针对冲击载荷识别中存在病态矩阵求逆的不适定问题和噪声敏感问题，给出一种增广Tikhonov正则化技术的改进贝叶斯方法。通过引入小波阈值方法解决高噪声水平下多源/连续冲击载荷识别精度不佳的问题，在识别过程中自适应地确定最优正则化参数,并有效地剔除噪声对冲击载荷识别的影响。通过开展飞机壁板结构在不同冲击载荷和信噪比噪声下的数值仿真分析，以相关系数和相对误差作为评价指标，对比讨论了基于L曲线法和广义交叉检验法的Tikhonov正则化方法、贝叶斯正则化方法以及本文方法的识别效果，结果表明本文方法兼顾了曲线的光滑性与峰值识别的准确性，在20dB高噪声水平连续冲击载荷识别时峰值平均误差不超过14%。开展了典型加筋壁板结构的冲击试验，验证了本文方法对实际工程中典型多源/连续冲击载荷的识别能力，峰值平均误差控制在18%以内，为解决工程应用中的载荷识别问题提供了有效途径。
Abstract
To solve the ill-posed problem and noise sensitivity in the recognition technology of shock load, an improved Bayesian regularization method based on Tikhonov regularization technology was proposed. By introducing the wavelet thresholding method to the Bayesian regularization method, it further solved the poor recognition accuracy of multi-source/continuous shock loads under high noise level, allowing for more accurate selection of regularization parameters and more reasonable elimination of noise influence. By carrying out the finite element simulation analysis of different impact loads and signal-to-noise ratio noise of aviation aluminum wall plate structures, and taking the correlation coefficient and relative error as the evaluation indexes, the recognition effects of the Tikhonov regularization method based on the L-curve method, the Tikhonov regularization method based on the Generalized Cross Validation method and the improved Bayesian regularization method are compared and discussed. The results show that the improved Bayesian method takes into account the smoothness of the curve and the accuracy of peak recognition. At the high noise level of 20dB, the average error of the peak value is controlled within 14% when the continuous shock load is recognized. In addition, the impact test based on the actual reinforced aviation aluminum wall plate structure is carried out, which verifies the ability of the method of this article to accurately identify the peak value of typical impact load in practical application, and the average error of the peak is controlled within 18%, which provides an effective way to solve the load identification problem in engineering.
关键词
载荷识别；贝叶斯正则化；小波阈值法；不适定问题 /
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Key words
Load identification /
Bayesian regularization /
Wavelet thresholding method /
Ill-posed problem
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