Abstract
The original problem of reliability-based design optimization (RBDO) is mathematically a nested two-level structure that is computationally time consuming for real engineering problems. In order to overcome the computational difficulties, many formulations have been proposed in the literature. These include SORA (sequential optimization and reliability assessment) that decouples the nested problems. SLA (single loop approach) further improves efficiency in that reliability analysis becomes an integrated part of the optimization problem. However, even SLA method can become computationally challenging for real engineering problems involving many reliability constraints. This paper presents an enhanced version of SLA where the first phase is based on approximation at nominal design point. After convergence of first iterative phase is reached the process transitions to a second phase where approximations of reliability constraints are carried out at their respective minimum performance target point (MPTP). The solution is implemented in Altair OptiStruct, where adaptive approximation and constraint screening strategies are utilized in the RBDO process. Examples show that the proposed two-phase approach leads to reduction in finite element analyses while preserving equal solution quality.
Highlights
The original problem of reliability-based design optimization (RBDO) is mathematically a nested two-level structure (Tu et al 1999), consisting of a design optimization loop which repeatedly calls reliability analyses in a series of inner loops
This paper presents an enhanced version of Single-loop approach (SLA) where the first phase is based on approximation of performance functions at nominal design point
A two-phase approach based on sequential approximation is proposed for reliability based structural optimization within the general framework of single loop approach (SLA)
Summary
The original problem of reliability-based design optimization (RBDO) is mathematically a nested two-level structure (Tu et al 1999), consisting of a design optimization loop which repeatedly calls reliability analyses in a series of inner loops. Performance function contains a separate optimization loop, and a sequence of deterministic optimization is processed before converging to the optimal design, the decoupled approach still involves extensive computation (Lim and Lee 2016). The process becomes essentially a deterministic optimization problem wherein constraints are shifted by approximation of MPTP points resolved from the KKT conditions of the reliability analyses. Single-loop methods are more efficient than the two-level approach including unnested SORA, with potential drawbacks of reduced solution accuracy and robustness (Aoues and Chatteauneuf 2010). The desired behavior of this process is: (1) to achieve an approximate RBDO solution with the first phase that is as efficient as solving the corresponding deterministic optimization; (2) to reduce the number of iterations in the full SLA process when starts at a near optimum, and achieve reasonable solution accuracy.
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