考虑混合不确定性的转子临界转速的灵敏度快速计算方法  

Rapid sensitivity calculation method for rotor critical speeds considering hybrid uncertainties

作　　者：林海东 邓振鸿 邓旺群 聂卫健 刘文魁 张保强 冯吴俊 LIN Haidong;DENG Zhenhong;DENG Wangqun;NIE Weijian;LIU Wenkui;ZHANG Baoqiang;FENG Wujun(School of Aerospace Engineering,Xiamen University,Xiamen 361102,China;AECC Hunan Aviation Powerplant Research Institute,Zhuzhou 412002,China;Key Laboratory of Aero-engine Vibration Technology,Aero Engine Corporation of China,Zhuzhou 412002,China;School of Energy and Power Engineering,Beihang University,Beijing 102206,China)

机构地区：[1]厦门大学航空航天学院,福建厦门361102 [2]中国航发湖南动力机械研究所,湖南株洲412002 [3]中国航空发动机集团航空发动机振动技术重点实验室,湖南株洲412002 [4]北京航空航天大学能源与动力工程学院,北京102206

出　　处：《厦门大学学报(自然科学版)》2025年第2期277-285,共9页Journal of Xiamen University:Natural Science

基　　金：中国航发产学研合作项目(HFZL2020CXY004,HFZL2020CXY009)。

摘　　要：[目的]为了实现转子系统中存在不确定性时各变量对临界转速影响程度的快速求解,提出一种考虑混合不确定性的全局灵敏度快速计算方法.[方法]采用概率盒表征输入参数的混合不确定性;再将混沌多项式展开(polynomial chaos expansion,PCE)与切比雪夫(Chebyshev)区间法相结合,分别用于处理随机和认知不确定性;最后通过不确定性传递求解Sobol灵敏度指标的上下界实现全局灵敏度分析.建立某动力涡轮模拟转子的有限元模型,以系统参数对其临界转速的灵敏度分析为例,对所提出方法进行验证,并与传统的双层蒙特卡洛采样法(Monte Carlo sampling,MCS)进行对比.[结果]在计算精度相当的情况下,与双层MCS相比,本文所提方法计算时间减少了98.63%,显著提高了灵敏度分析的效率.[结论]该方法可快速获得考虑混合不确定性情况下与转子临界转速有关参数的重要性排序.[Objective]To rapidly determine the impact of various variables on the critical speed of rotor systems with uncertainty,herein we propose a rapid global sensitivity calculation method in which hybrid uncertainties are considered.[Methods]In this method,probability boxes are used to represent the mixed uncertainty of input parameters.Then combine the Chebyshev interval method with the polynomial chaos expansion(PCE)to handle cognitive and random uncertainties,respectively.Finally,global sensitivity analysis is achieved by solving the upper and lower bounds of the Sobol sensitivity index through uncertainty transfer.A finite element model of a simulated power turbine rotor is established to verify the proposed method through sensitivity analyses of system parameters on its critical speeds.[Results]Our simulation results are compared with those obtained by the traditional double-loop Monte Carlo sampling(MCS)method.They indicate that,with comparable computational accuracy,the proposed method reduces computation time by 98.63%compared to the double-loop MCS,thus significantly enhancing the efficiency of sensitivity analyses.[Conclusions]The proposed method can quickly obtain the importance ranking of parameters related to the critical speed of rotor-considering mixed uncertainties.

关 键 词：临界转速 混合不确定性 多项式混沌展开 切比雪夫区间法 全局灵敏度 Sobol指标 

分 类 号：V23[航空宇航科学与技术—航空宇航推进理论与工程]