Updating an uncertain and expensive computational model in structural dynamics based on one single target FRF using a probabilistic learning tool

The paper presents an appropriate and efficient methodology for updating the control parameters of very large uncertain computational models, which are used for analyzing the linear vibrations in the frequency domain of highly complex structures for which there are an enormous number of intertwined local and global elastic structural modes in the broad frequency band of analysis. Moreover, the numerical cost of a single evaluation of the frequency response functions with the computational model is assumed to be very high and only one experimental frequency response function is available as a target. For decreasing the numerical cost of this challenging problem, a parameterized reduced-order model is constructed. Nevertheless, this reduction is not sufficient to be able to solve the non-convex optimization problem related to the updating. Consequently, for avoiding the call to the computational model, the probabilistic learning on manifolds is used for generating a learned set from a training set, which, coupled with conditional statistics, allows the evaluation of the cost function without calling the computational model. A numerical illustration is presented for validating the proposed methodology.