• Title/Summary/Keyword: Mathematical journal

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System Reliability-Based Design Optimization Using Performance Measure Approach (성능치 접근법을 이용한 시스템 신뢰도 기반 최적설계)

  • Kang, Soo-Chang;Koh, Hyun-Moo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.3A
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    • pp.193-200
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    • 2010
  • Structural design requires simultaneously to ensure safety by considering quantitatively uncertainties in the applied loadings, material properties and fabrication error and to maximize economical efficiency. As a solution, system reliability-based design optimization (SRBDO), which takes into consideration both uncertainties and economical efficiency, has been extensively researched and numerous attempts have been done to apply it to structural design. Contrary to conventional deterministic optimization, SRBDO involves the evaluation of component and system probabilistic constraints. However, because of the complicated algorithm for calculating component reliability indices and system reliability, excessive computational time is required when the large-scale finite element analysis is involved in evaluating the probabilistic constraints. Accordingly, an algorithm for SRBDO exhibiting improved stability and efficiency needs to be developed for the large-scale problems. In this study, a more stable and efficient SRBDO based on the performance measure approach (PMA) is developed. PMA shows good performance when it is applied to reliability-based design optimization (RBDO) which has only component probabilistic constraints. However, PMA could not be applied to SRBDO because PMA only calculates the probabilistic performance measure for limit state functions and does not evaluate the reliability indices. In order to overcome these difficulties, the decoupled algorithm is proposed where RBDO based on PMA is sequentially performed with updated target component reliability indices until the calculated system reliability index approaches the target system reliability index. Through a mathematical problem and ten-bar truss problem, the proposed method shows better convergence and efficiency than other approaches.

An Improved Structural Reliability Analysis using Moving Least Squares Approximation (이동최소제곱근사법을 이용한 개선된 구조 신뢰성 해석)

  • Kang, Soo-Chang;Koh, Hyun-Moo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.28 no.6A
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    • pp.835-842
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    • 2008
  • The response surface method (RSM) is widely adopted for the structural reliability analysis because of its numerical efficiency. However, the RSM is still time consuming for large-scale applications and sometimes shows large errors in the calculation of sensitivity of reliability index with respect to random variables. Therefore, this study proposes a new RSM in which moving least squares (MLS) approximation is applied. Least squares approximation generally used in the common RSM gives equal weight to the coefficients of the response surface function (RSF). On the other hand, The MLS approximation gives higher weight to the experimental points closer to the design point, which yields the RSF more similar to the limit state at the design point. In the procedure of the proposed method, a linear RSF is constructed initially and then a quadratic RSF is formed using the axial experimental points selected from the reduced region where the design point is likely to exist. The RSF is updated successively by adding one more experimental point to the previously sampled experimental points. In order to demonstrate the effectiveness of the proposed method, mathematical problems and ten-bar truss are considered as numerical examples. As a result, the proposed method shows better accuracy and computational efficiency than the common RSM.

Estimation of Perceived Curve Radius Considering Visual Distortion at Curve Sections (곡선부 시각왜곡현상을 고려한 인지곡선반경 산정에 관한 연구)

  • Shin, Jae-Man;Park, Je-Jin;Son, Sang-Ho;Ha, Tae-Jun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.4D
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    • pp.395-402
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    • 2010
  • The seriousness of a traffic accident appears relatively higher on the curve sections compared with the straight sections due to a change in speed caused by a change in the driver's sight. In particular, the visual distortion phenomenon, one of the dangerous factors taking place on the curve sections, appears different according to the road's geometric design. Although it is a genuinely principal design factor which should be necessarily considered in designing a road, the previous researches on establishing the design standards for it have been insufficiently conducted. As a result, the establishment of the road design standards for the curve sections considering the sight distortion phenomenon is desperately required. This research examined the previous researches on the driver's behaviors, the driver's sight characteristics and the perceived curve radius on the curve sections, and developed the theoretical model of perceived curve radius to which a mathematical technique is applied in consideration of the visual distortion phenomenon on the two-lane curve sections in a local area. In addition, after the theoretical visual distortion was calculated on the basis of the theoretical model of perceived curve radius, the range of error on the theoretical recognition radius model formula was verified through comparing it with the previous researches' experiential visual distortion level and analyzing both of them. As a result, it was observed that as the curve radius practically increases in the theoretical recognition curve radius, the range of error tends to go down, which reflects well the characteristics of the curve sections on the road. Based on this research, it is expected that this research will be helpful to eliminate the safety defects when designing the curve sections and contribute to develop the road design standards considering human factors in the future.

