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Daniel Guggenheim School of Aerospace Engineering
Daniel Guggenheim School of Aerospace Engineering
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ItemA Design of Experiments-Based Method for Point Selection in Approximating Output Distributions(Georgia Institute of Technology, 2002-09) McCormick, David Jeremy ; Olds, John R.The goal of this research is to find a computationally efficient and easy-to-use alternative to current approximation or direct Monte Carlo methods for robust design. More specifically, a technique is sought to use selected deterministic analyses to obtain probability distributions for analyses with large inherent uncertainties. Previous research by the authors has presented a promising class of methods known as Discrete Probability Matching Distributions (DPOMD). This paper introduces a new type of DPOMD better suited to problems with larger numbers of random variables. This new type utilizes a fractional factorial design of experiments array in combination with an inverse Hasofer-Lind standard normal space transform. The method defines points in the problem space that represent the moment characteristics of the input random variables. This new method is compared to two other approximation techniques, Descriptive Sampling and Response Surface/Monte Carlo Simulation, for three common aerospace analyses (Mass Properties and Sizing, Propulsion Analysis and Trajectory Simulation). A Monte Carlo analysis with corresponding error bands is used for reference. Preferences for probabilistic analysis each of these problems are determined based on the speed and accuracy of analysis. These results are presented here. The new DPOMD technique is shown to be advantageous in terms of speed and accuracy for two of the three problems tested.
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ItemA Distributed Framework for Probabilistic Analysis(Georgia Institute of Technology, 2002-09) McCormick, David Jeremy ; Olds, John R.Probabilistic multidisciplinary design optimization promises to incorporate critical design uncertainty in order to create optimal products with a high probability of meeting design constraints under a wide variety of circumstances. Several methods of accelerated probability analysis are available to designers. What is not available is a formal method for tying contributing analysis-level probability analysis into an integrated design framework capable of optimization. This would allow probability methods to be tailored to the characteristics of a particular contributing analysis as well as potentially reduce the dimensionality of the problems considered. This research presents such a method, and then tests it on a conceptual launch vehicle design problem. This probabilistic optimization problem consisted of 84 noise variables and four design variables. This problem setup consistently found system optimums in 6-8 hrs. It utilized several probability approximation methods run in an iterative manner to generate probabilistic vehicle sizing information. Once the probabilistic optimum was identified and confirmed using this process, a system-level Monte Carlo random simulation of the vehicle design was conducted around the optimum point to confirm the accuracy of the distributed approximation method. Because this simulation was prohibitively expensive, it was only conducted at the single optimum point. Following this accuracy confirmation, a comparison to a deterministic optimization of the same problem illustrated the difference between probabilistic and deterministic optimums.
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ItemSpace Tourism: Making it Work for Fun and Profit(Georgia Institute of Technology, 2000-10) Olds, John R. ; McCormick, David Jeremy ; Charania, Ashraf ; Marcus, Leland R.This paper summarizes the findings of a recent study of space tourism markets and vehicles conducted by the Space Systems Design Laboratory at Georgia Tech under sponsorship of the NASA Langley Research Center. The purpose of the study was to investigate and quantitatively model the driving economic factors and launch vehicle characteristics that affect businesses entering the space tourism industry. If the growing public interest in space tourism can be combined with an economically sound business plan, the opportunity to create a new and profitable era for space flight is possible. This new era will be one in which human space flight is routine and affordable for many more people. The results of the current study will hopefully serve as a guide to commercial businesses wishing to enter this potentially profitable emerging market.
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ItemComparison of Collaborative Optimization to Conventional Design Techniques for a Conceptual RLV(Georgia Institute of Technology, 2000-09) Cormier, Timothy A. ; Scott, Andrew ; Ledsinger, Laura Anne ; McCormick, David Jeremy ; Way, David Wesley ; Olds, John R.Initial results are reported from an ongoing investigation into optimization techniques applicable to multidisciplinary reusable launch vehicle (RLV) design. The test problem chosen for investigation is neither particularly large in scale nor complex in implementation. However, it does have a number of characteristics relevant to more general problems from this class including (1) the use of legacy analysis codes as contributing analyses and (2) non-hierarchical variable coupling between disciplines. Propulsion, trajectory optimization, and mass properties analyses are included in the RLV problem formulation. A commercial design framework is used to assist data exchange and legacy code integration. The need for a formal multidisciplinary design optimization (MDO) approach is introduced by first investigating two or more conventional approaches to solving the sample problem. A rather naive approach using iterative sublevel optimizations is clearly shown to produce non-optimal results for the overall RLV. The second approach using a system-level response surface equation constructed from a small number of RLV point designs is shown to produce better results when the independent variables are judiciously chosen. However, the response surface method approach cannot produce a truly optimum solution due to the presence of uncoordinated sublevel optimizers in the three contributing analyses. Collaborative optimization (CO) appears to be an attractive MDO approach to solving this problem. Initial implementation attempts using CO have exhibited noisy gradients and other numerical problems. Work to overcome these issues is currently in progress.
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ItemApproximation of Probabilistic Distributions Using Selected Discrete Simulations(Georgia Institute of Technology, 2000-09) McCormick, David Jeremy ; Olds, John R.The goal of this research is to find a computationally efficient and easy to use alternative to current approximation of direct Monte Carlo methods for robust design. More specifically, a new technique is sought to use selected deterministic analyses to obtain probability distributions for analyses with large inherent uncertainties. Two techniques for this task are investigated. The first uses a design of experiments array to find key points in the algorithm space upon which deterministic analyses will be performed. An expectation value error minimization routine is then used to assign discrete probabilities to the individual runs in the array based on the joint probability distribution of the inputs. This creates a representative distribution that can be used to estimate expectation values for the output distribution. The second technique uses a similar error minimization algorithm, but this time alters the location of the points to be sampled from the function space. This means that for every change in input variable distribution, the algorithm will generate a table of runs at input locations that minimize the error in expectation values. The advantages of these techniques include a small time savings over approximation or direct Monte Carlo methods as well as elimination of numerical noise due to random number generation. This noise will be shown to be a hindrance when converging multiple Monte Carlo analyses. In additional, when the variable location sampling point algorithm is used, this takes away the arbitrary task of defining levels for the input variables and provides enhanced accuracy.