• 한국전산구조공학회논문집
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• 제23권6호
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• pp.641-649
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• 2010

Estimation of uncertain parameters is required in many engineering problems which involve probabilistic structural analysis as well as prognosis of existing structures. In this case, Bayesian framework is often employed, which is to represent the uncertainty of parameters in terms of probability distributions conditional on the provided data. The resulting form of distribution, however, is not amenable to the practical application due to its complex nature making the standard probability functions useless. In this study, Markov chain Monte Carlo (MCMC) method is proposed to overcome this difficulty, which is a modern computational technique for the efficient and straightforward estimation of parameters. Three case studies that implement the estimation are presented to illustrate the concept. The first one is an inverse estimation, in which the unknown input parameters are inversely estimated based on a finite number of measured response data. The next one is a metamodel uncertainty problem that arises when the original response function is approximated by a metamodel using a finite set of response values. The last one is a prognostics problem, in which the unknown parameters of the degradation model are estimated based on the monitored data.

• 응용통계연구
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• 제23권1호
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• pp.13-28
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• 2010

혼합분포를 가정한 신용평가연구에서 부도차주를 정상으로 예측하거나 정상차주를 부도로 예측하는 오류를 최소화하는 분류점을 추정하는 방법을 토론한다. 확률변수 스코어와 정상과 부도상태의 모수공간으로 정의된 확률밀도함수들에 대하여 강력검정과 일반화가능도비검정을 이용하여 최적분류점의 추정방법을 제안하고, ROC와 CAP 곡선에서 분류정확도를 측정하는 정확도(accuarcy)와 진실율(true rate)을 이용하여 이 측도를 최대로 하는 최적분류점을 확률밀도함수의 관계식으로 추정하는 방법을 제안한다. 다양한 정규분포에서 가설검정, 정확도 그러고 진실율을 이용하는 세가지 방법의 최적분류점을 구하고 각최적분류점에 대응하는 제 I 종과 제 II 종 오류합의 크기를 비교하여 효율성을 토론한다.

• 전자공학회논문지
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• 제51권8호
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• pp.126-135
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• 2014

오차 신호의 확률분포 사이의 유클리드 거리 (Euclidean distance between error probability density functions, EDEP)는 충격성 잡음 환경의 적응 신호 처리를 위한 성능 지수로 사용되었다. 이 EDEP 알고리듬의 단점 중의 하나로 각 반복 시간마다 수행하는 이중적분에 의해 과다한 계산상의 복잡성이 있다. 이 논문에서는 EDEP 와 그 기울기 계산에서 계산상의 부담을 줄일 수 있는 반복적 추정 방법을 제안하였다. 데이터 블록 크기 N에 대하여, 기존의 추정 방식에 의한 EDEP와 그 기울기 계산량은 $O(N^2)$인 반면, 제안한 방식의 계산량은 O(N)이다. 성능 시험에서 제안한 방식의 EDEP와 그 기울기는 정상상태에서 기존의 블록 처리 방식과 동일한 추정결과를 나타냈다. 이러한 시뮬레이션 결과로부터, 제안한 방식이 실제 적응신호처리 분야에서 효과적인 방식임을 알 수 있다.

• 한국수자원학회논문집
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• 제39권8호
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• pp.691-702
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• 2006

본 연구에서는 우리나라 가뭄의 공간적인 특성을 파악하고 가뭄의 진행에 따른 피해규모를 산정하기 위하여 가뭄 심도-영향면적-생기빈도 곡선을 작성하여 제시하였다. 이를 위하여 전국의 기상관측소 지점별로 SPI를 산정하였으며, 산정된 지점별 SPI 자료를 이용하여 EOF 분석을 실시하였다. EOF 분석으로부터 추출된 핵심 공간패턴자료들은 다시 공간적으로는 Kriging 기법을 이용하여 보다 세밀한 공간정보를 갖는 자료로 확장되었으며, ARMA 모형을 이용하여 장기간의 가뭄사상을 모의발생하였다. 모의발생된 공간적인 장기간의 가뭄사상들로부터 특정 가뭄심도별 영향면적별 생기빈도 곡선을 작성할 수 있었다.

• Structural Engineering and Mechanics
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• 제62권4호
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• pp.507-517
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• 2017

Due to the discontinuous nature of uncertainty quantification in conventional evidence theory(ET), the computational cost of reliability analysis based on ET model is very high. A novel ET model based on fuzzy distribution and the corresponding combination rule to synthesize the judgments of experts are put forward in this paper. The intersection and union of membership functions are defined as belief and plausible membership function respectively, and the Murfhy's average combination rule is adopted to combine the basic probability assignment for focal elements. Then the combined membership functions are transformed to the equivalent probability density function by a normalizing factor. Finally, a reliability analysis procedure for structures with the mixture of epistemic and aleatory uncertainties is presented, in which the equivalent normalization method is adopted to solve the upper and lower bound of reliability. The effectiveness of the procedure is demonstrated by a numerical example and an engineering example. The results also show that the reliability interval calculated by the suggested method is almost identical to that solved by conventional method. Moreover, the results indicate that the computational cost of the suggested procedure is much less than that of conventional method. The suggested ET model provides a new way to flexibly represent epistemic uncertainty, and provides an efficiency method to estimate the reliability of structures with the mixture of epistemic and aleatory uncertainties.

