Generalized Grouping Regularization for Time Domain Force Reconstruction Problems

Grouping regularization has received attention in recent studies because it offers flexibility and better noise immunity than traditional methods. In this paper, we propose the generalized grouping regularization (GGR). With different parameter settings, GGR provides localization ability, adaptive basis selection ability, and at the same time reconstruct forces in low signal-to-noise ratio (SNR) conditions. And with specific parameter settings, the proposed method degenerates to traditional Tikhonov regularization and compressed sensing. GGR is supposed to serve as the general regularization scheme for time domain force reconstruction problems. A cantilever beam simulation shows its superiority.