Ensemble deep-learning methods are developed to swiftly differentiate between similar solid rocket motor variants using early-flight trajectory data. Two classes of rockets were defined, and fly-out data were generated using a 6-DOF code. Three studies were conducted, each with varying levels of similarity between the two classes. The individual model architectures were optimized with a genetic algorithm, and comparisons were made with unoptimized (weaker learning) ensembles. Ensembles consisting of optimized models achieved a few percent increase in classification accuracy over the best individual model accuracies.

This paper investigates applying statistical learning techniques to solid rocket motor simulation. A solid rocket motor (SRM) internal ballistics tool is used to generate large databases of thrust-time profiles for various SRM grain designs. This work will focus on various star and circular perforated SRM grain designs. Ample data generated regression methods and neural networks are used to solve the regression problem for the response variables of interest. For this analysis, the maximum thrust, average thrust, burn time, and total impulse are to be studied. Once the statistical learning analysis has been performed, Shapley Additive exPlanations (SHAP) will be used to help explain the regression and neural network models. In this analysis, SHAP values are used to better explain the results of the machine learning analysis, especially the neural network results. These SHAP values show the predictor variables that have an impact on the response variables, something not typically available for neural networks. This paper will cover the data generated using the solid rocket motor 1D internal ballistics tool, the statistical learning approaches, along with the results and interpretation of the analysis.

Solid propellant-fueled missile systems can be largely characterized by the properties of their solid propellants. These solid propellant properties are first-order variables in the performance of a solid rocket motor system. This paper investigated the classification of a given missile system based on the propellant used in the system and the prediction of propellant parameters of the missile system. These methods used neural networks built with scikit-learn and TensorFlow with Keras in Python. Using the Auburn University Solid Rocket Code (AUSRC), a dataset was generated for a given missile system that varied the propellant used in the system across 8 different propellant types; this dataset was used to classify missiles based upon the 8 propellant types. In another generated dataset, while still using the same 8 propellant types, each of the four propellant properties was varied by +/- 5% using Latin Hypercube sampling. Lastly, another dataset was generated in which one propellant property was increased while the other properties remained constant. These datasets were used to predict the four propellant properties and classify between missiles using slightly altered solid propellants. Shapley Additive Explanations (SHAP) was used with each model to detail the importance of features in the model and to give insights as to how the model classified missile systems and predicted propellant properties. It was found that using output data from the missiles' trajectories as the inputs to a neural network, a 98.3% classification accuracy was achieved when classifying between propellant types 1-8, while classification accuracy between marginally modified propellants ranged from 78% to 82%.

This paper describes classification methods of missiles using solid rocket motors. Two classification scenarios are described: one shows how to classify shortly after launch, and another shows how to use the "max" parameters of the trajectory for classification. The first scenario will show that, within the first 30 s of telemetry data, the missile class can be quickly and accurately determined. To extend this scenario, we will then determine how much data are necessary to classify, so classification will then be attempted in the first 10 and 20 s. The importance of the telemetry data can then be quantified by a direct calculation of the Shapley values. To analyze robustness, missing data are simulated and imputed for classification. The second scenario utilizes the max parameters of the telemetry, such as apogee, to classify the missile. This scenario is more akin to analyzing trajectories that have already been completed. Various classifications using different inputs for classification are shown. Both scenarios will utilize Fisher's discriminant analysis and neural networks to compare performance, and the main goal is to classify missiles. Using discriminant analysis and neural networks provides high accuracy.

This paper investigates applying statistical learning techniques to solid rocket motor simulation. A solid rocket motor (SRM) internal ballistics tool is used to generate large databases of thrust-time profiles for various SRM grain designs. This work will focus on various star and circular perforated SRM grain designs. With ample data generated regression methods along with neural networks are used to solve the regression problem for the response variables of interest. For this analysis the maximum thrust, average thrust, burn time, and total impulse are to be studied. Once the statistical learning analysis has been performed, SHAP (Shapley Additive exPlanations) will be used to help explain the regression and neural network models. In this analysis SHAP values will be used to better explain the results of the machine learning analysis, especially the neural network results. These SHAP values show the predictor variables that have an impact on the response variables, something not typically available for neural networks. This paper will cover the data generated using the solid rocket motor 1D internal ballistics tool, the statistical learning approaches, along with the results and interpretation of the analysis.

This paper investigates applying statistical learning techniques to tapered grain solid rocket motors. Tapered grain geometries offer an alternative to complex cross sections to control the thrust profile of the motor and are common in defense and space launch applications. Lagrangian flow assumptions were used to develop a tool that can robustly model the internal ballistics for tapered grain motors with fidelity suitable for conceptual design applications. Using a lumped parameter burn rate model, the burning area can be modeled to produce thrust vs. time curves with high computational efficiency. Once validated, the solid rocket motor internal ballistics tool was used to generate large databases practical for statistical learning applications. In this paper, we use statistical learning techniques for predicting thrust profiles based on the provided geometries. Tapered right circularly perforated star grain families are included in the paper. This paper includes a discussion of the physics equations governing the internal ballistics tool, the validation cases for the tapered solid rocket motor tool, the statistical learning approaches, and the accompanying results.

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.

