基于L1范数正则化和最小二乘优化的冲击载荷识别研究

Research on Impact Load Identification Based on L1-Norm Regularization and Least Squares Optimization

为了改善冲击载荷识别问题的病态特性,最大限度提高识别精度,在时域内提出一种基于L1范数正则化和最小二乘优化的改进冲击载荷识别方法。采用L1范数正则化方法构建冲击载荷稀疏反卷积模型,使用截断牛顿内点法求解L1范数的最小二乘优化问题,同时根据预条件共轭梯度法确定最优搜索路径和计算方向。最后,考虑不同冲击工况、不同响应位置对识别结果的影响。通过对铝合金板进行冲击载荷识别试验进行验证,发现在铝板受单次冲击和多次冲击工况下所识别载荷与施加的实际载荷吻合良好。结果还表明,与Tikhonov正则化方法相比,该方法能够提高冲击载荷识别的准确性和稳定性。

In order to improve the ill-conditioned characteristics of the impact load identification and maximize the accuracy of identification, an improved method of impact load identification in time domain based on L1-norm regularization and least square optimization is proposed. Firstly, the L1-norm regularization method is used to construct the impact load sparse deconvolution model, and the truncated Newton interior point method is used to solve the least squares optimization problem of the L1-norm, Then, the optimal search path and calculation direction are determined according to the preconditioned conjugate gradient method. Finally, considering the influence of different impact conditions and different response positions on the identification results, the impact load identification test of the aluminum alloy plate is carried out to verify the identification method. It is found that the identified load of the aluminum alloy plate under single impact and multiple impacts is in good agreement with the actual load applied. The results also show that compared with the Tikhonov regularization method, this method can improve the accuracy and stability of impact load identification.