Uncertainty quantification of shock to detonation experiment of PBX 9502 based on probability learning on manifold

LIANG Xiao; ZHAO Yanfei; WANG Ruili

doi:10.11883/bzycj-2025-0042

Article Contents

Article Navigation > Explosion And Shock Waves > 2026 > Accepted Manuscript

LIANG Xiao, ZHAO Yanfei, WANG Ruili. Uncertainty quantification of shock to detonation experiment of PBX 9502 based on probability learning on manifold[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0042

Citation:

LIANG Xiao, ZHAO Yanfei, WANG Ruili. Uncertainty quantification of shock to detonation experiment of PBX 9502 based on probability learning on manifold[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0042

Citation:

PDF( 1095 KB)

Uncertainty quantification of shock to detonation experiment of PBX 9502 based on probability learning on manifold

doi: 10.11883/bzycj-2025-0042

1.
School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
2.
Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450052, Henan, China
3.
Beijing Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received Date: 2025-02-14
Rev Recd Date: 2025-04-01

Available Online: 2025-04-08

Abstract

Abstract

To address the challenges posed by insufficient statistical sampling density and inherent irreducible uncertainties in multi-physical property detonation experiments, probability learning on manifold (PLoM) involving diffusion map and Itô projection sampling are used to generate sufficient dataset satisfying the detonation physical mechanism and therefore, to fulfill the uncertainty quantification of experiment. Firstly, scale transformation is implemented on the experimental data with multi-physical asset of insensitive high explosive PBX 9502. The training set is obtained through the normalization of the scale matrix by means of principal component analysis. Secondly, an improved high-dimensional Gaussian kernel density estimation is utilized to calibrate the probability measure of the random matrix associated with the training dataset. Diffusion map is used to deduce the nonlinear manifold based on the training dataset. Sampling on the manifold is fulfilled through Itô-MCMC generator defined by a dissipative Hamilton system driven by the Wiener process. Finally, the learning set is obtained via inverse transformation. The result shows that the Gaussian statistics obtained from random numbers generated by PLoM coincide with the statistical information of density of PBX 9502 calibrated in the literature. Furthermore, the double logarithm model related to the distance to detonation and initial impact stress is constructed through the data generated. It also holds for the relationship between the time of detonation and initial shock stress. Fitting precision of the curve is almost equivalent to the accuracy of result in literature, however the cost is negligible. More accurate digital test result is obtained through the learning and processing of existing experimental data via PLoM. The PLoM method demonstrates strong generalization capability, enabling its extension to detonation experiments with various types of explosive.
- probability learning on manifold,
- uncertainty quantification,
- small sample size,
- detonation,
- experimental uncertainty

FullText(HTML)

References(26)

