Uncertainty quantification of dynamical systems by a POD-Kriging surrogate model

Uncertainty quantification (UQ) of dynamical systems with a surrogate model is difficult as the surrogate model parameters often need to be computed at each time step. For that reason, a different kind of surrogate model is presented in this article by representing the stochastic response quantity using lower number of bases. Proper orthogonal decomposition (POD) is used to project the response quantity with low number of POD bases and the uncertainty is propagated using the Kriging model. The combined POD-Kriging model is used for UQ of four dynamical systems and all the results are compared with the Monte Carlo simulation results. The first three problems are long time integration problems and the time-dependent statistical moments are predicted well by the POD-Kriging model using low number of model evaluations. For the last example (a building subjected to Gaussian white noise base acceleration), the prediction accuracy of the POD-Kriging model is also high as compared to a similar surrogate model.