Efficient model reduction in non-linear dynamics using the Karhunen-Loeve expansion and dual-weighted-residual methods

We look at the task of computing the time-evolution of a non-linear system for a long time, in our case under random external influences. Our specific example is the fatigue evaluation of a wind turbine. To facilitate such a computation, we look at a reduction of the computational effort by projecting everything on a low-dimensional basis. In this case we take the Karhunen-Loeve basis generated from running the model a little while under the random loading. It is important that the error which is caused by this reduction process can be controlled. We estimate the error by dual or adjoint methods. This in turn allows the process of model reduction to be performed adaptively.