A Deep Learning Neural Network Approach to Missile Systems using Liquid Propulsion

This paper describes a statistical learning approach for modeling the performance of single stage missile systems with the speed and fidelity required for conceptual and early preliminary design. Developing a Response Surface Model (RSM) using statistical learning approaches not only enables design from first principles, but it also facilitates the determination of design parameters given system performance. This “two-way” predictive capability further speeds conceptual design while providing the observer with potentially valuable information about a missile using only limited information such as telemetry. For the purposes of demonstrating the overall approach for this paper, models are developed for a single stage liquid propellant system. For this paper, the authors identify the framework necessary to build the RSM consisting of characteristics used to define the liquid propellant missile design and launch settings. These inputs form the essence of a conventional design process. The most important design variables are missile diameter and length, nozzle expansion ratio, nozzle throat diameter, and initial launch angle. In tandem, these inputs are fed into the statistical learning algorithm, which in turn is trained to predict telemetry parameters that include range, apogee, max thrust, and the time of flight (TOF). A physics model is used to generate training data for the statistical learning exercise. This model is described in the paper and is the “glue” that connects the input and output necessary for statistical learning. Furthermore, it is necessary to use design of experiments to develop an appropriate database without agglomerating an excessively massive database. The AU Liquid Rocket Code (AULRC) uses a Latin hypercube design to randomly generate missile designs (inputs) and then simulate the missile thrust, time, and its trajectory. For this effort, the output is transformed into max thrust, TOF, range, and apogee. The bulk of the paper is methodology adopted for the Model development. Multiple software packages can implement foundational elements of the modeling process and models are developed with TensorFlow using Python, Flux using JULIA, Matlab, and SAS. The authors compare and contrast the platforms and their suitability for this problem, but ultimately TensorFlow is the preferred approach and the one used to develop the results for the paper. The performance capabilities of the RSM's from each software program are training time, error history, and the general mean absolute percentage error computed on each output characteristic and are used as the basis for choosing the best tools and models. All models are validated and/or cross-validated, then evaluated based on their performance on independent test data. Statistical/machine learning methods include, among others, deep learning neural networks, linear and non-linear regression (through basis expansion) and ensemble methods. This paper shows that the statistical learning RSM approach can yield results with sufficient fidelity to support conceptual and early preliminary design. Ongoing efforts address occasionally spuriously large errors while most of the output has error not exceeding 1%-2% of accepted values. Finally, the data set requirements and constraints required to produce results of this quality are discussed in the paper.