基于频率和模态保证准则的结构内部多缺陷反演

IDENTIFICATION OF MULTIPLE FLAWS IN STRUCTURES BASED ON FREQUENCY AND MODAL ASSURANCE CRITERIA

静响应(位移、应变等)在实际问题的反演分析中很难由安装在结构上的一组传感器记录得到,而结构的动力特性(频率、振型)和动力响应(加速度、速度、动位移)在实际问题中较易通过传感器采集得到.文中基于频率残差和模态保证准则构建了反演分析模型的目标函数,并结合频域内动力扩展有限元法和人工蜂群智能优化算法的优点,扩展有限元法通过引入非连续位移模式在不重新划分网格的情况下通过改变水平集函数反映缺陷的数量、位置及大小,避免了反演分析每次迭代过程中的网格重剖分,人工蜂群智能优化算法在每次迭代中都采用全局和局部搜索,找到最优解的概率大幅增大并可很好地避免局部最优,同时,通过引入拓扑变量,将缺陷的数量纳入到反演分析过程中,迭代过程中可智能反演出缺陷的数目,建立了结构内部多缺陷(孔洞、裂纹)的反演分析模型.通过若干算例的分析表明:建立的反演分析模型能够较为准确地探测出结构内部圆形、椭圆形以及裂纹状缺陷的数量、位置及大小,且算法具有较好的鲁棒性.

Static response (displacement, strain, etc.) can hardly be recorded by a group of sensors installed on the structure in the inversion analysis of practical problems, while the dynamic characteristics (frequency, mode) and dynamic response (acceleration, velocity, dynamic displacement) of the structure can be easily acquired by sensors in practical problems. In this paper, the objective function of the inversion analysis model is constructed based on frequency residuals and modal assurance criteria. Combining the advantages of dynamic extended finite element method in frequency domain and artificial bee colony intelligent optimization algorithm, the extended finite element method avoids re-meshing in each iteration by introducing discontinuous displacement approximation and can reflect the number, location and size of defects by changing the level set function. In each iteration, the artificial bee colony intelligent optimization algorithm uses global and local searches. The probability of finding the optimal solution increases greatly and avoids local optimum. At the same time, by introducing topological variables, the number of flaws is incorporated into the inversion analysis process. The number of flaws can be intelligently inverted in the iteration process. Then, the inversion analysis model of multiple flaws (voids, cracks) in the structure is established. The analysis of several examples shows that the inversion analysis model can accurately detect the number, location and size of circular flaws, elliptical flaws, or crack in the structure. The result also shows the good robustness of the algorithm.