• Structural Engineering and Mechanics
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• 제32권1호
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• pp.55-69
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• 2009

A quasi ideal importance sampling simulation method combined in the conditional expectation is proposed for the structural reliability estimation. The quasi ideal importance sampling joint probability density function (p.d.f.) is so composed on the basis of the ideal importance sampling concept as to be proportional to the conditional failure probability multiplied by the p.d.f. of the sampling variables. The respective marginal p.d.f.s of the ideal importance sampling joint p.d.f. are determined numerically by the simulations and partly by the piecewise integrations. The quasi ideal importance sampling simulations combined in the conditional expectation are executed to estimate the failure probabilities of structures with multiple failure surfaces and it is shown that the proposed method gives accurate estimations efficiently.

• Communications for Statistical Applications and Methods
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• 제31권1호
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• pp.65-85
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• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1991년도 봄 학술발표회 논문집
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• pp.34-42
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• 1991

This study is directed for the development of an efficient system-level Importance Sampling Technique for system reliability analysis of bridge structures Many methods have been proposed for structural reliability assessment purposes, such as the First-order Second-Moment Method, the Advanced Second-Moment Method, Computer Simulation, etc. The Importance Sampling Technique can be employed to obtain accurate estimates of the required probability with reasonable computation effort. Based on the observation and the results of application, it nay be concluded that Importance Sampling Method is a very effective tool for the system reliability analysis.

• 한국시뮬레이션학회논문지
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• 제8권3호
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• pp.77-89
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• 1999

Simulating rare events, such as probability of cell loss in ATM networks, machine failure in highly reliable systems, requires huge simulation efforts due to the low chance of occurrence. Importance Sampling (IS) has been applied to accelerate the occurrence of rare events. However, it has a drawback of effective biasing scheme to make the estimator of IS unbiased. Adaptive Importance Sampling (AIS) employs an estimated sampling distribution of IS to the system of interest during the course of simulation. We propose Nonparametric Adaptive Importance Sampling (NAIS) technique which is nonparametrical version of AIS. We test NAIS to estimate a probability of rare event in M/M/1 queueing model. Comparing with classical Monte Carlo simulation, the computational efficiency and variance reductions gained via NAIS are substantial. A possible extension of NAIS regarding with random number generation is also discussed.

• 한국통신학회논문지
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• 제22권5호
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• pp.1097-1106
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• 1997

Most works on importance sampling (IS) as an efficient evaluation technique havd been done in an additibe white gaussian noise channel (Awgn). In this paper we propose a CQ(conventional importance sampling and quasi-translantion) IS technique for the mobile radio channel modeled as Rician fading, and analyze the IS estimator's variance to determine optimum IS parameters and the minimum number of run times. Reference showed that CIS technique has a poor performance for systems with meories, but it is shown that the CIS technique can be improved by combining with quasi-translation technique even for systems with memories. Here the CQ IS technique modifies the variance of additive noise and also performs quasi-translation for the fading distribution. We determine the optimum IS parameters of the proposed CQ IS estimator and whow that the simulation gains are about 10$^{3}$~10$^{6}$ for the mobile communication systems with memories in case of the expected BERs 10$^{-5}$ ~10$^{-8}$ .

• Structural Engineering and Mechanics
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• 제38권1호
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• pp.125-140
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• 2011

This study presents an innovative method to estimate the reliability sensitivity based on the low-discrepancy sampling which is a new technique for structural reliability analysis. Two advantages are contributed to the method: one is that, by developing a general importance sampling procedure for reliability sensitivity analysis, the partial derivative of the failure probability with respect to the distribution parameter can be directly obtained with typically insignificant additional computations on the basis of structural reliability analysis; and the other is that, by combining various low-discrepancy sequences with the above importance sampling procedure, the proposed method is far more efficient than that based on the classical Monte Carlo method in estimating reliability sensitivity, especially for problems of small failure probability or problems that require a large number of costly finite element analyses. Examples involving both numerical and structural problems illustrate the application and effectiveness of the method developed, which indicate that the proposed method can provide accurate and computationally efficient estimates of reliability sensitivity.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1996년도 춘계공동학술대회논문집; 공군사관학교, 청주; 26-27 Apr. 1996
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• pp.553-556
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• 1996

The cell loss probability recommended in the B-ISDN is in the range of 10$^{-8}$ ~ 10$^{-12}$ . When a simulation technique is used to analyze the performance of the ATM switching system, an enormous amount of computer time is required. In this study, we derive an importance sampling simulation technique that can be used to evaluate the loss probability obtained by the importance sampling simulation is very close to that obtained by the ordinary simulation and the computer time can be reduced drastically by the importance sampling simulation.

• 전산구조공학
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• 제4권2호
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• pp.119-129
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• 1991

본 논문은 교량구조의 체계신뢰도를 추정하기 위한 효율적인 중요도 표본추출기법의 개발을 목적으로 한다. 기존의 체계신뢰성 해석을 위한 방법은 1차 모멘트법, 2차 모멘트법, AFOSM 근사해법, 그리고 시뮬레이션 방법등이 있다. 중요도 표본추출기법은 아주 적은 경비와 노력으로 정확한 해를 구하는 시뮬레이션 방법이다. 적용 예를 통하여 중요도 표본추출기법은 교량구조의 체계신뢰성해석에 아주 효과적인 방법임을 알 수 있었다.

• Journal of the Korean Statistical Society
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• 제35권2호
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• pp.157-166
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• 2006

This research proposes an efficient Monte Carlo algorithm for computing error probability in high performance digital communication st stems. It characterizes special features of the problem and suggests an importance sampling algorithm specially designed to handle the problem. It uses a shifted exponential density as the importance sampling density, and shows an adaptive way of choosing the rate and the origin of the shifted exponential density. Instead of equal allocation, an intelligent allocation of the samples is proposed so that more samples are allocated to more important part of the error probability. The algorithm uses the nested feature of the error space and avoids redundancy in estimating the probability. The algorithm is applied to an example data set and shows a great improvement in accuracy of the error probability estimation.

• 한국시뮬레이션학회:학술대회논문집
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• 한국시뮬레이션학회 1999년도 춘계학술대회 논문집
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• pp.70-79
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• 1999

Importance Sampling (IS) has been applied to accelerate the occurrence of rare events. However, it has a drawback of effective biasing scheme to make the estimator from IS unbiased. Adaptive Importance Sampling (AIS) employs an estimated sampling distribution of IS to the systems of interest during the course of simulation. We propose Nonparametric Adaptive Importance Sampling (NAIS) technique which is nonparametrically modified version of AIS and test it to estimate a probability of rare event in M/M/1 queueing model. Comparing with classical Monte Carlo simulation, the computational efficiency and variance reductions gained via NAIS are substantial. A possible extension of NAIS regarding with random number generation is also discussed.