Spectral SFEM analysis of structures with stochastic parameters under stochastic excitation

Galal, O.H.,El-Tahan, W.,El-Tawil, M.A.,Mahmoud, A.A. Techno-Press 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.3

In this paper, linear elastic isotropic structures under the effects of both stochastic operators and stochastic excitations are studied. The analysis utilizes the spectral stochastic finite elements (SSFEM) with its two main expansions namely; Neumann and Homogeneous Chaos expansions. The random excitation and the random operator fields are assumed to be second order stochastic processes. The formulations are obtained for the system solution of the two dimensional problems of plane strain and plate bending structures under stochastic loading and relevant rigidity using the previously mentioned expansions. Two finite element programs were developed to incorporate such formulations. Two illustrative examples are introduced: the first is a reinforced concrete culvert with stochastic rigidity subjected to a stochastic load where the culvert is modeled as plane strain problem. The second example is a simply supported square reinforced concrete slab subjected to out of plane loading in which the slab flexural rigidity and the applied load are considered stochastic. In each of the two examples, the first two statistical moments of displacement are evaluated using both expansions. The probability density function of the structure response of each problem is obtained using Homogeneous Chaos expansion.

Spectral SFEM analysis of structures with stochastic parameters under stochastic excitation

O.H. Galal,W. El-Tahan,M.A. El-Tawil,A.A. Mahmoud 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.3

In this paper, linear elastic isotropic structures under the effects of both stochastic operators and stochastic excitations are studied. The analysis utilizes the spectral stochastic finite elements (SSFEM) with its two main expansions namely; Neumann and Homogeneous Chaos expansions. The random excitation and the random operator fields are assumed to be second order stochastic processes. The formulations are obtained for the system solution of the two dimensional problems of plane strain and plate bending structures under stochastic loading and relevant rigidity using the previously mentioned expansions. Two finite element programs were developed to incorporate such formulations. Two illustrative examples are introduced: the first is a reinforced concrete culvert with stochastic rigidity subjected to a stochastic load where the culvert is modeled as plane strain problem. The second example is a simply supported square reinforced concrete slab subjected to out of plane loading in which the slab flexural rigidity and the applied load are considered stochastic. In each of the two examples, the first two statistical moments of displacement are evaluated using both expansions. The probability density function of the structure response of each problem is obtained using Homogeneous Chaos expansion.

STOCHASTIC법에 의한 STOCK RETURN 극대화 연구

정원길 慶山大學校 1993 論文集 Vol.11 No.1

This paper tests 3 Stochastic models-No Band Rule, 3% Band Rule, and 5% Band Rule-by utilizing the Korean Composite Stock Index from Jan. 1992 to Sep. 1993. The result of empirical test shows that the average Return of Stochastic model is higher than that of C.S.P.I. The optimum Stochastic model for Korean stock market is No band rule with 6day holding period which generated 37.83% return with σ-0.034 The result proves that technical analysis is a very useful investment tool worth studying.

