Robust Optimization Utilizing the Second-Order Design Sensitivity Information

Abstract

This paper presents an effective methodology for robust optimization of electromagnetic devices. To achieve the goal, the method improves the robustness of the minimum of the objective function chosen as a design solution by minimizing the second-order sensitivity information, called a gradient index (GI) and defined by a function of gradients of performance functions with respect to uncertain variables. The constraint feasibility is also enhanced by adding a GI corresponding to the constraint value. The distinctive feature of the method is that it requires neither statistical information on design variables nor calculation of the performance reliability during the robust optimization process. The validity of the proposed method is tested with the TEAM Workshop Problem 22.

Reliability-Based Design Optimization of a Superconducting Magnetic Energy Storage System (SMES) Utilizing Reliability Index Approach

“…Starting with an initial design, the deterministic and RBDO optima are presented in Table 1. The result of RDO in the previous article [2], where the gradients of performance function required for the second-order sensitivity information were exploited, is added in Table 1 for proving the validity of RBDO. It is observed that total number of function calls of RBDO is more than four times as high as that of DO because of the inherent double-loop optimization structure.…”

“…[1][2][3][4][5][6]. The methodology for treating optimization problems in the presence of uncertainties of design parameters/variables can be categorized into two approaches.…”

“…The methodology for treating optimization problems in the presence of uncertainties of design parameters/variables can be categorized into two approaches. The first is robust design optimization (RDO) based on several approaches, such as the worst-case analysis, gradient index, six sigma, etc., to improve the product quality by minimizing variability of the output performance functions [1][2][3]. However, it does not address the quantitative assessment of performance reliability (i.e.…”

“…Using the proposed method, RBDO optimum of SMES windings was obtained where two design constraints (stored energy and geometrical constraint) maintain high reliabilities (greater than 95%) under the uncertainties of design variables. In addition, DO, RDO [2], and RBDO optima were compared to each other in terms of reliability of design. To validate the accuracy and efficiency of the RBDO model based on RIA, Monte Carlo simulation (MCS) was performed.…”

A Robust Optimization Method Utilizing the Variance Decomposition Method for Electromagnetic Devices

“…A number of robust optimization methods have been proposed to be applied to electromagnetic devices [2][3][4][5][6]. A large part of the optimization approaches use the gradient index (GI) of parameters to represent the robustness due to its simplicity and low computational cost [7].…”