An Improved Reliability-Based Design Optimization using Moving Least Squares Approximation (이동최소자승근사법을 이용한 개선된 신뢰도 기반 최적설계)

  • Kang, Soo-Chang;Koh, Hyun-Moo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.1A
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    • pp.45-52
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    • 2009
  • In conventional structural design, deterministic optimization which satisfies codified constraints is performed to ensure safety and maximize economical efficiency. However, uncertainties are inevitable due to the stochastic nature of structural materials and applied loads. Thus, deterministic optimization without considering these uncertainties could lead to unreliable design. Recently, there has been much research in reliability-based design optimization (RBDO) taking into consideration both the reliability and optimization. RBDO involves the evaluation of probabilistic constraint that can be estimated using the RIA (Reliability Index Approach) and the PMA(Performance Measure Approach). It is generally known that PMA is more stable and efficient than RIA. Despite the significant advancement in PMA, RBDO still requires large computation time for large-scale applications. In this paper, A new reliability-based design optimization (RBDO) method is presented to achieve the more stable and efficient algorithm. The idea of the new method is to integrate a response surface method (RSM) with PMA. For the approximation of a limit state equation, the moving least squares (MLS) method is used. Through a mathematical example and ten-bar truss problem, the proposed method shows better convergence and efficiency than other approaches.

[Retracted]Analysis of Slope Safety by Tension Wire Data ([논문철회]지표변위계를 활용한 비탈면 안정성 예측)

  • Lee, Seokyoung;Jang, Seoyong;Kim, Taesoo;Han, Heuisoo
    • Journal of the Korean GEO-environmental Society
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    • v.16 no.4
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    • pp.5-12
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    • 2015
  • Civil engineers have taken the numerous slope monitoring data for an engineering project subjected to hazard potential of slide. However, the topics on how to deal with and draw out proper information from the data related to the slope behavior have not been widely discussed. Recently, several researchers had installed the real-time monitoring system to cope with slope failure; however they are mainly focused on the hardware system installation. Therefore, this study tries to show how the measured data could be grouped and connected each other. The basic idea of analyzing method studied in this paper came from the clustering, which is the part of data mining analysis. Therefore, at the base of classification of time series data, the authors suggest three mathematical data analyzing methods; Average Index of different displacement ($AD_{i,j}$), Difference of average relative displacement ($\overline{RD}_{i,j}$) and Coordinate system of average and relative displacement ($\overline{RD}$, AD). These analyzing methods are based on the statistical method and failure mechanism of slope. Therefore they showed clustering relationships of the similar parts of the slope which makes the same sliding mechanism.

A Study on Pose Control for Inverted Pendulum System using PID Algorithm (PID 알고리즘을 이용한 역 진자 시스템의 자세 제어에 관한 연구)

  • Jin-Gu Kang
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.16 no.6
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    • pp.400-405
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    • 2023
  • Currently, inverted pendulums are being studied in many fields, including posture control of missiles, rockets, etc, and bipedal robots. In this study, the vertical posture control of the pendulum was studied by constructing a rotary inverted pendulum using a 256-pulse rotary encoder and a DC motor. In the case of nonlinear systems, complex algorithms and controllers are required, but a control method using the classic and relatively simple PID(Proportional Integral Derivation) algorithm was applied to the rotating inverted pendulum system, and a simple but desired method was studied. The rotating inverted pendulum system used in this study is a nonlinear and unstable system, and a PID controller using Microchip's dsPIC30F4013 embedded processor was designed and implemented in linear modeling. Usually, PID controllers are designed by combining one or two or more types, and have the advantage of having a simple structure compared to excellent control performance and that control gain adjustment is relatively easy compared to other controllers. In this study, the physical structure of the system was analyzed using mathematical methods and control for vertical balance of a rotating inverted pendulum was realized through modeling. In addition, the feasibility of controlling with a PID controller using a rotating inverted pendulum was verified through simulation and experiment.

A New Method for Aortic Valve Planimetry with High-Resolution 3-Dimensional MRI and Its Comparison with Conventional Cine MRI and Echocardiography for Assessing the Severity of Aortic Valvular Stenosis

  • Hae Jin Kim;Yeon Hyeon Choe;Sung Mok Kim;Eun Kyung Kim;Mirae Lee;Sung-Ji Park;Joonghyun Ahn;Keumhee C. Carriere
    • Korean Journal of Radiology
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    • v.22 no.8
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    • pp.1266-1278
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    • 2021
  • Objective: We aimed to compare the aortic valve area (AVA) calculated using fast high-resolution three-dimensional (3D) magnetic resonance (MR) image acquisition with that of the conventional two-dimensional (2D) cine MR technique. Materials and Methods: We included 139 consecutive patients (mean age ± standard deviation [SD], 68.5 ± 9.4 years) with aortic valvular stenosis (AS) and 21 asymptomatic controls (52.3 ± 14.2 years). High-resolution T2-prepared 3D steady-state free precession (SSFP) images (2.0 mm slice thickness, 10 contiguous slices) for 3D planimetry (3DP) were acquired with a single breath hold during mid-systole. 2D SSFP cine MR images (6.0 mm slice thickness) for 2D planimetry (2DP) were also obtained at three aortic valve levels. The calculations for the effective AVA based on the MR images were compared with the transthoracic echocardiographic (TTE) measurements using the continuity equation. Results: The mean AVA ± SD derived by 3DP, 2DP, and TTE in the AS group were 0.81 ± 0.26 cm2, 0.82 ± 0.34 cm2, and 0.80 ± 0.26 cm2, respectively (p = 0.366). The intra-observer agreement was higher for 3DP than 2DP in one observer: intraclass correlation coefficient (ICC) of 0.95 (95% confidence interval [CI], 0.94-0.97) and 0.87 (95% CI, 0.82-0.91), respectively, for observer 1 and 0.97 (95% CI, 0.96-0.98) and 0.98 (95% CI, 0.97-0.99), respectively, for observer 2. Inter-observer agreement was similar between 3DP and 2DP, with the ICC of 0.92 (95% CI, 0.89-0.94) and 0.91 (95% CI, 0.88-0.93), respectively. 3DP-derived AVA showed a slightly higher agreement with AVA measured by TTE than the 2DP-derived AVA, with the ICC of 0.87 (95% CI, 0.82-0.91) vs. 0.85 (95% CI, 0.79-0.89). Conclusion: High-resolution 3D MR image acquisition, with single-breath-hold SSFP sequences, gave AVA measurement with low observer variability that correlated highly with those obtained by TTE.

