Estimation of probability of failure with dependent variables using copulas and support vector machines

Peng Jiang, Samy Missoum

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents an approach to estimate probabilities of failure in the case of dependent random variables. The approach is based on copulas and support vector machines (SVMs). A copula is used to generate dependent Monte Carlo samples and an SVM is used to construct the explicit boundary of the failure domain. It is shown that this construction of the failure boundary cannot be made in the original space due to the lack of "isotropy" of the probability densities. In this work the SVM is built in the uncorrelated standard normal space and refined using an adaptive sampling scheme. A transformation is used to map SVM training points and Monte-Carlo samples between the original space and the uncorrelated standard normal space. Because SVM is a classification-based approach, it can handle discontinuous responses and, more importantly, several limit states using one single SVM. Several analytical examples are used to demonstrate the methodology.

Original languageEnglish (US)
Title of host publication22nd Reliability, Stress Analysis, and Failure Prevention Conference; 25th Conference on Mechanical Vibration and Noise
PublisherAmerican Society of Mechanical Engineers
ISBN (Print)9780791855997
DOIs
StatePublished - 2013
EventASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States
Duration: Aug 4 2013Aug 7 2013

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume8

Other

OtherASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013
CountryUnited States
CityPortland, OR
Period8/4/138/7/13

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Fingerprint Dive into the research topics of 'Estimation of probability of failure with dependent variables using copulas and support vector machines'. Together they form a unique fingerprint.

Cite this