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International Journal for Uncertainty Quantification
IF: 4.911 5-Year IF: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2020032977
pages 277-296

MODEL CALIBRATION FOR DETONATION PRODUCTS: A PHYSICS-INFORMED, TIME-DEPENDENT SURROGATE METHOD BASED ON MACHINE LEARNING

Juan Zhang
Institute of Applied Physics and Computational Mathematics, Beijing, 100094, People's Republic of China
J. Yin
Institute of Applied Physics and Computational Mathematics, Beijing, 100094, People's Republic of China
Ruili Wang
Institute of Applied Physics and Computational Mathematics, Beijing, 100094, People’s Republic of China
J. Chen
China Aerodynamics Research and Development Center, Mianyang, Sichuan, 621000, People's Republic of China

ABSTRACT

This paper proposes an innovative physics-informed and time-dependent surrogate method based on machine learning to calibrate the parameters of detonation products for cylinder test. Model calibration is a step of model validation, verification, and uncertainty quantification. A good calibration result will effectively enhance the credibility of a simulation, even model and software. This method extracts and quantifies the features of data, and corresponds them to the specific physical processes, such as the fluctuation caused by shock wave and the damping effect caused by energy dissipation. Different from the conventional surrogate models, our method gives a special consideration to the time variable and couples it with the detonation parameters properly through feature extraction and correlation analysis. The use of feature screening and variable selection enables this method to deal with high-dimensional and nonlinear situations. Models based on the Cramer-von Mises conditional statistic can reduce the complexity and improve the generalization performance by screening out the variables with strong correlation. And with the Oracle property of adaptive lasso, the convergence property of the method is guaranteed. Numerical examples of PBX9501 show, that the calibration results effectively improve the accuracy of simulation. With the relation between parameters and feature coefficients, we offer an instructive parameter adjusting strategy. Last but not least it can be generalized to other explosives. Model comparison results on 17 types of explosives show that our method has a better agreement with the cylinder test than the classical exponential form.

REFERENCES

  1. Wang, R.L. and Jiang, S., Mathematical Methods for Uncertainty Quantification in Nonlinear Multi-Physics Systems and Their Numerical Simulations, Sci. China: Math., 45(6):723-738, 2015. (in Chinese).

  2. Liang, X. and Wang, R.L., Verification and Validation of Detonation Modeling, Defence Technol., 15:398-408, 2019.

  3. Schobi, R., Surrogate Models for Uncertainty Quantification in the Context of Imprecise Probability Modelling, PhD, ETH Zurich, Zurich, Switzerland, 2017.

  4. Hill, M.C., Methods and Guidelines for Effective Model Calibration; with Application to UCODE, a Computer Code for Universal Inverse Modeling, and MODFLOWP, a Computer Code for Inverse Modeling with MODFLOW, Tech. Rep. 98-4005, Water-Resources Investigations, Denver, CO, USA, 1998.

  5. Bhuvanagiri, P., Pichika, S., Akkur, R., Chaganti, K., Madhusoodhanan, R., andPusapati, S.V., Chapter 9: Integrated Approach for Modeling Coastal Lagoons: A Case for Chilka Lake, A.S.S. Rao and C. Rao, Eds., in Integrated Population Biology and Modeling, Part A, vol. 39 of Handbook of Statistics, pp. 343-402, Elsevier, 2018.

  6. Ma, Z.B. and Yu, M., Uncertainty Quantification for Modeling and Simulation with Calibration, ADVCOMP 2015: The 9th Int. Conf. on Advanced Engineering Computing and Applications in Sciences, Nice, France, pp. 7-12, 2015.

  7. Ma, Z.B., Li, H.J., Yin, J.W., and Huang, W.B., Uncertainty Quantification of Numerical Simulation for Reliability Analysis, Chin. J. Comput. Phys, 31(4):424-430, 2014. (in Chinese).

  8. Mortensen, C. and Souers, P.C., Optimizing Code Calibration of the JWL Explosive Equation-of-State to the Cylinder Test, Propel. Explos. Pyrotech., 42(6):616-622, 2017.

  9. Nan, Y.X., Jiang, J.W., Wang, S.Y., and Men, J.B., One Parameter-Obtained Method for JWL Equation of State Considered Detonation Parameter, Explos. Shock Waves, 35(2):157-163, 2015. (in Chinese).

