Inverse problems applied to the experimental thermal and hygric analysis of engineering materials

Abstract

Several relevant real-world applications rely on an inverse problem, which involves recovering unknown causes from observing their effects. This differs from the corresponding direct problem, whose solution involves predicting effects from a complete description of their causes. Naturally, inverse problems are more challenging than direct problems because, in general, they are ill-posed, i.e., the solution either does not exist, is not unique or it does not depend continuously on the input data. To soften this problematic aspect, applied inverse modeling requires detailed mathematical-physical modeling and well-designed experiments since the desired parameters are estimated by comparing calculated data with experimental measurements. In this PhD thesis, inverse approach was applied to experimentally investigate three case studies: • complementary experiments to simultaneously estimate the parameters describing the temperature-dependent thermal conductivity and specific heat of 304 austenitic stainless steel. Parameter estimation takes advantage of additional information provided by two heat-conducting solids with different geometries. It is an alternative approach to standard thermal characterization techniques, which are often beyond the reach of many laboratories. • one-year on-site measurements to estimate various hygrothermal properties and thus calibrate the simulation model of a lightweight multilayer wall. A 2D fully coupled heat and moisture transfer model was used to investigate the in-use response of the panel junction region, which is critical in terms of airtightness. The results enable an accurate assessment of building operating conditions by reducing uncertainties in material input data. • field data to determine the annual heat conduction flux through a wall assembly in an occupied house. Inverse modeling accounted for the physical interactions between outdoor environment and indoor occupancy. The methodology and the findings are useful to support decision-making on energy performance, as there is a lack of longterm field monitoring and information on dynamic heat flux related to prefabricated occupied dwellings. All the above inverse analyzes were based on evaluating the match between data predicted by numerical simulations in COMSOL Multiphysics and measurements conveying the physical behavior of the component under study. Numerical and experimental data were processed and used for inverse estimation purposes in MATLAB environment. After careful analysis of sensitivity coefficients, different optimization approaches were used to solve the inverse problems. Bayesian statistical inference was applied to determine the estimates and corresponding uncertainties of the thermal properties of 304 stainless steel. The Broyden– Fletcher–Goldfarb–Shanno (BFGS) algorithm, which determines the descent direction by preconditioning the gradient with curvature information, was used in the second case study. The wall heat flux was estimated using the sequential function specification method (SFSM), which expresses temperature as function of heat flux by means of a first-order Taylor series. The results show that inverse modeling is a reliable tool for obtaining valuable information about the hygrothermal mechanisms and parameters involved in applied engineering problems.