基于JS-BP模型和JS散度的随机有限元模型修正

Stochastic Finite Element Model Updating Based on JS-BP Model and Jensen-Shannon Divergence

对考虑试验参数不确定性的有限元模型修正方法展开研究。首先假设待修正参数和响应特征量都服从正态分布,将不确定性模型修正问题转化为均值和标准差的修正问题;其次采用拉丁超立方抽样选取待修正参数样本点作为输入,并计算其对应的频响函数进行常数[Q]变换提取第一层系数作为输出,通过海蜇算法(JS)优化BP神经网络的权值和阈值,构建JS-BP神经网络模型;最后以最小化JS散度作为目标函数,实现对待修正参数的均值和标准差的同步修正。空间桁架算例表明,所提方法能够有效地修正结构参数的均值和标准差,并且在试验数据标准差不同时仍能得到较好的修正效果。

The finite element model updating method considering the uncertainty of test parameters is studied.Firstly,assuming that the parameters to be updated and the response characteristic variables obey normal distribution,the uncertainty model updating problem is translated to the mean value and standard deviation updating problem.Secondly,Latin hypercube sampling is used to extract the sample points of the parameters to be updated as the input,and the corresponding frequency response function is calculated,the constant[Q]transform is used to extract the first layer coefficient as the output.The artificial jellyfish search optimizer(JS)is used to optimize the weights and thresholds of BP neural network,and the JS-BP neural network model is constructed.Finally,with the minimum JS divergence as the objective function,the synchronous updating of the mean value and standard deviation of the parameters is realized.The results of a space truss example show that the proposed method can effectively update the mean value and standard deviation of structural parameters,and can still get better updating effect even if the standard deviation of test data is different.