Improved hybrid method as a robust tool for reliability-based design optimization

• Published in: Structural and multidisciplinary optimization 2006-09, Vol.32 (3), p.203-213
• Main Authors: Mohsine, A, Kharmanda, G, El-Hami, A
• Format: Article
• Language: English
• Subjects: Computational efficiency; Computing time; Design optimization; Limit states; Parameter uncertainty; Probabilistic methods; Probabilistic models; Probability theory; Reliability engineering; Robustness (mathematics); Standard deviation
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-006-0013-2

In the engineering problems, the randomness and the uncertainties of the distribution of the structural parameters are a crucial problem. In the case of reliability-based design optimization (RBDO), it is the objective to play a dominant role in the structural optimization problem introducing the reliability concept. The RBDO problem is often formulated as a minimization of the initial structural cost under constraints imposed on the values of elemental reliability indices corresponding to various limit states. The classical RBDO leads to high computing time and weak convergence, but a Hybrid Method (HM) has been proposed to overcome these two drawbacks. As the hybrid method successfully reduces the computing time, we can increase the number of variables by introducing the standard deviations as optimization variables to minimize the error values in the probabilistic model. The efficiency of the hybrid method has been demonstrated on static and dynamic cases with extension to the variability of the probabilistic model. In this paper, we propose a modification on the formulation of the hybrid method to improve the optimal solutions. The proposed method is called, Improved Hybrid Method (IHM). The main benefit of this method is to improve the structure performance by much more minimizing the objective function than the hybrid method. It is also shown to demonstrate the optimality conditions. The improved hybrid method is next applied to two numerical examples, with consideration of the standard deviations as optimization variables (for linear and nonlinear distributions). When integrating the improved hybrid method within the probabilistic model variability, we minimize the objective function more and more.