  10. Faissol, D., Approaches for Calibrating Agent-Based Models to Data, Lawrence Livermore National Laboratory, Livermore, CA, LDRD Annual Rep. 16-FS-041,2017.

  11. Lee, E.L., Hornig, H.C., and Kury, J.W., Adiabatic Expansion of High Explosive Detonation Products, Lawrence Radiation Laboratory, Livermore, CA, Tech. Rep. UCRL505422, 1968.

  12. Wilkins, C.L., Calculation of Elastic-Plastic Flow, Lawrence Radiation Laboratory, Livermore, CA, Tech. Rep. UCRL-7322, 1963.

  13. Lan, I.F., Hung, S.C., Chen, C.Y., Niu, Y.M., and Shiuan, J.H., An Improved Simple Method of Deducing JWL Parameters from Cylinder Expansion Test, Propel. Explos. Pyrotech., 18(1):18-24, 1993.

  14. Bailey, W.A., Belcher, R.A., Eden, G., and Chilvers, D.K., Explosive Equation of State Determination by the AWRE Method, 7th Symp. (Int.) on Detonation, Annapolis, MD, USA, pp. 678-685, 1981.

  15. Hornberg, H., Determination of Fume State Parameters from Expansion Measurements of Metal Tubes, Propel. Explos. Pyrotech., 11(1):23-31, 1986.

  16. Ye, Z.F., Liu, H.B., and Zhu, G.X., Parameter Calculation of JWL with DYNA, Pyrotech. Technol, 20(1):35-48, 2004. (in Chinese).

  17. Aslam, T.D., Detonation Shock Dynamics Calibration of PBX 9501, Bull. Am. Phys. Soc, 955(1):813-816, 2008.

  18. Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T., Numerical Recipes, Art Sci. Comput., 994(4):423-426, 2007.

  19. Chen, Q.C., Jiang, X.H., Li, M., Lu, X.J., and Peng, Q.X., Study on JWLEOS of Detonation Product for HNS-IV, Initiators Pyrotech., 1(4):21-24,2010. (in Chinese).

  20. Chen, Q.C., Jiang, X.H., Li, M., and Lu, X.J., JWL Equation of State for RDX-Based PBX, Chin. J. Energetic Mater., 19(2):213-216,2011. (in Chinese).

  21. Baker, E.L., Stunzenas, G., Stiel, L.I., and Murphy, D., On the Calibration of High Explosive Thermodynamic Equations of State for Broad Application, COMPDYN2011IIIECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece, pp. 1-9,2011.

  22. Walls, K.C., Littlefield, D.L., Dorgan, R., and Lambert, D., An Optimization Framework for Calibration of Material Models, Procedia Eng., 58:279-288, 2013.

  23. Hertel, E.S., Bell, R.L., Elrick, M.G., Farnsworth, A.V., Kerley, G.I., McGlaun, J.M., Petney, S.V., Silling, S.A., Taylor, P.A., and Yarrington, L., CTH: A Software Family for Multi-Dimensional Shock Physics Analysis, R. Brun and L.Z. Dumitrescu, Eds., in Shock Waves Marseille I, Berlin: Springer, pp. 377-382, 1995.

  24. Ma, Z.B., Li, H.J., Yin, J.W., and Huang, W.B., Uncertainty Quantification of Numerical Simulation for Reliability Analysis, Chin. j. Computat. Phys, 31(4):424-430,2014. (in Chinese).

  25. Liu, D.Y., Chen, L., Yang, K., and Zhang, L.S., Calibration Method of Parameters in JWL Equation of State for Detonation Products of CL-20-Based Explosives, Acta Armamentarii, 37(1):141-145,2016. (in Chinese).

  26. Souers, P.C., Wu, B., andHaselman, L.C.J., Detonation Equation of State atLLNL, Lawrence Livermore National Laboratory, Livermore, CA, Tech. Rep. UCRL-ID119262, 1995.

  27. Polk, J.F., Determination of the Equation of State of Explosive Detonation Products from the Cylinder Expansion Test, 6th Int. Symp. Ballistics, Orlando, FL, USA, 1981.

  28. Urtiew, P.A. and Hayes, B., Parametric Study of the Dynamic JWL-EOS for Detonation Products, Combust. Explos. Shock Waves, 27(4):505-514, 1991.

