A General Approach for Robust Optimal Design

Abstract

This paper describes a general, rigorous approach for robust optimal design. The method allows a designer to explicitly consider and control, as an integrated part of the optimization process, the effects of variability in design variables and parameters on a design. Variability is defined in terms of tolerances which bracket the variation of fluctuating quantities. A designer can apply tolerances to any model input and can analyze how the tolerances affect the design using either a worst case or statistical analysis. As part of design optimization, the designer can apply the method to find an optimum that will remain feasible when subject to variation, and/or the designer can minimize or constrain the effects of tolerances as one of the objectives or constraints of the design problem.

Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation

“…(46) can be used to solve the optimization problem defined by Eq. (47). If N is still sufficiently large such that Eq.…”

“…Consequently, we have to solve the optimization problem defined by Eq. (47) for which the objective function is defined by Eq. (48) with ν exp = 1 and N defined hereinafter.…”

“…For instance, robust updating (or robust identification) has recently been proposed in the context of structural dynamics [34,41,42,45]. Similarly, robust design optimization has been proposed in different areas [16,33,37,46,47,49,51,65,67]. It should be noted that such robust updating (or robust identification) and robust design optimization are developed in the context of parameter uncertainties but not in the context of both parameter uncertainties and model uncertainties.…”

Robust design optimization using the price of robustness, robust least squares and regularization methods

“…When G = 2, we return to Soyster's formulation (2) which gives the following max À ð13:84x 1 þ 50:24x 2 Þ s:t: À ð13:84x 1 þ 50:24x 2 Þ þ 1:38y 1 þ 5:02y 2 À 250…”

“…This methodology ensures that the design solution remains feasible and close to optimal even if there is a change in data. Different methodologies for robust design and optimization in mechanical systems have been extensively discussed in literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Most of these methods assume some kind of distribution for the uncertain variable to optimize the problem.…”