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Multi-Criteria Shape Optimization of a Funnel in Cathode Ray Tubes Using Response Surface Model
Tae Hee Lee, Kwangki Lee, Kwang Soon Lee
July 10, 2001
Abstract
The ultimate goal of simulation that represents the behaviour of structures is to optimize their response performances within the specific requirements and needs with respect to the design variables. The f irst step of the design of cathode ray tubes is to design the glass geometry, called funnel geometry, to endure the vacuum stress because it is a main structure of cathode ray tubes. In order to create 3-dimensional funnel geometry in the cathode ray tubes, higher order response surface model is used instead of NURBS (non-uniform rational Bsplines) or Bezier curve because it is more robust for understanding the geometry change in finite element analysis. By combining finite element analysis , response surface model and sequential quadratic programming within the process integration framework, the shape optimization of a funnel is successfully performed and the maximum stress is reduced to almost half of the current one.
Introduction
Multi-criteria shape optimization based on finite element analysis has been increasingly concerned in the practical applications but it is difficult to describe the continuous shape changes without the mesh distortion of finite element analysis. In order to characterize the continuous shape changes with a finite number of design variables, the reduced-basis method that a few of design vectors are often used to sufficiently describe the shape changes in finite element analysis has been implemented into finite element analysis in the literature.
In this research, higher order response surface models based on design of experiments are proposed as one of the ways to represent the continuous shape changes for multi-criteria shape optimization instead of using the reduced-basis method. Design of experiments is utilized for exploring the design space and for constructing the response surface models to facilitate the effective solution of multi-criteria optimization problems. Response surface models provide an efficient means to rapidly model the trade-off among many conflicting goals under given constraints.
Usually in most practical optimization processes, engineers want to know which goals are in their degree of uncertainty, the so-called confidence levels , or not. In order to manipulate the confidence level of multicriteria optimization, conventional optimization method can be revised by using the fuzzy set theory that is called weighted geometric mean and product operator. The confidence level can be described by a design range and a fuzzy membership function. Fuzzy decisionmaking algorithm is then introduced and investigated to manipulate the engineer’s confidence level in the optimization process because the fuzzy model may be used to quantify the confidence level in the range from 0 to 1. The membership function value of 1 indicates the greatest confidence and the value of 0 corresponds to the weakest belief of the objective function. Fuzzy set theory is utilized to form a realistic description of the optimization objectives. The membership function reflects the degree of certainty from the viewpoint of engineer associated with the confidence level of multicriteria functions. For simplicity, a linear variation of membership is employed in this study.
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