### Abstract

This note introduces a derivation of the sensitivities of a probability of failure with respect to decision variables. For instance, the gradient of the probability of failure with respect to deterministic design variables might be needed in RBDO. These sensitivities might also be useful for Uncertainty-based Multidisciplinary Design Optimization. The difficulty stems from the dependence of the failure domain on variations of the decision variables. This dependence leads to a derivative of the indicator function in the form of a Dirac distribution in the expression of the sensitivities. Based on an approximation of the Dirac, an estimator of the sensitivities is analytically derived in the case of Crude Monte Carlo first and Subset Simulation. The choice of the Dirac approximation is discussed.

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

Pages (from-to) | 375-381 |

Number of pages | 7 |

Journal | Structural and Multidisciplinary Optimization |

Volume | 52 |

Issue number | 2 |

DOIs | |

State | Published - Apr 25 2015 |

### Fingerprint

### Keywords

- Decision variables
- Probability of failure
- Sensitivity

### ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design
- Computer Science Applications
- Control and Systems Engineering
- Control and Optimization

### Cite this

*Structural and Multidisciplinary Optimization*,

*52*(2), 375-381. https://doi.org/10.1007/s00158-015-1232-1

**Probability of failure sensitivity with respect to decision variables.** / Lacaze, Sylvain; Brevault, Loïc; Missoum, Samy; Balesdent, Mathieu.

Research output: Contribution to journal › Article

*Structural and Multidisciplinary Optimization*, vol. 52, no. 2, pp. 375-381. https://doi.org/10.1007/s00158-015-1232-1

}

TY - JOUR

T1 - Probability of failure sensitivity with respect to decision variables

AU - Lacaze, Sylvain

AU - Brevault, Loïc

AU - Missoum, Samy

AU - Balesdent, Mathieu

PY - 2015/4/25

Y1 - 2015/4/25

N2 - This note introduces a derivation of the sensitivities of a probability of failure with respect to decision variables. For instance, the gradient of the probability of failure with respect to deterministic design variables might be needed in RBDO. These sensitivities might also be useful for Uncertainty-based Multidisciplinary Design Optimization. The difficulty stems from the dependence of the failure domain on variations of the decision variables. This dependence leads to a derivative of the indicator function in the form of a Dirac distribution in the expression of the sensitivities. Based on an approximation of the Dirac, an estimator of the sensitivities is analytically derived in the case of Crude Monte Carlo first and Subset Simulation. The choice of the Dirac approximation is discussed.

AB - This note introduces a derivation of the sensitivities of a probability of failure with respect to decision variables. For instance, the gradient of the probability of failure with respect to deterministic design variables might be needed in RBDO. These sensitivities might also be useful for Uncertainty-based Multidisciplinary Design Optimization. The difficulty stems from the dependence of the failure domain on variations of the decision variables. This dependence leads to a derivative of the indicator function in the form of a Dirac distribution in the expression of the sensitivities. Based on an approximation of the Dirac, an estimator of the sensitivities is analytically derived in the case of Crude Monte Carlo first and Subset Simulation. The choice of the Dirac approximation is discussed.

KW - Decision variables

KW - Probability of failure

KW - Sensitivity

UR - http://www.scopus.com/inward/record.url?scp=84945436467&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945436467&partnerID=8YFLogxK

U2 - 10.1007/s00158-015-1232-1

DO - 10.1007/s00158-015-1232-1

M3 - Article

VL - 52

SP - 375

EP - 381

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 2

ER -