Some observations on uncertainty propagation through a simple nonlinear system

This paper discusses a number of issues relating to the analysis of uncertain systems or data in the context of (low-frequency) structural dynamics. In order to illustrate potential problems in applying 'classical' uncertainty analysis methods to nonlinear systems, a simple nonlinear system is simulated and the breakdown of two standard approaches is demonstrated on data from the system. By relaxing the requirements of the analysis, it is shown that an alternative uncertainty theory gives useful qualitative information about the system. This motivates a discussion of how uncertainty frameworks should be chosen to suit the problem in hand and leads to a clustering of uncertainty problems in structural dynamics into three types: quantification, fusion and propagation.