Uncertainty quantification of subcritical bifurcations

Abstract

Analysing and quantifying parametric uncertainties numerically is a tedious task, even more so when the system exhibits subcritical bifurcations. Here a novel interpolation based approach is presented and applied to two simple models exhibiting subcritical Hopf bifurcation. It is seen that this integrated interpolation scheme is significantly faster than traditional Monte Carlo based simulations. The advantages of using this scheme and the reason for its success compared to other uncertainty quantification schemes like Polynomial Chaos Expansion (PCE) are highlighted. The paper also discusses advantages of using an equi-probable node distribution which is seen to improve the accuracy of the proposed scheme. The probabilities of failure (POF) are defined and plotted for various operating conditions. The possibilities of extending the above scheme to experiments are also discussed.