• Computers and Concrete
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• 제32권1호
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• pp.99-117
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• 2023

The crack under the influence of the higher intensities of the stresses grows and the structure gets collapsed with the time when the crack length reaches to critical value. Therefore, the fracture behavior of a structure in terms of stress intensity factors (SIF) becomes important to determine the remaining fracture strength and capacity of material and structure for avoiding catastrophic failure, increasing safety and further improvement in the design. The robustness of the method has been demonstrated by comparing the numerical results with analytical and experimental results of some problems. XFEM is used to model cracks and holes in structures and predict their strength and reliability under service conditions. Further, XFEM is extended with a stochastic method for predicting the sensitivity in terms of output COVs and fracture strength in terms of mean values of stress intensity factors (SIFs) of a structure with discontinuities (cracks and holes) under tensile loading condition with input individual and combined randomness in different system parameters. In stochastic technique, the second order perturbation technique (SOPT) has been used for the predicting the fracture behavior of the structures. The stochastic/perturbation technique is also known as Taylor series expansion method and it provides the reliable results if the input randomness is less than twenty percentage. From the present numerical analysis it is observed that, the crack tip near to the hole is under the influence of the stress concentration and the variational effect of the input random parameters on the crack tip in terms of the SIFs are lesser so the COVs are the less sensitive. The COVs of mixed mode SIFs are the most sensitive for the crack angles (α=45° to 90°) for all the values of c₁ and d₁. The plate with the shorter distance between hole and crack is the most sensitive with all the crack angles but the crack tip which is much nearer to the hole has the highest sensitivity.

• Advances in aircraft and spacecraft science
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• 제3권4호
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• pp.471-502
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• 2016

This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).

• 한국항행학회논문지
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• 제19권6호
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• pp.636-642
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• 2015

본 논문에서는 계단응답으로부터 시 지연을 갖는 선형 연속시스템을 식별하기 위해 HS 최적화 알고리즘을 적용에 관하여 연구하였다. 인식 모델은 1차 시 지연 모델 (FOPDT)로써, FOPDT은 많은 화학 공정과 HAVC 공정에 실효성이 있으며 PID 튜닝에도 적합하다. 최근에 개발된 HS 알고리즘은 완벽한 하모니를 찾아가는 음악적 과정을 개념화 한 것이다. 수학을 기반으로 하는 전통적 기법과 달리 HS는 확률적인 방법을 사용하므로 미분과 같은 수학적 접근을 필요로 하지 않는다. 제시된 인식 방법의 효과를 입증하기 위해 많은 수치 예를 수행하여 결과를 제시하였다.

• 경영과학
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• 제29권3호
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• pp.121-134
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• 2012

In this study, we consider a component procurement planning problem where the procurement amounts of components are determined under assemble-to-order systems with demand uncertainty. In the problem, procurement amount of each component is decided before the demands of finished products are known and after the demands are identified the assembly amounts of the finished products are decided. In this study, the objective function of the problem is minimizing the total costs which are composed of purchase and inventory costs of the components and the backorder costs of the finished products. We assume that the uncertain demand information is given as multiple scenarios of the demands, and we propose procurement planning methods based on stochastic models which considering the multiple demand scenarios. To evaluate the performances of the proposed methods, computational experiments were carried out on the proposed methods as well as benchmarks including a method based on deterministic mathematical model and a heuristic. From the results of the computational tests, the superiorities of the proposed methods were shown.

• Industrial Engineering and Management Systems
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• 제12권3호
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• pp.172-180
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• 2013

We herein consider a stochastic multi-item inventory management problem in which a warehouse sells multiple items with stochastic demand and periodic replenishment from a supplier. Inventory management requires the timing and amounts of orders to be determined. For inventory replenishment, trucks of finite capacity are available. Most inventory management models consider either a single item or assume that multiple items are ordered independently, and whether there is sufficient space in trucks. The order cost is commonly calculated based on the number of carriers and the usage fees of carriers. In this situation, we can reduce future shipments by supplementing items to an order, even if the item is not scheduled to be ordered. On the other hand, we can reduce the average number of items in storage by reducing the order volume and at the risk of running out of stock. The primary variables of interest in the present research are the average number of items in storage, the stock-out volume, and the number of carriers used. We formulate this problem as a multi-objective optimization problem. In a numerical experiment based on actual shipment data, we consider the item shipping characteristics and simulate the warehouse replenishing items coordinately. The results of the simulation indicate that applying a conventional ordering policy individually will not provide effective inventory management.

