Comparison of methods for parameter selection in Tikhonov regularization with application to inverse force determination

Choi, Hyun-Ki; Thite, A.N.; Thompson, D.J.

doi:10.1016/j.jsv.2007.03.040

Cited by 110 publications

(52 citation statements)

References 15 publications

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“…The full dynamic response time history is divided into 3 time units with equal length. In Scale 0, the responses (0, 01 , 02 , and 03 ) and Scale 0 Lagrange wavelet scaling functions ( 0,1 and 0,2 ) are adopted to establish the force-response equation (denoted as Scale 0 force-response equation) as (10). The size of the coefficient matrix is 4 × 4.…”

Section: Numerical Studymentioning

confidence: 99%

“…Dynamic force reconstruction methods can generally be categorized into two groups: frequency-domain [1][2][3][4] and time-domain [5][6][7][8] methods. The frequency-and time-domain methods estimate dynamic forces by establishing the relationship between dynamic forces and structural responses based on frequency response functions [9,10] and impulse response functions [11,12], respectively. Compared to the frequency-domain methods, the time-domain methods have received increasing attention in the past years because of their distinct physical meaning and relatively higher accuracy [13].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Numerical Studymentioning

confidence: 99%

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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“…See e.g. Choi et al (2007) On the other hand better results may be expected if the operator L and the value of λ are adapted to the problem under investigation. The following references deal with the inversion of atmospheric state parameters.…”

Section: Theoretical Basismentioning

confidence: 99%

A self-adapting and altitude-dependent regularization method for atmospheric profile retrievals

Ridolfi

Sgheri

2009

Atmos. Chem. Phys.

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Abstract. MIPAS is a Fourier transform spectrometer, operating onboard of the ENVISAT satellite since July 2002. The online retrieval algorithm produces geolocated profiles of temperature and of volume mixing ratios of six key atmospheric constituents: H 2 O, O 3 , HNO 3 , CH 4 , N 2 O and NO 2 . In the validation phase, oscillations beyond the error bars were observed in several profiles, particularly in CH 4 and N 2 O.To tackle this problem, a Tikhonov regularization scheme has been implemented in the retrieval algorithm. The applied regularization is however rather weak in order to preserve the vertical resolution of the profiles.In this paper we present a self-adapting and altitudedependent regularization approach that detects whether the analyzed observations contain information about small-scale profile features, and determines the strength of the regularization accordingly. The objective of the method is to smooth out artificial oscillations as much as possible, while preserving the fine detail features of the profile when related information is detected in the observations. The proposed method is checked for self consistency, its performance is tested on MIPAS observations and compared with that of some other regularization schemes available in the literature. In all the considered cases the proposed scheme achieves a good performance, thanks to its altitude dependence and to the constraints employed, which are specific of the inversion problem under consideration. The proposed method is generally applicable to iterative GaussNewton algorithms for the retrieval of vertical distribution profiles from atmospheric remote sounding measurements.

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“…Djamaa et al [3] had further understood about the dynamic loads distribution of the thin pilaster structure using the finite differential method; and eliminated the error amplification through normalized. Choi et al [4,5] improved the stability of the load identification results and studied the affect on loads identification accuracy selecting different normalization parameter. In order to identify a two-dimensional dynamic loads distribution, Paper [6] utilized the tensor theory to generate the high-dimensional moment basis function in the high dimensional orthogonal space and then represented the unknown two-dimensional dynamic load distribution with the undetermined coefficient in the form of high dimensional orthogonal function series.…”

Section: Introductionmentioning

confidence: 99%

“…Paper [8] put forward the condition number weighted algorithm based on inverse pseudo-excitation method, which improves the error amplifier problems of the identification results generated when matrix is "sick" in random loads identification. The methods offered in [2][3][4][5][6][7][8] solve the problem of identifying the dynamic loads mathematically, but they were all limited to be academic because of the complexities of the theory and the difficulty of large amount of calculation.…”

Section: Introductionmentioning

confidence: 99%

On the Identification Technology for the Random Load Spectrums

Li¹,

Wang²,

Qiu³

et al. 2015

Proceedings of the 2015 International Conference on Electrical, Automation and Mechanical Engineering

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Abstract-This paper deduces the relationship between the frequency response and loads for a structure within the frequency domain, and puts forward a new method for identifying the random loads spectrum. Firstly, the response power spectrum of structural control points is calculated based on the white noise loads spectrum. Then in order to get the corresponding random loads spectrum, the response power spectrum and the desired output response spectrum are compared. Finally, a specific cabin structure is analyzed by using the above method. The FEA (Finite Element Analysis) simulation results show that the method is valid in identifying the fundamental acceleration loads spectrum.

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Comparison of methods for parameter selection in Tikhonov regularization with application to inverse force determination

Cited by 110 publications

References 15 publications

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

A self-adapting and altitude-dependent regularization method for atmospheric profile retrievals

On the Identification Technology for the Random Load Spectrums

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