基于倒数变量与广义柔度矩阵的桁架损伤识别

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中图分类号：TH113.1；O346.5 文献标志码：A 文章编号：1000-4939（2025）03-0639-07

Abstract：In order to improve the accuracy damage identification，this paper introduces the concept reciprocal variable and proposes a truss damage identification method combining reciprocal variable and generalized flexibility matrix.This method only needs low order modal parameters.In this paper，a control equation based on incomplete modes is introduced，and an iterative strategy based on non-negative least square method is used to solve the damage identification problem.In each cycle，the non-negative least square method is used to determine the damage location and degree the structure.By excluding the nondamaged elements，a new coefficient matrix is reconstructed，and the new coefficient matrix and the original right-hand term are used to solve the next cycle until the convergence accuracy requirements are met. Numerical simulation results show that compared with the original recognition method based on generalized flexibility matrix，the recognition effect the method combining reciprocal variable with generalized flexibility matrix is better.In the case noise and incomplete measured mode shapes，the method combining the incomplete mode shape control equation with the iterative strategy can maintain certain identification accuracy.

Key words： truss damage identification；reciprocal variable；generalized flexibility matrix；incomplete mode shape ； iteration；non-negative least squares method

结构在其使用寿命周期内可能会由于自身老化或者环境因素的影响而受损，这将降低结构的使用性能，甚至可能因为结构失效而导致灾难性事故的发生。（剩余9524字）