Reconstructing the surface velocity of a vibrating structure using a weighted transfer matrix mode method

•The weighted transfer matrix mode (TMM) is used for reconstructing surface velocity.•Two kinds of TMMs are described and compared.•A method for selecting the proper sparsity level is given. The transfer matrix mode (TMM) has been successfully applied for reconstructing sound field with sparse measurement, as the sound field can be sparsely represented by a series of TMMs. In order to mitigate the influence of noise, the TMM-based methods usually require truncating the high-order TMMs which are deemed as evanescent waves. However, the determination of the cut-off order for truncation remains an open issue. The present paper proposes a method combining a weighted TMM with the match pursuit to reconstruct the source velocity with sparse pressure measurement. The method employs a weighted strategy during the iteration of matching pursuit, which will encourage the selection of low-order TMMs, and release the risk of instability caused by the high-order TMMs. Two kinds of TMMs, the p-mode obtained from the pressure transfer matrix and the v-mode obtained from the velocity transfer matrix, are used to construct the reconstruction model and their performance are compared. Numerical simulation and experimental results demonstrate the advantages of weighting the TMMs and the validity of the proposed method.