Uncertainty quantification method based on interval random moment
To tackle the problem of quantitative analysis of inherent characteristics of gear-rotor systems which lacked sufficient information to build an accurate probability model,an uncertainty quantification method based on interval random moment technology was proposed.Rayleigh quotient formula was firstly introduced to derive the approxi-mate solution of the natural frequency of gear-rotor systems with random interval mixed variables.Then,the inter-val variables were expressed as the distribution parameters of random variables,and the uncertainty modeling was carried out with the established random variables.Combined with Taylor expansion of multi-dimensional interval random functions and ordered moment method,the expressions of the mean and variance of the natural frequency of the gear-rotor system were derived.Furthermore,the upper and lower bounds of the mean and variance were ob-tained according to the fundamental algebraic operations and interval budget rule,and the influence law of random and interval variables on the natural frequency of the system was analyzed through the fluctuation of the upper and lower bounds and the concavity and convexity of the function curve.A numerical example of a gear-rotor system was used to verify the correctness and effectiveness of the proposed method.
interval random moment technologyuncertainty quantificationapproximate solutionnatural frequencygear-rotor systems
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