Automatic Differentiation as a Tool in Engineering Design.pdf

NASA TECHNICAL MEMORANDUM 107661 __// Automatic Differentiation as a Tool in Engineering Design Jean-Francois Laura E. Hall Barthelemy I P,j (7, Z ul M U C _0 _0 _0 p._ 0 _0 August 1992 NASA National Aeronautics and Space Administration Langley Reseamh Center Hampton, Virginia 23665 ,-,4 Z_ I-4 A I-- _j ,,￠ u_Z -, _, ,-_Z _DI.u P-k- I-.- W _ _uJZ ?_, z_ t/,j AUTOMATIC DIFFERENTIATION AS A TOOL IN ENGINEERING DESIGN Jean-Francois M. Barthelemyl NASA/Langley Research Center Laura E. Hall, Unisys Corporation Abstract Automatic Differentiation (AD) is a tool that system- atically implements the chain rule of differentiation to obtain the derivatives of functions calculated by com- puter programs. In this paper, it is assessed as a tool for engineering design. The paper discusses the for: ward and reverse modes of AD, their computing re: quirements as well as approaches to implementing AD. It continues with application of two different tools to two medium-size structural analysis problems to gen- erate sensitivity information typically necessary in an optimization or design situation. The paper concludes with the observation that AD is to be preferred to fi- of a programs input, generates approximate deriva- tives which can be affected by round-off and trunca- tion errors (Haftka and Gurdal, 1992 is. While an ex- act technique, the later tends to generate very cum- bersome expressions for the derivatives. There are a number of applications of AD in the literature, although a surprisingly limited number of them have to do with engineering design. This paper describes an effort underway to assess the applicability of AD in engineering design. It has two major sections. The first is a brief introduction to AD based on some of the most recent publications on the subject. It discusses the two modes of AD, addresses nite differencing in most cases, as long as sufficient the issue of computer cost, presents different forms of AD tools and briefly discusses some results. The c