• Earthquakes and Structures
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• 제14권3호
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• pp.203-214
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• 2018

Predictive demand and collapse fragility functions are two essential components of the probabilistic seismic demand analysis that are commonly developed based on statistics with enormous, costly and time consuming data gathering. Although this approach might be justified for research purposes, it is not appealing for practical applications because of its computational cost. Thus, in this paper, Bayesian regression-based demand and collapse models are proposed to eliminate the need of time-consuming analyses. The demand model developed in the form of linear equation predicts overall maximum inter-story drift of the lowto mid-rise regular steel moment resisting frames (SMRFs), while the collapse model mathematically expressed by lognormal cumulative distribution function provides collapse occurrence probability for a given spectral acceleration at the fundamental period of the structure. Next, as an application, the proposed demand and collapse functions are implemented in a seismic fragility analysis to develop fragility and consequently seismic demand curves of three example buildings. The accuracy provided by utilization of the proposed models, with considering computation reduction, are compared with those directly obtained from Incremental Dynamic analysis, which is a computer-intensive procedure.

• 대한의용생체공학회:의공학회지
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• 제37권1호
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• pp.21-30
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• 2016

Weibull distribution with two parameters, shape (k) and scale (s) parameters are used to model the fatigue failure analysis due to periodic vortex shedding of the synovial fluid in knee joints. In order to determine the later parameter, a suitable statistical model is required for velocity distribution of synovial fluid flow. Hence, wide applicability of Weibull distribution in life testing and reliability analysis can be applied to describe the probability distribution of synovial fluid flow velocity. In this work, comparisons of three most widely used methods for estimating Weibull parameters are carried out; i.e. the least square estimation method (LSEM), maximum likelihood estimator (MLE) and the method of moment (MOM), to study fatigue failure of bone joint due to periodic vortex shedding of synovial fluid. The performances of these methods are compared through the analysis of computer generated synovial fluidflow velocity distribution in the physiological range. Significant values for the (k) and (s) parameters are obtained by comparing these methods. The criterions such as root mean square error (RMSE), coefficient of determination ($R^2$), maximum error between the cumulative distribution functions (CDFs) or Kolmogorov-Smirnov (K-S) and the chi square tests are used for the comparison of the suitability of these methods. The results show that maximum likelihood method performs well for most of the cases studied and hence recommended.

• 한국산림과학회지
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• 제102권4호
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• pp.477-483
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• 2013

본 연구의 목적은 몬테 카를로 시뮬레이션을 이용하여 소나무 탄소배출계수 자료의 확률밀도를 추정하고 불확도를 제시하는데 있다. 이용된 탄소배출계수는 목재기본밀도, 바이오매스확장계수, 뿌리함량비이고 4개의 확률밀도 함수(정규분포, 로그정규분포, 감마분포, 와이불 분포)를 고려하였다. 2-표본 콜모그로프-스미르노프 검정통계량과 누적밀도그림을 비교하여 최적의 확률밀도함수를 선정하고 상한과 하한의 불확도를 제시하였다. 본 연구의 결과에 의하면, 각 탄소배출계수에서 추정된 확률밀도함수는 강원지방소나무에서 목재기본밀도는 감마분포, 바이오매스확장계수는 로그정규분포, 뿌리함량비는 정규분포이고 중부지방소나무에서 목재기본밀도는 정규분포, 바이오매스확장계수는 감마분포, 뿌리함량비는 감마분포를 나타내었다. 강원지방소나무 탄소배출계수의 불확도는 상한에서 62.1%, 하한에서 -52.6%이고 중부지방소나무는 상한에서 43.9%, 하한에서 -34.5%를 나타내었다.

• 한국물환경학회지
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• 제28권1호
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• pp.38-49
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• 2012

In this study, we analyze statistical characteristics of influent water quality in Daejeon waste water treatment plant and apply a stochastic model for data generation. In the analysis, the influent water quality data from year 2003 to 2008, except for year 2006, are used. Among water quality variables, we find strong correlations between BOD and T-N; T-N and T-P; BOD and T-P; $COD_{Mn}$ and T-P; and BOD and $COD_{Mn}$. We also find that different water quality variables follow different theoretical probability distribution functions, which also depends on whether the seasonal cycle is removed. Finally, we generate the influent water quality data using the multi-season 1st Markov model (Thomas-Fiering model). With model parameters calibrated for the period 2003~2005, the generated data for 2007~2008 are well compared with observed data showing good agreement in general. BOD and T-N are underestimated by the stochastic model. This is mainly due to the statistical difference in observed data itself between two periods of 2003~2005 and 2007~2008. Therefore, we expect the stochastic model can be applied with more confidence in the case that the data follows stationary pattern.

• Computers and Concrete
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• 제26권2호
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• pp.127-136
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• 2020

There is an inherent randomness for concrete microstructure even with the same manufacturing process. Meanwhile, the concrete material under the aqueous environment is usually not fully saturated by water. This study aimed to develop a stochastic micromechanical framework to investigate the probabilistic behavior of the unsaturated concrete from microscale level. The material is represented as a multiphase composite composed of the water, the pores and the intrinsic concrete (made up by the mortar, the coarse aggregates and their interfaces). The differential scheme based two-level micromechanical homogenization scheme is presented to quantitatively predict the concrete's effective properties. By modeling the volume fractions and properties of the constituents as stochastic, we extend the deterministic framework to stochastic to incorporate the material's inherent randomness. Monte Carlo simulations are adopted to reach the different order moments of the effective properties. A distribution-free method is employed to get the unbiased probability density function based on the maximum entropy principle. Numerical examples including limited experimental validations, comparisons with existing micromechanical models, commonly used probability density functions and the direct Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the material's effective properties. Finally, the effects of the saturation degrees and the pore shapes on the concrete macroscopic probabilistic behaviors are investigated based on our proposed stochastic micromechanical framework.