### Abstract

This paper presents a methodology to calculate probabilities of failure using Probabilistic Support Vector Machines (PSVMs). Support Vector Machines (SVMs) have recently gained attention for reliability assessment because of several inherent advantages. Specifically, SVMs allow one to construct explicitly the boundary of a failure domain. In addition, they provide a technical solution for problems with discontinuities, binary responses, and multiple failure modes. However, the basic SVM boundary might be inaccurate; therefore leading to erroneous probability of failure estimates. This paper proposes to account for the inaccuracies of the SVM boundary in the calculation of the Monte Carlo-based probability of failure. This is achieved using a PSVM which provides the probability of misclassification of Monte Carlo samples. The probability of failure estimate is based on a new sigmoidbased PSVM model along with the identification of a region where the probability of misclassification is large. The PSVM-based probabilities of failure are, by construction, always more conservative than the deterministic SVM-based probability estimates.

Original language | English (US) |
---|---|

Pages (from-to) | 156-173 |

Number of pages | 18 |

Journal | International Journal of Reliability and Safety |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - 2013 |

### Fingerprint

### Keywords

- Discontinuous and binary behaviour
- Multiple failure modes
- Probabilistic support vector machines
- Probability of failure
- Probability of misclassification

### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality

### Cite this

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

Research output: Contribution to journal › Article

*International Journal of Reliability and Safety*, vol. 7, no. 2, pp. 156-173. https://doi.org/10.1504/IJRS.2013.056378

}

TY - JOUR

T1 - Reliability assessment using probabilistic support vector machines'

AU - Basudhar, Anirban

AU - Missoum, Samy

PY - 2013

Y1 - 2013

N2 - This paper presents a methodology to calculate probabilities of failure using Probabilistic Support Vector Machines (PSVMs). Support Vector Machines (SVMs) have recently gained attention for reliability assessment because of several inherent advantages. Specifically, SVMs allow one to construct explicitly the boundary of a failure domain. In addition, they provide a technical solution for problems with discontinuities, binary responses, and multiple failure modes. However, the basic SVM boundary might be inaccurate; therefore leading to erroneous probability of failure estimates. This paper proposes to account for the inaccuracies of the SVM boundary in the calculation of the Monte Carlo-based probability of failure. This is achieved using a PSVM which provides the probability of misclassification of Monte Carlo samples. The probability of failure estimate is based on a new sigmoidbased PSVM model along with the identification of a region where the probability of misclassification is large. The PSVM-based probabilities of failure are, by construction, always more conservative than the deterministic SVM-based probability estimates.

AB - This paper presents a methodology to calculate probabilities of failure using Probabilistic Support Vector Machines (PSVMs). Support Vector Machines (SVMs) have recently gained attention for reliability assessment because of several inherent advantages. Specifically, SVMs allow one to construct explicitly the boundary of a failure domain. In addition, they provide a technical solution for problems with discontinuities, binary responses, and multiple failure modes. However, the basic SVM boundary might be inaccurate; therefore leading to erroneous probability of failure estimates. This paper proposes to account for the inaccuracies of the SVM boundary in the calculation of the Monte Carlo-based probability of failure. This is achieved using a PSVM which provides the probability of misclassification of Monte Carlo samples. The probability of failure estimate is based on a new sigmoidbased PSVM model along with the identification of a region where the probability of misclassification is large. The PSVM-based probabilities of failure are, by construction, always more conservative than the deterministic SVM-based probability estimates.

KW - Discontinuous and binary behaviour

KW - Multiple failure modes

KW - Probabilistic support vector machines

KW - Probability of failure

KW - Probability of misclassification

UR - http://www.scopus.com/inward/record.url?scp=84880769654&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880769654&partnerID=8YFLogxK

U2 - 10.1504/IJRS.2013.056378

DO - 10.1504/IJRS.2013.056378

M3 - Article

AN - SCOPUS:84880769654

VL - 7

SP - 156

EP - 173

JO - International Journal of Reliability and Safety

JF - International Journal of Reliability and Safety

SN - 1479-389X

IS - 2

ER -