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Abstract: A general procedure is proposed to estimate the reliability of a dual-span rotor based on nonparametric modeling on random uncertainty. First, the vibration equation of the rotor with random uncertainty is constructed based on random matrices through the nonparametric modeling approach. Second, the reliability estimation is then performed by response spectral analysis and the moment method. By making full use of the advantages of nonparametric method and response spectral analysis, not only is the requirement on probability density function (PDF) avoided, but also the first and second moments are no longer needed to be estimated or assumed for calculating the reliability. Finally, the statistical index Z^*-value based on short-term predictability is introduced to investigate the influence of random uncertainties on the reliability of the dual-span rotor. Illustrating examples show that the results obtained from the proposed procedure are consistent with those from short-term predictability, such that dangerous ranges can be well identified during the start-up process of the rotor.

The central topic of this paper is the study of the reliability of a dual span rotor based on the nonparametric modeling on random uncertainty. With what appears to be well conducted mathematical derivation and numerical verification, the authors establish some interesting results, which states that the reliability calculation can be continued without knowing discrete movements by their procedure, and also, a large amount of information needed for determining the PDF is avoided in the reliability analysis. From their simulation results, the safe or failure ranges of the dual-span rotor system can be clearly estimated from the curves of the proposed reliability indices. The results are certainly of important significance for random uncertainty modeling and reliability analysis of rotating machinery.

双跨转子的随机不确定性非参数建模与可靠性分析

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