基于BFGS摄动法的固定梁损伤检测  

BFGS Perturbation Method for Damage Detection of Fixed-Fixed Beam

作　　者：黄振南[1] 胡彪[2] 

机构地区：[1]兰州理工大学机电工程学院,兰州730050 [2]电子科技大学机械电子工程学院,成都611731

出　　处：《振动．测试与诊断》2016年第3期536-540,607,共5页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(50905028;51275554)

摘　　要：运用损伤结构的特征值问题,建立拟牛顿法的BFGS优化摄动方法来检测固定梁的损伤情况。多单元两端固定梁的损伤位置与程度,可以从首几对振动模态在数次迭代內准確获取。首先,摄动展开损伤结构的刚度矩阵、特征值和特征向量,并代入损伤结构的特征值方程;然后,集合p阶的弹性模量摄动项,以显式直接推导特征参数的p阶摄动系数;最后,把系数代入摄动方程,对于多个弹性模量进行BFGS拟牛顿优化迭代,其目标函数由摄动方程剩余项的总和产生。使用两端固定梁的有限元模型,五单元至九单元梁的损伤检测验证了该方法在有限模态参数与减少自由度模型的有效性。在终止准则方面,使用了d-模与t-模比较不同迭代阶段的收敛性,并精确地在0.06~0.001弹性模量误差內检测了小至大损伤的各个单元号及其损伤程度。Using the eigenvalue problem of damaged structure,the BFGS perturbation method is constructed to detect the damage situation of a fixed beam.Damaged locations and their extents of fixed-fixed beam with multiple elements can be accurately obtained in a few iterations using several vibration modes.First,perturbation expansions of the stiffness matrix,eigenvalue and eigenvector perturbation equations of the damaged structure are carried out and will be substituted into the eigenvalue equation of the damaged structure.Then,eigen-parameter p-th order perturbation terms of all orders are derived explicitly and directly by gathering p-th elastic modulus perturbed terms.Finally,by substituting the perturbation terms into the perturbation equations,multiple elastic moduli are optimized using the BFGS quasi-Newton iteration.Its objective function is generated from the summation of the remaining terms in the perturbation equation.Using the finite element model of fixed-fixed beam,the applicability of the algorithm under limited modes and reduced-order models is validated by damage detections on the five to nine elements beam.In termination criterion aspect,convergences of different iteration statuses are compared using d-norm and tnorm indicators.Various element numbers and their damage extents are accurately detected with 0.06to0.001 elastic modulus errors.

关 键 词：BFGS摄动法 两端固定梁 损伤检测 拟牛顿优化 

分 类 号：TH113.1[机械工程—机械设计及理论]