References

[1]	孙承纬, 卫玉章, 周之奎. 应用爆轰物理 [M]. 北京: 国防工业出版社, 2000. SUN C W, WEI Y Z, ZHOU Z K. Applied detonation physics [M]. Beijing: National Defense Industry Press, 2000.
[2]	FICKETT W, DAVIS W C. Detonation: theory and experiment [M]. New York: Dover Publication, 2011.
[3]	LIANG X, WANG R, GHANEM R. Uncertainty quantification of detonation through adapted polynomial chaos [J]. International Journal for Uncertainty Quantification, 2020, 10(1): 83–100. DOI: 10.1615/Int.J.UncertaintyQuantification.2020030630.
[4]	梁霄, 王瑞利. 基于冲击Hugoniot关系的爆压性质和不确定度量化 [J]. 兵工学报, 2024, 45(5): 1673–1680. DOI: 10.12382/bgxb.2022.1207. LIANG X, WANG R L. Property and uncertainty quantification of detonation pressure based on shock Hugoniot relationship [J]. Acta Armamentarii, 2024, 45(5): 1673–1680. DOI: 10.12382/bgxb.2022.1207.
[5]	LIANG X, WANG R L. Verification and validation of detonation modeling [J]. Defence Technology, 2019, 15(3): 398–408. DOI: 10.1016/j.dt.2018.11.005.
[6]	梁霄, 王瑞利. 爆轰流体力学模型敏感度分析与模型确认 [J]. 物理学报, 2017, 66(11): 116401. DOI: 10.7498/aps.66.116401. LIANG X, WANG R L. Sensitivity analysis and validation of detonation computational fluid dynamics model [J]. Acta Physica Sinica, 2017, 66(11): 116401. DOI: 10.7498/aps.66.116401.
[7]	WESCOTT B L, STEWART D S, DAVIS W C. Equation of state and reaction rate for condensed-phase explosives [J]. Journal of Applied Physics, 2005, 98(5): 053514. DOI: 10.1063/1.2035310.
[8]	CAMPBELL A W. Diameter effect and failure diameter of a TATB-based explosive [J]. Propellants, Explosives, Pyrotechnics, 1984, 9(6): 183–187. DOI: 10.1002/prep.19840090602.
[9]	PETERSON P D, IDAR D J. Microstructural differences between virgin and recycled lots of PBX 9502 [J]. Propellants, Explosives, Pyrotechnics, 2005, 30(2): 88–94. DOI: 10.1002/prep.200400088.
[10]	HANDLEY C A, LAMBOURN B D, WHITWORTH N J, et al. Understanding the shock and detonation response of high explosives at the continuum and meso scales [J]. Applied Physics Reviews, 2018, 5(1): 011303. DOI: 10.1063/1.5005997.
[11]	GUSTAVSEN R L, SHEFFIELD S A, ALCON R R. Measurements of shock initiation in the tri-amino-tri-nitro-benzene based explosive PBX 9502: wave forms from embedded gauges and comparison of four different material lots [J]. Journal of Applied Physics, 2006, 99(11): 114907. DOI: 10.1063/1.2195191.
[12]	PARK C, NILI S, MATHEW J T, et al. Uncertainty reduction for model error detection in multiphase shock tube simulation [J]. Journal of Verification, Validation and Uncertainty Quantification, 2021, 6(3): 031004. DOI: 10.1115/1.4051407.
[13]	LINDQUIST B A, JADRICH R B, RIVERA J E H, et al. Uncertainty quantification for high explosive reactant and product equations of state [J]. Journal of Applied Physics, 2023, 134(7): 075102. DOI: 10.1063/5.0157842.
[14]	ANDREWS S A, LEIDING J A, THRUSSELL J, et al. Calibration and uncertainty quantification for Davis Equation of State Models for the High Explosive PBX 9501 products [J]. Propellants, Explosives, Pyrotechnics, 2024, 49(2): e202300110. DOI: 10.1002/prep.202300110.
[15]	NELMS M, SCHILL W, WILLIAM KUO I F, et al. Uncertainty quantification of material parameters in modeling coupled metal and high explosive experiments [J]. Journal of Applied Physics, 2024, 136(19): 195101. DOI: 10.1063/5.0226642.
[16]	ANDREWS S A, FRASER A M. Estimating physics models and quantifying their uncertainty using optimization with a Bayesian objective function [J]. Journal of Verification, Validation and Uncertainty Quantification, 2019, 4(1): 011002. DOI: 10.1115/1.4043807.
[17]	GARNO J, OUELLET F, BAE S, et al. Calibration of reactive burn and Jones-Wilkins-Lee parameters for simulations of a detonation-driven flow experiment with uncertainty quantification [J]. Physical Review Fluids, 2020, 5(12): 123201. DOI: 10.1103/physrevfluids.5.123201.
[18]	戴诚达, 王翔, 谭华. Hugoniot实验的粒子速度测量不确定度分析 [J]. 高压物理学报, 2005, 19(2): 113–119. DOI: 10.11858/gywlxb.2005.02.003. DAI C D, WANG X, TAN H. Evaluation for uncertainty of particle velocity in Hugoniot measurements [J]. Chinese Journal of High Pressure Physics, 2005, 19(2): 113–119. DOI: 10.11858/gywlxb.2005.02.003.
[19]	刘俊明, 张旭, 裴红波, 等. JB-9014钝感炸药冲击Hugoniot关系测量 [J]. 高压物理学报, 2018, 32(3): 033202. DOI: 10.11858/gywlxb.20170669. LIU J M, ZHANG X, PEI H B, et al. Measurement of Hugoniot relation for JB-9014 insensitive explosive [J]. Chinese Journal of High Pressure Physics, 2018, 32(3): 033202. DOI: 10.11858/gywlxb.20170669.
[20]	SOIZE C, GHANEM R. Data-driven probability concentration and sampling on manifold [J]. Journal of Computational Physics, 2016, 321: 242–258. DOI: 10.1016/j.jcp.2016.05.044.
[21]	GHANEM R G, SOIZE C, SAFTA C, et al. Design optimization of a scramjet under uncertainty using probabilistic learning on manifolds [J]. Journal of Computational Physics, 2019, 399: 108930. DOI: 10.1016/j.jcp.2019.108930.
[22]	CAPIEZ-LERNOUT E, EZVAN O, SOIZE C. Updating nonlinear stochastic dynamics of an uncertain nozzle model using probabilistic learning with partial observability and incomplete dataset [J]. Journal of Computing and Information Science in Engineering, 2024, 24(6): 061006. DOI: 10.1115/1.4065312.
[23]	NESPOULOUS J, PERRIN G, FUNFSCHILLING C, et al. Measurements-based constrained control optimization in presence of uncertainties with application to the driver commands for high-speed trains [J]. Physica D: Nonlinear Phenomena, 2024, 457: 133977. DOI: 10.1016/j.physd.2023.133977.
[24]	CAPIEZ-LERNOUT E, SOIZE C. Nonlinear stochastic dynamics of detuned bladed-disks with uncertain mistuning and detuning optimization using a probabilistic machine learning tool [J]. International Journal of Non-Linear Mechanics, 2022, 143: 104023. DOI: 10.1016/j.ijnonlinmec.2022.104023.
[25]	DALLMAN J C, WACKERLE J. Temperature-dependent shock initiation of TATB-based high explosives [C]//Tenth International Detonation Symposium. Arlington, VA, 1993.
[26]	DICK J J, FOREST C A, RAMSAY J B, et al. The Hugoniot and shock sensitivity of a plastic-bonded TATB explosive PBX 9502 [J]. Journal of Applied Physics, 1988, 63(10): 4881–4888. DOI: 10.1063/1.340428.