• Structural Engineering and Mechanics
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• 제50권5호
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• pp.679-695
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• 2014

A design method of second generation wavelet (SGW)-based multivariable finite elements is proposed for static and vibration beam analysis. An important property of SGWs is that they can be custom designed by selecting appropriate lifting coefficients depending on the application. The SGW-based multivariable finite element equations of static and vibration analysis of beam problems with two and three kinds of variables are derived based on the generalized variational principles. Compared to classical finite element method (FEM), the second generation wavelet-based multivariable finite element method (SGW-MFEM) combines the advantages of high approximation performance of the SGW method and independent solution of field functions of the MFEM. A multiscale algorithm for SGW-MFEM is presented to solve structural engineering problems. Numerical examples demonstrate the proposed method is a flexible and accurate method in static and vibration beam analysis.

• Structural Engineering and Mechanics
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• 제33권5호
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• pp.543-560
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• 2009

The rotating Rayleigh-Timoshenko beam element based on B-spline wavelet on the interval (BSWI) is constructed to discrete short shaft and stiffness disc. The crack is represented by non-dimensional linear spring using linear fracture mechanics theory. The wavelet-based finite element model of rotor system is constructed to solve the first three natural frequencies functions of normalized crack location and depth. The normalized crack location, normalized crack depth and the first three natural frequencies are then employed as the training samples to achieve the neural networks for crack diagnosis. Measured natural frequencies are served as inputs of the trained neural networks and the normalized crack location and depth can be identified. The experimental results of fatigue crack in short shaft is also given.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
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• pp.281-282
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• 2007

We address a new representation of DCT/DFT/Wavelet matrices via one hybrid architecture. Based on an element inverse matrix factorization algorithm, we show that the OCT, OFT and Wavelet which based on Haar matrix have the similarrecursive computational pattern, all of them can be decomposed to one orthogonal character matrix and a special sparse matrix. The special sparse matrix belongs to Jacket matrix, whose inverse can be from element-wise inverse or block-wise inverse. Based on this trait, we can develop a hybrid architecture.

• Structural Monitoring and Maintenance
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• 제9권2호
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• pp.157-177
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• 2022

In this paper, an innovative finite element updating method is presented based on the variation wavelet transform coefficients of Auto/cross-correlations function (WTCF). The Quasi-linear sensitivity of the wavelet coefficients of the WTCF concerning the structural parameters is evaluated based on incomplete measured structural responses. The proposed algorithm is used to estimate the structural parameters of truss and plate models. By the solution of the sensitivity equation through the least-squares method, the finite element model of the structure is updated for estimation of the location and severity of structural damages simultaneously. Several damage scenarios have been considered for the studied structure. The parameter estimation results prove the high accuracy of the method considering measurement and mass modeling errors.

• Journal of Mechanical Science and Technology
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• 제19권8호
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• pp.1611-1620
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• 2005

This paper shows the use of wavelet transformation combined with inverse acoustics to reconstruct the surface velocity of a noise source. This approach uses the boundary element analysis based on the measured sound pressure at a set of field points, the Helmholtz integral equations and wavelet transformation for reconstructing the normal surface velocity field. The reconstructed field can be diverged due to the small measurement errors in the case of nearfield acoustic holography (NAH) using an inverse boundary element method. In order to avoid this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the order of an optimal truncation is difficult to determine. In this paper, a wavelet transformation is applied to reduce the computation time for inverse acoustics and to enhance the reconstructed vibration field. The computational speed-up is achieved, with solution time being reduced to $14.5\%$.

• Structural Engineering and Mechanics
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• 제38권6호
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• pp.733-751
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• 2011

In the present study, a new kind of multivariable Reissner-Mindlin plate elements with two kinds of variables based on B-spline wavelet on the interval (BSWI) is constructed to solve the static and vibration problems of a square Reissner-Mindlin plate, a skew Reissner-Mindlin plate, and a Reissner-Mindlin plate on an elastic foundation. Based on generalized variational principle, finite element formulations are derived from generalized potential energy functional. The two-dimensional tensor product BSWI is employed to form the shape functions and construct multivariable BSWI elements. The multivariable wavelet finite element method proposed here can improve the solving accuracy apparently because generalized stress and strain are interpolated separately. In addition, compared with commonly used Daubechies wavelet finite element method, BSWI has explicit expression and a very good approximation property which guarantee the satisfying results. The efficiency of the proposed multivariable Reissner-Mindlin plate elements are verified through some numerical examples in the end.

• Structural Engineering and Mechanics
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• 제54권2호
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• pp.239-256
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• 2015

An adaptive-scale damage detection strategy based on a wavelet finite element model (WFEM) for thin plate structures is established in this study. Equations of motion and corresponding lifting schemes for thin plate structures are derived with the tensor products of cubic Hermite multi-wavelets as the elemental interpolation functions. Sub-element damages are localized by using of the change ratio of modal strain energy. Subsequently, such damages are adaptively quantified by a damage quantification equation deduced from differential equations of plate structure motion. WFEM scales vary spatially and change dynamically according to actual needs. Numerical examples clearly demonstrate that the proposed strategy can progressively locate and quantify plate damages. The strategy can operate efficiently in terms of the degrees-of-freedom in WFEM and sensors in the vibration test.

• Computers and Concrete
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• 제2권6호
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• pp.481-498
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• 2005

A wavelet based approach is proposed for structural damage detection in beams, plate and delamination of composite plates. Wavelet theory is applied here for crack identification of a beam element with a transverse on edge non-propagating open crack. Finite difference method was used for generating a general displacement equation for the cracked beam in the first example. In the second and third example, damage is detected from the deformed shape of a loaded simply supported plate applying the wavelet theory. Delamination in composite plate is identified using wavelet theory in the fourth example. The main concept used is the breaking down of the dynamic signal of a structural response into a series of local basis function called wavelets, so as to detect the special characteristics of the structure by scaling and transformation property of wavelets. In the light of the results obtained, limitations of the proposed method as well as suggestions for future work are presented. Results show great promise of wavelet approach for damage detection and structural health monitoring.

• 전자공학회논문지CI
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• 제39권6호
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• pp.24-35
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• 2002

Maxwell 방정식을 효율적으로 풀기 위해 웨이브렛 행렬 변환(wavelet matrix transformation)과 경계요소법(Boundary Element Method)을 결합하는 방법을 제안하였으며, 2차원 위상변이 마스크(phase- shifting mask) 문제에 적용하였다. 계산 결과를 해석적인 해 및 참고문헌의 결과와 비교함으로써 구현된 모듈의 정확도를 검증하였으며, 제안된 방법이 경계요소법만을 적용한 경우에 비해 연산 시간과 메모리 사용 측면에서 효율적임을 확인하였다.

• Smart Structures and Systems
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• 제22권3호
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• pp.277-290
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• 2018

In this paper, wavelet finite element model (WFEM) updating technique is employed to detect sub-element damage in thin plate structures progressively. The procedure of WFEM-based detection method, which can detect sub-element damage gradually, is established. This method involves the optimization of an objective function that combines frequencies and modal assurance criteria (MAC). During the damage detection process, the scales of wavelet elements in the concerned regions are adaptively enhanced or reduced to remain compatible with the gradually identified damage scenarios, while the modal properties from the tests remains the same, i.e., no measurement point replacement or addition are needed. Numerical and experimental examples were conducted to examine the effectiveness of the proposed method. A scanning Doppler laser vibrometer system was employed to measure the plate mode shapes in the experimental study. The results indicate that the proposed method can detect structural damage with satisfactory accuracy by using minimal degrees-of-freedoms (DOFs) in the model and minimal updating parameters in optimization.