TOWSON UNIVERSITY OFFICE OF GRADUATE STUDIES PREDICTING THE TERMINAL BALLISTICS OF KINETIC ENERGY PROJECTILES USING ARTIFICIAL NEURAL NETWORKS by John Robert Auten Sr. A Dissertation Presented to the faculty of Towson University in partial fulfillment of the requirements for the degree Doctor of Science Department of Computer & Information Sciences Towson University 8000 York Rd. Towson, MD. 21252 Date of Submission: December 7, 2016 ii Acknowledgments I would like to thank my advisor Dr. Robert J. Hammell II he has been a mentor, colleague, and friend. Without his guidance and encouragement, completion of this work would not have been possible. I would also like to thank my wife, Karen Lee Auten and son, John Robert Auten Jr. for their support and understanding. iii Abstract Predicting the Terminal Ballistics of Kinetic Energy Rods Using Artificial Neural Networks John Robert Auten Sr. The U.S. Army requires the evaluation of new weapon and vehicle systems through the use of experimental testing and Modeling & Simulation (M&S). Traditional M&S has worked well over the years but can be a lengthy process and often cannot provide quick results for studies involving new threats encountered in theater. So, there is increased focus on rapid M&S efforts that can provide accurate and fast results. Accurately modeling the penetration and residual properties of a ballistic threat as it progresses through a target is an extremely important part of determining the effectiveness of the threat against that target. This dissertation presents research on the application of Artificial Neural Networks (ANNs) to the prediction of the terminal ballistics of Kinetic Energy Projectiles (KEPs). By shifting the computational complexity of the problem to the fitting (regression) phase of the methodology, performance during analyses are improved when compared to other terminal ballistic models for KEPs. Another improvement in performance can be realized by removing the need for input preparation by a Subject Matter Expert (SME) prior to using the methodology for an analysis. This research shows that ANNs can be used to model the terminal ballistics of KEPs and that they are capable of being used for single element and multiple element targets. It is also shown that the runtimes of an ANN are drastically faster than the current state-of-the-art model. iv iv Contents List of Tables vii List of Figures viii Acronyms x 1 Introduction 1 1.1 Background . .1 1.2 Problem Definition . .5 1.3 Objectives . .5 1.4 Research Questions . .5 1.5 Approach . .7 1.5.1 Phases of Approach . .7 1.5.2 Methods and Tools . .9 1.6 Chapter Summary . 11 1.7 Roadmap . 11 2 Literature Review 12 2.1 Vulnerability/Lethality (V/L) Modeling . 12 2.2 Terminal Ballistics Modeling . 16 2.3 Kinetic Energy Projectiles . 17 2.3.1 Kinetic Energy Projectile Penetration Process . 19 2.4 Kinetic Energy Projectile Terminal Ballistics Models . 21 2.4.1 Empirical Models . 22 2.4.2 Phenomenological Models . 24 2.4.3 Generalization Methods for All Models . 29 2.5 Artificial Neural Networks . 33 2.5.1 Multi-Layered Perceptron . 35 2.5.2 Artificial Neural Network Characteristics . 36 2.6 Applications of Artificial Neural Networks in the Field of Ballistics . 49 2.7 Deep Learning . 52 2.8 Summary . 53 3 Software Overview and Implementation Details 54 3.1 Software Overview . 54 3.1.1 Encog . 54 3.1.2 PenDataModel . 56 3.1.3 PDMLEditor . 56 3.1.4 BallisticsANN . 57 3.1.5 ANNPlotter . 60 3.2 Implementation Details . 60 3.2.1 K-fold Cross-Validation . 60 3.2.2 Splitting of the data into data sets . 61 3.2.3 Early Stopping Strategies . 63 3.2.4 Back-Propagation Method . 64 3.2.5 Global Optimization . 64 3.2.6 Cost Function . 65 3.2.7 Topology Selection . 66 3.2.8 Data Quality and Cleaning . 67 3.2.9 Analysis Methods . 71 3.3 Summary . 82 4 Experimental Test Data 83 4.1 Database Design . 83 4.1.1 Test . 85 4.1.2 Source . 86 4.1.3 Impact . 87 4.1.4 Projectile . 87 4.1.5 Target . 87 4.1.6 Results . 88 4.2 Data Acquisition . 88 4.3 Data Preparation . 89 4.4 Parameter Selection . 95 4.5 Data Analysis . 96 4.6 Summary . 101 5 MLP for Monolithic Metallic Armor 103 5.1 Methodology . 103 5.2 Training Process Results . 110 5.3 Comparison to Segletes Model . 111 5.3.1 Perforation Prediction Results . 112 5.3.2 Residual Value Estimation Results . 113 5.3.3 Runtime Comparison . 116 5.4 Summary . 117 6 MLP for Multi-Layer Metallic Armor 125 6.1 Methodology . 125 6.2 Results . 126 6.3 Comparison to Segletes Model . 128 6.3.1 Perforation Prediction Results . 128 6.3.2 Residual Value Estimation Results . 130 6.3.3 Runtime Comparison . 134 6.4 Summary . 134 v 7 Conclusion 148 7.1 Revisit of Research Questions . 148 7.2 Summary of Contributions . 155 7.2.1 Publications . 155 7.2.2 Impact . 157 7.3 Discussion of Limitations . 157 7.4 Future Work . 158 8 References 160 9 Bibliography 171 Appendix A Vitae 245 Appendix B Penetration Database Markup Language 249 B.1 PDML Schema . 249 B.2 PDML Design Diagrams . 256 vi vii List of Tables 1.1 Phases of approach . .7 2.1 Minimum and maximum bounds for normalization . 39 3.1 Confusion matrix . 72 3.2 MPE and MAPE Example . 75 3.3 MAPE and SMAPE Example . 76 4.1 Database Hardness Columns . 91 4.2 Statistics for the input and output values of the ANN . 97 4.3 The normalization values used for the parameter box and whisker plots . 102 5.1 Perforation Prediction Statistics for Monolithic Targets . 112 5.2 Mean square error and symmetric mean absolute percentage error statistics for residual value predictions of monolithic targets . 114 6.1 Perforation Prediction Statistics for Multiple Element Targets . 129 6.2 Mean square error and symmetric mean absolute percentage error statistics for residual value predictions of multiple element targets . 131 viii List of Figures 1.1 Rod plastic zone entrainment in multiple elements . .9 2.1 A Computer Aided Design (CAD) target model . 13 2.2 V/L taxonomy (Level 1 to Level 4) . 14 2.3 A shotline through a target . 15 2.4 Types of Armor Piercing (AP) rounds . 18 2.5 An Armor Piercing Fin Stabilized Discarding Sabot (APFSDS) round . 19 2.6 Example of erosion during penetration of Tungsten Heavy Alloy and Depleted Uranium . 20 2.7 Finite element analysis of KEP . 21 2.8 Illustration of the difference between normal thickness and line-of-sight thick- ness ........................................ 31 2.9 Example topology of a Multi-Layered Perceptron (MLP) . 33 2.10 Incorrect extrapolation predictions . 38 2.11 Example of three activation functions . 41 2.12 Example of how a neuron's output is effected by weight adjustment . 42 2.13 Example of how a neuron's output is effected.