• Structural Engineering and Mechanics
• /
• 제28권2호
• /
• pp.129-152
• /
• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Structural Engineering and Mechanics
• /
• 제38권1호
• /
• pp.39-63
• /
• 2011

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

• 한국경영과학회지
• /
• 제36권3호
• /
• pp.91-105
• /
• 2011

In this paper, we analyze a logistic system involving a supplier who produces and delivers multiple types of items and a buyer who receives and sells the products to end customers. The buyer controls the inventory level by replenishing each product item up to a given order-up-to-level to cope with stochastic demand of end customers. In response to the buyer's order, the supplier produces or outsources the ordered item and delivers them at the start of each period. For the system described above, a mathematical model for a single type of item was developed from the buyer's perspective. Based on the model, an efficient method to find the cycle length and safety factor which correspond to a local minimum solution is proposed. This single product model was extended to cover a multiple item situation. From the model, algorithms to decide the base cycle length and order interval of each item were proposed. The results of the computational experiment show that the algorithms were able to determine the global optimum solution for all tested cases within a reasonable amount of time.

• 한국전산구조공학회논문집
• /
• 제20권6호
• /
• pp.789-799
• /
• 2007

본 논문에서는 구조의 재료물성치와 기하학적 인수의 공간적 불확실성에 의한 구조 응답변화도 산정을 위한 정식화를 제안하였다. 정식화는 추계론적 유한요소해석의 해석법 중의 하나인 가중적분법을 기본으로 하였다. 해석 대상 구조는 전단변형을 포함하는 평판구조로서, 평판구조에 나타날 수 있는 불확실 인수로는 재료적 측면에서는 재료탄성계수와 포아송비가 있으며, 기하학적 인수로는 평판의 두께를 들 수 있다. 선형탄성 영역에서 선형성을 나타내는 재료탄성계수와는 달리 평판의 두께는 3차함수로 강성에 기여하고, 포아송비의 경우 분수의 형태로 강성에 기여하므로 직접적으로는 이를 추계론적 해석에 고려할 수 없다. 따라서 본 연구에서는 적합행렬내의 포아송비를 Taylor전개하여 사용하였다. 제안된 정식화에 의한 결과는 기존 연구결과는 물론 몬테카를로 해석에 의한 결과와도 비교하여 제안한 정식화를 검증하였다.

• Wind and Structures
• /
• 제10권1호
• /
• pp.45-60
• /
• 2007

Transmission tower is a vital component in electrical system. In order to accurately compute the dynamic response and reliability of transmission tower under the excitation of wind loading, a new method termed as probability density evolution method (PDEM) is introduced in the paper. The PDEM had been proved to be of high accuracy and efficiency in most kinds of stochastic structural analysis. Consequently, it is very hopeful for the above needs to apply the PDEM in dynamic response of wind-excited transmission towers. Meanwhile, this paper explores the wind stochastic field from stochastic Fourier spectrum. Based on this new viewpoint, the basic random parameters of the wind stochastic field, the roughness length $z_0$ and the mean wind velocity at 10 m heigh $U_{10}$, as well as their probability density functions, are investigated. A latticed steel transmission tower subject to wind loading is studied in detail. It is shown that not only the statistic quantities of the dynamic response, but also the instantaneous PDF of the response and the time varying reliability can be worked out by the proposed method. The results demonstrate that the PDEM is feasible and efficient in the dynamic response and reliability analysis of wind-excited transmission towers.

• 한국정보통신학회논문지
• /
• 제18권11호
• /
• pp.2634-2639
• /
• 2014

시스템 및 네트워크의 안정적인 서비스를 위한 기본적인 구조로 다양한 이중화 방식이 있다. 또한 시스템 및 네트워크의 성능을 분석하기 위하여 페트리네트에서부터 Stochastic Reward Net(SRN)에 이르기까지 다양한 성능 분석 모형이 존재한다. 본 논문에서는 정상 상태에서 하나의 액티브 서비스 유닛과 하나의 스탠바이 서비스 유닛을 가진 2N 이중화 방식을 SRN으로 모형화 한다. 성능 분석 소프트웨어인 추계적 페트리네트 패키지 SPNP를 사용하여 2N 이중화 방식의 가용도를 분석한다.

