Improving the accuracy of normal form analysis

In second-order normal form (NF) analysis, the nonlinear dynamical system being analyzed is modeled with nonlinearities up to second order. Due to the presence of nonlinearities in the model, the results of second order NF analysis are initial condition dependent [1], [2]. There are two assumptions in the theory of NIT analysis and in this paper it has been shown that if the initial condition chosen do not satisfy these two main assumptions, then NF analysis is inaccurate. This paper also proposes three criteria to identify whether the initial condition satisfies one of the assumptions or not. This paper proposes to use a snap shot of state variables at an instant subsequent to the clearing of disturbance in situations where the state variables immediately after clearing the disturbance is not suitable for NF analysis. The time-domain simulations are presented to support the analysis.