基于神经网络及自适应随机采样的桥梁颤振可靠度分析

Reliability analysis of bridge flutter based on neural network and adaptive stochastic sampling

文章采用径向基函数(radial basis function,RBF)神经网络替代复杂的有限元模型分析,结合基于加权抽样和动态距离约束的自适应采样策略,建立一种颤振可靠度分析方法。基于全模态理论建立参数化颤振临界风速分析有限元模型,并将试验设计生成的样本代入有限元模型求解得到训练集,进而构建RBF模型;通过定义的自适应采样策略,在迭代过程中不断从蒙特卡洛(Monte Carlo,MC)方法生成的样本中筛选出失效面附近的样本点添加至训练集,重新训练RBF模型直至满足收敛要求,并基于该RBF模型和MC样本直接计算得出颤振失效概率。通过2个经典数值算例对文中所提方法的有效性和准确性进行验证。结果表明,该文提出的可靠度分析方法及其自适应随机采样策略在保证计算精度的同时,能够大幅减少海量有限元模型运算带来的计算耗费,并降低功能函数的高维非线性和非显性带来的计算复杂度。

A modified method for calculating the flutter reliability of bridges is presented by using radial basis function(RBF)neural network instead of complex finite element model analysis,which is integrated with the adaptive stochastic sampling technique based on weighted sampling and dynamic distance constraint.Firstly,a parametric finite element model of critical flutter wind speed is established based on the full-mode theory,and the samples generated by design of experiments(DOE)method are substituted into the finite element model to solve the training set,so as to build the initial RBF neural network.Secondly,the points near the limit state that are picked up from samples generated by Monte Carlo(MC)method with the pre-defined adaptive sampling rule are added into the training set to update the RBF model.The procedure of the filter-update continues until the convergence of the RBF,and then the failure probability can be calculated directly.Finally,the effectiveness and accuracy of the proposed method is verified by two classical numerical examples.The results show that at the precondition of keeping precision,the proposed method can not only reduce the calculation cost caused by massive finite element model operation,but also reduce the computational complexity caused by the high-dimensional nonlinear and implicit functions.