• Title/Summary/Keyword: Variational methods

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Closed-form and numerical solution of the static and dynamic analysis of coupled shear walls by the continuous method and the modified transfer matrix method

  • Mao C. Pinto
    • Structural Engineering and Mechanics
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    • v.86 no.1
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    • pp.49-68
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    • 2023
  • This study investigates the static and dynamic structural analysis of symmetrical and asymmetrical coupled shear walls using the continuous and modified transfer matrix methods by idealizing the coupled shear wall as a three-field CTB-type replacement beam. The coupled shear wall is modeled as a continuous structure consisting of the parallel coupling of a Timoshenko beam in tension (with axial extensibility in the shear walls) and a shear beam (replacing the beam coupling effect between the shear walls). The variational method using the Hamilton principle is used to obtain the coupled differential equations and the boundary conditions associated with the model. Using the continuous method, closed-form analytical solutions to the differential equation for the coupled shear wall with uniform properties along the height are derived and a numerical solution using the modified transfer matrix is proposed to overcome the difficulty of coupled shear walls with non-uniform properties along height. The computational advantage of the modified transfer matrix method compared to the classical method is shown. The results of the numerical examples and the parametric analysis show that the proposed analytical and numerical model and method is accurate, reliable and involves reduced processing time for generalized static and dynamic structural analysis of coupled shear walls at a preliminary stage and can used as a verification method in the final stage of the project.

Analytical nonlocal elasticity solution and ANN approximate for free vibration response of layered carbon nanotube reinforced composite beams

  • Emrah Madenci;Saban Gulcu;Kada Draiche
    • Advances in nano research
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    • v.16 no.3
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    • pp.251-263
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    • 2024
  • This article investigates the free vibration behavior of carbon nanotube reinforced composite (CNTRC) beams embedded using variational analytical methods and artificial neural networks (ANN). The material properties of layered functionally graded CNTRC (FG-CNTRC) beams are estimated using nonlocal parameters modified power-law with different types of CNT distributions through the thickness direction of the beam. Adopting Eringen's nonlocal elasticity theory to capture the small size effects, the nonlocal governing equations are derived and solved using the analytical method. And also, the problem was analyzed using the ANN method. The architecture of the proposed ANN model is 3-9-1. In the experiments, we used 112 different data to predict the natural frequency using ANN. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton's principle. The classical beam theory is used to formulate a governing equation for predicting the free vibration of laminated CNTRC beams. According to the experimental results, the prediction ability of the ANN model is very good and the natural frequency can be predicted in ANN without attempting any experiments.

Comparison of Data Assimilation Methods in a Regional Ocean Circulation Model for the Yellow and East China Seas (자료동화 기법에 따른 황·동중국해 지역 해양순환모델 결과 비교)

  • Lee, Joon-Ho;Moon, Jae-Hong;Choi, Youngjin
    • Ocean and Polar Research
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    • v.42 no.3
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    • pp.179-194
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    • 2020
  • The present study aims to evaluate the effects of satellite-based SST (OSTIA) assimilation on a regional ocean circulation model for the Yellow and East China Seas (YECS), using three different assimilation methods: the Ensemble Optimal Interpolation (EnOI), Ensemble Kalman Filter (EnKF), and 4-Dimensional Variational (4DVAR) techniques, which are widely used in the ocean modeling communities. The model experiments show that an improved initial condition by assimilating the SST affects the seasonal water temperature and water mass distributions of the YECS. In particular, the SST data assimilation influences the temperature structures horizontally and vertically in winter, thereby improving the behavior of the YS warm current water. This is due to the fact that during wintertime the water column is well mixed, which is directly updated by the SST assimilation. The model comparisons indicate that the SST assimilation can improve the model performance in resolving the subsurface structures in wintertime, but has a relatively small impact in summertime due to the strong stratification. The differences among the different assimilation experiments are obvious when the SST was sharply changed due to a typhoon passage. Overall, the EnKF and 4DVAR show better agreement with the observations than the EnOI. The relatively low performance of EnOI under storm conditions may be related with a limitation of EnOI method whereby an analysis is obtained from a number of climatological fields, and thus the typhoon-induced SST changes in short-time scales may not be adequately reflected in the data assimilation.

Study on the pre-processors to improve the generalized-cross-correlation based time delay estimation under the narrow band single tone signal environments (협대역 단일 주파수 신호 환경에서 일반 상호 상관 시간 지연 추정 향상을 위한 전처리기 연구)

  • Lim, Jun Seok;Kim, Seongil
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.3
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    • pp.207-215
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    • 2020
  • There are several methods for the time delay estimation between signals to two receivers. Among these methods, Generalized Cross Correlation (GCC), which estimates the relative delay from the cross-correlation between the different signals at the two receivers, is a traditionally well-known method. However, when using a narrow band Continuous Wave (CW) signal, the GCC method degrades the estimation performance from relatively higher signal-to-noise ratio than when using a wideband signal. To improve this phenomenon, this paper examines four different pre-processors for GCC using narrow band single frequency signals. Simulation shows that the performance gain of the preprocessed GCC is up to 9 dB for a 100 msec CW signal as well as up to 4 dB for a 1 s CW signal.

