Radial Basis Function Extreme Response Surface Method for Reliability Analysis of Mistune Blisk Vibration
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摘要: 为了研究随机刚度失谐对叶盘振动可靠性的影响,将径向基函数神经网络与极值响应面结合提出了径向基极值响应面法。选取叶盘材料密度、工作转速、激振力幅值作为随机输入变量,叶盘振幅极值为输出响应,利用拉丁超立方抽样法抽取不同输入样本点,通过有限元分析计算得到各样本点对应的振幅极值响应,用抽取的样本点构建径向基极值响应面,并结合蒙特卡洛法对随机变量进行大批量抽样,将其带入径向基极值响应面分析得到叶盘振动可靠度。结果表明,在随机刚度失谐因素影响下,叶盘振动可靠性降低,更容易发生振动失效。通过与蒙特卡洛法、极值响应面法进行对比,得出径向基极值响应面在保证计算精度的情况下提高了计算效率。Abstract: In order to study the vibration reliability of aeroengine blisk under the influence of random stiffness mistuning, a radial basis function extreme response surface method (RBFERSM) is proposed by combining the radial basis function artificial neural nets (RBFANN) with extreme response surface method (ERSM). The material density, angular velocity and amplitude of force of the blisk are taken as random input variables, the extreme response of blisk vibration as the output response, the RBFERSM is constructed with the sample points, which are sampled by Latin hypercube sampling method. Than a large number of input random variables are sampled with Monte Carlo method and are taken into the RBFERSM to calculate the output responses. The results show that vibration reliability of the mistune blisk is reduced and its vibration failure is more likely to occur. By comparing with MCM and ERSM, it concluded that RBFERSM in this study can improve the calculation efficiency on the premise of ensuring the accuracy of calculation.
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表 1 叶盘固有频率
阶次 1 2 3 4 5 6 谐调叶
盘/Hz203.28 217.34 217.34 396.25 396.25 427.12 失谐
叶/Hz203.28 217.34 217.37 396.2 396.22 426.39 表 2 失谐叶盘振动可靠性分析随机变量选择
变量 均值 标准差 密度/(kg·m3) 4 620 231 转速/(rad·s-1) 1 168 58.4 气体激振力幅值/MPa 0.1 0.005 表 3 叶盘可靠性分析对比
叶盘类型 振幅均值μ/mm 振幅标准差σ/mm 总体失效数 可靠度/% 谐调叶盘 0.444 88 0.001 084 3 0 100 失谐叶盘 0.517 91 0.000 675 74 94 99.06 变化率/% 15.37 37.68 - 0.94 表 4 RBFERSM和ERSM的训练速度与均方误差
方法 训练速度/s 均方误差 ERSM 2.856 2.496×10-3 RBFERSM 0.157 2.566 7×10-4 表 5 MCM、ERSM和RBFERSM的抽样时间
s 方法 102 103 104 105 106 MCM 10 800 14 400 - - - ERSM 1.854 1.861 1.859 1.956 3.216 RBFERSM 1.517 1.527 1.571 1.684 2.741 表 6 不同抽样次数下可靠性分析方法精度对比
样本数量 MCM/可靠度 ERSM/可靠度 ERSM/% RBFERSM/可靠度 RBFERSM/% 102 0.875 0.708 3 80.94 0.86 98.85 103 0.97 0.846 1 87.22 0.963 99.27 104 - 0.942 4 - 0.990 6 - 105 - 0.941 81 - 0.992 42 - 106 - 0.941 35 - 0.994 86 - -
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