Epistemic uncertainty propagation in energy flows between structural vibrating systems

• A dimension-wise method for the epistemic uncertainty propagation is proposed.
• Cuts of the response through a point at each dimensionality are approximated.
• Min/max point vectors are dimension-wisely obtained via Legendre approximations.
• DWM also applies to the dynamic analysis of systems with interval parameters.

A dimension-wise method for predicting fuzzy energy flows between structural vibrating systems coupled by joints with epistemic uncertainties is established. Based on its Legendre polynomial approximation at α=0, both the minimum and maximum point vectors of the energy flow of interest are calculated dimension by dimension within the space spanned by the interval parameters determined by fuzzy those at α=0 and the resulted interval bounds are used to assemble the concerned fuzzy energy flows. Besides the proposed method, vertex method as well as two current methods is also applied. Comparisons among results by different methods are accomplished by two numerical examples and the accuracy of all methods is simultaneously verified by Monte Carlo simulation.