基于神经网络响应面法的汽轮机叶片强度可靠性分析

Artificial neural network-based response surface method for strength reliability analysis of steam turbine blade

对叶片强度进行可靠性分析,当功能函数为随机输入变量的隐性函数时,就无法直接用常规可靠性分析方法得到叶片的可靠度,因此将有限元,神经网络响应面和一阶可靠性方法(FORM)相结合,针对某汽轮机振动实验台的等直叶片,考虑几何参数、材料参数和载荷参数的随机性,在合理构造神经网络结构的基础上,利用有限元数值计算获得神经网络训练样本,通过对样本的学习和训练,获得叶片功能函数与随机变量之间的映射关系;选择非线性S型函数作为网络隐含层的激励函数,利用该函数的一阶导数是其自身函数的特点,推导出了功能函数对随机变量的一阶偏导数,进而采用FORM方法得到了叶片可靠性指标β并完成叶片强度的可靠性分析。将计算结果与Monte-Carlo模拟法进行对比,证明了该方法的正确性和有效性。该方法为后续进一步研究多失效模式下叶片的可靠性分析提供了新的思路。

As the performance function of steam turbine blade is implicit function in terms of the input random variables, the traditional reliability analysis method such as first-order reliability method （FORM） is not directly used to obtain the blade strength reliability. So, this paper proposed a method which combines the finite element method （FEM）, artificial neural network-based response surface method and FORM to analyze the blade rdiability. An equal cross-section blade was investigated and its geometrical parameters, material parameters and loading parameters are considered as input random variables. A reasonable artificial neural network is constructed and its training samples are obtained via finite element numerical calculation. The mapping relationship between the performance function and in- put random variables are obtained by successful training network. The logistic sigrnoid function is used as activation function in the hidden layer in that its derivative is easily found and can be expressed in terms of the function itself. So, the first order partial derivatives of the performance function with respect to the design random variables can be obtained and the strength rdiability indexβ of the blade can also be calculated by FORM. Moreover, the calculation result is compared with that of traditional Monte Carlo simulation method, which proves the approach in this paper is correct and valid and can also provide a new idea for further research about reliability analysis of the blade under multi- failure mode.