研究了考虑试验频响函数不确定性的有限元模型修正法。首先,假设待修正参数和响应特征量服从高斯分布，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,构造径向基模型，将频响函数经过小波变换并提取第5层低频小波系数作为径向基模型输出，并通过土狼优化算法对径向基模型的方差进行优化；然后,以最小化巴氏距离为目标，引入花朵授粉算法，分别实施待修正参数的均值和标准差的两步和同步求解；最后,通过平面桁架结构和空间桁架结构验证了所提方法的可行性。结果表明，所提随机有限元模型修正法皆能有效地修正结构参数的均值和标准差，同时在不同的试验响应下对参数均值和标准差的修正具有鲁棒性。
Abstract
Here, the finite element model updating method considering the uncertainty of test frequency response function was studied. Firstly, assuming parameters to be modified and response characteristics obeying Gaussian distribution, the uncertainty model correction problem was converted into the mean and standard deviation correction problem. Secondly, the radial basis model was constructed, the frequency response function was transformed by wavelet transform, the 5th layer low frequency wavelet coefficients were extracted as the output of the radial basis model, and the variance of the radial basis model was optimized using the hyena optimization algorithm. Thirdly, in order to minimize Bhattacharyya distance, the flower pollination algorithm was introduced to perform solving the mean and standard deviation of parameters to be modified in two steps and simultaneously. Finally, the feasibility of the proposed method was verified with plane truss structure and space truss structure. The results showed that the proposed stochastic finite element model updating method can effectively modify the mean and standard deviation of structural parameters; the correction of mean and standard deviation of parameters has robustness under different test responses.
关键词
模型修正 /
不确定性 /
径向基模型 /
频响函数 /
巴氏距离
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Key words
model updating /
uncertainty /
radial basis model /
frequency response function /
Bhattacharyya distance
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