TY - GEN
T1 - Adjoint-FORM for efficient reliability analysis of large-scale structural problems
AU - Gao, Yi
AU - Liu, Yongming
N1 - Funding Information:
The work is sponsored by NSF (1536994, Program Officer: Y. Grace Hsuan) and the financial support is greatly appreciated.
Publisher Copyright:
© 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
PY - 2018
Y1 - 2018
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.
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U2 - 10.2514/6.2018-0435
DO - 10.2514/6.2018-0435
M3 - Conference contribution
AN - SCOPUS:85141565716
SN - 9781624105296
T3 - AIAA Non-Deterministic Approaches Conference, 2018
BT - AIAA Non-Deterministic Approaches
PB - American Institute of Aeronautics and Astronautics Inc, AIAA
T2 - AIAA Non-Deterministic Approaches Conference, 2018
Y2 - 8 January 2018 through 12 January 2018
ER -