• KDI Journal of Economic Policy
• /
• 제40권4호
• /
• pp.1-22
• /
• 2018

We estimate three continuous-time stochastic volatility models following the approach by Aït-Sahalia and Kimmel (2007) to compare the Korean and US stock markets. To do this, the Heston, GARCH, and CEV models are applied to the KOSPI 200 and S&P 500 Index. For the latent volatility variable, we generate and use the integrated volatility proxy using the implied volatility of short-dated at-the-money option prices. We conduct MLE in order to estimate the parameters of the stochastic volatility models. To do this we need the transition probability density function (TPDF), but the true TPDF is not available for any of the models in this paper. Therefore, the TPDFs are approximated using the irreducible method introduced in Aït-Sahalia (2008). Among three stochastic volatility models, the Heston model and the CEV model are found to be best for the Korean and US stock markets, respectively. There exist relatively strong leverage effects in both countries. Despite the fact that the long-run mean level of the integrated volatility proxy (IV) was not statistically significant in either market, the speeds of the mean reversion parameters are statistically significant and meaningful in both markets. The IV is found to return to its long-run mean value more rapidly in Korea than in the US. All parameters related to the volatility function of the IV are statistically significant. Although the volatility of the IV is more elastic in the US stock market, the volatility itself is greater in Korea than in the US over the range of the observed IV.

• Wind and Structures
• /
• 제38권1호
• /
• pp.1-13
• /
• 2024

In order to effectively simulate nonstationary stochastic turbulent wind fields, four separation hybrid (SEP-H) models are proposed in the present study. Based on the assumption that the lateral turbulence component at one single-point is uncorrelated with the longitudinal and vertical turbulence components, the fluctuating wind is separated into 2nV-1D and nV1D nonstationary stochastic vector processes. The first process can be expressed as double proper orthogonal decomposition (DPOD) or proper orthogonal decomposition and spectral representation method (POD-SRM), and the second process can be expressed as POD or SRM. On this basis, four SEP-H models of nonstationary stochastic turbulent wind fields are developed. In addition, the orthogonal random variables in the SEP-H models are presented as random orthogonal functions of elementary random variables. Meanwhile, the number theoretical method (NTM) is conveniently adopted to select representative points set of the elementary random variables. The POD-FFT (Fast Fourier transform) technique is introduced in frequency to give full play to the computational efficiency of the SEP-H models. Finally, taking a long-span bridge as the engineering background, the SEP-H models are compared with the dimension-reduction DPOD (DR-DPOD) model to verify the effectiveness and superiority of the proposed models.

• Structural Engineering and Mechanics
• /
• 제4권4호
• /
• pp.425-436
• /
• 1996

An application of the perturbation method to optimum structural design with random parameters is presented. It is formulated on the basis of the first-order stochastic finite element perturbation method. It also takes into full account the stress, displacement and eigenvalue constraints, together with the rates of change of the random variables. A method for calculating the sensitivity coefficients in regard to the governing equation and the first-order perturbed equation has been derived, by using a direct differentiation approach. A gradient-based nonlinear programming technique is used to solve the problem. The numerical results are specifically noted, where the stiffness parameter and external load are treated as random variables.

• 산업경영시스템학회지
• /
• 제42권4호
• /
• pp.183-193
• /
• 2019

Process mining is an analytical technique aimed at obtaining useful information about a process by extracting a process model from events log. However, most existing process models are deterministic because they do not include stochastic elements such as the occurrence probabilities or execution times of activities. Therefore, available information is limited, resulting in the limitations on analyzing and understanding the process. Furthermore, it is also important to develop an efficient methodology to discover the process model. Although genetic process mining algorithm is one of the methods that can handle data with noises, it has a limitation of large computation time when it is applied to data with large capacity. To resolve these issues, in this paper, we define a stochastic process tree and propose a tabu search-genetic process mining (TS-GPM) algorithm for a stochastic process tree. Specifically, we define a two-dimensional array as a chromosome to represent a stochastic process tree, fitness function, a procedure for generating stochastic process tree and a model trace as a string of activities generated from the process tree. Furthermore, by storing and comparing model traces with low fitness values in the tabu list, we can prevent duplicated searches for process trees with low fitness value being performed. In order to verify the performance of the proposed algorithm, we performed a numerical experiment by using two kinds of event log data used in the previous research. The results showed that the suggested TS-GPM algorithm outperformed the GPM algorithm in terms of fitness and computation time.