涡轮叶片模糊响应面可靠性分析方法

The Fuzzy Response Surface Reliability Analysis Method of Turbine Blades

为提高涡轮叶片可靠性分析的精度,在考虑输入变量模糊性和极限状态模糊性的基础上,提出了结构可靠性分析的模糊响应面法(fuzzy response surface method,FRSM)。首先,采用等价转换的方法,将带有模糊性的输入变量转换为当量随机变量;然后,基于二次多项式响应面函数,建立结构可靠性分析的模糊响应面数学模型。利用蒙特卡洛法对该模型进行大量的联动抽样,得到叶片应力、径向变形的均值及方差;最后,基于概率积分法计算事件失效概率及模糊随机可靠性指标。分析结果表明,叶片的可靠性指标随模糊系数的增大而减小;与传统基于随机变量的方法相比,该方法对不确定性的描述更为合理,理论上对可靠性的评估更为准确。

In order to improve the reliability analysis precision of turbine blades,the fuzzy response surface method(FRSM,Fuzzy Response Surface Method)of structural reliability analysis is put forward considering the fuzziness of input variables and limit states.First,using the method of equivalent transformation,the input variables with fuzziness is converted into equivalent random variables.Then,the mathematic model of fuzzy response surface for structural reliability analysis is established based on the quadratic polynomial response surface function.The mean value and the variance of the stresses and radial deformations of the blades were gained through a lot of joint sampling of the model using the Monte Carlo method.Finally,the event failure probability and the fuzzy random reliability index are calculated based on the probability integral method.The analysis result shows that the blade reliability indexes decrease with the increase of fuzzy coefficient.Compared with the traditional method based on random variables,this method is more reasonable for the description of uncertainty,and the evaluation of reliability is more accurate theoretically.