Abstract: Impact force identification plays an important role in structural health monitoring, dynamics optimization design, milling force measurement, etc. However, the traditional L2 norm-based regularization methods run into the bottleneck and limitation on identification accuracy, stability, computational efficiency, parameter selection, etc. Sparse regularization theory widely developed in recent years is a promising technique for impact force identification. Considering the prior information that the impact force is sparse in time domain, a general impact force sparse identification model is proposed, where the traditional minimization L2 norm penalty is replaced by the minimization L1 norm penalty. A sparse regularization model based on L1 norm is established, leading to breaking through the limitation of the low identification accuracy of the traditional L2 norm-based regularization methods in impact force identification. The sparse identification method based on L1 norm is examined and compared with the Tikhonov regularization method based on L2 norm under single impact force and multiple impact forces. Experimental results of identifying impact force acting on a thin plate structure demonstrate that the sparse regularization solution based on L1 norm is sufficiently sparse in time domain, where the noise in the unloading stage of impact force is greatly inhibited; the proposed sparse identification method has great advantages of reconstructing impact force history, stability and computational efficiency over the traditional Tikhonov regularization method.

Key words: impact force identification, inverse problem, regularization, sparse identification