Group sparsity extension of "Non-convex sparse regularization via convex optimization for impact force

We recently proposed a non-convex sparse regularization method in the ADMM framework to reconstruct and localize unknown impact forces. This method surpasses the convex l(1) regularization not only in inducing sparsity but also in avoiding the high-amplitude underestimation of solutions. In this work, we aim to improve the identification performance and enable the monitoring of unknown impact forces with fewer sensors by incorporating prior information in the form of natural grouping of the solution components. To achieve this, we extend our previous work on non-convex sparse regularization by incorporating group information into the method. The resulting group sparsity problem is challenging to solve due to the mixed structure and possible grouping irregularity. To address this, we develop an efficient ADMM solver in a grouped manner, featuring a novel shrinkage operator. We validate our approach both numerically and experimentally on aircraft-like composite laminated plates. Our case studies demonstrate that the proposed method achieves high accuracy and strong robustness in impact localization and time-history reconstruction from single-sensor-based measurements.