외환시장의 변동성과 거래량의 관계 분석: 충격정보 확률변동성 모형 이용

박범조 한국은행 2008 經濟分析 Vol.14 No.4

Modifying the MDH(mixture of distribution hypothesis) theory, Park(2007) showed that the effect of ‘surprising information’ on the relationship between volatility and trading volumes contrasts with that of general information. On the basis of his study, this paper proposes surprising-information-stochastic- volatility(SISV) model to capture their nonlinear relationship that is caused by the state change of volatility due to the surprising information flow. To estimate the SISV model efficiently this paper also suggests Markov chain Monte Carlo(MCMC) method. Strong evidence in favor of SISV model over the standard stochastic volatility model is based on empirical application with high frequency data of Won/Dollar exchange rates. Interestingly, while their positive relationship is not significant in the stochastic volatility model with a volume variable, it becomes significant and the persistence of volatility is remarkably reduced in the SISV model. According to the estimation results of the bivariate SISV model, furthermore, the surprising information flow increases the volatility of returns highly, whereas it little changes the volatility of trading volume. These empirical findings are consistent with the modified MDH and imply that ignoring the feature of surprising information can lead to a model misspecification. 충격정보가 자산시장의 변동성과 거래량의 관계에 미치는 영향이 일반정보와 다르다는 수정된 혼합분포가설(MDH)(박범조, 2007)에 기초하여 본 연구는 충격정보의 유입에 따라 변동성의 상태(states)가 변함으로써 발생되는 두 변수의 비선형적 관계를 동태적으로 고려하기 위한 충격정보 확률변동성(surprising-information-stochastic volatility: SISV) 모형을 새롭게 제안하였다. 이 모형을 추정하기 위해 효율적인 베이지언 추정법인 마코프 체인 몬테칼로(MCMC) 알고리즘을 적용하고 고빈도 원/달러 환율 자료와 일별 거래량 자료를 이용하여 실증분석을 수행하였다. 거래량 변수만을 포함한 단변량 확률변동성 모형을 이용한 분석결과에 의하면 GARCH 유형의 모형을 이용한 일반적 연구결과와 다르게 변동성과 거래량이 통계적으로 유의한 관계를 갖지 않았다. 하지만 충격정보를 고려할 경우 유의한 관계를 가지게 되며 변동성의 지속성도 현격히 감소하였다. 한편 동시편의(simultaneity bias) 문제 없이 두 변수의 관계를 동태적으로 분석할 수 있는 이변량 SISV 모형에서도 유사한 결과를 보여줄 뿐만 아니라 충격정보가 유입되는 경우 수익률의 변동성은 통계적으로 유의하게 증가되지만 거래량의 변동성은 유의하게 변화되지 않는다는 흥미로운 사실을 보여주었다. 이런 실증분석 결과들은 수정된 혼합분포가설과 일치하며 변동성 모형에 충격정보를 고려하지 않는 경우 심각한 모형설정 오류가 발생할 수 있음을 암시한다.

Individual-based and stochastic modeling of cell population dynamics considering substrate dependency

Lee, Min Woo,Vassiliadis, Vassilios S.,Park, Jong Moon Wiley Subscription Services, Inc., A Wiley Company 2009 Biotechnology and bioengineering Vol.103 No.5

<P>In this article, we propose an individual-based and stochastic modeling approach that is capable of describing the bacterial cell population dynamics during a batch culture. All stochastic nature inherent in intracellular molecular level reactions and cell division processes were considered in a single model framework by embedding a sub-model describing individual cell's growth kinetics in a discrete event simulation algorithm. The resultant unique feature of the model is that the effects of the stochasticities on the cell population dynamics can be investigated for different substrate-dependent cell growth kinetics. When Monod kinetics was used as the sub-model, the stochasticities only slightly affected the cell mass increase and substrate consumption profiles during the batch culture although they were still important in describing the changes of cell population distributions. When Andrews substrate inhibition kinetics was used, however, it was revealed that the overall cell population dynamics could be seriously influenced by the stochasticities. Under a critical initial substrate level, the cell population could proliferate against the substrate inhibition only when the stochasticities were considered. Biotechnol. Bioeng. 2009;103: 891–899. © 2009 Wiley Periodicals, Inc.</P>

STOCHASTIC SINGLE MACHINE SCHEDULING SUBJECT TO MACHINES BREAKDOWNS WITH QUADRATIC EARLY-TARDY PENALTIES FOR THE PREEMPTIVE-REPEAT MODEL

Tang, Hengyong,Zhao, Chuanli 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1

In this paper we research the problem in which the objective is to minimize the sum of squared deviations of job expected completion times from the due date, and the job processing times are stochastic. In the problem the machine is subject to stochastic breakdowns and all jobs are preempt-repeat. In order to show that the replacing ESSD by SSDE is reasonable, we discuss difference between ESSD function and SSDE function. We first give an express of the expected completion times for both cases without resampling and with resampling. Then we show that the optimal sequence of the problem V-shaped with respect to expected occupying time. A dynamic programming algorithm based on the V-shape property of the optimal sequence is suggested. The time complexity of the algorithm is pseudopolynomial.

