### Abstract

For large scale structural reliability analysis, most of the current methods have the difficulty associated with the “curse of dimensionality”. A novel and efficient Adjoint-FORM (first order reliability method) is proposed to solve extremely large dimensional structural reliability problems. The method formulates the reliability problem as the optimization problem using the additional physical equation of the state variables (responses of the system). The responses and gradients in each iteration are efficiently evaluated by the adjoint method. Then the sequential quadratic programming (SQP) algorithm is applied to obtain the optimal reliability index. Its application is demonstrated by several extremely large dimension examples extracted from a truss structure with varying dimensions. The results of the proposed method are compared with those of FORM and direct Monte Carlo simulation. It is shown that the proposed model has the same failure probability estimation as the classical FORM, which is applicable to linear and weakly nonlinear problem. The major benefit is that the computational cost is almost independent of the dimensionality of the system, which is due to the adjoint formulation of the sensitivity problem. This characteristic offers a significant improvement of computational efficiency for large dimension problems. Finally, some future work are discussed.

Original language | English (US) |
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Title of host publication | AIAA Non-Deterministic Approaches |

Publisher | American Institute of Aeronautics and Astronautics Inc, AIAA |

Edition | 209969 |

ISBN (Print) | 9781624105296 |

State | Published - Jan 1 2018 |

Event | AIAA Non-Deterministic Approaches Conference, 2018 - Kissimmee, United States Duration: Jan 8 2018 → Jan 12 2018 |

### Other

Other | AIAA Non-Deterministic Approaches Conference, 2018 |
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Country | United States |

City | Kissimmee |

Period | 1/8/18 → 1/12/18 |

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### ASJC Scopus subject areas

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

### Cite this

*AIAA Non-Deterministic Approaches*(209969 ed.). American Institute of Aeronautics and Astronautics Inc, AIAA.

**Adjoint-FORM for efficient reliability analysis of large-scale structural problems.** / Gao, Yi; Liu, Yongming.

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

*AIAA Non-Deterministic Approaches.*209969 edn, American Institute of Aeronautics and Astronautics Inc, AIAA, AIAA Non-Deterministic Approaches Conference, 2018, Kissimmee, United States, 1/8/18.

}

TY - GEN

T1 - Adjoint-FORM for efficient reliability analysis of large-scale structural problems

AU - Gao, Yi

AU - Liu, Yongming

PY - 2018/1/1

Y1 - 2018/1/1

N2 - For large scale structural reliability analysis, most of the current methods have the difficulty associated with the “curse of dimensionality”. A novel and efficient Adjoint-FORM (first order reliability method) is proposed to solve extremely large dimensional structural reliability problems. The method formulates the reliability problem as the optimization problem using the additional physical equation of the state variables (responses of the system). The responses and gradients in each iteration are efficiently evaluated by the adjoint method. Then the sequential quadratic programming (SQP) algorithm is applied to obtain the optimal reliability index. Its application is demonstrated by several extremely large dimension examples extracted from a truss structure with varying dimensions. The results of the proposed method are compared with those of FORM and direct Monte Carlo simulation. It is shown that the proposed model has the same failure probability estimation as the classical FORM, which is applicable to linear and weakly nonlinear problem. The major benefit is that the computational cost is almost independent of the dimensionality of the system, which is due to the adjoint formulation of the sensitivity problem. This characteristic offers a significant improvement of computational efficiency for large dimension problems. Finally, some future work are discussed.

AB - For large scale structural reliability analysis, most of the current methods have the difficulty associated with the “curse of dimensionality”. A novel and efficient Adjoint-FORM (first order reliability method) is proposed to solve extremely large dimensional structural reliability problems. The method formulates the reliability problem as the optimization problem using the additional physical equation of the state variables (responses of the system). The responses and gradients in each iteration are efficiently evaluated by the adjoint method. Then the sequential quadratic programming (SQP) algorithm is applied to obtain the optimal reliability index. Its application is demonstrated by several extremely large dimension examples extracted from a truss structure with varying dimensions. The results of the proposed method are compared with those of FORM and direct Monte Carlo simulation. It is shown that the proposed model has the same failure probability estimation as the classical FORM, which is applicable to linear and weakly nonlinear problem. The major benefit is that the computational cost is almost independent of the dimensionality of the system, which is due to the adjoint formulation of the sensitivity problem. This characteristic offers a significant improvement of computational efficiency for large dimension problems. Finally, some future work are discussed.

UR - http://www.scopus.com/inward/record.url?scp=85044254328&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044254328&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85044254328

SN - 9781624105296

BT - AIAA Non-Deterministic Approaches

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

ER -