FAST NON-CONVEX SPARSE REGULARIZATION FOR IMPACT FORCE IDENTIFICATION

Impact force identification as a typical inverse problem is definitely a challenging task to simultaneously reconstruct and localize impact forces. While sparse solutions can be induced, the standard ℓ₁ sparse regularization tends to underestimate the amplitude of impact forces, thus it may interfere with the subsequent damage assessment of mechanical structures. With regards to this, we propose a fast non-convex(FNC) sparse regularization method that incorporates a non-convex generalized minimax-concave penalty as a regularizer and introduces an acceleration strategy to rapidly achieve the global optimum. This non-convex penalty can not only promote sparsity of the estimation, but also preserve the convexity of the cost function, so that it avoids the case of convergence to a locally optimal solution. This method is applied to solve the impact force identification problem in the underdetermined case to simultaneously reconstruct and localize impact forces. Experiments are performed on a composite fan blade to validate the FNC method in its computational efficiency and identification accuracy in terms of impact force reconstruction and localization. Results indicate that proposed FNC method converges faster and it simultaneously reconstructs and localizes impact forces with higher accuracy than the classic ℓ₁ sparse regularization method.