Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Abstract

The shape function-based method is one of the very promising time-domain methods for dynamic force reconstruction, because it can significantly reduce the number of unknowns and shorten the reconstruction time. However, it is challenging to determine the optimum time unit length that can balance the tradeoff between reconstruction accuracy and efficiency in advance. To address this challenge, this paper develops an adaptive dynamic force reconstruction method based on multiscale wavelet shape functions and time-domain deconvolution. A concentrated dynamic force is discretized into units in time domain and the local force in each unit is approximated by wavelet scale functions at an initial scale. Subsequently, the whole response matrix is formulated by assembling the responses induced by the wavelet shape function forces of all time units which are calculated by the structural finite element model (FEM). Then, the wavelet shape function-based force-response equation is established for force reconstruction. Finally, the scale of the force-response equation is lifted by refining the wavelet shape function with high-scale wavelets and dynamic responses with more point data to improve the reconstruction accuracy gradually. Numerical examples of different structural types are analyzed to verify the feasibility and effectiveness of the proposed method.

Wavelets for Differential Equations and Numerical Operator Calculus

“…Note that starting from a ϕ that satisfies a two-scale equation like (37), it is possible to recover a full multiresolution analysis. Indeed, one defines V 0 according to (36) and V n by repeated applications of (35). Two-scale Eq.…”

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Study on an Integral Algorithm of Load Identification Based on Displacement Response

“…For this reason, much research has been carried out on the modeling of random loads. He et al represented the loads to be identified by means of the second-generation Lagrangian wavelet [ 6 , 7 ]. Lei et al applied the Daubechies wavelet to fit spatially distributed dynamic loads [ 8 ].…”

A Comparative Study of Regularization Method in Structure Load Identification

“…In the past two decades, a large number of researchers have carried out many effective research studies on inverse problems such as structural load identification and damage identification [1][2][3][4][5][6], and many of the results have been applied to the structural health monitoring technology of structural integrity and safety assessment [7][8][9][10]. Most of the load identification techniques use these regularization methods, such as the Tikhonov method and the truncated singular value decomposition (TSVD) method.…”