한국전산구조공학회논문집 (Journal of the Computational Structural Engineering Institute of Korea)

  • 제32권1호
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  • Pages.55-63
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  • 2019
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  • 1229-3059(pISSN)
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  • 2287-2302(eISSN)
한국전산구조공학회 (Computational Structural Engineering Institute of Korea)
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다변량 확률분포함수의 추정을 위한 MKDE-ebd 개발

Development of MKDE-ebd for Estimation of Multivariate Probabilistic Distribution Functions

  • Kang, Young-Jin (Research Institute of Mechanical Technology, Pusan Nat'l Univ.) ;
  • Noh, Yoojeong (School of Mechanical Engineering, Pusan Nat'l Univ.) ;
  • Lim, O-Kaung (School of Mechanical Engineering, Pusan Nat'l Univ.)
  • 투고 : 2018.11.05
  • 심사 : 2018.11.14
  • 발행 : 2019.02.28
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초록

공학문제에서 많은 확률 변수들은 상관성을 가지고 있고, 입력변수의 상관성은 기계시스템의 통계적 성능 분석 결과에 큰 영향을 미친다. 하지만, 상관 변수들은 결합분포함수를 모델링하기 어렵다는 이유로 종종 독립변수로 취급되거나 특정한 모수적 모델로 표현되는 경우가 많으며, 특히 데이터가 적은 경우 결합분포함수를 정확히 모델링하는데 더 큰 어려움이 있다. 본 연구에서 개발된 경계데이터를 이용한 다변량 커널밀도추정은 비선형성을 갖는 다양한 형태의 다변량 확률 분포 추정을 위해 개발되었다. 다변량 커널밀도추정은 주어진 데이터와 균등분포함수의 파라미터의 신뢰구간으로부터 생성된 경계데이터를 결합하여 데이터의 질과 수에 덜 민감하다. 따라서 제안된 방법은 보수적인 통계모델링과 신뢰성 해석 결과를 도출할 수 있으며, 통계시뮬레이션과 공학예제를 통해 그 성능을 검증하였다.

In engineering problems, many random variables have correlation, and the correlation of input random variables has a great influence on reliability analysis results of the mechanical systems. However, correlated variables are often treated as independent variables or modeled by specific parametric joint distributions due to difficulty in modeling joint distributions. Especially, when there are insufficient correlated data, it becomes more difficult to correctly model the joint distribution. In this study, multivariate kernel density estimation with bounded data is proposed to estimate various types of joint distributions with highly nonlinearity. Since it combines given data with bounded data, which are generated from confidence intervals of uniform distribution parameters for given data, it is less sensitive to data quality and number of data. Thus, it yields conservative statistical modeling and reliability analysis results, and its performance is verified through statistical simulation and engineering examples.

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참고문헌

  1. Noh, Y., Choi, K.K., Lee, I. (2010) Identification of Marginal and Joint CDFs using Baeysian Method for RBDO, Struct. Multidisc. Optim., 40(1), pp.35-51. https://doi.org/10.1007/s00158-009-0385-1
  2. Chen, S. (2015) Optimal Bandwidth Selection for Kernel Density Functionals Estimation, J. Probab. Stat., pp.1-21.
  3. Eldred, M.S., Agarwal, H., Perez, V.M., Wojtkiewicz Jr, S.F., Renaud, J.E. (2007) Investigation of Reliability Method Formulations in DAKOTA/UQ, Struct. & Infrastruct. Eng., 3(3), pp.199-213. https://doi.org/10.1080/15732470500254618
  4. Frigge, M., Hoaglin, D.C., Iglewicz, B. (1989) Some Implementations of the Boxplot, The American Statistician, 43(1), pp.50-54. https://doi.org/10.2307/2685173
  5. Hong, J., Kang, Y.J., Lim, O.K., Noh, Y. (2018) Comparison of Multivariate Statistical Modeling Methods for Limited Correlated Data, Trans. Korean Soc. Mech. Eng. A, 42(5), pp.445-453. https://doi.org/10.3795/KSME-A.2018.42.5.445
  6. Jamieson, P.D., Porter, J.R., Wilson, D.R. (1991) A Test of the Computer Simulation Model ARCWHEAT1 on Wheat Crops Grown in New Zealand, Field Crops Res., 27(4), pp.337-350. https://doi.org/10.1016/0378-4290(91)90040-3
  7. Kang, Y.J., Hong J., Lim, O.K., Noh, Y. (2017) Reliability Analysis Using Parametric and Nonparametric Input Modeling Methods, J. Comput. Struct. Eng. Inst. Korea, 30(1), pp.87-94. https://doi.org/10.7734/COSEIK.2017.30.1.87
  8. Kang, Y.J., Noh, Y., Lim, O.K. (2018a) Kernel Density Estimation with Bounded Data, Struct. Multidisc. Optim., 57(1), pp.95-113. https://doi.org/10.1007/s00158-017-1873-3
  9. Kang, Y.J. (2018b) Development of Integrated Statistical Modeling Method for Reliability Analysis, Ph.D. Dissertation, Pusan National University.
  10. Li, M.F., Tang, X.P., Wu, W., Liu, H.B. (2013) General Models for Estimating Daily Global Solar Radiation for Different Solar Radiation Zones in Mainland China, Energy Convers. & Manag., 70, pp.139-148. https://doi.org/10.1016/j.enconman.2013.03.004
  11. Park, C., Kim, N.H., Haftka, R.T. (2015) The Effect of Ignoring Dependence Between Failure Modes on Evaluating System Reliability, Struct. Multidisc. Optim., 52(2), pp.251-268. https://doi.org/10.1007/s00158-015-1239-7
  12. Scott, D.W. (2015) Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, New Jersey, p.416.
  13. Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis, 26, CRC Press, London.
  14. Tukey, J.W. (1977) Exploratory Data Analysis, Pearson, New York, p.23.
  15. Verma, A.K, Srividya, A, Karanki, D.R. (2010) Reliability and Safety Engineering, Springer, London, p.571.