Uncertainty quantification of subcritical bifurcations

• Uncertainty quantification is performed in subcritical bifurcation systems.
• Parametric uncertainties in such dynamical systems result in bimodal probability density functions (PDFs).
• For accurate predictions of the response PDFs, the discontinuities of the response surface needs to be resolved.
• A new interpolation based algorithm is proposed here to capture discontinuous response surfaces and PDFs accurately.
• Stochastic bifurcation and probability of failure are also discussed.

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.