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Uncertainty quantification of shock to detonation experiment of PBX9502 based on probability learning on manifold
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Xiao LIANG1, Yanfei ZHAO1, Ruili WANG2, 3
Explosion and Shock Waves | 2026, 46(9) : 094102-1 - 094102-10
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Explosion and Shock Waves | 2026, 46(9): 094102-1-094102-10
• Experimental Techniques & Numerical Methods •
Uncertainty quantification of shock to detonation experiment of PBX9502 based on probability learning on manifold
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Xiao LIANG1, Yanfei ZHAO1, Ruili WANG2, 3
Affiliations
  • 1School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
  • 2Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450052, Henan, China
  • 3Beijing Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
Published: 2026-09-05 doi: 10.11883/bzycj-2025-0042
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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 PBX9502. 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 PBX9502 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
梁霄, 赵延菲, 王瑞利. 基于流形上概率学习的PBX9502冲击起爆试验不确定度量化. 爆炸与冲击, 2026 , 46 (9) : 094102-1 -094102-10 . DOI: 10.11883/bzycj-2025-0042
Xiao LIANG, Yanfei ZHAO, Ruili WANG. Uncertainty quantification of shock to detonation experiment of PBX9502 based on probability learning on manifold[J]. Explosion and Shock Waves, 2026 , 46 (9) : 094102-1 -094102-10 . DOI: 10.11883/bzycj-2025-0042
Year 2026 volume 46 Issue 9
118
58
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Article Info
doi: 10.11883/bzycj-2025-0042
  • Receive Date:2025-02-14
  • Online Date:2026-10-10
  • Published:2026-09-05
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  • Received:2025-02-14
  • Revised:2025-04-01
Affiliations
    1School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
    2Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450052, Henan, China
    3Beijing Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
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表12种不同金属材料的力学参数
科
Family
属数
Number of
genus
种数
Number of
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Genus
种数
Number of
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Percentage of total
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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