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Expansion of Sensitivity Analysis for Statistical Moments and Probability Constraints to Non-Normal Variables

비정규 분포에 대한 통계적 모멘트와 확률 제한조건의 민감도 해석

  • 허재성 (한국항공우주연구원 회전익기사업단) ;
  • 곽병만 (한국과학기술원 기계공학과)
  • Received : 2010.06.24
  • Accepted : 2010.08.30
  • Published : 2010.11.01

Abstract

The efforts of reflecting the system's uncertainties in design step have been made and robust optimization or reliabilitybased design optimization are examples of the most famous methodologies. The statistical moments of a performance function and the constraints corresponding to probability conditions are involved in the formulation of these methodologies. Therefore, it is essential to effectively and accurately calculate them. The sensitivities of these methodologies have to be determined when nonlinear programming is utilized during the optimization process. The sensitivity of statistical moments and probability constraints is expressed in the integral form and limited to the normal random variable; we aim to expand the sensitivity formulation to nonnormal variables. Additional functional calculation will not be required when statistical moments and failure or satisfaction probabilities are already obtained at a design point. On the other hand, the accuracy of the sensitivity results could be worse than that of the moments because the target function is expressed as a product of the performance function and the explicit functions derived from probability density functions.

Keywords

Sensitivity Analysis;Statistical Moment;Probability Constraint;Moment Method;Non-Normal Distributions

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