基于空间-频域联合稀疏的复合材料结构冲击载荷识别

Impact ForceIdentification of Composite Structures Based on Spatial-frequency Domain Joint Sparse Prior

冲击载荷识别反问题具有典型的不适定,经典冲击载荷识别方法如Tikhonov正则化方法,在识别精度、超参数选取、传感器数量选取等方面存在局限性。近年来兴起的稀疏正则化方法为冲击载荷识别提供了新思路,可依据冲击载荷在空间-频域联合稀疏先验,建立具有稀疏结构约束的冲击载荷识别数学模型。提出利用改进的正交匹配追踪算法对模型进行求解,实现少测点欠定条件下,对作用于复合材料结构的冲击载荷的同时定位与重构。将所提出方法与经典的Tikhonov正则化方法以及L1稀疏正则化方法进行对比,复合材料层合板的数值仿真和试验均表明,所提出方法允许稀疏的传感器布局,实现了3个应变片监测9个载荷作用点,冲击定位、载荷重构精度高、抗噪性能好,并且表现均超过Tikhonov正则化方法和L1标准稀疏正则化方法。

The inverse problem of impact force identification is typically ill-posed,classical methods for impact force identification,such as the Tikhonov regularization method,have limitations in terms of identification accuracy,hyper-parameter determination and sensor selection.In recent years,the emerging sparse regularization methods have provided new ideas for impact force identification.By means of the joint sparse prior of impact forces in space-frequency domain,a novel model of impact force identification with sparse structure constraints is established.The model is solved by the improved orthogonal matching pursuit algorithm,and the simultaneous localization and reconstruction of the impact forces can be realized in the under-determined circumstances of less measurements.The proposed method is compared with the Tikhonovand L1 regularization methods.Numerical and experimental validations show that the proposed method allows for sparse sensor placement,and can monitor nine potential impact locations using three strain gauges,with high accuracy and good anti-noise performanceand outperforms the Tikhonov regularization and the L1 regularization methods.