Impact-force sparse reconstruction from highly incomplete and inaccurate measurements

• Published in: Journal of sound and vibration 2016-08, Vol.376, p.72-94
• Main Authors: Qiao, Baijie, Zhang, Xingwu, Gao, Jiawei, Chen, Xuefeng
• Format: Article
• Language: English
• Subjects: Algorithms; Computer simulation; Frames; Impact-force reconstruction; Iterative shrinkage/thresholding algorithm; l1-norm regularization; Noise; Reconstruction; Regularization; Shrinkage; Sparse reconstruction; Underdetermined model; Vibration
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2016.04.040

The classical l2-norm-based regularization methods applied for force reconstruction inverse problem require that the number of measurements should not be less than the number of unknown sources. Taking into account the sparse nature of impact-force in time domain, we develop a general sparse methodology based on minimizing l1-norm for solving the highly underdetermined model of impact-force reconstruction. A monotonic two-step iterative shrinkage/thresholding (MTWIST) algorithm is proposed to find the sparse solution to such an underdetermined model from highly incomplete and inaccurate measurements, which can be problematic with Tikhonov regularization. MTWIST is highly efficient for large-scale ill-posed problems since it mainly involves matrix-vector multiplies without matrix factorization. In sparsity frame, the proposed sparse regularization method can not only determine the actual impact location from many candidate sources but also simultaneously reconstruct the time history of impact-force. Simulation and experiment including single-source and two-source impact-force reconstruction are conducted on a simply supported rectangular plate and a shell structure to illustrate the effectiveness and applicability of MTWIST, respectively. Both the locations and force time histories of the single-source and two-source cases are accurately reconstructed from a single accelerometer, where the high noise level is considered in simulation and the primary noise in experiment is supposed to be colored noise. Meanwhile, the consecutive impact-forces reconstruction in a large-scale (greater than 104) sparse frame illustrates that MTWIST has advantages of computational efficiency and identification accuracy over Tikhonov regularization. •The sparsity nature of impact-force in time domain is considered.•MTWIST based on l1-norm is proposed to solve highly underdetermined problems.•The performance of sparse regularization is verified by simulation and experiment.•The impact location and force time history are simultaneously identified by MTWIST.•Compared with Tikhonov regularization, MTWIST is highly accurate and efficient.