• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.113-140
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• 2004

A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.

• Nuclear Engineering and Technology
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• v.55 no.12
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• pp.4350-4356
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• 2023

Radiation detection systems working at high count rates suffer from the overlapping of their output electric pulses, known as pulse pile-up phenomenon, resulting in spectrum distortion and degradation of the energy resolution. Pulse tail extrapolation is a pile-up correction method which tries to restore the shifted baseline of a piled-up pulse by extrapolating the overlapped part of its preceding pulse. This needs a mathematical model which is almost always nonlinear, fitted usually by a nonlinear least squares (NLS) technique. NLS is an iterative, potentially time-consuming method. The main idea of the present study is to replace the NLS technique by an integration-based non-iterative method (NIM) for pulse tail extrapolation by an exponential model. The idea of linear extrapolation, as another non-iterative method, is also investigated. Analysis of experimental data of a NaI(Tl) radiation detector shows that the proposed non-iterative method is able to provide a corrected spectrum quite similar with the NLS method, with a dramatically reduced computation time and complexity of the algorithm. The linear extrapolation approach suffers from a poor energy resolution and throughput rate in comparison with NIM and NLS techniques, but provides the shortest computation time.

• Geophysics and Geophysical Exploration
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• v.1 no.2
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• pp.116-126
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• 1998

I present a datuming scheme for poststack data that uses wavefield depth extrapolation. The method I have developed allows the use of any depth extrapolation technique, such as phase-shift, split-step, and finite-difference extrapolation. I derive the datuming algorithms by transposing and taking the complex conjugate (i.e. taking adjoint) of the corresponding forward modeling operator, which does upward extrapolation from a flat surface to an irregular surface. The exact adjoint relation between the forward modeling operator and the datuming operator is demonstrated algebraically. Testing the poststack datuming algorithms with synthetic data, using several depth extrapolation algorithms, has shown that the method works well.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.1
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• pp.25-31
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• 1984

An algorithm on time limited signal extrapolation technique is presented where the total extrapolation process of iteration method is achieved by a single matrix operation. The proposed technique and its implementation has many advantages over iteration method in terms of computational saving and accuracy of the results. As an examples in this paper, appling the proposed technique to ultrasonic diagnosis-device, we prove the excellence of the proposed technique.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.2
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• pp.31-38
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• 1990

An antenna gain measurement system using an extrapolation technique is described. The technique is similar to the usual two-antenna method for absolute gain measurement system, but involves the measurement of the received signal as a function of seperation in short distances, and the signal-versus-seperation data is processed in a way that allows an extrapolation of the signal to "infinite" seperation. In this technique it is possible to obtain the near field gain as function of distance by combining the far field gain and a proximity correction factor. The results of gain measurements of standard gain horn antennas and OEG (open ended waveguide) antennas are also presented.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4C
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• pp.207-216
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• 2011

Motion compensated extrapolation (MCE) techniques show inferior performance compared to motion compensated interpolation techniques, since only past frames are used in MCE. MCE techniques are used for the reconstruction of corrupted frames, the up-conversion of frame rates and the generation of side information in the distributed video coding system. In this paper, the performance of various MCE techniques are evaluated and an efficient MCE technique using the forward and backward motion estimation is proposed. In the proposed technique, the present frame is extrapolated by averaging two frames which are generated by forward and backward motion estimation respectively. It is shown that the proposed method produces better PSNR results and less blocking phenomena than conventional methods.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• Smart Structures and Systems
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• v.17 no.6
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• pp.995-1015
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• 2016

In the design and condition assessment of bridges, it is usually necessary to take into consideration the extreme conditions which are not expected to occur within a short time period and thus require an extrapolation from observations of limited duration. Long-term structural health monitoring (SHM) provides a rich database to evaluate the extreme conditions. This paper focuses on the extrapolation of extreme traffic load effects on bridges using long-term monitoring data of structural strain. The suspension Tsing Ma Bridge (TMB), which carries both highway and railway traffic and is instrumented with a long-term SHM system, is taken as a testbed for the present study. Two popular extreme value extrapolation methods: the block maxima approach and the peaks-over-threshold approach, are employed to extrapolate the extreme stresses induced by highway traffic and railway traffic, respectively. Characteristic values of the extreme stresses with a return period of 120 years (the design life of the bridge) obtained by the two methods are compared. It is found that the extrapolated extreme stresses are robust to the extrapolation technique. It may owe to the richness and good quality of the long-term strain data acquired. These characteristic extremes are also compared with the design values and found to be much smaller than the design values, indicating conservative design values of traffic loading and a safe traffic-loading condition of the bridge. The results of this study can be used as a reference for the design and condition assessment of similar bridges carrying heavy traffic, analogous to the TMB.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.673-687
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• 2022

In this study, we solve the Cayley inclusion problem and the fixed point problem in real Hilbert space using Tseng's technique with inertial extrapolation in order to obtain more efficient results. We provide a strong convergence theorem to approximate a common solution to the Cayley inclusion problem and the fixed point problem under some appropriate assumptions. Finally, we present a numerical example that satisfies the problem and shows the computational performance of our suggested technique.