• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.4
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• pp.432-446
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• 1996

A stochastic Hamilton variational principle(SHVP) is formulated for dynamic problems of linear continuum. The SHVP allows incorporation of probabilistic distributions into the finite element analysis. The formulation is simplified by transformation of correlated random variables to a set of uncorrelated random variables through a standard eigenproblem. A procedure based on the Fourier analysis and synthesis is presented for eliminating secularities from the perturbation approach. In addition to, a method to analyse stochastic design sensitivity for structural dynamics is present. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element codes. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The algorithms developed can readily be adapted to existing deterministic finite element codes. The numerical results for stochastic analysis by proceeding approach of cantilever, 2D-frame and 3D-frame illustrates in this paper.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.391-399
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• 2006

In order to solve the optimization problem of designing the trajectory of three-dimensional horizontal well, we establish a multi-phase, nonlinear, stochastic dynamic system of the trajectory of horizontal well. We take the precision of hitting target and the total length of the trajectory as the performance index. By the integration of the state equation, this model can be transformed into a nonlinear stochastic programming. We discuss here the necessary conditions under which a local solution exists and depends in a continuous way on the parameter (perturbation). According to the properties we propose a revised Hooke-Jeeves algorithm and work out corresponding software to calculate the local solution of the nonlinear stochastic programming and the expectancy of the performance index. The numerical results illustrate the validity of the proposed model and algorithm.

• Proceedings of the KIEE Conference
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• 1999.07a
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• pp.200-202
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• 1999

A method of stochastic finite element analysis is developed for yield a uncertainty of engineering problems. Where, a stochastic finite-element method for shapes modeling is proposed a6 a means to solve the models with the uncertainty and variety. This method is based on the probability and illustrated by a first-Order Second-Moment Method and considering the covariance of random variables. The validity and accuracy of the stochastic finite element method is verified through comparing with those solved by the conventional 2-D finite element method.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.4
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• pp.425-438
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• 2007

In this paper, unsettled technical controversies concerning about fatigue strength analysis for FPSO, one of the representative floaters, associated with welding types, screening methods, fabrication tolerances, corrosion margins and Morison loads are described based on yard practices. Basic theory for stochastic fatigue analysis is introduced as detail as possible. In order to resolve large parts of the controversies, a new fully stochastic fatigue analysis program for FPSO is developed.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.187-207
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• 2016

Practical ambient excitations of engineering structures usually do not comply with the stationary-white-noise assumption in traditional operational modal analysis methods due to heavy traffic, wind guests, and other disturbances. In order to eliminate spurious modes induced by non-white noise inputs, the improved stochastic subspace identification based on a delay index is proposed in this paper for a representative kind of stationary non-white noise ambient excitations, which have nonzero autocorrelation values near the vertical axis. It relaxes the stationary-white-noise assumption of inputs by avoiding corresponding unqualified elements in the Hankel matrix. Details of the improved stochastic subspace identification algorithms and determination of the delay index are discussed. Numerical simulations on a four-story frame and laboratory vibration experiments on a simply supported beam have demonstrated the accuracy and reliability of the proposed method in eliminating spurious modes under non-white noise ambient excitations.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.107-122
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• 2022

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Management Science and Financial Engineering
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• v.15 no.1
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• pp.33-49
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• 2009

We examine the effectiveness of the conventional (Q, r) model in managing production-inventory systems with finite capacity, stochastic demand, and stochastic order processing times. We show that, for systems with finite production capacity, order replenishment lead times are highly sensitive to loading and order quantity. Consequently, the choice of optimal order quantity and optimal reorder point can vary significantly from those obtained under the usual assumption of a load-independent lead time. More importantly, we show that for a given (Q, r) policy the conventional model can grossly under or over-estimate the actual cost of the policy. In cases where a setup time is associated with placing a production order, we show that the optimal (Q, r) policy derived from the conventional model can, in fact, be infeasible.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.595-611
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• 2013

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlighted. Three examples are presented to demonstrate the accuracy and efficiency of the three methods. The results indicate that the condition that the Hermite polynomial information matrix evaluated at the collocation points has a full rank should be satisfied to yield reliability results with a sufficient accuracy. The point method and the without origin method are much more efficient than the root method, especially for the reliability problems involving a large number of random variables or requiring complex finite element analysis. The without origin method can also produce sufficiently accurate reliability results in comparison with the point and root methods. Therefore, the origin often used as a collocation point is not absolutely necessary. The odd order SRSMs with the point method and the without origin method are recommended for the reliability analysis due to their computational accuracy and efficiency. The order of SRSM has a significant influence on the results associated with the three collocation point methods. For normal random variables, the SRSM with an order equaling or exceeding the order of a performance function can produce reliability results with a sufficient accuracy. The order of SRSM should significantly exceed the order of the performance function involving strongly non-normal random variables.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.4
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• pp.53-62
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• 2009

Lee[15] examined quantity discount contracts between a manufacturer and a retailer in a stochastic, two-period inventory model where quantity discounts are provided based on the previous order size. During the two periods, the retailer faces stochastic (truncated Poisson distributed) demands and he/she places orders to meet the demands. The manufacturer provides for the retailer a price discount for the second period order if its quantity exceeds the first period order quantity. In this paper we extend the above two-period model to a k-period one (where k < 2) and propose a stochastic nonlinear mixed binary integer program for it. In order to make the program tractable, the nonlinear term involving the sum of truncated Poisson cumulative probability function values over a certain range of demand is approximated by an i-interval piecewise linear function. With the value of i selected and fixed, the piecewise linear function is determined using an evolutionary algorithm where its fitness to the original nonlinear term is maximized. The resulting piecewise linear mixed binary integer program is then transformed to a mixed binary integer linear program. With the k-period model developed, we suggest a solution procedure of receding horizon control style to solve n-period (n < k) order decision problems. We implement Lee's two-period model and the proposed k-period model for the use in receding horizon control style to solve n-period order decision problems, and compare between the two models in terms of the pattern of order quantities and the total profits. Our computational study shows that the proposed model is superior to the two-period model with respect to the total profits, and that order quantities from the proposed model have higher fluctuations over periods.