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ISSN : 1229-3059(Print)
ISSN : 2287-2302(Online)
Journal of the Computational Structural Engineering Institute of Korea Vol.32 No.1 pp.55-63

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

Young-Jin Kang1,Yoojeong Noh2†,O-Kaung Lim2
1Research Institute of Mechanical Technology, Pusan Nat’l Univ., Busan, 46241, Korea
2School of Mechanical Engineering, Pusan Nat’l Univ., Busan, 46241, Korea
Corresponding author: Tel: +82-51-510-2308; E-mail:


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.

다변량 확률분포함수의 추정을 위한 MKDE-ebd 개발

1부산대학교 기계기술연구원, 2부산대학교 기계공학부