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

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 called texpander 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.