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基于灵敏度分析的有限元模型修正方法与Tikhonov正则化方法相结合,可以有效抑制实测模态参数中噪声的影响,正确识别结构损伤,但也存在着识别结果过度光滑的缺陷。通过在Tikhonov罚函数项中引入光滑函数,改善Tikhonov正则化方法对非光滑解的描述能力,在保持识别算法鲁棒性的同时,提高模型修正方法对于结构损伤的识别精度。以简支梁模型为例的损伤识别数值模拟表明,该文方法不仅能扩大正则化参数的可选择范围,还能显著降低噪声对识别结果的干扰,提高单元损伤程度的识别精度。
The combination of Tikhonov regularization method and finite element method based on sensitivity analysis can effectively suppress the influence of noise in the measured modal parameters and correctly identify the structural damage. However, there is a defect that the recognition result is too smooth. By introducing a smoothing function into the Tikhonov penalty function, the Tikhonov regularization method can improve the description ability of nonsmooth solutions. While maintaining the robustness of the recognition algorithm, the recognition accuracy of the model correction method for structural damage is improved. The numerical simulation of damage identification with simple support beam model shows that this method not only can expand the range of regularization parameters, but also can significantly reduce the interference of noise to the recognition result and improve the accuracy of unit damage identification.