• Communications for Statistical Applications and Methods
• /
• v.31 no.1
• /
• pp.65-85
• /
• 2024

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

• Journal of the Korean Society of Safety
• /
• v.32 no.3
• /
• pp.54-59
• /
• 2017

This paper presents an efficient finite analysis model and a simulation-based reliability analysis method for stowage device system failure of a container crane with respect to lateral load. A quasi-static analysis model is introduced to simulate the nonlinear resistance characteristics and failure of tie-down and stowage pin, which are the main structural stowage devices of a crane. As a reliability analysis method, a subset simulation method is applied considering the uncertainties of later load and mechanical characteristic parameters of stowage devices. An efficient Markov chain Monte Carlo (MCMC) method is applied to sample random variables. Analysis result shows that the proposed model is able to estimate the probability of failure of crane system effectively which cannot be calculated practically by crude Monte Carlo simulation method.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.4
• /
• pp.573-583
• /
• 2008

In this paper, we introduce the techniques of estimating the probability of failure in reliability analysis. The basic idea of each technique is explained and drawbacks of these techniques are examined.

• Computational Structural Engineering
• /
• v.7 no.1
• /
• pp.109-116
• /
• 1994

In this paper, various reliability analysis methods for calculating a probability of failure are investigated for their accuracy and efficiency. Crude Monte Carlo method is used as a basis for the comparison of various numerical results. For the sampling methods, Importance Sampling method and Directional Simulation method are considered for overcoming a drawback of Crude Monte Carlo method. For the approximate methods, conventional Rackwitz-Fiessler method. 3-parameter Chen-Lind method, and Rosenblatt transformation method are compared on the basis of First order reliability method. As a Second-order reliability method, Curvature-Fitting paraboloid method, Point-fitting paraboloid method, and Log-likelihood function method are explored in order to verify the accuracy of the reliability calculation results. These methods mentioned above would have some difficulty unless the limit state equation is expressed explicitly in terms of random design variables. Thus, there is a need to develop some general reliability methods for the case where an implicit limit state equation is given. For this purpose, Response surface method is used where the limit state equation is approximated by regression analysis of the response surface outcomes resulted from the structural analysis. From the application of these various reliability methods to three examples, it is found that Directional Simulation method and Response Surface method are very efficient and recommendable for the general reliability analysis problem cases.

• Computational Structural Engineering
• /
• v.4 no.2
• /
• pp.111-117
• /
• 1991

The analysis method calculating the mean and standard deviation for the eigenvalue of complicated structures in which the limit state equation is implicitly expressed is formulated and applied to the buckling analysis by combining probabilistic finite element method with direct differential method which is a kind of sensitivity analysis technique. Also, the probability of buckling failure is calculated by combining classical reliability techniques such a MVFOSM and AFOSM. As random variables external load, elastic modulus, sectional moment of inertia and member length are chosen and Parkinson's iteration algorithm in AFOSM is used. The accuracy of the results by this study is verified by comparing the results with the crude Monte Carlo simulation and Importance Sampling Method. Through the case study of some structures the important aspects of buckling reliability analysis are discussed.

• The Journal of the Korea Contents Association
• /
• v.13 no.4
• /
• pp.53-63
• /
• 2013

This paper presents an importance sampling(IS) embedded experimental frame(EF) design for efficient Monte Carlo (MC) simulation. To achieve IS principles, the proposed EF contains two embedded sub-models, which are classified into Importance Sampler(IS) and Bias Compensator(BC) models. The IS and BC models stand between the existing system model and EF, which leads to enhancement of model reusability. Furthermore, the proposed EF enables to achieve fast stochastic simulation as compared with the crude MC technique. From the abstract two case studies with the utilization of the proposed EF, we can gain interesting experimental results regarding remarkable enhancement of simulation performance. Finally, we expect that this work will serve various content areas for enhancing simulation performance, and besides, it will be utilized as a tool to understand and analyze social phenomena.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1993.04a
• /
• pp.109-116
• /
• 1993