Development of Quantification Methods for the Myocardial Blood Flow Using Ensemble Independent Component Analysis for Dynamic $H_2^{15}O$ PET (동적 $H_2^{15}O$ PET에서 앙상블 독립성분분석법을 이용한 심근 혈류 정량화 방법 개발)

  • Lee, Byeong-Il;Lee, Jae-Sung;Lee, Dong-Soo;Kang, Won-Jun;Lee, Jong-Jin;Kim, Soo-Jin;Choi, Seung-Jin;Chung, June-Key;Lee, Myung-Chul
    • The Korean Journal of Nuclear Medicine
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    • v.38 no.6
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    • pp.486-491
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    • 2004
  • Purpose: factor analysis and independent component analysis (ICA) has been used for handling dynamic image sequences. Theoretical advantages of a newly suggested ICA method, ensemble ICA, leaded us to consider applying this method to the analysis of dynamic myocardial $H_2^{15}O$ PET data. In this study, we quantified patients' blood flow using the ensemble ICA method. Materials and Methods: Twenty subjects underwent $H_2^{15}O$ PET scans using ECAT EXACT 47 scanner and myocardial perfusion SPECT using Vertex scanner. After transmission scanning, dynamic emission scans were initiated simultaneously with the injection of $555{\sim}740$ MBq $H_2^{15}O$. Hidden independent components can be extracted from the observed mixed data (PET image) by means of ICA algorithms. Ensemble learning is a variational Bayesian method that provides an analytical approximation to the parameter posterior using a tractable distribution. Variational approximation forms a lower bound on the ensemble likelihood and the maximization of the lower bound is achieved through minimizing the Kullback-Leibler divergence between the true posterior and the variational posterior. In this study, posterior pdf was approximated by a rectified Gaussian distribution to incorporate non-negativity constraint, which is suitable to dynamic images in nuclear medicine. Blood flow was measured in 9 regions - apex, four areas in mid wall, and four areas in base wall. Myocardial perfusion SPECT score and angiography results were compared with the regional blood flow. Results: Major cardiac components were separated successfully by the ensemble ICA method and blood flow could be estimated in 15 among 20 patients. Mean myocardial blood flow was $1.2{\pm}0.40$ ml/min/g in rest, $1.85{\pm}1.12$ ml/min/g in stress state. Blood flow values obtained by an operator in two different occasion were highly correlated (r=0.99). In myocardium component image, the image contrast between left ventricle and myocardium was 1:2.7 in average. Perfusion reserve was significantly different between the regions with and without stenosis detected by the coronary angiography (P<0.01). In 66 segment with stenosis confirmed by angiography, the segments with reversible perfusion decrease in perfusion SPECT showed lower perfusion reserve values in $H_2^{15}O$ PET. Conclusions: Myocardial blood flow could be estimated using an ICA method with ensemble learning. We suggest that the ensemble ICA incorporating non-negative constraint is a feasible method to handle dynamic image sequence obtained by the nuclear medicine techniques.

Comparison of Ensemble Perturbations using Lorenz-95 Model: Bred vectors, Orthogonal Bred vectors and Ensemble Transform Kalman Filter(ETKF) (로렌쯔-95 모델을 이용한 앙상블 섭동 비교: 브레드벡터, 직교 브레드벡터와 앙상블 칼만 필터)

  • Chung, Kwan-Young;Barker, Dale;Moon, Sun-Ok;Jeon, Eun-Hee;Lee, Hee-Sang
    • Atmosphere
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    • v.17 no.3
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    • pp.217-230
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    • 2007
  • Using the Lorenz-95 simple model, which can simulate many atmospheric characteristics, we compare the performance of ensemble strategies such as bred vectors, the bred vectors rotated (to be orthogonal to each bred member), and the Ensemble Transform Kalman Filter (ETKF). The performance metrics used are the RMSE of ensemble means, the ratio of RMS error of ensemble mean to the spread of ensemble, rank histograms to see if the ensemble member can well represent the true probability density function (pdf), and the distribution of eigen-values of the forecast ensemble, which can provide useful information on the independence of each member. In the meantime, the orthogonal bred vectors can achieve the considerable progress comparing the bred vectors in all aspects of RMSE, spread, and independence of members. When we rotate the bred vectors for orthogonalization, the improvement rate for the spread of ensemble is almost as double as that for RMS error of ensemble mean compared to the non-rotated bred vectors on a simple model. It appears that the result is consistent with the tentative test on the operational model in KMA. In conclusion, ETKF is superior to the other two methods in all terms of the assesment ways we used when it comes to ensemble prediction. But we cannot decide which perturbation strategy is better in aspect of the structure of the background error covariance. It appears that further studies on the best perturbation way for hybrid variational data assimilation to consider an error-of-the-day(EOTD) should be needed.