  29. Chen, C.Y., Shiuan, J.H., and Lan, I.F., The Equation of State of Detonation Products Obtained from Cylinder Expansion Test, Propel. Explos. Pyrotech., 19(1):9-14, 1994.

  30. Hill, L.G., Detonation Product Equation-of-State Directly from the Cylinder Test, Office of Scientific & Technical Information, Oak Ridge, TN, Tech. Rep. LA-UR-97-2213, 1997.

  31. Jiang, H.M. and Zhang, R.Q., Application ofNonlinear Optimization to Parameters in JWL Equation of State, J. Ballistics, 10(2):25-28, 1998. (in Chinese).

  32. Trebinski, R. and Trzcinski, W., Determination of an Expansion Isentrope for Detonation Products of Condensed Explosives, J Tech. Phys, 40(4):447-456, 1999.

  33. Sun, Z.F., Xu, H., Li, Q.Z., and Zhang, C.Y., Further Study on JWL Equation of State of Detonation Product for Insensitive High Explosive, Chin. J. High Pressure Phys, 24(1):55-60, 2010. (in Chinese).

  34. Elek,P. andMickovic,D., Cylinder Test: Analytical and Numerical Modeling, in 4th Int. Sci. Conf. on Defensive Technologies, Belgrade, Serbia, pp. 324-330, 2011.

  35. Miller, P.J. and Carlson, K.E., Determining JWL Equation of State Parameters Using the Gurney Equation Approximation, in 9th Symp. (Int.) on Detonation, Portland, OR, USA, pp. 930-936, 1989.

  36. Shen, F., Wang, H., and Yuan, J.F., A Simple Method for Determining the Parameters of JWL Equation of State, J. Vibr. Shock, 33(9):107-110,2014. (in Chinese).

  37. Sanchidrian, J.A., Castedo, R., Lopez, L.M., Segarra, P., and Santos, A.P., Determination of the JWL Constants for ANFO and Emulsion Explosives from Cylinder Test Data, Central Eur. J. Energetic Mater, 12(2):177-194,2015.

  38. Ijsselstein, R.R., On the Expansion of High-Explosive Loaded Cylinders and JWL Equation of State, in 9th Int. Symp. on Ballistics, Shrivenham, UK, 1986.

  39. Liu, J., Xu, C., Han, X., Jiang, C., and Liu, G.P., Determination of the State Parameters of Explosive Detonation Products by Computational Inverse Method, Inv. Prob. Sci. Eng., 24(1):22-41, 2016.

  40. Wang, Y.J., Zhang, S.D., Li, H., and Zhou, H.B., Uncertain Parameters of Jones-Wilkin-Lee Equation of State for Detonation Products of Explosive, Acta Phys. Sinica, 65(10):106401,2016. (in Chinese).

  41. Kennedy, M.C. and O'Hagan, A., Bayesian Calibration of Computer Models, J. R Stat. Soc., 63(3):425-464,2001.

  42. Higdon, D., Kennedy, M.C., Cavendish, J.C., Cafeo, J.A., and Ryne, R.D., Combining Field Data and Computer Simulations for Calibration and Prediction, Comput. Sci. Eng., 26(2):448-466,2005.

  43. Rasmussen, C.E. and Williams, C.K.I., Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning), The MIT Press, 2005.

  44. Chen, H., Zhou, H.B., Liu, G.Z., Sun, Z.F., and Zhang, S.D., Bayesian Calibration for Parameters of JWL Equation of State in Cylinder Test, Explos. Shock Waves, 37(4):585-590, 2017. (in Chinese).

  45. Souers, P.C. and Vitello, P.A., Detonation Energy Densities from the Cylinder Test, Lawrence Livermore National Laboratory, Livermore, CA, Tech. Rep. LLNL-TR-666420, 2015.

  46. Wang, R.L., Liu, Q., and Wen, W.Z., Uncertainty Quantification for JWL EOS Parameters Using Non-Intrusive Polynomial Chaos, Explos. Shock Waves, 35(1):9-15, 2015. (in Chinese).

  47. Liang, X. and Wang, R.L., Sensitivity Analysis and Validation of Detonation Computational Fluid Dynamics Model, Acta Phys. Sinica, 66(11):233-242,2017. (in Chinese).

