• Smart Structures and Systems
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• 제29권2호
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• pp.321-336
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• 2022

Model uncertainty is a key factor that could influence the accuracy and reliability of numerical model-based analysis. It is necessary to acquire an appropriate updating approach which could search and determine the realistic model parameter values from measurements. In this paper, the Bayesian model updating theory combined with the transitional Markov chain Monte Carlo (TMCMC) method and K-means cluster analysis is utilized in the updating of the structural model parameters. Kriging and polynomial chaos expansion (PCE) are employed to generate surrogate models to reduce the computational burden in TMCMC. The selected updating approaches are applied to three structural examples with different complexity, including a two-storey frame, a ten-storey frame, and the national stadium model. These models stand for the low-dimensional linear model, the high-dimensional linear model, and the nonlinear model, respectively. The performances of updating in these three models are assessed in terms of the prediction uncertainty, numerical efforts, and prior information. This study also investigates the updating scenarios using the analytical approach and surrogate models. The uncertainty quantification in the Bayesian approach is further discussed to verify the validity and accuracy of the surrogate models. Finally, the advantages and limitations of the surrogate model-based updating approaches are discussed for different structural complexity. The possibility of utilizing the boosting algorithm as an ensemble learning method for improving the surrogate models is also presented.

• Journal of information and communication convergence engineering
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• 제20권2호
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• pp.79-89
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• 2022

To compute the mean and variance of component-based reliability software, we focused on path-based reliability analysis. System reliability depends on the transition probabilities of components within a system and reliability of the individual components as basic input parameters. The uncertainty in these parameters is estimated from the test data of the corresponding components and arises from the software architecture, failure behaviors, software growth models etc. Typically, researchers perform Monte Carlo simulations to study uncertainty. Thus, we considered a Markov chain Monte Carlo (MCMC) simulation to calculate uncertainty, as it generates random samples through sequential methods. The MCMC approach determines the input parameters from the probability distribution, and then calculates the average approximate expectations for a reliability estimation. The comparison of different techniques for uncertainty analysis helps in selecting the most suitable technique based on data requirements and reliability measures related to the number of components.

• Nuclear Engineering and Technology
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• 제55권8호
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• pp.2844-2853
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• 2023

A sophisticated Bayesian multilevel model for estimating group bias was developed to improve the utility of the ASTM E900-15 embrittlement trend curve (ETC) to assess the conditions of nuclear power plants (NPPs). For multilevel model development, the Baseline 22 surveillance dataset was basically classified into groups based on the NPP name, product form, and notch orientation. By including the notch direction in the grouping criteria, the developed model could account for TTS differences among NPP groups with different notch orientations, which have not been considered in previous ETCs. The parameters of the multilevel model and biases of the NPP groups were calculated using the Markov Chain Monte Carlo method. As the number of data points within a group increased, the group bias approached the mean residual, resulting in reduced credible intervals of the mean, and vice versa. Even when the number of surveillance test data points was less than three, the multilevel model could estimate appropriate biases without overfitting. The model also allowed for a quantitative estimate of the changes in the bias and prediction interval that occurred as a result of adding more surveillance test data. The biases estimated through the multilevel model significantly improved the performance of E900-15.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2021년도 학술발표회
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• pp.127-127
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• 2021

In order to estimate parameter uncertainty of hydrological models, the consideration of the likelihood functions which provide reliable parameters of model is necessary. In this study, the Bayesian Markov Chain Monte Carlo (MCMC) method with informal likelihood functions is used to analyze the uncertainty of parameters of the SURR model for estimating the hourly streamflow of Gunnam station of Imjin basin, Korea. Three events were used to calibrate and one event was used to validate the posterior distributions of parameters. Moreover, the performance of four informal likelihood functions (Nash-Sutcliffe efficiency, Normalized absolute error, Index of agreement, and Chiew-McMahon efficiency) on uncertainty of parameter is assessed. The indicators used to assess the uncertainty of the streamflow simulation were P-factor (percentage of observed streamflow included in the uncertainty interval) and R-factor (the average width of the uncertainty interval). The results showed that the sensitivities of parameters strongly depend on the likelihood functions and vary for different likelihood functions. The uncertainty bounds illustrated the slight differences from various likelihood functions. This study confirms the importance of the likelihood function selection in the application of Bayesian MCMC to the uncertainty assessment of the SURR model.

• 응용통계연구
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• 제19권3호
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• pp.505-519
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• 2006

셀 수 있는 이산 자료(discrete count data)에 대한 분석은 여러 분야에서 활용되고 있지만 영(zero)을 과도하게 포함하고 있는 영과잉 자료는 자료의 성격상 포아송 분포를 따르지 못할 때가 있어 분석에 어려움이 따른다. Zero-Inflated Poisson(ZIP)모형은 이런 어려움을 극복하기 위하여 영에 대한 점확률을 가지는 분포와 포아송 분포를 합성하여 과도한 영과 영이 아닌 자료를 설명하는 모형이다. 설명 변수가 존재할 때는 포아송 분포 부분에서 반응변수의 평균과 공변량사이에 로그선형 연결함수를 사용한 Zero-Inflated Poisson Regression(ZIPR)모형이 사용될 수 있다. 본 논문에서는 Markov Chain Monte Carlo 기법을 이용한 ZIPR모형의 베이지안 추론방법을 제안하고, 이를 실제 구강위생 자료에 적용하며 다른 모형들과 비교한다. 그 결과 베이지안 추론 방법을 적용한 영과잉 모형의 추정오차가 다른 모형들의 추정오차보다 작았고, 예측치가 더 정확했다는 점에서 우수함을 알 수 있었다.

