A methodology for ballistic missile defense systems analysis using nested neural networks

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Weaver, Brian Lee
Mavris, Dimitri N.
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The high costs and political tensions associated with Ballistic Missile Defense Systems (BMDS) has driven much of the testing and evaluation of BMDS to be performed through high fidelity Modeling and Simulation (M&S). In response, the M&S environments have become highly complex, extremely computationally intensive, and far too slow to be of use to systems engineers and high level decision makers. Regression models can be used to map the system characteristics to the metrics of interest, bringing about large quantities of data and allowing for real-time interaction with high-fidelity M&S environments, however the abundance of discontinuities and non-unique solutions makes the application of regression techniques hazardous. Due to these ambiguities, the transfer function from the characteristics to the metrics appears to have multiple solutions for a given set of inputs, which combined with the multiple inputs yielding the same set of outputs, causes troubles in creating a mapping. Due to the abundance of discontinuities, the existence of a neural network mapping from the system attributes to the performance metrics is not guaranteed, and if the mapping does exist, it requires a large amount of data to be for creating a regression model, making regression techniques less suitable to BMDS analysis. By employing Nested Neural Networks (NNNs), intermediate data can be associated with an ambiguous output which can allow for a regression model to be made. The addition of intermediate data incorporates more knowledge of the design space into the analysis. Nested neural networks divide the design space to form a piece-wise continuous function, which allows for the user to incorporate system knowledge into the surrogate modeling process while reducing the size of a data set required to form the regression model. This thesis defines nested neural networks along with methods and techniques for using NNNs to relieve the effects of discontinuities and non-unique solutions. To show the benefit of the approach, these techniques are applies them to a BMDS simulation. Case studies are performed to optimize the system configurations and assess robustness which could not be done without the regression models.
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