In this paper the problem of updating the parameters of a probabilistic computational model, describing overall behavior of spatially large structures, based on uncertain output information is analyzed. An Unscented Kalman Filter (UKF) variant is successfully used in order to solve this computationally intensive inverse problem although the analysis has not been cast in this case as a state estimation problem of a dynamic system. The performance of this inverse solver is also compared with other generic gradient-free methods. To reduce the computational demands of the stochastic model a series of steps is taken consisting of sensitivity analysis for functional model inputs and probabilistic homogenization techniques, in relation to moments of the output quantities. For improved clarity and readability, and without loss of generality for this type of problems, the whole process is described along a specific application concerning diffusion phenomena in a reinforced concrete slab and spatial steel damage.