• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.63-69
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• 2001

In this study, we shall be concerned with computing in parallel a few of the smallest eigenvalues and their corresponding eigenvectors of the eigenvalue problem, $Ax={\lambda}Bx$, where A is symmetric, and B is symmetric positive definite. Both A and B are large and sparse. Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for small extreme eigenvalues. As in the case of a system of linear equations, successful application of the CG scheme to eigenproblems depends also upon the preconditioning techniques. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. The idea underlying the present work is a parallel computation of the Multi-Color Block SSOR preconditioning for the CG optimization of the Rayleigh quotient together with deflation techniques. Multi-Coloring is a simple technique to obatin the parallelism of order n, where n is the dimension of the matrix. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI(Message Passing Interface) library was adopted for the interprocessor communications. The test problems were drawn from the discretizations of partial differential equations by finite difference methods.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.3
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• pp.91-98
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• 2016

Detection and classification of underwater objects in sonar imagery are challenging problems. This paper proposes a system that detects and identifies underwater objects at the sea floor level using a sonar image and image processing techniques. The identification process of underwater objects consists of two steps; detection of candidate regions and identification of underwater objects. The candidate regions of underwater objects are extracted by image registration through the detection of common feature points between the reference background image and the current scanning image. And then, underwater objects are identified as the closest pattern within the database using eigenvectors and eigenvalues as features. The proposed system is expected to be used in efficient securement of Q route in vessel navigation.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.6
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• pp.979-994
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• 2015

The mode shapes of a segmented hull model towed in a model basin were predicted using both the Proper Orthogonal Decomposition (POD) and cross random decrement technique. The proper orthogonal decomposition, which is also known as Karhunen-Loeve decomposition, is an emerging technology as a useful signal processing technique in structural dynamics. The technique is based on the fact that the eigenvectors of a spatial coherence matrix become the mode shapes of the system under free and randomly excited forced vibration conditions. Taking advantage of the simplicity of POD, efforts have been made to reveal the mode shapes of vibrating flexible hull under random wave excitation. First, the segmented hull model of a 400 K ore carrier with 3 flexible connections was towed in a model basin under different sea states and the time histories of the vertical bending moment at three different locations were measured. The measured response time histories were processed using the proper orthogonal decomposition, eventually to obtain both the first and second vertical vibration modes of the flexible hull. A comparison of the obtained mode shapes with those obtained using the cross random decrement technique showed excellent correspondence between the two results.

• Steel and Composite Structures
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• v.31 no.5
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• pp.489-502
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• 2019

This article presents a unified mathematical model to investigate free and forced vibration responses of perforated thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively. Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS) based on perforated structure.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.3
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• pp.894-907
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• 2022

The features extracted by convolutional neural networks are more descriptive of images than traditional features, and their convolutional layers are more suitable for retrieving images than are fully connected layers. The convolutional layer features will consume considerable time and memory if used directly to match an image. Therefore, this paper proposes a feature weighting and region integration method for convolutional layer features to form global feature vectors and subsequently use them for image matching. First, the 3D feature of the last convolutional layer is extracted, and the convolutional feature is subsequently weighted again to highlight the edge information and position information of the image. Next, we integrate several regional eigenvectors that are processed by sliding windows into a global eigenvector. Finally, the initial ranking of the retrieval is obtained by measuring the similarity of the query image and the test image using the cosine distance, and the final mean Average Precision (mAP) is obtained by using the extended query method for rearrangement. We conduct experiments using the Oxford5k and Paris6k datasets and their extended datasets, Paris106k and Oxford105k. These experimental results indicate that the global feature extracted by the new method can better describe an image.

• Advances in Computational Design
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• v.7 no.1
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• pp.81-98
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• 2022

This study presents the application of two indices for the locating of cracks in Reinforced Concrete (RC) structures, as well as the development of their modified forms to overcome limitations. The first index is based on mode shape curvature and the second index is based on the fourth derivative of the mode shape. In order to confirm the indices' effectiveness, both eigenvalues coupled with nonlinear static analyses were carried out and the eigenvectors for two different damage locations and intensities of load were obtained from the finite element model of RC beams. The values of the damage-locating indices derived using both indices were then compared. Generally, the mode shape curvature-based index suffered from insensitivity when attempting to detect the damage location; this also applied to the mode shape fourth derivative-based index at lower modes. However, at higher modes, the mode shape fourth derivative-based index gave an acceptable indication of the damage location. Both the indices showed inconsistencies and anomalies at the supports. This study proposed modification to both indices to overcome identified flaws. The results proved that modified forms exhibited better sensitivity for identifying the damage location. In addition, anomalies at the supports were eliminated.

• Journal of the Society of Naval Architects of Korea
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• v.61 no.1
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• pp.29-43
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• 2024

The present study concerns a feasibility study for applying principal component analysis to ship dynamics in maneuver. Using the four degrees of freedom standard modular model for ship dynamics maneuver simulations of large angle zigzag tests with rudder deflection angle variations are conducted. The datasets of ship motion, hydrodynamic force, and moment during the maneuver are acquired to identify the principal modes. The covariance matrix of obtained ship dynamics variables shows a strong linear correlation between the motion, hydrodynamic force, and moment, except the surge force. Four eigenvectors of the covariance matrix are selected as the principal modes of ship dynamics. Using the principal modes, ship motion in turning circle and zigzag tests is reconstructed, showing good agreement with the original data.

• Structural Engineering and Mechanics
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• v.90 no.6
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• pp.601-610
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• 2024

Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.2
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• pp.827-833
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• 2012

In this paper, we propose an improved optical flow algorithm which reduces computational complexity as well as noise level. This algorithm reduces computational time by applying level simplification technique and removes noise by using eigenvectors of objects. Optical flow is one of the accurate algorithms used to generate depth information from two image frames using the vectors which track the motions of pixels. This technique, however, has disadvantage of taking very long computational time because of the pixel-based calculation and can cause some noise problems. The level simplifying technique is applied to reduce the computational time, and the noise is removed by applying optical flow only to the area of having eigenvector, then using the edge image to generate the depth information of background area. Three-dimensional images were created from two-dimensional images using the proposed method which generates the depth information first and then converts into three-dimensional image using the depth information and DIBR(Depth Image Based Rendering) technique. The error rate was obtained using the SSIM(Structural SIMilarity index).

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.271-286
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• 2020

Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.