Abstract
This study considers structural optimization under a reliability constraint, in which the input distribution is only partially known. Specifically, when it is only known that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, it is required that the failure probability of a structure should be no greater than a specified target value for any realization of the input distribution. We demonstrate that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can handle a reliability-based design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization; in particular, nonlinear semidefinite programming. Two numerical examples are solved to demonstrate the relation between the optimal value and either the target reliability or the uncertainty magnitude.
Highlights
Reliability-based design optimization (RBDO) is a crucial tool for structural design in the presence of uncertainty [2, 44, 56, 60]
This paper has dealt with the reliability-based design optimization (RBDO) of structures, in which the knowledge of the input distribution that is followed by the design variables is imprecise
It is only known that the expected value vector and the variance-covariance matrix of the input distribution belong to a specified convex set, and their true values are not known
Summary
Reliability-based design optimization (RBDO) is a crucial tool for structural design in the presence of uncertainty [2, 44, 56, 60]. In this paper we consider a possibilistic model of the input distribution parameters What this approach guarantees is a level of robustness [4] of the satisfaction of structural the reliability. We demonstrate that the robust reliability constraint, i.e., the constraint that the structural reliability is no less than a specified value for any possible realizations of the input distribution moments, can be reduced to a system of nonlinear matrix inequalities This reduction essentially follows the concept presented by El Ghaoui et al [15] for computing the worst-case value-at-risk in financial engineering..
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