KSME International Journal

, Volume 15, Issue 7, pp 876–888

Efficient approximation method for constructing quadratic response surface model

Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design


For a large scaled optimization based on response surface methods, an efficient quadratic approximation method is presented in the context of the trust region model management strategy. If the number of design variables inn, the proposed method requires only 2n+1 design points for one approximation, which are a center point and two additional axial points within a systematically adjusted trust region. These design points are used to uniquely determine the main effect terms such as the linear and quadratic regression coefficients. A quasi-Newton formula then uses these linear and quadratic coefficients to progressively update the two-factor interaction effect terms as the sequential approximate optimization progresses. In order to show the numerical performance of the proposed method, a typical unconstrained optimization problem and two dynamic response optimization problems with multiple objective are solved. Finally, their optimization results compared with those of the central composite designs (CCD) or the over-determined D-optimality criterion show that the proposed method gives more efficient results than others.

Key Words

Efficient Quadratic Approximation Response Surface Trust Region Approximate Optimization 


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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2001

Authors and Affiliations

  1. 1.Department of Mechanical Design and Production EngineeringHanyang UniversitySeoulKorea
  2. 2.BK21 Division for Research and Education in Mechanical EngineeringHanyang UniversitySeoulKorea
  3. 3.Center of Innovative Design Optimization TechnologyHanyang UniversitySeoulKorea

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