基于应变模态和贝叶斯方法的杆件损伤识别

Damage Detection of Bars Based on Strain Mode and Bayesian Statistical Method

提出了一种基于空间杆系结构应变模态和贝叶斯统计方法的损伤识别方法。对于空间杆系结构,认为其杆件只承受轴向应力,因此,由节点位移可得出各杆件应变。文中采用一个转换矩阵来表示这种关系,进而得出应变模态的摄动矩阵。然后,对可能损伤的杆件乘以一刚度系数,由于应变模态误差能用高斯分布近似模拟,应用贝叶斯统计方法便可得到这些参数的概率密度函数。由此函数值的最大化构造目标函数进行优化,通过得到的各参数的最优解就能判断杆件的损伤状况。最后,通过数值算例对该方法进行了验证。

A damage detection approach was proposed by employing strain mode of structure and Bayesian statistical method. For spatial truss structures, they are consisted of steel pipes, which were regarded as space bars. The strains of all elements could be obtained by the displacements of all nodes owing to axial stress was predominant, and the relationship can be expresses by a transition matrix. Then the perturbation matrix of strain mode was deduced further. Potential damaged elements were allocated uncertain parameters to scale their contributions to the global stiff matrix. As the uncertain strain modes can be well approximated by a Gaussian distribution, the probability density function （PDF） of the uncertain parameters was constructed by Bayesian statistical method. Consequently, by maximizing the PDF, the optimal parameters were determined, which expressed the damage conditions of the potential damaged elements. At last, a numerical example was presented to demonstrate the efficiency of the approach.