Application of Sequential Approximate Optimization for Designing Linear Systems Under Gaussian Excitation

Abstract eng:
This contribution explores the application of sequential approximate optimization (Svanberg 2002) for optimal design of linear structural systems subject to dynamic excitation characterized as a Gaussian process. The focus is on analyzing and comparing the performance of two different schemes for constructing conservative convex and separable approximations of the objective function and constraints involved in the optimization problem. These schemes correspond to the Diagonal Quadratic approximation (Snyman and Hay 2002) and the Conservative approximation (Zhang and Fleury 1997). The associated reliability problem comprises high dimensional spaces and thus, it is evaluated by means of an efficient Importance Sampling scheme (Au and Beck 2001). The sensitivity of the reliability is evaluated using a scheme based on local approximations introduced recently (Valdebenito et al. 2011). The results obtained show that the sequential approximate optimization scheme is quite efficient, as only few function evaluations are required in order to determine the optimum. Moreover, the results indicate that the particular scheme that is used to construct approximations of the objective function and constraints may have an impact on the associated numerical costs. In fact, for the particular example studied here, the conservative approximation outperforms the diagonal quadratic approximation.

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