A model-based deep learning approach to interpretable impact force localization and reconstruction

Model-based and deep learning-based methods have been widely studied for force identification. However, model-based methods usually have high computational complexity and face challenges in parameter setting, while the generic network structures in deep learning methods are mostly designed empirically. In this paper, a model-based deep learning network is proposed to simultaneously localize and reconstruct impact f[orces. The proposed network, dubbed NSC-Net, is obtained by unrolling the iterative shrinkage-thresholding algorithm (ISTA) for the non-negative sparse coding (NSC) model. NSC-Net combines the interpretability of the model-based ISTA with the powerful parameter learning capability of deep learning. The transfer matrix is embedded into the network as physical information through learnable scaling. The structure of NSC-Net is based on explicit theoretical analysis, which enhances its interpretability in terms of structural design. In contrast to ISTA, the parameters in NSC-Net can be trained end-to-end from the training data without manual setting. Simulations and experiments on composite panels are conducted to validate the performance of the proposed method. The results demonstrate that NSC-Net accurately localizes and reconstructs impact forces, outperforming both ISTA and learned iterative shrinkage-thresholding algorithm (LISTA) network. Additionally, NSC-Net exhibits excellent noise immunity. Furthermore, the systematic approach of constructing an algorithm unrolling network for impact force identification is summarized, aiming to facilitate further related research. •A novel model-based deep learning method is proposed for impact force identification.•A deep network named NSC-Net is constructed by unrolling the ISTA for the NSC model.•The NSC-Net is based on explicit theoretical analysis for interpretable structure.•The proposed NSC-Net is verified in simulations and experiments.