基于复变量求导及Levenberg-Marquardt法对梁的损伤识别研究

Damage Identification of Beams Based on Complex-variable-differentiation and Levenberg-Marquardt Method

文中结合复变量求导方法,利用Levenberg-Marquardt算法,构建了一种损伤识别模式,并以此实现对简支梁结构的损伤识别。该模式以单元弹性模量的减少模拟损伤,采用有限元方法获得结构的振动加速度响应,构造用振动响应与计算响应差值的最小二乘函数作为目标函数的识别依据。在识别过程中,采用Levenberg-Marquardt算法进行弹性模量的迭代计算,引用复变量求导法解决在识别过程中灵敏度计算困难的问题,并通过极小化目标函数求得损伤的弹性模量。分析了不同工况中有无噪声条件下梁的损伤识别效果。数值算例表明,该方法具有一定的鲁棒性。

Combined with the complex-variable-differentiation method, a damage recognition mode was constructed by Levenberg-Marquardt algorithm to identify the damage of simply supported beam. The simulated damage could be adopted by decreasing the elastic modulus, and the structure vibration acceleration response was obtained through using the finite element method. Then through the least square function of the difference between the vibration response and the calculated response, an objective function identification basis could be constructed. In the identification process, Levenberg-Marquardt algorithm was used to perform elastic modulus iterative calculation, the complex-variable-differentiation was used to solve the difficulty of sensitivity calculation in recognition process, and the damage modulus was taken by minimizing the objective function. In this paper, the damage identification effect of beams under different working conditions with or without noise was analyzed. Numerical examples show that the method has good robustness.