一种改进的残余力向量法在结构损伤识别中的应用

残余力向量法是结构损伤识别中常用的方法，复杂结构中单元数量较多而损伤位置较少，容易造成无关变量增多，进而导致计算量过大的问题。鉴于此，本文提出一种改进的残余力向量法用于结构的损伤识别。该方法利用刚度联系向量与残余力向量之间线性相关的特性，以向量投影值作为损伤定位的影响系数，初步筛选出结构可能出现损伤的单元范围。在此基础上，构建出残余力向量对应的线性方程组，根据顺序主子式不为零的条件，对线性方程组进行行初等变换，再根据单元的数量保留前n维线性方程，通过求解该方程组的代数解可得到该结构单元的刚度损伤参数。以简支梁为例的数值模拟表明，本文方法可减少无关单元变量的计算，降低残余力向量的维度并且具有较好的抗噪能力。

Application of an improved residual force vector method in structural damage identification

Residual force vector method is a commonly used method in structural damage identification.Considering that a complex structure has many elements and few damage locations,it is easy to define too many unwanted variables,which leads to the problem of excessive computation.Therefore,this study presents an improved residual force vector method for structural damage identification.The method utilizes the linear correlation between the stiffness connection vector and the residual force vector.It uses the vector projection value as the influence coefficient of damage location.The suspect elements of possible structural damage are first located.In addition,a set of linear equations about residual force vector is constructed.According to the condition that the order principal form is not zero,this study conducts an elementary row transformation on the linear equations.According to the number of elements,the method can retain n-dimensional linear equations.From the algebraic solution of the equations,this study has obtained the stiffness and damage parameters of the structural elements are obtained.A simply-supported beam is simulated numerically.The results show that the proposed method can not only reduce the calculation of unrelated element variables,and the dimension of the residual force vector but also have better anti-noise ability.