利用冗余扩展余弦字典的复杂动载荷识别研究

Identification of complex dynamic load using redundant extended cosinetransform dictionary

针对真实测量噪声影响下复杂动载荷识别精度低的问题,提出了一种基于冗余扩展余弦字典的L1范数正则化载荷识别方法。根据系统响应与外部动载荷的卷积关系,建立用于载荷识别的离散系统控制方程;选择与动载荷相适应的离散余弦基函数进行时延扩展,构造了扩展余弦字典与Db10小波字典相级联的冗余扩展字典,对复杂载荷进行稀疏表示;使用L1范数正则化方法求解稀疏表示系数,基于改进L曲线准则获取最优正则化参数,通过在GARTEUR飞机模型上试验得到的响应数据,实现不同噪声水平下对拍频载荷与连续冲击载荷时间历程的识别。试验研究结果表明:本文提出的冗余扩展余弦字典对拍频载荷与连续冲击载荷的表示稀疏性高,基于冗余扩展余弦字典的L1范数正则化载荷识别方法的识别精度高、抗噪性能好。

Considering the low accuracy problem of complex dynamic load identification under the effect of real measurement noise,an L1 norm regularized load identification method based on redundant extended cosine transform dictionary is proposed.Ac-cording to the convolutional relationship between the system response and the external load,the discrete system control equation for load identification is established.According to the main characteristics of the vibration response signal,appropriate discrete co-sine basis functions are selected and extended,and the extended cosine dictionary and the Db10 wavelet dictionary are used to cas-cade a redundant extended dictionary to represent the complex load sparsely.By using the L1 norm regularization method to solve the sparse representation vector under the proposed redundant extended cosine transform dictionary,the optimal regularization pa-rameter is obtained by improved L curve criterion,and the identification of beat load and repetitive impact load at different noise levels is realized.The experimental verification results show that the constructed redundant extended cosine transform dictionary has much better performance in sparse representation of beat load and repetitive impact load,and the load identification method based on the redundant extended cosine transform dictionary has great advantages to obtain accurate inversion results and good ro-bustness.