• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.296-311
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• 2021

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.

• Structural Engineering and Mechanics
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• 제70권6호
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• pp.737-750
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• 2019

This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young's modulus and Poisson's ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integropartial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton's method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

• 한국가시화정보학회지
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• 제17권2호
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• pp.10-16
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• 2019

Considering the role of viscosity in the hemorheology, the characteristics of non-Newtonian fluid are important in the pulsatile blood flows. Stenosis, with an abnormal narrowing of the vessel, contributes to block blood flows to downstream tissue and lead to plaque rupture. Therefore, systematic analysis of blood flow around stenosed vessels is crucial. In this study, non-Newtonian behaviors of blood analog fluids around the micro-stenosis with 60 % severity in diameter of $500{\mu}m$ was examined by using CFX under the pulsatile flow conditions with the period of 10 s. Viscosity information of two non-Newtonian fluids were obtained by fitting the value of normal blood and highly viscous blood. As the Newtonian fluid, the water at room temperature was used. During the pulsatile phase, wall shear stress (WSS) is highly oscillated. In addition, high viscous solution gives rise to increases the variation in the WSS around the micro-stenosis. Highly oscillating WSS enhance increasing tendency of plaque instability or rupture and damage of the tissue layer. These results, related to the influence on the damage to the endothelium or stenotic lesion, may help clinicians understand relevant mechanisms.

• 한국추진공학회지
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• 제23권2호
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• pp.38-45
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• 2019

본 연구에서는 항공용 가스터빈의 연소실에서의 연소불안정 해석을 위한 고유값 도출을 목적으로 하는 1D 네트워크 모델을 개발하였다. 모델은 면적 변화가 있는 음향 네트워크 요소들 사이의 각종 지배 방정식을 통하여 개발되었고, 이를 이용하여 현재 개발 중인 복잡한 유로 형상을 갖는 실제 항공용 가스터빈 연소기에서의 음향장 해석에 적용되었다. 본 모델을 통하여 도출된 음향장 해석 결과는 3차원 유한요소해석 기반의 헬름홀츠 솔버의 계산 결과와 비교하였다.

• 호남수학학술지
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• 제41권2호
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• 한국추진공학회지
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• 제24권4호
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• pp.25-32
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• 2020

모형 연소기에서 동축형 분사기에 의한 연소불안정성을 운동량비 변화에 따라 수치적으로 분석하였다. 실제 로켓 엔진의 경계조건을 기반으로 총 5개의 운동량비를 선택하였다. 운동량비가 증가할수록 분사기 출구에서의 확산각도는 감소하는 경향을 보였으며, 축방향 운동량이 증가할수록 연소기 내부의 압력진폭이 크게 감소함을 확인하였다. 동적 모드 분해 기법(dynamic mode decomposition)을 통해 연소기내의 음향 모드를 파악하였고 관심 섭동 주파수를 갖는 2L 모드(mode)의 감쇠계수를 구하고 이를 통해 운동량비가 증가할수록 연소기의 안정성이 증가함을 보였다.

• Geomechanics and Engineering
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• 제23권6호
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• pp.587-600
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• 2020

Shear-induced instability of jointed rock mass has greatly threatened the safety of underground openings. To better understand the failure mechanism of surrounding rock mass under shear, the flawed specimens containing a circular opening and two open joints are prepared and used to conduct direct shear tests. Both experimental and numerical results show that joint inclination (β) has a significant effect on the shear strength, dilation, cracking behavior and stress distribution around flaws. The maximum shear strength, occurring at β=30°, usually corresponds to a unifrom stress state around joint and an intense energy release. However, a larger joint inclination, such as β=90°~150°, will cause a more uneven stress distribution and a stronger stress concentration, thus a lower shear strength. The stress distribution around opening changes little with joint inclination, while the magnitude varys much. Both compression and tension around opening will be greatly enhanced by the 30°-joints. In addition, a higher normal stress tends to enhance the compression and suppress the tension around flaws, resulting in an earlier generation and a larger proportion of shear cracks.

• Communications for Statistical Applications and Methods
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• 제28권4호
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• pp.339-350
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• 2021

In medical research, the risk factors associated with human diseases need to be identified to predict the incidence rate and determine the treatment plan. Logistic regression analysis is primarily used in order to select risk factors. However, individuals who are unfamiliar with statistics outcomes have trouble using these methods. In this study, we develop a nomogram that graphically represents the numerical association between the disease and risk factors in order to identify the risk factors for delirium and to interpret and use the results more effectively. By using the logistic regression model, we identify risk factors related to delirium, construct a nomogram and predict incidence rates. Additionally, we verify the developed nomogram using a receiver operation characteristics (ROC) curve and calibration plot. Nursing home, stroke/epilepsy, metabolic abnormality, hemodynamic instability, and analgesics were selected as risk factors. The validation results of the nomogram, built with the factors of training set and the test set of the AUC showed a statistically significant determination of 0.893 and 0.717, respectively. As a result of drawing the calibration plot, the coefficient of determination was 0.820. By using the nomogram developed in this paper, health professionals can easily predict the incidence rate of delirium for individual patients. Based on this information, the nomogram could be used as a useful tool to establish an individual's treatment plan.

• 한국정밀공학회지
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• 제13권3호
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• pp.110-122
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• 1996

Finite element analysis tool was developed to analyze the casting process. Generally, casting process consists of mold filling and solidification. Both filling and solidication process were simulated simultaneously to investigate the effects of process variables and to predict the defect. At filling process, thermal coupling was especially considered to investigate thermal history of material during the filling stage. And thermal condition at the final stage of filling is used as the initial conditions in a solidification process for the exact simullation of the actual casting processes. At mold filling process, Lagragian-type finite element method with automatic remeshing scheme was used to find the material flow. A perturbation method with artificial viscosity is adopted to avoid numerical instability in low viscous fluid. At solidification process, enthalpy-based finite element method was used to solove the heat transfer problem with phase change. And elastic stress analysis has been performed to predict the thermal residual stress. Through the FE analysis, solidification time, position of solidus line, liquidus line and thermal residual stress are found. Through the study, the importance of combined analysis has been emphasized. Finite element tools developed in this study will be used process design of casting process and may be basic structure for total CAE system of castings which will be constructed afterward.

• Geomechanics and Engineering
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• 제33권2호
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• pp.167-174
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• 2023

This study evaluated slope stability through a case study to determine the disaster risks associated with increased deforestation in structures, including schools and apartments, located in urban areas adjacent to slopes. The slope behind the ○○ High School in Gwangju, Korea, collapsed owing to heavy rain in August 2018. Historically, rainwater drained well around the slope during the rainy season. However, during the collapse, a large amount of seepage water flowed out of the slope surface and a shallow failure occurred along the saturated soil layer. To analyze the cause of the collapse, the images of the upper area of the slope, which could not be directly identified, were captured using unmanned aerial vehicles (UAVs). A digital elevation model of the slope was constructed through image analysis, making it possible to calculate the rainfall flow direction and the area, width, and length of logging areas. The change in the instability of the slope over time owing to rainfall lasting ten days before the collapse was analyzed through numerical analysis. Imaging techniques based on the UAV images were found to be effective in analyzing ground disaster risk maps in urban areas. Furthermore, the analysis was found to predict the failure before its actual occurrence.