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Applying an automatic differentiation technique to sensitivity analysis in design optimization problems

- Article in a journal -

Published in
Finite Elements in Analysis and Design

Year
1993

Abstract
For the design of optimal mechanical structures, the design sensitivity analysis technique using high-order derivatives is important. However, the usual techniques for computing the derivatives, for example a numerical differential method, are very hard to apply to real scale structures because of excessive computation time. To overcome the problem, we have used a code generator to compute differential coefficients of high-order derivatives of complex functions calledtexpander and written in fortran. texpander automatically transforms a user's fortran functions into special purpose ones, which can compute both the value of the given functions and their derivatives. The algorithm used in texpander can automatically and efficiently compute accurate values of high-order partial derivatives of a given function with many variables. This paper reports the basic principle of the automatic differentiation method, and some experiments on the design sensitivity analysis of mechanical structures. The original program of structures analysis by using the finite element method was implemented in fortran, as developed by us. Using the proposed method, we get accurate sensitivity and prediction values compared with the usual numerical differentiation, with less computing time. We also discuss the effectiveness of the proposed method.

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BibTeX
@ARTICLE{
         Ozaki1993Aaa,
       title = "Applying an automatic differentiation technique to sensitivity analysis in design
         optimization problems",
       journal = "Finite Elements in Analysis and Design",
       volume = "14",
       number = "2--3",
       pages = "143--151",
       year = "1993",
       note = "Special Issue Optimum Design in Japan",
       issn = "0168-874X",
       doi = "DOI: 10.1016/0168-874X(93)90015-I",
       url =
         "http://www.sciencedirect.com/science/article/B6V36-47X7CVD-R/2/bb8e33cd734fbb3d668e9017e7837a25",
       author = "Ikuo Ozaki and Takao Terano",
       abstract = "For the design of optimal mechanical structures, the design sensitivity analysis
         technique using high-order derivatives is important. However, the usual techniques for computing the
         derivatives, for example a numerical differential method, are very hard to apply to real scale
         structures because of excessive computation time. To overcome the problem, we have used a code
         generator to compute differential coefficients of high-order derivatives of complex functions
         calledtexpander and written in fortran. texpander automatically transforms a user's fortran
         functions into special purpose ones, which can compute both the value of the given functions and
         their derivatives. The algorithm used in texpander can automatically and efficiently compute
         accurate values of high-order partial derivatives of a given function with many variables. This
         paper reports the basic principle of the automatic differentiation method, and some experiments on
         the design sensitivity analysis of mechanical structures. The original program of structures
         analysis by using the finite element method was implemented in fortran, as developed by us. Using
         the proposed method, we get accurate sensitivity and prediction values compared with the usual
         numerical differentiation, with less computing time. We also discuss the effectiveness of the
         proposed method.",
       ad_tools = "TEXPANDER"
}

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