The Monte Carlo method is computationally demanding. Consequently, applying that method to high-dimensional nonlinear systems is practically not feasible. Therefore, a new strategy is proposed in this article, which enables the evaluation of the response statistics of high-dimensional structures subject to random seismic excitations in a nonlinear reduced low-order subspace. It is shown that the new model order reduction method provides the possibility to overcome the computational issue of large-scale Monte Carlo simulations. It provides reliable approximations of the response statistics, when compared with those of the non-reduced Monte Carlo method.
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