A stochastic finite element method for dynamic analysis of bridge structures under moving loads

Xiang Liu,Lizhong Jiang,Ping Xiang,Zhipeng Lai,Yuntai Zhang,Lili Liu 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.82 No.1

In structural engineering, the material properties of the structures such as elastic modulus, shear modulus, density, and size may not be deterministic and may vary at different locations. The dynamic response analysis of such structures may need to consider these properties as stochastic. This paper introduces a stochastic finite element method (SFEM) approach to analyze moving loads problems. Firstly, Karhunen-Loéve expansion (KLE) is applied for expressing the stochastic field of material properties. Then the mathematical expression of the random field is substituted into the finite element model to formulate the corresponding random matrix. Finally, the statistical moment of the dynamic response is calculated by the point estimation method (PEM). The accuracy and efficiency of the dynamic response obtained from the KLE-PEM are demonstrated by the example of a moving load passing through a simply supported Euler-Bernoulli beam, in which the material properties (including elastic modulus and density) are considered as random fields. The results from the KLE-PEM are compared with those from the Monte Carlo simulation. The results demonstrate that the proposed method of KLE-PEM has high accuracy and efficiency. By using the proposed SFEM, the random vertical deflection of a high-speed railway (HSR) bridge is analyzed by considering the random fields of material properties under the moving load of a train.

Empty Container Repositioning with Stochastic Demand/Supply and Transportation Capacity

Zong Bin Qui,문일경 한국SCM학회 2008 한국SCM학회지 Vol.8 No.1

We study the empty container repositioning problem for a shipping company in this paper. We develop a mathematical model with stochastic parameters. The model seeks to minimize the total costs of repositioning, leasing, and inventory holding of empty containers, subject to meeting the requirements for empty containers. We consider that the demand/supply for empty containers consists of two parts; one is deterministic and the other is stochastic. We also consider the transportation capacity of ships used for the transportation of empty containers as a stochastic factor. In order to solve the model, Chance-Constrained Programming is applied. The developed model can be an effective decision support for a shipping company.

대일정 생산 계획에 따른 조선소 생산 용량의 초기 평가를 위한 이산사건 시뮬레이션

김광식(Kwang Sik Kim),황호진(Ho Jin Hwang),이장현(Jang Hyun Lee) (사)한국CDE학회 2012 한국CDE학회 논문집 Vol.17 No.2

Capacity planning plays an important role not only for master production plan but also for facility or layout design in shipbuilding. Product work breakdown structure, attributes of production resources, and production method or process data are associated in order to make the discrete event simulation model of shipyard layout plan. The production amount of each process and the process time is assumed to be stochastic. Based on the stochastic discrete event simulation model, the production capacity of each facility in shipyard is estimated. The stochastic model of product arrival time, process time and transferring time is introduced for each process. Also, the production capacity is estimated for the assumed master production schedule.

New Optimization Model for Multi-Period Multi-Product Production Planning System with Uncertainty

Asmaa A. Mahmoud,Mohamed F. Aly,Ahmed M. Mohib,Islam H. Afefy 대한산업공학회 2019 Industrial Engineeering & Management Systems Vol.18 No.4

The focus of this study is to develop a multi-period multi-product (MPMP) production planning system with uncertainty, and products demand (seasonal demand) uncertainty. Mainly, the problem aims reach the production levels ofeach product according to the uncertain demand for various periods, which depend on constraints of capacity, inventory, and resources. An analytical model proposed for this problem that can be categorized into two classes: non-linearand stochastic. The objective is to minimize the summation of variable production costs. As uncertain demand is adynamic stochastic data process in the planning horizon, it is considered as a tree model. Each stage in the demandtree model is related to a cluster of a period time. Hence, depending on the tree model for the fluctuation demand;Two-Stage Stochastic Programming (TSP) model is presented as an alternative for all demand scenarios. In some ofthe reviewed articles validation of the analytical model were missing, while other studies were missing either manufacturing set up costs or assumptions of seasonal demand. Therefore, this study proposes TSP model using SamplingAverage Approximation method (SAA) that is suitable for a production planning system in any manufacturing environment considering seasonal demand using optimization program (Lingo 16) to solve the mathematical model. Further, investigation of seasonal demand is performed using the multiplicative seasonal method, and the model validation was checked using Mathworks Matlab R2015a (64-Bit) considering manufacturing set up costs. Finally, somerecommendations for future research are suggested.