Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction

Gunawan, Fergyanto E.; Homma, Hiroomi; Kanto, Yasuhiro

doi:10.1016/j.jsv.2006.03.036

Cited by 77 publications

(31 citation statements)

References 8 publications

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“…Here, four noise levels, i.e., 10%, 20%, 30% and 40% respectively correspond to noise-to-signal ratios of the measured response ‖e‖ 2 =‖y‖ 2 , i.e., 5.82%, 11.54%, 17.47% and 23.29%. Here, the noise levels are higher than those in [10][11][12]43]. For instance, the highest noise level in [43] is 10%; the highest one in [12] is 30%.…”

Section: Problem Descriptionmentioning

confidence: 82%

See 1 more Smart Citation

Impact-force sparse reconstruction from highly incomplete and inaccurate measurements

Qiao

Zhang

Gao

2016

Journal of Sound and Vibration

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Section: Problem Descriptionmentioning

confidence: 82%

“…Transfer functions can be determined analytically [5,9,11] numerically [16,18,29,30] or experimentally [10,[12][13][14]. An experiment method using impact testing of experimental modal analysis has the advantage of being applicable to various types of structures.…”

Section: Impact-force Sparse Reconstruction Using Mtwistmentioning

confidence: 99%

Impact-force sparse reconstruction from highly incomplete and inaccurate measurements

Qiao

Zhang

Gao

2016

Journal of Sound and Vibration

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“…Therefore, it is challenging to set an optimal sampling time interval to balance the tradeoff between reconstruction accuracy and efficiency. Approaches based on various basis functions were proposed to address this challenge, in which unknown dynamic forces were approximated by 2 Shock and Vibration basis functions, such as Gaussian basis functions [14], Bspline functions [15,16], triangle functions [17], exponential function [18], and Daubechies wavelet [19], and subsequently they were reconstructed by identifying the coefficients in these basis functions. These approaches could significantly reduce the number of unknowns (considerably less than that of data points) and shorten the identification time.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Yang

Zhu

2018

Shock and Vibration

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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.

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“…Hashemi and Kargarnovin [3] present the identification method for the amplitude of the impact load acting on a simply supported beam and its location using the genetic algorithm. Gunawan et al [4] proposed two-step bspline regularization method for solving an ill-posed problem of impact-load reconstruction. Gunawan et al [5] also proposed a method to approximate the impact-load by quadratic spline approximation.…”

Section: Introductionmentioning

confidence: 99%

Numerical experiments on determination of spatially concentrated time-varying loads on a beam: an iterative regularization method

Jang

Han

2009

J Mech Sci Technol

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This paper treats a solution for the ill-posed (inverse) load determination problem for a time-varying load on a beam. The ill-posed nature of the problem causes numerical instability. Conventional numerical approach for solutions results in arbitrarily large errors in solution. The Tikhonov regularization method, which is a non-iterative stabilization technique, has been widely adopted for overcoming the ill-posed nature (or numerical instability). However, in this paper, we introduce an "iterative" regularization method, specifically, the iterated Tikhonov regularization method. The iterated method is applied to the present load determination problem. The result of the iterative method is compared with that of the (non-iterative) Tikhonov regularization. The rate of convergence for the introduced iterative method turned out to be very fast. The accuracy and applicability of the introduced method are examined through a numerical experiment.

show abstract

Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction

Cited by 77 publications

References 8 publications

Impact-force sparse reconstruction from highly incomplete and inaccurate measurements

Impact-force sparse reconstruction from highly incomplete and inaccurate measurements

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Numerical experiments on determination of spatially concentrated time-varying loads on a beam: an iterative regularization method

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