Robust optimization using a gradient index: MEMS applications

Han, Jeong Sam; Kwak, Byung Man

doi:10.1007/s00158-004-0410-3

Cited by 41 publications

(25 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to simplify the design problem, a constraint of the current quench condition on the superconductivity magnet is not considered here. A typical optimization problem for minimizing an objective function subject to a set of constraints is expressed as (5) where is the stray field values calculated at the th measurement point along line a and line b, is the stored magnetic energy, and is the energy target value of 180 MJ. The design variable vector consists of six parameters describing the dimensions of the magnet and the two current densities.…”

Section: Resultsmentioning

confidence: 99%

“…[1]- [5]. Until now, most of the reported attempts have used the Taguchi's robust design concept or Monte Carlo simulation based on the assumption that design parameters are random variables with a probability distribution [2]- [4].…”

mentioning

confidence: 99%

“…To overcome the aforementioned drawbacks, this paper proposes an effective methodology utilizing the second-order sensitivity information, defined as a "gradient index" (GI) in [5], for the robust optimization of electromagnetic systems. The basic concept of the method is to obtain robustness of the objective function by minimizing a GI value calculated from the gradients of performance functions with respect to uncertain variables.…”

mentioning

confidence: 99%

“…A modified feasible direction algorithm with the secondorder sensitivity information by finite differencing is used to [5] in mechanical engineering, its basic concepts are briefly summarized.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Robust Optimization Utilizing the Second-Order Design Sensitivity Information

Kim

et al. 2010

IEEE Trans. Magn.

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Robust Optimization Utilizing the Second-Order Design Sensitivity Information

Kim

et al. 2010

IEEE Trans. Magn.

View full text Add to dashboard Cite

show abstract

“…However, the aforementioned method requires the additional efforts on the handling of multi-objective function, and derivative information about both objective function and constraints should be provided; the evaluation of derivative based design sensitivity is computation-ally expensive, especially when commercial CAE tools are used. A number of studies have been conducted to develop design methodologies (6) - (8) and engineering applications (9) - (12) in the context of robust optimization. The present paper describes a new robust optimization method to account for both the tolerance in design variable (controllable factor) and the variation in problem parameter (uncontrollable factor).…”

Section: Introductionmentioning

confidence: 99%

DOE Based Robust Optimization Considering Tolerance Bands of Design Parameters

Lee

Ahn

2006

JSME Int. J., Ser. C

View full text Add to dashboard Cite

The paper describes a robust optimization method to account for the tolerance of design variable and the variation in problem parameter. The proposed post-optimization effort is initiated from the deterministic optimum as a baseline. The successive process to find search directions and step sizes toward the robust optimum is conducted by determining the worst design that has the highest level in constraint violation. During the selection of the worst design, an orthogonal array table in the context of design of experiemtns (DOE) is used to reduce the constraint function evaluations especially for higher dimensionality problem. The analysis of means (ANOM) is adopted in a case where the variation in problem parameter is considered. The measurement criterion to select the worst design is based on the degree of cumulative constraint violation. A mathematical function problem is first conducted to examine the tolerance of design variable. A cantilever beam problem described by four design variables and a bracket problem with seven design variables are subsequently explored by considering both tolerance of design variable and variation in problem parameter.

show abstract

Sensitivity importance‐based robust optimization of structures with incomplete probabilistic information

Chakraborty

Bhattacharjya

Haldar

2012

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARY Robust design optimization (RDO) is usually performed by minimizing the nominal value of a performance function and its dispersion considering equal importance to each individual gradient of the performance function. However, it is well known that all gradients are not equally important. An efficient sensitivity importance‐based RDO technique is proposed in the present study for optimum design of structures characterized by bounded uncertain input parameters. The basic idea of the proposed RDO formulation is to improve the robustness of a performance function by using a new gradient index that utilizes the importance factors proportional to the importance of the gradients of the performance function. The same concept is also extended to the constraints. To enhance the robustness of the constraints, the constraint functions are also modified by using the importance factor proportional to the importance of the associated gradient of the constraint. Because all the variables are not equally important to capture the presence of uncertainty, an improved robust solution is obtained by the proposed approach compared with the conventional RDO approach. The present formulation is illustrated with the help of three informative examples. The results are compared with the conventional RDO results to study the effectiveness of the proposed RDO approach. Copyright © 2012 John Wiley & Sons, Ltd.

show abstract

Robust optimization using a gradient index: MEMS applications

Cited by 41 publications

References 13 publications

Robust Optimization Utilizing the Second-Order Design Sensitivity Information

Robust Optimization Utilizing the Second-Order Design Sensitivity Information

DOE Based Robust Optimization Considering Tolerance Bands of Design Parameters

Sensitivity importance‐based robust optimization of structures with incomplete probabilistic information

Contact Info

Product

Resources

About