Probabilistic collocation method for strongly nonlinear problems: 3. Transform by time

The probabilistic collocation method (PCM) has drawn wide attention for stochastic analysis recently. Its results may become inaccurate in case of a strongly nonlinear relation between random parameters and model responses. To tackle this problem, we proposed a location‐based transformed PCM (xTPCM) and a displacement‐based transformed PCM (dTPCM) in previous parts of this series. Making use of the transform between response and space, the above two methods, however, have certain limitations. In this study, we introduce a time‐based transformed PCM (tTPCM) employing the transform between response and time. We conduct numerical experiments to investigate its performance in uncertainty quantification. The results show that the tTPCM greatly improves the accuracy of the traditional PCM in a cost‐effective manner and is more general and convenient than the xTPCM/dTPCM.