Equivalent reconstruction of local distributed dynamic load based on block sparse Bayesian learning

A method for reconstructing equivalent loads using block sparse Bayesian learning (BSBL) is proposed for local distributed dynamic load (LDDL) without prior information on its spatiotemporal distribution. Considering the continuous variation of LDDL, a temporal distribution pattern consistency assumption is introduced, compressing LDDL into an equivalent load temporal distribution pattern function. First, the vibration response is transformed into modal loads in the modal space. Subsequently, based on BSBL, a structured redundant dictionary of basis functions derived from the pattern function is learned, enabling the reconstruction of the equivalent time distribution for the LDDL. Next, considering the structure's spatial characteristics, a redundant dictionary of structural mode shapes is constructed. BSBL is again applied to the non-zero encoding of the basis functions for sparse decomposition, solving for the spatial distribution corresponding to the basis functions and achieving the equivalent spatial distribution reconstruction of the LDDL. The reconstructed equivalent load obtained by the proposed method not only achieves equivalence in the response field but also reflects the spatiotemporal characteristics of the actual load to a certain extent. Numerical examples validate the effectiveness of this method.