• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.523-529
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• 2004

In Korea, mathematics education has been changed according to the 7th national mathematics curriculum renovated by the Ministry of Education and Human Resources Development announcement in 1997. The education of probability and Statistics has been carried out as a part of this curriculum. We analyze and compare 3 kinds of mathematics textbooks for 10-12 grade students. Descriptions of random variable, sample variance and sample standard deviation, distribution of sample mean, and etc. which are on some textbooks, are misleaded in school education. We suggest the unbiased estimator of sample variance in textbooks and distributions of sample means with normal population assumption.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.351-358
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• 1999

The structural responses of underground structures are examined in probability by using the elasto-plastic stochastic finite element method in which the spatial distributions of material properties are assumed to be stochastic fields. In addition, the adaptive importance sampling method using the response surface technique is used to improve simulation efficiency. The method is found to provide appropriate information although the nonlinear Limit State involves a large number of basic random variables and the failure probability is small. The probability of plastic local failures around an excavated area is effectively evaluated and the reliability for the limit displacement of the ground is investigated. It is demonstrated that the adaptive importance sampling method can be very efficiently used to evaluate the reliability of a large scale stochastic finite element model, such as the underground structures located in the multi-layered ground.

• Journal of electromagnetic engineering and science
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• v.11 no.4
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• pp.262-268
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• 2011

In this paper, we evaluate the outage performance of cooperative transmission in two-dimensional random networks. Firstly, we derive the joint distributions of the source-relay and the relay-destination links. Secondly, the outage probability for the decode-and-forward relaying system is derived when selection combining (SC) is employed at the destination. Finally, we calculate the average outage probability of the system and then attempt to express it by a simple approximate expression. The simulation results are presented to verify the accuracy of the derivations. Similar to deterministic networks, the cooperative transmission in random networks outperforms direct transmission at a high signal-to-noise ratio (SNR).

• Communications for Statistical Applications and Methods
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• v.31 no.1
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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.

• Structural Engineering and Mechanics
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• v.11 no.6
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• pp.663-672
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• 2001

Numerous failures in welded connections in steel moment-resisting building frames (SMRF) were observed when buildings were inspected after the 1994 Northridge Earthquake. These observations raised concerns about the effectiveness of such frames for resisting strong earthquake ground motions. The behavior of SMRFs during an earthquake must be assessed using nonlinear dynamic analysis, and such assessments must permit the deterioration in connection strength to capture the behavior of the frame. The uncertainties that underlie both structural and dynamic loading also need to be included in the analysis process. This paper describes the analysis of one of approximately 200 SMRFs that suffered damage to its welded beam-to-column connections from the Northridge Earthquake is evaluated. Nonlinear static and dynamic analysis of this SMRF in the time domain is performed using ground motions representing the Northridge Earthquake. Subsequently, a detailed uncertainty analysis is conducted for the building using an ensemble of earthquake ground motions. Probability distributions for deformation-related limit states, described in terms of maximum roof displacement or interstory drift, are constructed. Building fragilities that are useful for condition assessment of damaged building structures and for performance-based design are developed from these distributions.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.631-634
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• 2004

In this paper, the Bayesian recurrent neural network (BRNN) is proposed to predict time series data. Among the various traditional prediction methodologies, a neural network method is considered to be more effective in case of non-linear and non-stationary time series data. A neural network predictor requests proper learning strategy to adjust the network weights, and one need to prepare for non-linear and non-stationary evolution of network weights. The Bayesian neural network in this paper estimates not the single set of weights but the probability distributions of weights. In other words, we sets the weight vector as a state vector of state space method, and estimates its probability distributions in accordance with the Bayesian inference. This approach makes it possible to obtain more exact estimation of the weights. Moreover, in the aspect of network architecture, it is known that the recurrent feedback structure is superior to the feedforward structure for the problem of time series prediction. Therefore, the recurrent network with Bayesian inference, what we call BRNN, is expected to show higher performance than the normal neural network. To verify the performance of the proposed method, the time series data are numerically generated and a neural network predictor is applied on it. As a result, BRNN is proved to show better prediction result than common feedforward Bayesian neural network.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.11
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• pp.2421-2428
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• 2002

In this study, the failure probability of the degraded LP turbine blade steel was performed using the Monte Carlo simulation to apply variation of applied stress and strength. For this purpose, applied stress under the service condition of steady state was obtained by theoretical stress analysis and the maximum Von-Mises stress was 219MPa. The fatigue strength under rotating-bending load was evaluated by the staircase method. Furthermore, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probabilistic distributions of tensile and fatigue strength were determined by the proposed analysis. The failure probability with various loading conditions was derived from the strength-stress interference model and the characteristic factor of safety was also estimated.

• Journal of Korean Society for Atmospheric Environment
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• v.12 no.2
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• pp.167-177
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• 1996

To investigate the source-receptor relationships aerosol model has been used to simulate the distribution behavior of the yellow sand. Data for meteorological fields were obtained by Meso-scale Analysis and Prediction Model System/Seoul National University (MAPMS/SNU) for five days (10-14 April 1988). To obtain the distributions of concentration of yellow sand,the aerosol model has been modified to allow quantifications of relative concentration distributions of yellow sand. Source regions of yellow sand were delineated by soil maps of China and emission rate as a function of wind stress(Westphal et al., 1987). Using 3-dimensional wind fields the backward trajectories from 3 receptor grids at the layer of .sigma. =0.95, 0.9, 0.85, 0.8 were calculated. In order to facilitate quantitative assessment of source-receptor relationships, it was assumed that the perturbations in along-trajectory and cross-trajectory proceed linearly with time, in accord with Gaussian distribution characteristics. On the basis of this assumption, the probability fields were calculated from every grid point with source strength 1. Using these probability fields and emission retes, the potential contributions of upstream sources along the trajectories were estimated. The results of this study indicate that the application of trajectory modeling is useful in investigating the quantitative relationship between source and receptor regions.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.427-436
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• 2000

In this paper, we consider a Bayesian model selection problem of lifetime distributions using fractional Bayes factor with noninformative prior when type II censored data are given. For a given type II censored data, we calculate the posterior probability of exponential, Weibull and lognormal distributions and select the model which gives the highest posterior probability. Our proposed methodology is explained and applied to real data and simulated data.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.467-471
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• 2014

The natural frequencies of a mechanical system are determined by the system parameters such as masses and stiffness of the system. Since material irregularities and manufacturing tolerances always exist in most of practical engineering situations, the system parameters always have uncertainties. As the uncertainties of the parameters increase, the uncertainties of the system natural frequencies also increases. Then, the reliability of the system deteriorates. So, the uncertainty of the system natural frequencies should be analyzed accurately and considered in the design of the system. In order to analyze the uncertainty of the system natural frequencies employing most of existing uncertainty analysis methods, the probability distributions of the uncertain system parameters should be identified. In most practical situations, however, identification of the probability distributions is almost impossible because of limited time and cost. For that case, the reliability should be estimated based on finite samples of the system parameters. In this paper, sample based reliability estimation method employing extreme value theory was proposed. Using the proposed estimation method, sample based reliability design of the system natural frequencies was conducted.