This paper describes an approach to developing a robust real-coded genetic algorithm (GA) that is implemented for three representative Aerospace Applications, a propeller optimization, a solid rocket motor missile system optimization, and a liquid rocket engine powered missile system optimization. The propeller design and optimization analysis using Bernstein polynomials to develop the geometries is optimized for a cruise condition. The full propeller design optimization problem requires a GA that can overcome abundant local maxima and find a real solution as there are a multitude of parameters for the GA to adjust. The GA makes use of demes (subpopulations) to avoid local maxima. The development of this genetic algorithm uses a tournament style parent selection to obtain the four fittest members of a given subpopulation. The results for the GA applied to the two different genres of aerospace analysis are provided here. The propeller geometry is optimized for thrust and efficiency, and the missile applications are optimized for range and apogee. The number of subpopulations used to generate the main population is varied for both applications to provide insight into their assistance to the GA model.

Classifying the sentiments of online reviews of products or services is important in that it provides the analysts with the ability to extract critical information which can be used to improve the corresponding product or service. The objective of this study is to classify the customer reviews (on a five-star and binary scale) that were collected for four different types of products/services. To achieve this goal, a novel classification framework is built by devising a unique classifier (composite variable), which includes rich information gathered by using all of the extracted features. The proposed framework is compared to commonly used Singular Value Decomposition (SVD) and chi-square-based feature selection (selected features, SF). These approaches are separately deployed in tree-based machine learning algorithms and Logistic Regression using a five-fold cross validation strategy. The results indicate that the proposed methodology outperforms the alternatives for each dataset employed.

This paper describes a methodology to rapidly model the performance of solid rocket motors and classify motors according to their geometries using statistical learning approaches. Star grain configurations are considered in this analysis. A variety of statistical learning approaches including neural networks have been applied to the problem of mapping pressure time curves for solid rocket motors and, using convolutional neural networks, backwardly map pressure time curves to the motor geometries which produced the pressure time profiles. This classification application is useful in reverse engineering applications and in identifying a range of possible options for achieving a given design goal. This paper contains a description of the physical model, the statistical learning methods required to robustly replicate the physics model, and the convolutional neural network approach used for the classification, along with results for both functions.

For flight dynamics modeling of a missile system to predict trajectories, very efficient aerodynamic models with at least conceptual design level fidelity are required because of the extreme diversity in flight conditions encountered. This paper presents a Deep Learning Neural Network (DNN) based approach for predicting 5 missile aerodynamic coefficients (dependent variables). This approach has been implemented for a diversity of grid fin equipped missile configurations. For this paper, no canards are incorporated in the training data sets. For this demonstration effort, a lower order physics model for the aerodynamics has been used to generate training and validation data. A single center body geometry has been considered in this analysis with a full range of grid fin semi spans, cell sizes, Mach numbers, incident angles, and angles of attack have been considered (a total of 8 predictor variables). In this investigation, techniques were developed for selecting an appropriately small subset of the data for training DNNs and using the larger remainder of the data for testing. Results presented in this work point the way toward modeling aerodynamics of grid fin equipped missile systems with high fidelity using a very limited set of high resolutions computational fluid dynamics solutions.

This paper describes a Deep Learning Neural Network (DNN) approach to intermediate range missile system rapid classification during engagement. This paper is an update on a strategy to develop live fire analysis capability starting with the idea that if a known set of missile classes is to be fired, the measured telemetry of a missile from the given class can be used to rapidly determine which of the classes of missiles is flying. The ultimate goal of this work is to rapidly identify characteristics of unknown missiles during flight. These initial steps rely on characterizations derived from large numbers of flight histories or simulated trajectories identified by class. Deep learning neural networks were applied, as well as, other statistical learning procedures, which yielded extremely accurate class predictions on both non-noisy and noisy fly-outs.

In this paper, we give a new feature selection algorithm for the binary class classification problem in sparse high-dimensional spaces. Singular value decomposition (SVD) is a popular dimension reduction method in higher-dimensional classification. The traditional SVD method begins by ranking the Singular Dimensions (SDs) from largest singular value to the smallest. However, when the number of signals is fewer than the number of noise, the first few ranked SDs are not necessarily the best for classification. We demonstrate, theoretically and empirically, that our method efficiently selects the SDs most appropriate for classification and significantly reduces the misclassification error. We also apply our method to real data text mining applications.

This paper offers a statistical methodology for evaluating Pb-free solder alloy performance for high-reliability products using Cox proportional regression analysis and provides a detailed application of the technique based upon a 15-mm BGA package. Specifically, the effects of doping SAC305 solder balls with small amounts of Bi, Co, In, Mn, Ni, and Sb either directly or from the solder paste used for assembly have been studied. The test results have led to a downselection of optimum material combinations that offer a potential solution to the well-known material degradation of SAC305 solder alloys with aging. The test conditions had two different time/temperature periods: 10 days at 25 degrees C and an accelerated condition of 180 days at 125 degrees C. Each test board was temperature shocked 3000 times (-40 degrees C-125 degrees C) with a 15-min thermal profile (5-min dwell time and 2.5-min transition time). The electrical continuity of solder interconnect was examined during the tests, and the effect of solder doping and aging on the failure rate (hazard rate) were assessed at 90% confidence level using the proportional hazard model. We found that the solder doping combination, aging time and temperature, and the interactions between these parameters have significant impacts on the failure rate. BGA with Sn-Ag-Cu doped with Sb, Bi, Co, and Ni can significantly reduce the failure rate after aging with a 90% level of confidence. The failure analysis shows recrystallized assisted crack nucleation in the solder joints.