A numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticity

Marin, Liviu; Karageorghis, Andréas; Lesnic, D.

doi:10.1002/num.21898

Cited by 13 publications

(2 citation statements)

References 38 publications

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“…They derived new particular solutions for the nonhomogeneous equilibrium equations. Karageorghis (2013a, 2013b); Marin, Karageorghis and Lesnic (2015)] used the MFS for inverse analysis of inverse thermoelastic problems too. Sun et al [Sun and Marin (2017)] proposed an invariant method of fundamental solutions for analysis of 2D elastostatic problems.…”

Section: Introductionmentioning

confidence: 99%

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Hematiyan¹,

Arezou²,

Dezfouli³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

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In this paper, some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made. First, the effects of the distance between pseudo and main boundaries on the solution are investigated and by a numerical study a lower bound for the distance of each source point to the main boundary is suggested. In some cases, the resulting system of equations becomes ill-conditioned for which, the truncated singular value decomposition with a criterion based on the accuracy of the imposition of boundary conditions is used. Moreover, a procedure for normalizing the shear modulus is presented that significantly reduces the condition number of the system of equations. By solving two example problems with stress concentration, the effectiveness of the proposed methods is demonstrated.

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Section: Introductionmentioning

confidence: 99%

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Hematiyan¹,

Arezou²,

Dezfouli³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

show abstract

“…Based on the SVD principle, the vectors ⎯ → u i are mutually orthonormal and they form an orthonormal basis of m-dimensional space; the vectors ⎯→ v i are also orthonormal to one another and they form the orthonormal basis of n-dimensional space [20,21].…”

Section: Amentioning

confidence: 99%

SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient

Qiao

Pan

2015

Meas. Sci. Technol.

129

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Aiming at solving the existing sharp problems by using singular value decomposition (SVD) in the fault diagnosis of rolling bearings, such as the determination of the delay step k for creating the Hankel matrix and selection of effective singular values, the present study proposes a novel adaptive SVD method for fault feature detection based on the correlation coefficient by analyzing the principles of the SVD method. This proposed method achieves not only the optimal determination of the delay step k by means of the absolute value of the autocorrelation function sequence of the collected vibration signal, but also the adaptive selection of effective singular values using the index corresponding to useful component signals including weak fault information to detect weak fault signals for rolling bearings, especially weak impulse signals. The effectiveness of this method has been verified by contrastive results between the proposed method and traditional SVD, even using the wavelet-based method through simulated experiments. Finally, the proposed method has been applied to fault diagnosis for a deep-groove ball bearing in which a single point fault located on either the inner or outer race of rolling bearings is obtained successfully. Therefore, it can be stated that the proposed method is of great practical value in engineering applications.

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Finite element method for the reconstruction of a time-dependent heat source in isotropic thermoelasticity systems of type-III

Bockstal

Marin

2022

Z. Angew. Math. Phys.

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The isotropic thermoelasticity system of type-III, describing both the mechanical and the thermal behaviours of a body occupying a bounded domain with a Lipschitz boundary, is considered. The displacement vector and either the normal heat flux or the temperature are prescribed on the boundary. Both the theoretical and the numerical reconstructions of a time-dependent heat source from the knowledge of an additional weighted integral measurement of the temperature are investigated. It is showed that the appropriate type of measurement depends on the thermal boundary condition available, whilst the existence and uniqueness of a weak solution for exact data is also proved. For each of the two inverse source problems investigated herein, a numerical algorithm is also proposed and the convergence of these numerical schemes for exact data is proved. Four numerical examples with noisy measurements are implemented using the finite element method and thoroughly investigated to validate the convergence and stability of the proposed algorithms.

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A numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticity

Cited by 13 publications

References 38 publications

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient

Finite element method for the reconstruction of a time-dependent heat source in isotropic thermoelasticity systems of type-III

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