John E. Burkhalter

Aerospace design optimization using a steady state real-coded genetic algorithm

Abstract This study demonstrates the advantages of using a real coded genetic algorithm (GA) for aerospace engineering design applications. The GA developed for this study runs steady state, meaning that after every function evaluation the worst performer is determined and that worst performer is then thrown out and replaced by a new member that has been evaluated. The new member is produced by mating two successful parents through a crossover routine, and then mutating that new member. For this study three different preliminary design studies were conducted using both a binary and a real coded GA including a single stage solid propellant missile systems design, a two stage solid propellant missile systems design and a single stage liquid propellant missile systems design.

Missile Aerodynamic Shape Optimization Using Genetic Algorithms

The use of pareto genetic algorithms (GAs)to determine high-efe ciency missile geometries is examined, and the capabilityofthesealgorithmstodeterminehighlyefe cientandrobustmissileaerodynamicdesignsisdemonstrated, given a variety of design goals and constraints. The design study presented documents both thelearning capability of GAs and the power of such algorithms for multiobjective optimization. Results indicate that the GA is clearly capable of designing aerodynamic shapes that perform well in either single or multiple goal applications.

Genetic-Algorithm Optimization of Liquid-Propellant Missile Systems

The use of computer programs driven by genetic algorithms has become an increasingly popular method for optimizing engineering designs. This paper focuses on the modeling and optimization of liquid-rocket-enginepropelled missiles with a computer program that is composed of a series of codes that simulate the performance of liquid-propelled rockets andare controlledby a genetic algorithm.Because the entiremissile design is considered, the complete system performance must be modeled accurately and efficiently. The methodology described in this paper has been extended to both the preliminary design and reverse-engineering of liquid-propelled missiles. The performance model has been validated against the performance of a liquid-propelled missile and the results are provided. Two different fast-aerodynamic-prediction codes are used and their results are compared. A complete preliminary design of a liquid-propelled missile system is considered with a variety of goals and constraints. Results from the preliminary design optimization are also shown and discussed in detail.

Ramjet Powered Missile Design Using a Genetic Algorithm

A methodology for developing optimized designs for symmetric - centerbody ramjet powered missiles, using genetic algorithms as the central driver for the system optimization process, has been developed. This paper contains discussion of that methodology and shows results for a typical design scenario.

Design of an air to air interceptor using genetic algorithms

For this preliminary design study an apportioned pareto genetic algorithm, unique to the software package IMPROVE?“‘, was used to manipulate a solid rocket design code, an aerodynamic design code, and a three-loop autopilot to produce interceptor designs capable of accurately engaging a target. Twenty-nine design variables were required to define the optimization problem, and four primary goals were established to access the’performance of the interceptor designs. Design goals included 1) minimize miss distance, 2) minimize intercept time, 3) minimize takeoff weight, and 4) minimize maximum G-loading. In 100 generations the genetic algorithm was able to develop several basic types of external aerodynamic designs that ,performed nearly the same, with miss distances less than 10.0 feet. The solid rocket motors that propelled these external shapes shared one common characteristic: a large initial burning area. Initial combustion chamber volumes varied significantly, but the fastest interceptors generally had less fuel than would have been expected. The genetic algorithm did not prefer maximizing the amount of fuel within the rocket motor case (high fuel volume ratio). Introduction With the addition of guidance, an autopilot, and an airframe with movable control surfaces, basic rocketry expands into a more lethal and much more precise means of waging war. Rather than increasing the size of the warhead being delivered (to make-up for a loss in delivery accuracy), modem weaponeering has tended to use a small warhead coupled with an accurate control system. For ground launched systems, ideas such as “smart rocks” and “brilliant pebbles” that sprang from early Strategic Defense Initiative (SDI) research were based on the belief that the energy delivered by a small fast moving projectile without an explosive could be as lethal as a less accurate system with an explosive warhead. Similarly for air-launched ground attack weapons, Vietnam proved that delivery accuracy was paramount to defeating tough targets, and the Air Force devoted billions of dollars to the development of precise warhead delivery systems. Certainly the Persian Gulf War showed the benefit of the highly accurate weapon systems the Air Force developed. In more human terms, increased delivery accuracy means less collateral damage to nonmilitary facilities and less civilian casualties. While it is difficult to argue with .the success of the air-launched ground attack weapons that have been demonstrated in combat, these systems, and air-to-air missile systems, share a common design ‘philosophy with the less successful ground launch interceptors. When a system has a guidance system and autopilot, there is a tendency to compensate for less than stellar aerodynamic designs by shifting more and more of the delivery problems over to the autopilot. As a result, autopilots are typically very good and very robust, but the airframe and aerodynamics of the overall system are almost an afterthought. Overall system performance and system capability, therefore, suffers because of the overreliance on the autopilot to compensate for weaknesses in the aerodynamic performance of the weapon, system’. The goal of this research is to let an artificial intelligence tool, a genetic algorithm, design the aerodynamic shape while at the same time designing the propulsion system and key autopilot variables. This all-at-once approach to missile design is intended to provide a system capable of producing good aerodynamic shapes in addition to the good performance expected from an autopilot. Previous Work Rather than discuss the historical development of the autopilot, propulsion system, or’aerodynamics used for this research, it is more pertinent to discuss previous applications of genetic algorithms to autopilot and control systems. Norris and Crossleyz recently used a genetic algorithm to find gains to control a standard pedagogical two-disk torsional spring system. The approach used a very simple two-loop proportional-integral control system with velocity feedback. The two loop controller had three gains that needed to be determined as a function of variable spring stiffness. The objective functions were defined such that good gain values produce little error between the commanded and achieved disk rotation angles. Since two separate disks were being commanded in twist, a pareto genetic algorithm was used to try to minimize the rotational errors in both disks simultaneously. At the conclusion of 80 .generations, the resulting family (i.e. population of 80 members) of three controller gains were hybrid performers that would work reasonably well for both disks. Two points worth noting from this study was that the crossover * Deputy Director, Development Test Department, Senior Member, AIAA ’ Professor, Auburn University, Associate Fellow, AIAA * Associate Professor, Auburn University, Senior Member, AIAA Copyright@ 19!