Design of Digital Phase-locked Loop based on Two-layer Frobenius norm Finite Impulse Response Filter (2계층 Frobenius norm 유한 임펄스 응답 필터 기반 디지털 위상 고정 루프 설계)

  • Sin Kim;Sung Shin;Sung-Hyun You;Hyun-Duck Choi
    • The Journal of the Korea institute of electronic communication sciences
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    • v.19 no.1
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    • pp.31-38
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    • 2024
  • The digital phase-locked loop(DPLL) is one of the circuits composed of a digital detector, digital loop filter, voltage-controlled oscillator, and divider as a fundamental circuit, widely used in many fields such as electrical and circuit fields. A state estimator using various mathematical algorithms is used to improve the performance of a digital phase-locked loop. Traditional state estimators have utilized Kalman filters of infinite impulse response state estimators, and digital phase-locked loops based on infinite impulse response state estimators can cause rapid performance degradation in unexpected situations such as inaccuracies in initial values, model errors, and various disturbances. In this paper, we propose a two-layer Frobenius norm-based finite impulse state estimator to design a new digital phase-locked loop. The proposed state estimator uses the estimated state of the first layer to estimate the state of the first layer with the accumulated measurement value. To verify the robust performance of the new finite impulse response state estimator-based digital phase locked-loop, simulations were performed by comparing it with the infinite impulse response state estimator in situations where noise covariance information was inaccurate.

Dose Assessment of Orbital Adnexa in Electron Beam Therapy for Orbital Lymphoma (안와림프종의 전자선 치료 시 안구 부속기관에 대한 선량평가)

  • Dong Hwan Kim;Yong In Cho
    • Journal of the Korean Society of Radiology
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    • v.18 no.3
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    • pp.283-292
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    • 2024
  • Radiation side effects and complications on the ocular adnexa during electron beam therapy for orbital lymphoma can increase the incidence of posterior subcapsular cataracts. This study simulated a medical linear accelerator and a mathematical model of the eye using monte carlo simulations to evaluate the dose to the ocular adnexa and compare the shielding effectiveness on different parts of the ocular adnexa based on lens shield thickness. The dose assessment results of the ocular adnexa showed that the lens's sensitive area had the highest absorbed dose distribution when no shield was used, followed by the lens's non-sensitive area, the anterior chamber, vitreous humor, cornea, and eyelid in descending order. With the use of a shield, a 2 mm thick shield demonstrated a dose reduction effect of over 90% in the lens's sensitive area, over 83% in the non-sensitive area and anterior chamber, and a dose reduction effect of 30 to 62% in the vitreous body, cornea, and eyelid. For dose reduction in the lens's sensitive area during electron beam therapy for orbital lymphoma, it is necessary to use a shield of at least 2 mm thickness. Additionally, shielding strategies considering the thickness and area of the shield for other ocular adnexa besides the lens are required.

Effect of Modified Atmosphere Packaging Gas Composition on Quality Preservation of Korean Rockfish Fillets (조피볼락 필렛의 변형기체포장에서 품질보존에 미치는 기체조성의 영향)

  • Eo Jin Park;Su Chan Kim;Duck Soon An
    • KOREAN JOURNAL OF PACKAGING SCIENCE & TECHNOLOGY
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    • v.29 no.3
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    • pp.145-151
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    • 2023
  • In order to extend shelf life for rockfish fillets by modified atmosphere packaging (MAP), different package atmospheres were compared in the product quality preservation. Firstly, CO2 solubility was measured at 0, 5, 10, and 15℃ to be incorporated into the mathematical model to predict the volume and CO2 concentration of the package at expected storage temperature. The CO2 solubility given in Henry's constant decreased with temperature to be fitted with a linear equation. Then air packaging as control and four MAP conditions of 100 g fillets were prepared and stored for duration of 5 days at 10℃ to compare them in the quality preservation effect. Four MAP conditions employed were CO2(60):O2(30):N2(10), CO2(60):O2(0):N2(40), CO2(30):O2(30):N2(40) andCO2(30):O2(0):N2(70). MAP conditions with high CO2 concentration inhibited total aerobic bacteria, and the conditions containing O2 led to low TVB-N. MAP of CO2(60):O2(30):N2(10) was found to be the best condition for rockfish fillet preservation considering total aerobic bacteria growth and nitrogenous volatiles production.