Dynamic system uncertainty propagation using polynomial chaos

The classic polynomial chaos method (PCM), characterized as an intrusive methodology, has been applied to uncertainty propagation (UP) in many dynamic systems. However, the intrusive polynomial chaos method (IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.