  48. Saltelli, A., Sensitivity Analysis for Importance Assessment, Risk Anal., 22(3):579-590,2002.

  49. Alam, M., Abedi, V., Bassaganya-Riera, J., Wendelsdorf, K., Bisset, K., Deng, X., Eubank, S., Hontecillas, R., Hoops, S., and Marathe, M., Agent-Based Modeling and High Performance Computing, Chapter 6, in Computational Immunology, New York: Academic Press, pp. 79-111,2016.

  50. Iooss, B. and Lemaitre, P., A Review on Global Sensitivity Analysis Methods, G. Dellino and C. Meloni, Eds., in Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications, Boston: Springer, pp. 101-122, 2015.

  51. O'Connor, T., Yang, X., Tian, G., Chatterjee, S., and Lee, S., Quality Risk Management for Pharmaceutical Manufacturing: The Role of Process Modeling and Simulations, G. Dellino and C. Meloni, Eds., in Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications, Boston: Springer, pp. 101-122, 2017.

  52. Sinclair, A., Convergence Rates for Monte Carlo Experiments, New York: Springer, 1998.

  53. Baker, E.L., Capellos, C., Pincay, J., and Stiel, I., Accuracy and Calibration of High Explosive Thermodynamic Equations of State, J. Energetic Mater., 28:140-153, 2010.

  54. Tripathy, R.K. and Bilionis, I., Deep UQ: Learning Deep Neural Network Surrogate Models for High Dimensional Uncertainty Quantification, J. Comput. Phys., 375:565-588, 2018.

  55. Hastie, T., Tibshirani, R., and Friedman, J.H., The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed., New York: Springer, 2009.

  56. Forrester, A.I.J., Sobester, A., and Keane, A.J., Engineering Design via Surrogate Modelling: A Practical Guide, Hoboken, NJ: John Wiley & Sons, 2008.

  57. Storlie, C.B., Swiler, L.P., Helton, J.C., and Sallaberry, C.J., Implementation and Evaluation of Nonparametric Regression Procedures for Sensitivity Analysis of Computationally Demanding Models, Reliab. Eng. Syst. Saf., 94(11):1735-1763,2009.

  58. Ghanem, R.G. and Spanos, P.D., Stochastic Finite Elements: A Spectral Approach, Mineola, NY: Dover Publications, 2003.

  59. Yan, L. and Zhou, T., Adaptive Multi-Fidelity Polynomial Chaos Approach to Bayesian Inference in Inverse Problems, J. Comput. Phys.,381:110-128,2019.

  60. Yan, L. and Zhou, T., An Adaptive Multi-Fidelity PC-Based Ensemble Kalman Inversion for Inverse Problems, Int. j. Uncertainty Quantif, 9(3):205-220, 2019.

  61. Sacks, J., Welch, W. J., Mitchell, T.J., and Wynn, H.P., Design and Analysis of Computer Experiments, Asta Adv. Stat. Anal, 4(4):409-423, 1989.

  62. Santner, T.J., Williams, B.J., andNotz, W.I., The Design and Analysis of Computer Experiments, New York: Springer, 2003.

  63. Rasmussen, C.E., Gaussian Processes in Machine Learning, Lect. Notes Comput. Sci., 3176:63-71, 2003.

  64. Gunn, S.R., Support Vector Machines for Classification and Regression, Department of Electronics and Computer Science, University of Southampton, Southampton, UK, Tech. Rep. ISIS-1-98, 1998.

  65. Vazquez, E. and Walter, E., Multi-Output Suppport Vector Regression, IFAC Proceedings Volumes, Livermore, CA, USA, pp. 1783-1788,2003.

  66. Clarke, S.M., Griebsch, J., and Simpson, T.W., Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses, J. Mech. Des., 127(6):1077-1087, 2005.

  67. Smola, A.J. and Scholkopf, B., A Tutorial on Support Vector Regression, Stat. Comput., 14(3):199-222,2004.

  68. Hurtado, J.E. and Alvarez, D.A., Neural-Network-Based Reliability Analysis: A Comparative Study, Comput. Methods Appl. Mech. Eng., 191(1):113-132, 2001.

  69. Schueremans, L. and Van Gemert, D., Benefit of Splines and Neural Networks in Simulation based Structural Reliability Analysis, Struct. Safety, 27(3):246-261,2005.

  70. Yan, L. and Zhou, T., An Adaptive Surrogate Modeling based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems, Numer. Anal, arXiv:1911.08926, 2019.

  71. Bhosekar, A. and Ierapetritou, M., Advances in Surrogate based Modeling, Feasibility Analysis, and Optimization: A Review, Comput. Chem. Eng., 108:250-267,2018.

