框架结构损伤识别的改进非线性直接解析法

IMPROVED NONLINEAR ANALYTICAL METHOD FOR DAMAGE IDENTIFICATION OF FRAME STRUCTURES

考虑到直接解析法求解速度快和非线性直接解析法求解精度高的特点,提出一种用于结构损伤识别的混合迭代算法,该算法用二阶非线性的解析解作为算法的第一次迭代值,用一阶灵敏度方程的求解值对该算法的第一次迭代值进行关于泰勒级数截尾误差的修正。通过对一个空间框架结构进行数值模拟分析验证了该方法的可行性。结果表明,提出的混合迭代算法由于采用了精确度较高的二阶非线性解析解作为迭代修正的初值,因此,迭代修正精度更高,收敛性更好,而且大幅地减少了运算时间,尤其对于多损伤或者大损伤,本算法优势更加明显。

The generalized inverse technique was used to solve the first order equation,and the trust-region reflective Newton method was used to solve the second order sensitivity equation.Considering the fast solving speed by the first order sensitivity equation and the high solving precision by the second order equation,a mixed iteration algorithm which was applied in structure damage detection was put forward.This algorithm uses the second order nonlinear analytical solution as the first substituting value,and then the first substituting value is modified based on the taylor series bias error using the solution of the first order sensitivity equation.The modal analysis program and damage identification program about space frame based on the finite element theory were carried out.Damage identification was studied using the mixed iteration algorithm which was mentioned in this paper.It shows that the mixed iteration algorithm has a better convergence and a faster iteration speed because the higher precision second order nonlinear analytical solution is adopted.