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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Comparison Study of Kernel Density Estimation according to Various Bandwidth Selectors

다양한 대역폭 선택법에 따른 커널밀도추정의 비교 연구

  • Kang, Young-Jin (Research Institute of Mechanical Technology, Pusan Nat'l Univ.) ;
  • Noh, Yoojeong (School of Mechanical Engineering, Pusan Nat'l Univ.)
  • 강영진 (부산대학교 기계기술연구원) ;
  • 노유정 (부산대학교 기계공학부)
  • Received : 2019.03.11
  • Accepted : 2019.05.10
  • Published : 2019.06.30
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Abstract

To estimate probabilistic distribution function from experimental data, kernel density estimation(KDE) is mostly used in cases when data is insufficient. The estimated distribution using KDE depends on bandwidth selectors that smoothen or overfit a kernel estimator to experimental data. In this study, various bandwidth selectors such as the Silverman's rule of thumb, rule using adaptive estimates, and oversmoothing rule, were compared for accuracy and conservativeness. For this, statistical simulations were carried out using assumed true models including unimodal and multimodal distributions, and, accuracies and conservativeness of estimating distribution functions were compared according to various data. In addition, it was verified how the estimated distributions using KDE with different bandwidth selectors affect reliability analysis results through simple reliability examples.

제한된 실험 데이터로부터 확률분포함수를 추정하기 위해서 KDE가 많이 사용되고 있다. KDE에 의한 분포함수는 대역폭 선택법에 따라서 실험 데이터에 대해 평활하거나 과대적합된 커널 추정치를 생성한다. 본 연구에서는 Silverman's rule of thumb, rule using adaptive estimate, oversmoothing rule을 사용해서 각 방법에 따른 정확성과 보수적인 성향을 비교하였다. 비교를 위해서 단봉분포와 다봉분포를 가지는 실제 모델을 가정하고 통계적 시뮬레이션을 수행한 다음 다양한 데이터의 개수에 따른 추정된 분포함수의 정확도와 보수성을 비교하였다. 또한, 간단한 신뢰성 예제를 통해 대역폭 선택법에 따른 KDE의 추정된 분포가 신뢰성 해석 결과에 어떻게 영향을 미치는지 확인하였다.

Keywords

References

  1. An, D., Won, J., Kim, E., Choi, J. (2009) Reliability Analysis under Input Variable and Metamodel Uncertainty using Simulation Method based on Bayesian Approach, Trans. Korean Soc. Mech. Eng. A, 33(10), pp.1163-1170. https://doi.org/10.3795/KSME-A.2009.33.10.1163
  2. Analytical Methods Committee (1989) Robust Statistics-how not to Reject Outliers, Part 1. Basic Concepts, Analyst, 114(12), pp.1693-1697. https://doi.org/10.1039/AN9891401693
  3. Chen, S. (2015) Optimal Bandwidth Selection for Kernel Density Functionals Estimation, J. Probab. & Stat., pp.1-21
  4. 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
  5. Jang, J., Cho, S.G., Lee, S.J., Kim, K.S., Kim, J.M., Hong, J.P., Lee, T.H. (2015) Reliability-based Robust Design Optimization with Kernel Density Estimation for Electric Power Steering Motor Considering Manufacturing Uncertainties, IEEE Transactions on Magnetics, 51(3), pp.1-4.
  6. Jung, J.H., Kang, Y.J., Lim, O.K., Noh, Y. (2017) A New Method to Determine the Number of Experimental Data using Statistical Modeling Methods, J. Mech. Sci. & Technol., 31(6), pp.2901-2910. https://doi.org/10.1007/s12206-017-0533-2
  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. Korea Meteorological Administration (KMA) https://data.kma.go.kr (accessed Mar., 6, 2019)
  9. Lee, D., Hwang, I.S. (2011) Analysis on the Dynamic Characteristics of a Rubber Mount Considering Temperature and Material Uncertainties, J. Comput. Struct. Eng. Inst. Korea, 24(4), pp.383-389.
  10. Scott, D.W. (2010) Scott's Rule, Wiley Interdiscip. Rev.: Comput. Stat., 2(4), pp.497-502 https://doi.org/10.1002/wics.103
  11. Scott, D.W. (2015) Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, New Jersey.
  12. Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis, 26, CRC Press, London.
  13. Terrell, G.R., Scott, D.W. (1985) Oversmoothed Nonparametric Density Estimates, J. Am. Stat. Assoc., 80(389), pp.209-214. https://doi.org/10.1080/01621459.1985.10477163
  14. Terrell, G.R. (1990) The Maximal Smoothing Principle in Density Estimation, J. Am. Stat. Assoc., 85(410), pp.470-477. https://doi.org/10.1080/01621459.1990.10476223
  15. Tukey, J.W. (1977) Exploratory Data Analysis, Pearson, New York.
  16. Wand, M.P., Jones, M.C. (1994) Kernel smoothing, CRC press, London.
  17. Zhang, F., Liu, Y., Chen, C., Li, Y.F., Huang, H.Z. (2014) Fault Diagnosis of Rotating Machinery based on Kernel Density Estimation and Kullback-Leibler Divergence, J. Mech. Sci. & Technol., 28(11), pp.4441-4454. https://doi.org/10.1007/s12206-014-1012-7