An inverse reliability analysis method for reliability-based design optimization with random and dependent interval variables constrained within ellipsoids

ABSTRACT

In practical design problems, interval variables exist. Many existing methods can handle only independent interval variables. Some interval variables, however, are dependent. In this work, dependent interval variables constrained within a multi-ellipsoid convex set are considered and incorporated into reliability-based design optimization (RBDO). An efficient RBDO method is proposed by employing the sequential single-loop procedure, which separates the coupled reliability analysis procedure from the deterministic optimization procedure. In the reliability analysis procedure, a single-loop optimization for the inverse reliability analysis is performed, and an efficient inverse reliability analysis method for searching for the worst-case most probable point (WMPP) is developed. The search method contains two stages. The first stage deals the situation where the WMPP is on the boundary of the feasible region, while the second stage accommodates the situation where the WMPP is inside the feasible region by interpolation. Three examples are used for a demonstration.

KEYWORDS:

• Dependent interval variable
• multi-ellipsoid convex model
• reliability-based design optimization
• inverse reliability analysis
• worst-case most probable point

Acknowledgements

The first two authors acknowledge the support from the National Natural Science Foundation of China. The third author would like to thank the Intelligent Systems Center at the Missouri University of Science and Technology for support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first two authors received support from the National Natural Science Foundation of China [grant number 51475425]. The third author received support from the Intelligent Systems Center at the Missouri University of Science and Technology.