Calculation of second order statistics of uncertain linear systems applying reduced order models

This contribution investigates the application of reduced order models for approximating the response of a class of uncertain linear systems. The basis associated with the reduced model is generated based on the results of a single analysis of the system plus a sensitivity analysis. The aforementioned strategy is applied in combination with control variates, thus allowing to estimate the second order statistics of the system's response. In this way, accurate estimates of these statistics can be generated with reduced numerical efforts, as a large number of samples of the system's response is evaluated with the reduced order model while only a small number of samples of the full model is required. Numerical examples comprising stochastic finite element models suggest that the proposed approach can produce estimates of the second order statistics with reduced variability.