A Review of Analytical Methods for Solid Rocket Motor Grain Analysis

lby Murray B. Anderson. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.

Design of a Guided Missile Interceptor Using a Genetic Algorithm

Analytical methods for solid rocket motor grain design are proving to be tremendously beneficial to some recent efforts to optimize solid-rocket propelled missiles. The analytical approach has fallen out of favor in recent decades; however, for some classes of grains, the analytical methods are much more efficient than grid-based techniques. This paper provides a review of analytical methods for calculating burn area and port area for a variety of cylindrically perforated solid rocket motor grains. The equations for the star, long spoke wagon wheel, and dendrite grains are summarized and the development of the burn-back equations for the short spoke wagon wheel and the truncated star configurations are included. This set of geometries and combinations of these geometries represent a very wide range of possibilities for two-dimensional grain design. Introduction In many practical solid rocket motor design efforts, final geometric designs for grains are arrived at using numerical layering techniques. This process is geometrically versatile and imminently practical for cases in which small numbers of final geometries are to be considered. However, for a grain design optimization process in which large numbers of grain configurations are to be considered, generating grids for each candidate design is often prohibitive. For such optimization processes, analytical developments of burn perimeter and port area for two-dimensional grains are critically important. Most modern texts on solid rocket propulsion do not provide geometric details for grain design. This paper will offer a review of analytical methods for determining burn area and port area as a function of burn distance for a selection of common grain designs. Analytical developments for solid rocket motor grains were much more prevalent in the decades before widespread use of microcomputers. A summary of one version of the burn back equations for the star grain and for part of one type of wagon wheel can be found in Barrere. Analytical methods have also been developed for the truncated star and for the dendrite. Other potential grain configurations are described in NASA publications but very few geometric details are given in such publications. 1 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit 20-23 July 2003, Huntsville, Alabama AIAA 2003-4506 Copyright

Propeller Performance Optimization Using Vortex Lattice Theory and a Genetic Algorithm

An apportioned pareto genetic algorithm was used to manipulate a solid rocket design code, an aerodynamic designcode,andathree-loopautopilottoproduceguidedmissileinterceptordesignscapableofaccuratelyengaging a high-speed/high-altitude target. Dee nition of the optimization problem required 29 design variables, and 4 primary goals were established to assess the performance of the interceptor designs. Design goals included the following: minimize miss distance, minimize intercept time, minimize takeoff weight, and minimize maximum g loading. In 50 generations, the genetic algorithm was able to develop 2 basic types of external aerodynamic designs that performed nearlythe same, with miss distances less than 1.0ft. The solid rocket motors that propelled these external shapes shared common characteristics such as a large initial burning area and a large combustion chambervolume. Thegeneticalgorithmdid not prefermaximizing theamount offuel within therocket motorcase (high fuel volume ratio). A higher fuel volume ratiotypicallymeans higher launch weight, but does not necessarily guarantee faster intercepts given enite thermal limits. Examination of the intercept trajectories themselves shows that standard proportional navigation guidance works adequately, but could probably be improved by thrust compensation,especiallyduringthelaunchtransient.Thethree-loopautopilotperformswellevenforhigh-altitude engagements, and the analytic gain determination makes the autopilot straightforward to implement.

Scramjet missile design using genetic algorithms

This paper describes the methodology for propeller performance optimization which uses the vortex lattice method as the performance prediction algorithm and a genetic algorithm (GA) for optimization. The performance optimization investigates thin airfoil propellers which can be simulated with a single lifting surface layer of vortex elements. The propeller wake is simulated by constant pitch and constant radius horseshoe elements, which extend from the last cordwise panel two blade revolutions downstream. The design space considered by the GA is defined by, the number of blades, airfoil shape, twist angle, sweep and cord length for a given free stream velocity and blade revolution rate. The optimization results include minimum power for given thrust and max thrust for given power at one specific advance ratio. Also the thrust was maximized for a given power setting with respect to two advance ratios.

Design Optimization of a Space Launch Vehicle Using a Genetic Algorithm

The objective of this effort was to show that scramjet powered vehicle designs which are optimized for a given flight condition can be found using predictive modeling tools and a genetic algorithm (GA). This required the assimilation of basic modeling tools for the external aerodynamics, the engine internal ballistics for thrust and additive drag predictions, and for the mass and inertia properties. The GA routines for optimizing the design have been used in other design optimization efforts. The basic models have been assembled and specific designs have been developed. Results indicate that the flight envelope for a scramjet is very narrow and dimensions are critical if the engine is to develop thrust at a given design point. For the designs considered in this investigation, specific Mach number and altitude limits were established and dimensional designs were identified. Utilization of these codes and representative results are documented in this paper.