Robust Nonconvex Sparse Optimization for Impact Force Identification

The inherent sparse structure of impact forces has garnered considerable attention in the field of impact force identification. However, conventional convex sparse regularization methods, including the widely used l(1) regularization, often encounter challenges such as underestimation of impact amplitudes and biased estimations. To address these limitations, we propose a robust nonconvex sparse regularization method for impact force identification. The key advantage of our method is the simultaneous retention of robustness and unbiasedness. The robustness of our method is primarily achieved through an efficient solver developed within the alternating direction method of multipliers (ADMM) framework. By combining convex and nonconvex strategies, the ADMM solver separates the intractable nonconvex problem into more manageable convex sub-problems. Additionally, the ADMM solver incorporates the firm-thresholding operator, which ensures an unbiased amplitude distribution and preserves the impact amplitudes. With a sparse and under-determined sensor configuration, our proposed method enables simultaneous impact localization and time-history reconstruction. We comprehensively demonstrate the algorithmic performance through a series of numerical simulations and laboratory experiments on typical composite structures. The comparative results clearly indicate that our proposed approach achieves significant improvements in identification accuracy compared to classical sparse regularization methods, such as l(1) and l(0) regularization.