Identification of external forces via truncated response sparse decomposition under unknown initial conditions

When structural dynamic design for smart control and health monitoring is executed, imposed excitations on structures are one of most important issues in structural engineering. Identification of structural excitations, such as force reconstruction, moving force identification, and so on, has drawn increasing attentions in the last decades. Assumption of known initial conditions is a precondition for existing deterministic force reconstruction methods. However, initial conditions are often unknown and hard to be estimated. To address this problem, a novel truncated response sparse decomposition method is proposed for calculating the external forces under unknown initial conditions. The truncated response sparse decomposition involves two basic steps, that is, response sparse decomposition and force estimation. First, a collection of basis vectors is defined for expressing unknown forces. Unknown initial conditions are represented in modal space. Structural responses induced by both external forces and initial conditions are then normalized as potential response features to form an image dictionary, which is adapted to decompose the measured responses via sparse regularization. Second, the response features with lower decomposed amplitudes and small scaling factors are eliminated from the decomposed results. The remaining features are used for estimating the external forces. In order to assess the accuracy and the feasibility of the proposed force reconstruction method, some numerical simulations on a planar truss structure and a series of experimental studies are carried out. The illustrated results show the robustness and the applicability of the proposed method for addressing the force reconstruction problem under unknown initial conditions. Some related issues are discussed as well.