### Abstract

This article presents a new probability of failure measure based on the notion of probabilistic support vector machines (PSVMs). A PSVM allows one to quantify the probability of having an error in the approximation of the failure boundary using a support vector machine (SVM). SVM can define explicitly the boundaries of disjoint and non-convex failure domains. The approximation of the failure boundary can be refined using an adaptive sampling scheme with a limited number of samples. However, the calculation of the probability of failure might still be inaccurate despite the adaptive sampling. In order to refine the probability estimate, the "quality" of the approximated boundary is quantified through the probability of misclassification of a sample by the SVM. A new measure of probability is then calculated using Monte-Carlo simulations that include the probability of misclassification. The proposed measure of probability of failure is such that it is always larger (i.e., more conservative) than the one obtained using a deterministic SVM. Several analytical examples are presented, including a case with two failure modes.

Original language | English (US) |
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Title of host publication | 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |

State | Published - Dec 16 2010 |

Event | 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Orlando, FL, United States Duration: Apr 12 2010 → Apr 15 2010 |

### Publication series

Name | Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |
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ISSN (Print) | 0273-4508 |

### Other

Other | 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |
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Country | United States |

City | Orlando, FL |

Period | 4/12/10 → 4/15/10 |

### Fingerprint

### ASJC Scopus subject areas

- Architecture
- Materials Science(all)
- Aerospace Engineering
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference*[2010-2764] (Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference).