Rhonald M. Jenkins

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

Numerical analysis of ignition transients in solid rocket motors

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.

Design Optimization of a Space Launch Vehicle Using a Genetic Algorithm

A model to analyze the unstready multidimensional turbulent flow in the head-end, star slot section of a solid rocket motor during the ignition transient is developed. The present paper examines the fluid dynamic aspects of the starting transient. A finite-difference solution of the unsteady, compressible, full Navier-Stokes equations, together with a two-equation k-epsilon turbulence model, is obtained utilizing the MacCormack explicit, predictor-corrector technique. Computed results for the flow in the slot are compared with experimental data obtained in cold flow tests of a scaled model of the Space Shuttle SRM head-end, star grain section. The agreement between the calculated flowfield and existing experimental data is very good.

Analytical Development of a Slotted-Grain Solid Rocket Motor

This paper describes an effort to optimize the design of an entire space launch vehicle to low-Earth (circular) orbit, consisting of multiple stages using a genetic algorithm (GA) with the goal of minimizing vehicle weight and ultimately vehicle cost. The entire launch vehicle system is analyzed using various multistage configurations to reach low-Earth orbit. Specifically, three and four-stage solid propellant vehicles have been analyzed. The vehicle performance modeling requires that analysis from four separate disciplines be integrated into the design optimization process. The disciplines of propulsion characteristics, aerodynamics, mass properties and flight dynamics have been integrated to produce a high fidelity system model of the entire vehicle. In addition, the system model has been validated using existing launch vehicle data. The cost model is mass-based and uses extensive historical data to produce a cost estimating relationship for a solid propellant vehicle. For the design optimization, the goals of the problem are for the GA to minimize the differences between the desired and actual orbital parameters. This ensures the payload achieves the desired orbit. One final goal is to minimize the overall vehicle mass thus minimizing the system cost per launch. The paper will represent the first effort of its kind to minimize solid propellant launch vehicle cost at the preliminary design level using a GA.

Solid Rocket Motor Performance Matching Using Pattern Search/Particle Swarm Optimization

In most practical solid-rocket-motor design processes, final designs for grains are determined using computer-generated grids. This process is 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. This paper offers a detailed development of the burn-back equations for a slotted grain with burning only on the slot faces. The result is a set of algebraic equations that can be used to predict burn perimeter and port area at a given burn distance for a given slotted grain design.