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基于信赖域的Levenberg-Marquardt法有限元模型修正

Finite Element Model Updating of Levenberg-Marquardt Method Based on Trust Region
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摘要 基于灵敏度的有限元模型修正方法常因灵敏度矩阵病态或非满秩问题而面临修正困难.虽然传统的Levenberg-Marquardt(L-M)算法能够解决这些问题,但其计算成本较高.为此,提出了一种基于信赖域的改进LM算法,并通过对T形尾翼的仿真算例进行修正对比,验证两种算法的修正速度和精度差异.结果显示,两种算法均能将参数基本修正至目标参数,但改进L-M算法计算成本更低,证明了改进算法在修正效率上的优势.以钢制T形尾翼模型为例,通过试验和有限元分析,分别获得了实际模型和有限元模型的前8阶固有频率.采用改进L-M算法对T形尾翼进行修正,经过3次迭代,前8阶频率的绝对平均误差从修正前的13.02%降至1.67%,频率精度显著提升.可以看出,改进算法也具有很高的工程应用价值. The finite element model updating method based on sensitivity often encounters difficulties due to the ill-conditioning or rank-deficiency issues of the sensitivity matrix.However,the traditional Levenberg-Marquardt(L-M)algorithm,while addressing these problems,has a high computational cost.To address this,a modified L-M algorithm based on the trust region method is proposed.The updating speed and accuracy differences between the two algorithms are compared through a simulation case of a T-tail wing.The results show that both algorithms can generally update the parameters to the target values,but the improved algorithm has a lower computational cost,demonstrating its advantage in updating efficiency.Using a steel T-tail wing model as an example,the first eight natural frequencies of the actual model and the finite element model are obtained through experiments and finite element analysis,respectively.The improved algorithm is used to update the T-tail wing model,and after three iterations,the absolute average error of the first eight frequencies is reduced from 13.02%to 1.67%,significantly enhancing the frequency accuracy.This demonstrates that the improved algorithm also holds substantial engineering application value.
作者 伍平 王立峰 刘欢 Wu Ping;Wang Lifeng;Liu Huan(State Key Laboratory of Mechanics and Control for Aerospace Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)
出处 《宁夏大学学报(自然科学版)》 CAS 2024年第4期333-339,共7页 Journal of Ningxia University(Natural Science Edition)
基金 国家自然科学基金资助项目(U2341230)。
关键词 模型修正 有限元模型 改进L-M算法 固有频率 model updating finite element model modified L-M method natural frequency
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