjected to a transient, one-dimensional conductive test. Then, from temperature and heat flux measurements on the boundary and at the interior of the specimen, the thermal conductivity and the specific heat are simultaneously reconstructed, as a function of temperature, by solving the associated inverse heat conduction problem. As well known, various systematic errors may affect measurements during the thermal transient with loss of accuracy in the identified thermophysical properties. In this work a strategy is proposed for handling some typical biases and many examples, coming both from numerical and true experiments, are reported and discussed. In particular the following three sources of error are considered and compensated: the uncertainty in the knowledge of the exact location of thermal sensors inside the specimen, the error of temperature measurement affecting the sensors (thermocouples) in dynamic regime and the statistical effect of the calibration uncertainty on the quality of the final estimates. In all cases the strategy adopted for handling the biases can be synthesized as follows: the improvement of the measurement process by adding appropriate physical models, to take into account each source of discovered error; the identification of the additional coefficients appearing in the models; the validation of the above procedure by means of proper indexes such as temperature or heat flux residuals, temperature dependent confidence regions of the estimated parameters, etc. The examples and the experimental results reported in this work refer to light insulating materials and show that a proper compensation of the effects of the above biases gives rise to a sensible improvement in the accuracy of the reconstructed thermophysical properties. Thermal conductivity and specific heat are reconstructed as a function of temperature with an accuracy comparable or even better than that obtainable with more consolidated standard methods.