Group Relevance Vector Machine for sparse force localization and reconstruction

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 loca-tions. 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 adaptiv -ity, 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. (c) 2021 Elsevier Ltd. All rights reserved. Information of external excitations acting on mechanical and civil structures is essential for their loading condition assessment [1-4], health monitoring [5-7], and fatigue analysis [8-11]. These excitations, in a substantial number of cases, cannot be measured directly with force transducers. For example, the external excitation locations may be forbidden to install transducers, inaccessible, or unknown in advance. In other cases, installing transducers may bring undesired or unacceptable changes to the dynamic properties of structures. Force identification techniques are developed to bypass these limitations, which combines the responses at accessible locations and the system dynamic model to indirectly estimate the external excitations. Force identification involves localizing the unknown forces and reconstructing their time histories. If force locations are a