• Journal of Information Processing Systems
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• 제19권3호
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• pp.275-288
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• 2023

Many image edge details are easily lost in the image denoising process, and the smooth image regions are prone to produce jagged. In this paper, we propose a wavelet-based image global k- singular value decomposition variational method to remove image noise. A layer of wavelet decomposition is applied to the noisy image first. Then, the image global k-singular value decomposition (IGK-SVD) method is used to remove the random noise of low-frequency components. Furthermore, a constructed variational denoising method (VDM) removes the random noise in the high-frequency component. Finally, the denoised image is obtained by wavelet reconstruction. The experimental results show that the proposed method's peak signal-to-noise ratio (PSNR) value is higher than other methods, and its structural similarity (SSIM) value is closer to one, indicating that the proposed method can effectively suppress image noise while retaining more image edge details. The denoised image has better denoising effects.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.381-394
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• 2011

In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1343-1359
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• 2009

In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.

• Journal of Information Processing Systems
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• 제15권6호
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• pp.1296-1305
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• 2019

To solve the problem of poor noise suppression capability and frequent loss of edge contour and detailed information in current fusion methods, an infrared and visible light image fusion method based on variational multiscale decomposition is proposed. Firstly, the fused images are separately processed through variational multiscale decomposition to obtain texture components and structural components. The method of guided filter is used to carry out the fusion of the texture components of the fused image. In the structural component fusion, a method is proposed to measure the fused weights with phase consistency, sharpness, and brightness comprehensive information. Finally, the texture components of the two images are fused. The structure components are added to obtain the final fused image. The experimental results show that the proposed method displays very good noise robustness, and it also helps realize better fusion quality.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1371-1377
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• 2008

In this paper, we have employed the variational iteration method to solve the boundary value problems. Numerical results reveal that it is a very effective method compared with the results obtained by using the Adomian decomposition method in Wazwaz, A. M. (2000).

• Smart Structures and Systems
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• 제30권1호
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• pp.75-88
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• 2022

Engineering structures in operation essentially belong to time-varying or nonlinear structures and the resultant response signals are usually non-stationary. For such time-varying structures, it is of great importance to extract time-dependent dynamic parameters from non-stationary response signals, which benefits structural health monitoring, safety assessment and vibration control. However, various traditional signal processing methods are unable to extract the embedded meaningful information. As a newly developed technique, variational mode decomposition (VMD) shows its superiority on signal decomposition, however, it still suffers two main problems. The foremost problem is that the number of modal components is required to be defined in advance. Another problem needs to be addressed is that VMD cannot effectively separate non-stationary signals composed of closely spaced or overlapped modes. As such, a new method named generalized adaptive variational modal decomposition (GAVMD) is proposed. In this new method, the number of component signals is adaptively estimated by an index of mean frequency, while the generalized demodulation algorithm is introduced to yield a generalized VMD that can decompose mode overlapped signals successfully. After that, synchrosqueezing wavelet transform (SWT) is applied to extract instantaneous frequencies (IFs) of the decomposed mono-component signals. To verify the validity and accuracy of the proposed method, three numerical examples and a steel cable with time-varying tension force are investigated. The results demonstrate that the proposed GAVMD method can decompose the multi-component signal with overlapped modes well and its combination with SWT enables a successful IF extraction of each individual component.

• 응용통계연구
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• 제28권2호
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• pp.159-174
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• 2015

최근에 Dragomiretskiy와 Zosso (2014)는 경험적모드분해의 단점을 보완하여 새로운 신호 분해방법인 변동모드분해법(Variational Mode Decomposition)을 고안하였다. 기본적으로 변동모드분해법은 경험적모드분해법에 비하여 주파수 탐색 및 분리(tone detection and tone separation)에 탁월한 성능을 보인다. 또한 고속퓨리에변환을 기반으로 한 알고리즘을 사용하여 경험적모드분해법보다 잡음에 강건하다는 장점이 있다. 하지만 변동모드분해법은 결측 등으로 신호가 동일한 시간간격 혹은 공간적 간격으로 측정되지 않은 경우 제대로 동작하지 않는 단점이 있다. 이를 보완하기 위해서 본 논문에서는 변동모드분해법에 다단계우도함수를 조합하는 새로운 방법을 제안한다. 여기에서 다단계우도함수는 변동모드분해법이 신호를 적절한 내재모드함수로 분해하기 전에 결측치를 대체하는 효율적인 방법을 제시한다. 모의실험과 실제 자료의 사례연구를 통하여 변동모드분해법이 기존의 방법보다 더 효율적으로 신호를 분해한다는 것을 보일 것이다.

• Wind and Structures
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• 제37권6호
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• pp.445-460
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• 2023

Accurate estimation of modal parameters (i.e., natural frequency, damping ratio) of tall buildings is of great importance to their structural design, structural health monitoring, vibration control, and state assessment. Based on the combination of variational mode decomposition, smoothed discrete energy separation algorithm-1, and Half-cycle energy operator (VMD-SH), this paper presents a method for structural modal parameter estimation. The variational mode decomposition is proved to be effective and reliable for decomposing the mixed-signal with low frequencies and damping ratios, and the validity of both smoothed discrete energy separation algorithm-1 and Half-cycle energy operator in the modal identification of a single modal system is verified. By incorporating these techniques, the VMD-SH method is able to accurately identify and extract the various modes present in a signal, providing improved insights into its underlying structure and behavior. Subsequently, a numerical study of a four-story frame structure is conducted using the Newmark-β method, and it is found that the relative errors of natural frequency and damping ratio estimated by the presented method are much smaller than those by traditional methods, validating the effectiveness and accuracy of the combined method for the modal identification of the multi-modal system. Furthermore, the presented method is employed to estimate modal parameters of a full-scale tall building utilizing acceleration responses. The identified results verify the applicability and accuracy of the presented VMD-SH method in field measurements. The study demonstrates the effectiveness and robustness of the proposed VMD-SH method in accurately estimating modal parameters of tall buildings from acceleration response data.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.189-201
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• 2022

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

• Nuclear Engineering and Technology
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• 제55권3호
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• pp.827-838
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• 2023

Centrifugal pump is a key part of nuclear power plant systems, and its health status is critical to the safety and reliability of nuclear power plants. Therefore, fault diagnosis is required for centrifugal pump. Traditional fault diagnosis methods have difficulty extracting fault features from nonlinear and non-stationary signals, resulting in low diagnostic accuracy. In this paper, a new fault diagnosis method is proposed based on the improved particle swarm optimization (IPSO) algorithm-based variational modal decomposition (VMD) and relevance vector machine (RVM). Firstly, a simulation test bench for rotor faults is built, in which vibration displacement signals of the rotor are also collected by eddy current sensors. Then, the improved particle swarm algorithm is used to optimize the VMD to achieve adaptive decomposition of vibration displacement signals. Meanwhile, a screening criterion based on the minimum Kullback-Leibler (K-L) divergence value is established to extract the primary intrinsic modal function (IMF) component. Eventually, the factors are obtained from the primary IMF component to form a fault feature vector, and fault patterns are recognized using the RVM model. The results show that the extraction of the fault information and fault diagnosis classification have been improved, and the average accuracy could reach 97.87%.