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以基于灵敏度分析的有限元模型修正方法为基础,提出了一种基于1范数正则化过程的结构损伤识别方法。通过与以Tikhonov正则化为代表的二次型正则化过程相比较,本文的理论分析表明1范数正则化方法在迭代计算过程中能根据上一迭代步损伤识别结果自适应地调整正则化项中的损伤参数权系数,从而显著改善了Tikhonov正则化识别结果过度光滑的缺陷,更利于识别结构的局部损伤。为解决引入1范数造成的数值计算困难,文中还对基于1范数正则化的模型修正算法进行了改进。以二维框架模型为例的损伤识别数值模拟表明:1范数正则化方法与模型修正方法相结合可以有效抑制实测模态参数中噪声的影响,体现出较好的鲁棒性;在模态噪声水平达到10%的情况下,仍能有效抑制噪声干扰,凸显结构局部损伤位置,准确识别损伤程度。
Based on the finite element model correction method based on sensitivity analysis, a structural damage identification method based on 1-norm regularization process is proposed. Compared with the quadratic regularization process represented by Tikhonov regularization, the theoretical analysis of this paper shows that the 1-norm regularization method can adaptively regularize the regularization term according to the damage identification results of the previous iteration during the iterative computation The damage coefficient weight coefficients in Tikhonov regularization can significantly improve the over-smoothness of the Tikhonov regularization recognition results, which is more conducive to the identification of local damage to the structure. In order to solve the numerical calculation difficulty caused by the introduction of 1-norm, the model modification algorithm based on 1-norm regularization is also improved. The numerical simulation of damage identification using two-dimensional frame model as an example shows that: 1 The combination of norm regularization method and model correction method can effectively restrain the influence of noise in the measured modal parameters, which shows better robustness; Under the condition that the noise level reaches 10%, the noise interference can still be effectively suppressed, the local damage position of the structure is highlighted, and the damage degree is accurately identified.