### Abstract

This paper introduces a novel approach for reliability assessment with dependent variables. In this work, the boundary of the failure domain, for a computational problem with expensive function evaluations, is approximated using a Support Vector Machine and an adaptive sampling scheme. The approximation is sequentially refined using a new adaptive sampling scheme referred to as generalized "max-min". This technique efficiently targets high probability density regions of the random space. This is achieved by modifying an adaptive sampling scheme originally tailored for deterministic spaces (Explicit Space Design Decomposition). In particular, the approach can handle any joint probability density function, even if the variables are dependent. In the latter case, the joint distribution might be obtained from copula. In addition, uncertainty on the probability of failure estimate are estimated using bootstrapping. A bootstrapped coefficient of variation of the probability of failure is used as an estimate of the true error to determine convergence. The proposed method is then applied to analytical examples and a beam bending reliability assessment using copulas.

Original language | English (US) |
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Title of host publication | 34th Computers and Information in Engineering Conference |

Publisher | American Society of Mechanical Engineers (ASME) |

Volume | 1A |

ISBN (Print) | 9780791846285 |

DOIs | |

State | Published - 2014 |

Event | ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014 - Buffalo, United States Duration: Aug 17 2014 → Aug 20 2014 |

### Other

Other | ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014 |
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Country | United States |

City | Buffalo |

Period | 8/17/14 → 8/20/14 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*34th Computers and Information in Engineering Conference*(Vol. 1A). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC201434051

**A generalized "max-min" sample for reliability assessment with dependent variables.** / Lacaze, Sylvain; Missoum, Samy.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*34th Computers and Information in Engineering Conference.*vol. 1A, American Society of Mechanical Engineers (ASME), ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014, Buffalo, United States, 8/17/14. https://doi.org/10.1115/DETC201434051

}

TY - GEN

T1 - A generalized "max-min" sample for reliability assessment with dependent variables

AU - Lacaze, Sylvain

AU - Missoum, Samy

PY - 2014

Y1 - 2014

N2 - This paper introduces a novel approach for reliability assessment with dependent variables. In this work, the boundary of the failure domain, for a computational problem with expensive function evaluations, is approximated using a Support Vector Machine and an adaptive sampling scheme. The approximation is sequentially refined using a new adaptive sampling scheme referred to as generalized "max-min". This technique efficiently targets high probability density regions of the random space. This is achieved by modifying an adaptive sampling scheme originally tailored for deterministic spaces (Explicit Space Design Decomposition). In particular, the approach can handle any joint probability density function, even if the variables are dependent. In the latter case, the joint distribution might be obtained from copula. In addition, uncertainty on the probability of failure estimate are estimated using bootstrapping. A bootstrapped coefficient of variation of the probability of failure is used as an estimate of the true error to determine convergence. The proposed method is then applied to analytical examples and a beam bending reliability assessment using copulas.

AB - This paper introduces a novel approach for reliability assessment with dependent variables. In this work, the boundary of the failure domain, for a computational problem with expensive function evaluations, is approximated using a Support Vector Machine and an adaptive sampling scheme. The approximation is sequentially refined using a new adaptive sampling scheme referred to as generalized "max-min". This technique efficiently targets high probability density regions of the random space. This is achieved by modifying an adaptive sampling scheme originally tailored for deterministic spaces (Explicit Space Design Decomposition). In particular, the approach can handle any joint probability density function, even if the variables are dependent. In the latter case, the joint distribution might be obtained from copula. In addition, uncertainty on the probability of failure estimate are estimated using bootstrapping. A bootstrapped coefficient of variation of the probability of failure is used as an estimate of the true error to determine convergence. The proposed method is then applied to analytical examples and a beam bending reliability assessment using copulas.

UR - http://www.scopus.com/inward/record.url?scp=84961323878&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961323878&partnerID=8YFLogxK

U2 - 10.1115/DETC201434051

DO - 10.1115/DETC201434051

M3 - Conference contribution

AN - SCOPUS:84961323878

SN - 9780791846285

VL - 1A

BT - 34th Computers and Information in Engineering Conference

PB - American Society of Mechanical Engineers (ASME)

ER -