Group Relevance Vector Machine for sparse force localization and reconstruction

Abstract Locations and amplitudes of external forces are essential information for design, loading assessment, and health monitoring of structures. In this paper, we propose an original time domain group sparsity regularization method, named Group Relevance Vector Machine, to localize and reconstruct external forces on structures based on structure responses only. Group Relevance Vector Machine constructs a structured regularization on the unknown forces, by binding the unknown amplitudes associated with different potential locations into separate groups and promoting the group-level sparsity between the potential locations. With this technique, we can adaptively localize and reconstruct dynamic point-forces in an underdetermined sensor configuration. Group Relevance Vector Machine is constructed and derived in detail under the hierarchical Bayesian framework. Its adaptivity, computational efficiency, and robustness with respect to noise and applied structure under underdetermined sensor configurations are comprehensively validated numerically on a cantilever beam and a cantilever plate, and experimentally on a cantilever plate and an engineering-scale tank.