### 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 | Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |

State | Published - 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 |

### 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

- Civil and Structural Engineering
- Mechanics of Materials
- Building and Construction
- Architecture

### Cite this

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

**Reliability assessment using probabilistic support vector machines (PSVMs).** / Basudhar, Anirban; Missoum, Samy.

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

*Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.*, 2010-2764, 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Orlando, FL, United States, 4/12/10.

}

TY - GEN

T1 - Reliability assessment using probabilistic support vector machines (PSVMs)

AU - Basudhar, Anirban

AU - Missoum, Samy

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84855617276&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855617276&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84855617276

SN - 9781600867422

BT - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

ER -