구조물의 신뢰도를 평가하는 방법을 살펴보고 각각의 장,단점을 비교한다. 각 방법의 정확성을 평가하는 기준으로 Crude Monte Carlo(CMC)방법을 택하여, Importance Sampling(IS)방법, 그리고 Directional Sampling(DS)방법을 살펴 보고, 1차 근사방법은 현재 많이 사용되고 있는 Rackwitz-Fiessler(RF)방법, Chen과 Lind가 제안한 3-parameter방법(CL), Hohenbichler가 제안한 Rosenblatt 변환방법(RT)을, 그리고 2차 근사방법은 Breitung이 제안한 곡률적합 포물선 (Curvature Fitted Paraboloid,CFP)공식과 Kiureghian이 제안한 점적합 포물선(Point Fitted Paraboloid,PFP)공식, 그리고 Log-Likelihood function을 이용하여 원변수공간에서 파괴확률을 구하는 2차 근사공식(LLF)을 비교한다. 그리고 한계상태식이 불명확할 때 효율적으로 사용할 수 있는 반웅웅답법(Response surface method, RSM)을 살펴본다. 각 방법의 효율성 특히 적용 가능성을 예제를 통해 해석한 결과 추출법의 경우는 DS 방법이, 그리고 근사방법에서는 RSM 방법이 효율적임을 알 수 있었다.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1996.10a
• /
• pp.95-102
• /
• 1996

In this study, a stochastic finite element model is proposed with a view to consider the uncertainty of physical properties of discontinuous rock mass in the analysis of structural behavior on underground caverns. In so doing, the LHS(Latin Hypercube sampling) technique has been applied to make up weak points of the Crude Monte Carlo technique. Concerning the effect of discontinuities, a joint finite element model is used that is known to be superior in explaining faults, cleavage, things of that nature. To reflect the uncertainty of material properties, the variables such as the the elastic modulus, the poisson's ratio, the joint shear stiffness, and the joint normal stiffness have been used, all of which can be applicable through normal distribution, log-normal distribution, and rectangulary uniform distribution. The validity of the newly developed computer program has been confirmed in terms of verification examples. And, the applicability of the program has been tested in terms of the analysis of the circular cavern in discontinuous rock mass.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.21 no.6
• /
• pp.495-507
• /
• 2009

The expected sliding distance for the lifetime of a caisson breakwater has a limitation to be used as the stability criterion of the breakwater. Since the expected sliding distance is calculated as the mean of simulated sliding distances for the lifetime, there is possibility for the actual sliding distance to exceed the expected sliding distance. To overcome this problem, the exceedance probability of the allowable sliding distance is used to assess the stability of sliding. Latin Hypercube sampling and Crude Monte Carlo simulation were used to calculate the exceedance probability. The doubly-truncated normal distribution was considered to complement the physical disadvantage of the normal distribution as the random variable distribution. In the case of using the normal distribution, the cross-sections of Okgye, Hwasun, and Donghae NI before reinforcement were found to be unstable in all the limit states. On the other hand, when applying the doubly-truncated normal distribution, the cross-sections of Hwasun and Donghae NI before reinforcement were evaluated to be unstable in the repairable limit state and all the limit states, respectively. Finally, the shortcoming of the expected sliding distance as the stability criterion was investigated, and we reasonably assessed the stability of sliding of caissons by using the exceedance probability of allowable sliding distance for the caisson breakwaters in Korea.

• Journal of Radiation Protection and Research
• /
• v.16 no.1
• /
• pp.53-72
• /
• 1991

An integrated model is developed in this paper for the performance assessment of high level radioactive waste repository. This integrated model consists of two simple mathematical models. One is a multiple-barrier failure model of the repository system based on constant failure rates which provides source terms to biosphere. The other is a biosphere model which has multiple pathways for radionuclides to reach to human. For the parametric uncertainty and sensitivity analysis for the risk assessment of high level radioactive waste repository, Latin hypercube sampling and rank correlation techniques are applied to this model. The former is cost-effective for large computer programs because it gives smaller error in estimating output distribution even with smaller number of runs compared to crude Monte Carlo technique. The latter is good for generating dependence structure among samples of input parameters. It is also used to find out the most sensitive, or important, parameter groups among given input parameters. The methodology of the mathematical modelling with statistical analysis will provide useful insights to the decision-making of radioactive waste repository selection and future researches related to uncertain and sensitive input parameters.