• Communications for Statistical Applications and Methods
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• 제13권3호
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• pp.491-501
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• 2006

We consider a multiple change point model with autoregressive conditional heteroscedasticity (ARCH). The model assumes that all or the part of the parameters in the ARCH equation change over time. The occurrence of the change points is modelled as the discrete time Markov process with unknown transition probabilities. The model is estimated by Markov chain Monte Carlo methods based on the approach of Chib (1998). Simulation is performed using a variant of perfect sampling algorithm to achieve the accuracy and efficiency. We apply the proposed model to the simulated data for verifying the usefulness of the model.

• 정보과학회 컴퓨팅의 실제 논문지
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• 제21권1호
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• pp.94-99
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• 2015

비모수 베이스 통계학, 확률적 표집에 기반한 추론 등이 기계학습의 주요 패러다임으로 등장하면서 디리슐레(Dirichlet) 분포는 최근 다양한 그래프 모형 곳곳에 등장하고 있다. 디리슐레 분포는 일변수 감마 분포를 벡터 분포로 확장한 형태의 하나이다. 본 논문에서는 감마 분포를 갖는 임의의 자연수 X를 K개의 자연수의 합으로 임의 분할 할 때 각 부분의 크기 비율을 디리슐레 분포에서 표집하는 방법을 제안한다. 일반적으로 디리슐레 분포는 연속적인 (K-1)-단체(simplex) 위에 정의 되지만 자연수로 분할하는 표본은 자연수라는 조건 때문에 단체 내부의 이산 그리드 점에만 정의된다. 본 논문에서는 단체 위의 그리드 상의 이웃 점들의 확률 분포로부터 마르코프연쇄 몬테 칼로(MCMC) 제안 분포를 정의하고 일련의 표본들의 마르코프 연쇄를 구현하는 알고리듬을 제안한다. 본 방법은 마르코프 모델, HMM 및 준-HMM 등에서 각 상태별 시간 지속 분포를 표현하는데 활용 가능하다. 나아가 최근 제안된 전역-지역(global-local) 상태지속 분포를 동시에 모형화하는 감마-디리슐레 HMM에도 응용가능하다.

• Journal of Electrical Engineering and Technology
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• 제11권3호
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• pp.575-584
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• 2016

Considering the randomness and uncertainty of wind power, a reliability model of WTGs is established based on the combination of the Weibull distribution and the Markov chain. To analyze the failure mode quickly, we use the switch-section partitioning method. After defining the first-level load zone node, we can obtain the supply power sets of the first-level load zone nodes with each WTG. Based on the supply sets, we propose the dynamic division strategy of island operation. By adopting the fault analysis method with the attributes defined in the switch-section, we evaluate the reliability of the distribution network with WTGs using a sequential Monte Carlo simulation method. Finally, using the IEEE RBTS Bus6 test system, we demonstrate the efficacy of the proposed model and method by comparing different schemes to access the WTGs.

• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.413-430
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• 2020

The multiply Type-II hybrid censoring scheme is disadvantaged by an experiment time that is too long. To overcome this limitation, we propose a generalized multiply Type-II hybrid censoring scheme. Some estimators of the scale parameter of the exponential distribution are derived under a generalized multiply Type-II hybrid censoring scheme. First, the maximum likelihood estimator of the scale parameter of the exponential distribution is obtained under the proposed censoring scheme. Second, we obtain the Bayes estimators under different loss functions with a noninformative prior and an informative prior. We approximate the Bayes estimators by Lindleys approximation and the Tierney-Kadane method since the posterior distributions obtained by the two priors are complicated. In addition, the Bayes estimators are obtained by using the Markov Chain Monte Carlo samples. Finally, all proposed estimators are compared in the sense of the mean squared error through the Monte Carlo simulation and applied to real data.

• 대한기계학회논문집A
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• 제39권8호
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• pp.751-758
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• 2015

수학적 해석모델은 물리적 현상을 파악하고 실험비용을 절감하는데 활발하게 사용되지만 편의를 위한 단순화 또는 파라미터가 가지고 있는 불확실성에 의해 해석모델에 의한 예측결과는 실제현상과 차이가 발생한다. 본 연구에서는 이러한 문제에 대해 통계적 기법을 이용하여 해석모델의 불확실성을 반영한 교정 및 검증 방법을 종이 헬리콥터를 통해 제시한다. 먼저, 같은 제원의 세 가지 종이 헬리콥터로 실시한 실험 데이터를 각 그룹으로 형성하여 두 가지 낙하해석모델에서 미지의 입력 파라미터인 항력계수를 교정하는데 사용했다. 그리고 확률분포로 예측된 낙하시간을 실험 데이터 분포와 비교하여 해석 모델을 검증하였다. 이 때, Markov Chain Monte Carlo 기법을 활용하여 항력계수의 불확실성을 정량화하였다. 또한 종이 헬리콥터의 그룹별 데이터에 대해 분산분석(Analysis of Variance)를 이용하여 제작오차와 실험오차의 관계를 비교하였고, 각 그룹이 모두 동일한 대상으로 간주해도 됨을 증명하였다.