  72. Romick, C.M., Aslam, T.D., and Powers, J.M., Verified and Validated Calculation of Unsteady Dynamics of Viscous Hydrogen-Air Detonations, J. Fluid Mech, 769:154-181,2015.

  73. Doebling, S.W., The Escape of High Explosive Products: An Exact-Solution Problem for Verification of Hydrodynamics Codes, J. Verification, Validation Uncertainty Quantif, 1(4):1-13,2016.

  74. von Neumann, J. and Richtmyer, R.D., A Method for the Numerical Calculation of Hydrodynamic Shocks, j. Appl. Phys., 21(3):232-237,1950.

  75. Hiermaier, S., Predictive Modeling of Dynamic Processes: A Tribute to Professor Klaus Thoma, Berlin: Springer, 2009.

  76. Campbell, J. and Vignjevic, R., Artificial Viscosity Methods for Modelling Shock Wave Propagation, Boston, MA: Springer, pp. 349-365, 2009.

  77. Lindsay, C.M., Butler, G.C., Rumchik, C., Schulze, B., Gustafson, R., and Maines, W.R., Increasing the Utility of the Copper Cylinder Expansion Test, Propel. Explos. Pyrotech., 35(5):433-439, 2010.

  78. Kury, J.W., Dorough, G.D., and Sharples, R.E., Energy Release from Chemical Systems, in 3rd (Int.) Symp. on Detonation, Princeton, NJ, pp. 738-760, 1960.

  79. Kury, J.W., Hornig, H.C., Lee, E.L., McDonnel, J.L., Ornellas, D.L., Finger, M., Strange, F.M., and Wilkins, M.K., Acceleration by Chemical Explosives, in 4th Symp. (Int.) on Detonation, Silverspring, MD, 1965.

  80. Military Standard, U.S., Safety and Performance Tests for Qualification of Explosives (High Explosives, Propellants, and Pyrotechnics), U.S. Department of Defense, Washington, DC, Tech. Rep. MIL-STD-1751, 1982.

  81. Wang, R.L., Lin, Z., Wen, W.Z., Wei, L., and Lin, W.Z., Development and Application of Adaptive Multi-Media Lagrangian Fluid Dynamics Software LAD2D, Comput. Aided Eng., 23(2):1-7, 2014. (in Chinese).

  82. Wang, R.L., Liang, X., and Liu, X.Z., Research on Verification and Validation Strategy of Detonation Fluid Dynamics Code of LAD2D, AIP Conf. Proc., 1863(1):030007, 2017.

  83. Tibshirani, R., Regression Shrinkage and Selection via the Lasso, Series B, J. R. Stat. Soc., 58(1):267-288, 1996.

  84. Wang, H., Li, R., and Tsai, C.L., Tuning Parameter Selectors for the Smoothly Clipped Absolute Deviation Method, Biometrika, 94(3):553-568, 2007.

  85. Fan, J.Q. and Li, R.Z., Variable Selection viaNonconcave Penalized Likelihood and Its Oracle Properties, J. Am. Stat. Assoc., 96(456):1348-1360,2001.

  86. Meinshausen, N. and Buhlmann, P., High-Dimensional Graphs and Variable Selection with the Lasso, Ann. Stat., 34(3):1436-1462, 2006.

  87. Leng, C.L., Yi, L., and Wahba, G., A Note on the Lasso and Related Procedures in Model Selection, Stat. Sinica, 16(4):1273-1284, 2004.

  88. Zou, H., The Adaptive Lasso and Its Oracle Properties, J. Am. Stat. Assoc, 101(476):1418-1429, 2006.

  89. Wang, L.H., Liu, J.Y., Li, Y., and Li, R.Z., Model-Free Conditional Independence Feature Screening for Ultrahigh Dimensional Data, Sci. China-Math, 60(3):551-568, 2017.

  90. Fan, J.Q. and Lv, J.C., Sure Independence Screening for Ultrahigh Dimensional Feature Space, J. R. Stat. Soc. Ser. B, 70(5):849-911,2008.

  91. Coleman, T.F. and Li, Y. Y., An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds, SIAM J. Opt:., 6(2):418-445, 1993.

  92. Coleman, T.F. and Li, Y.Y., On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds, Math. Prog., 67(2):189-224, 1992.


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