Shape Design Sensitivity Analysis using Isogeometric Approach (CAD 형상을 활용한 설계 민감도 해석)

  • Ha, Seung-Hyun;Cho, Seon-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.577-582
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    • 2007
  • A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

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Hydrodynamic scene separation from video imagery of ocean wave using autoencoder (오토인코더를 이용한 파랑 비디오 영상에서의 수리동역학적 장면 분리 연구)

  • Kim, Taekyung;Kim, Jaeil;Kim, Jinah
    • Journal of the Korea Computer Graphics Society
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    • v.25 no.4
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    • pp.9-16
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    • 2019
  • In this paper, we propose a hydrodynamic scene separation method for wave propagation from video imagery using autoencoder. In the coastal area, image analysis methods such as particle tracking and optical flow with video imagery are usually applied to measure ocean waves owing to some difficulties of direct wave observation using sensors. However, external factors such as ambient light and weather conditions considerably hamper accurate wave analysis in coastal video imagery. The proposed method extracts hydrodynamic scenes by separating only the wave motions through minimizing the effect of ambient light during wave propagation. We have visually confirmed that the separation of hydrodynamic scenes is reasonably well extracted from the ambient light and backgrounds in the two videos datasets acquired from real beach and wave flume experiments. In addition, the latent representation of the original video imagery obtained through the latent representation learning by the variational autoencoder was dominantly determined by ambient light and backgrounds, while the hydrodynamic scenes of wave propagation independently expressed well regardless of the external factors.

Consider the directional hole filling method for virtual view point synthesis (가상 시점 영상 합성을 위한 방향성 고려 홀 채움 방법)

  • Mun, Ji Hun;Ho, Yo Sung
    • Smart Media Journal
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    • v.3 no.4
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    • pp.28-34
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    • 2014
  • Recently the depth-image-based rendering (DIBR) method is usually used in 3D image application filed. Virtual view image is created by using a known view with associated depth map to make a virtual view point which did not taken by the camera. But, disocclusion area occur because the virtual view point is created using a depth image based image 3D warping. To remove those kind of disocclusion region, many hole filling methods are proposed until now. Constant color region searching, horizontal interpolation, horizontal extrapolation, and variational inpainting techniques are proposed as a hole filling methods. But when using those hole filling method some problem occurred. The different types of annoying artifacts are appear in texture region hole filling procedure. In this paper to solve those problem, the multi-directional extrapolation method is newly proposed for efficiency of expanded hole filling performance. The proposed method is efficient when performing hole filling which complex texture background region. Consideration of directionality for hole filling method use the hole neighbor texture pixel value when estimate the hole pixel value. We can check the proposed hole filling method can more efficiently fill the hole region which generated by virtual view synthesis result.

The influence of accumulated clinical experience with Soyang-type patients on the conceptualization of the Soyang pathology (소양인(少陽人) 치험례(治驗例)가 소양인(少陽人) 병리관(病理觀) 형성과정에 미친 영향에 대한 고찰)

  • Kang, Mi-Jeong;Lee, Ji-Won;Lee, Jun-Hee;Koh, Byung-Hee;Lee, Eui-Ju
    • Journal of Sasang Constitutional Medicine
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    • v.23 no.3
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    • pp.275-284
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    • 2011
  • 1. Objective: This literary review investigates Lee Jema's clinical experiences with Soyang-type patients and their influence on his conceptualization of the Soyang physiology and pathology. 2. Methods: 1) The case reports in "Soyang constitutional type: Spleen Cold-based Exterior-Cold disease" were compared before and after the Sinchuk revision to explore the temporal change in the Sasang medical concepts. 2) The texts in Donguisusebowon (Gabo edition) and Donguisusebowon (Sasangchobongwon) were analyzed to investigate the pathological concepts appearing before the completion of the Donguisusebowon (Gabo edition). 3) The texts in Donguisusebowon (Sinchuk edition) was analyzed to investigate the pathological concepts formed between the Gabo and Sinchuk editions of Donguisusebowon. 3. Results and Conclusions: 1) Gabo edition : The Gabo edition divided the External-origin Exterior disease into Cold-dominant (Heat-moderate) and Heat-dominant (Cold-moderate) patterns and differentiated the severity of Exterior-based Exterior disease and Interior-based Interior disease into mild, moderate, severe, and critical conditions. Cold-damage Delirium disease pattern was categorized as an Interior-based Interior disease, and the treatment protocol using Baekho-tang (Baihu-tang) was established. The stool condition and bowel movement reflecting the patient's defecation habits, the prime indicator of health in the Soyang constitutional type, were emphasized on their importance. 2) Sinchuk edition: The Delirium disease pattern was moved into the Exterior-cold disease, and the treatment protocol applying Jihwangbaekho-tang (Dihuangbaihu-tang) and Hyeongbangsabaek-san (Jingfangxiebai-san), with variational usage of Gypsum, was newly established. The Seong-Jeong and basal disease patterns were suggested as important factors in treating the patients. Also, it was proposed that the symptoms and signs reflecting the condition of the life-preserving energy be assessed to understand the patient's current condition. The importance of post-acute rehabilitation and aftercare as well as the most appropriate acute-stage treatment were emphasized.