Local mode-in-state participation factors for nonlinear systems

In this paper, a new definition for modal participation factors for nonlinear systems is proposed and used to obtain a formula for local mode-in-state participation factors. While the definition is general, the obtained formula depends on the assumption made regarding the distribution of the system initial condition. The definition extends work in the linear setting by Hashlamoun, Hassouneh and Abed (2009), and entails taking an average (or expectation) of a modal participation measure over an uncertain set of system initial conditions. As in the linear case, it is found that a symmetry assumption on the distribution of the initial state results in a tractable calculation and an analytical formula for mode-in-state participation factors. While the dichotomy discovered in the linear case between mode-in-state participation factors and state-in-mode participation factors exists also in the nonlinear setting, specific calculations for state-in-mode participation factors is more involved than for mode-in-state participations, and is left for further work.