基于空间稀疏先验的冲击载荷识别频域非凸稀疏正则化方法

Composite materials are widely used in aviation, aerospace and other fields because of their advantages such as high strength, high stiffness and low density. However, due to its poor impact resistance, monitoring the impact force acting on the composite structure is very important for timely detection of structural damage. The classic Tikhonov regularization method tends to obtain false forces in the non-loaded area when solving the force identification problem under the under-determined condition. The well-known LI sparse regularization method is prone to underestimate the amplitude of the impact force. In order to break through the limitations of these methods and identify impact forces with higher accuracy, a novel frequency-domain non-convex sparse regularization method was proposed for impact force identification based on the spatial sparse prior of impact forces. In the proposed method, the non-convex advantage of the generalized minmax concave penalty term was combined with the convexity-preserving characteristics, and the forward-backward splitting algorithm was utilized for convex optimization. This approach avoids the problem of non-convex optimization converging to local optima and promotes sparsity of the solution. Laboratory impact tests were conducted on composite beams and laminated composite plates to validate the proposed method. The results indicate that the proposed method can accurately localize the impact positions and reconstruct the time history of impact forces, in the case of either even-determined or under-determined scenarios. The performance of the proposed method in promoting solution sparsity and identifying force amplitudes is superior to the LI regularization method, with an improvement of over 50% in amplitude identification accuracy compared to the LI regularization method.