• 대한수학회보
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• 제54권3호
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• pp.839-874
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• 2017

Our goal is to establish and prove the almost sure central limit theorems for some order statistics $\{M_n^{(k)}\}$, $k=1,2,{\ldots}$, formed by stochastic processes ($X_1,X_2,{\ldots},X_n$), $n{\in}N$, the distributions of which are defined by certain Archimedean copulas. Some properties of generators of such the copulas are intensively used in our proofs. The first class of theorems stated and proved in the paper concerns sequences of ordinary maxima $\{M_n\}$, the second class of the presented results and proofs applies for sequences of the second largest maxima $\{M_n^{(2)}\}$ and the third (and the last) part of our investigations is devoted to the proofs of the almost sure central limit theorems for the k-th largest maxima $\{M_n^{(k)}\}$ in general. The assumptions imposed in the first two of the mentioned groups of claims significantly differ from the conditions used in the last - the most general - case.

• 산업경영시스템학회지
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• 제37권1호
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• pp.165-171
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• 2014

We develop an optimization algorithm for a periodic review inventory system under a stochastic budget constraint. While most conventional studies on the periodic review inventory system consider a simple budget limit in terms of the inventory investment being less than a fixed budget, this study adopts more realistic assumption in that purchasing costs are paid at the time an order is arrived. Therefore, probability is employed to express the budget constraint. That is, the probability of total inventory investment to be less than budget must be greater than a certain value assuming that purchasing costs are paid at the time an order is arrived. We express the budget constraint in terms of the Lagrange multiplier and suggest a numerical method to obtain optional values of the cycle time and the safety factor to the system. We also perform the sensitivity analysis in order to investigate the dependence of important quantities on the budget constraint. We find that, as the amount of budget increases, the cycle time and the average inventory level increase, whereas the Lagrange multiplier decreases. In addition, as budget increases, the safety factor increases and reaches to a certain level. In particular, we derive the condition for the maximum safety factor.

• 한국해안·해양공학회논문집
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• 제27권4호
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• pp.246-257
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• 2015

피해 자료의 부족에 따른 불확실성 뿐만 아니라 시간의 진행에 따른 불확실성을 고려하기 위하여 추계학적 확률과정을 이용하여 시간에 따른 구조물의 피해 경로를 정량적으로 추적하였다. 누적피해도와 내구년수의 분포함수를 시간의 함수로 산정하여 추계학적 확률과정을 적용할 때 주의해야 하는 중요한 특성들을 제시하였다. 특히, 본 연구에서는 추계학적 확률과정을 경사제 피복재에 적용하여 시간에 따른 누적 피해도를 추적할 수 있는 방법을 제안하였다. 확률과정의 매개변수들을 추정하기 위하여 개발된 표본경로기법을 이용하여 경사제 피복재의 시간에 따른 누적 피해도가 포화거동을 따른다는 사실이 확인되었다. 또한 누적 피해도 산정시 중요한 역할을 하는 멱함수의 지수를 정량적으로 산정하여 경사제 피복재의 누적 피해도를 시간에 따라 추적하는 것이 가능했다. 마지막으로 한계수준을 다양하게 변화시키면서 파괴확률의 거동특성을 해석하였다.

• 품질경영학회지
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• 제14권1호
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• pp.33-38
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• 1986

This paper deals with probabilistic order level inventory system which the quantity ordered at the end of the scheduling period is dependent on lead times. To find an optimal solution, pearson system of distributions is used to approximate the probability density function of the on-order quantity. An example is solved and sensitivity analysis is performed to examine the relation between lead times and the ordering quantity.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2002년도 봄 학술발표논문집 Vol.29 No.1 (B)
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• pp.289-291
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• 2002

Host of source separation methods focus on stationary sources so higher-order statistics is necessary In this paler we consider a problem of source separation when sources are second-order nonstationary stochastic processes . We employ the natural gradient method and develop learning algorithms for both 1inear feedback and feedforward neural networks. Thus our algorithms possess equivariant property Local stabi1iffy analysis shows that separating solutions are always locally stable stationary points of the proposed algorithms, regardless of probability distributions of