1 American Institute of Aeronautics and Astronautics R EDUCED O RDER G UIDANCE M ETHODS A ND P ROBABILISTIC T ECHNIQUES I N A DDRESSING M ISSION U NCERTAINTY Mr. Daniel DeLaurentis NASA Multidisciplinary Analysis Fellow Dr. Dimitri N. Mavris Assistant Professor & Associate Director ASDL Dr. Anthony J. Calise Professor, School of Aerospace Dr. Daniel P. Schrage Professor & Co-Director ASDL Aerospace Systems Design Laboratory (ASDL) * School of Aerospace Engineering Georgia Institute of Technology Atlanta, GA 30332-0150 * Copyright © 1996 by AIAA. Presented at the 6th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, Sept. 4-6, 1996. Abstract Recognizing that vehicle synthesis fulfills the role of integrator of the mutually interacting disciplines, difficulties persist in intelligently implementing disciplinary analysis into this synthesis process. This paper develops and describes analytical and statistical approximation techniques used to create design-oriented analyses which are implementable in the process. Specifically, techniques related to the vehicle guidance discipline are examined. The ultimate goal is to investigate the economic viability of an aerospace system in the face of uncertainty at the system and discipline design levels. The notion of a “design mission” as a requirement is replaced by a modeling of mission variability, since future aircraft will likely fly a variety of missions. Aircraft guidance laws are key components in the mission analysis portion of an aircraft sizing code, and thus they must be included in the investigation. Through the use of statistical modeling techniques, a link between mission uncertainty, optimal guidance, wing planform, and economic objectives is obtained. This linkage allows for the investigation of guidance and mission effects on such quantities as gross weight and ticket price (on a per mile basis). Further, the resulting solutions are robust since they are obtained by choosing control parameters which maximize the probability of meeting a target while simultaneously assuring that appropriate constraints (which are also probabilistic) are met. Introduction The consideration of economic uncertainty on the aircraft synthesis process is the focus of recent research as a means to generate robust solutions. 1,2 Building on the insights of this work, this paper expands the types of uncertainty considered to include variability related to the vehicle guidance discipline as well as to mission requirements. In general, defining requirements is a key first step to a successful design process. In fact, requirements definition is a key element of the Integrated Product and Process Development (IPPD)/Concurrent Engineering (CE) concept which has emerged recently as a viable means of implementing concurrent engineering practices in aerospace systems design. 3 Designing aircraft in an IPPD/CE framework is viewed as designing with a focus on affordability, which implies an understanding of how various discipline, mission, design, and economic variables affect the feasibility (“can it be built”) and viability (“should it be built”) of an aircraft. It is in evaluating feasibility and viability that one quickly realizes the non- deterministic nature of the design problem. This is because parameters traditionally treated as fixed assumptions are in reality distributions around a most likely value. For example, deterministic methods proceed “assuming a fuel price of $1/gallon” whereas probabilistic methods proceed “assuming a range of possible fuel prices represented by a probability distribution”. Probabilistic design methods have, until recently, been discipline specific. In recent years, research in the controls area has had its emphasis on robustness, focusing on the conflicting