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Detonation test suffers small experimental datasets due to high risk of implementation and substantial cost of samples production and measurement. The major challenges of limited data consist in constructing the probability distribution of physical quantities and application of machine learning. Probability learning on manifold (PLoM) can generate a large number of realizations reconcilable with practical common sense, and the underlying physical mechanism is preserved in these samples generated. So PLoM is viewed as an efficient tool of tackling small samples. To begin with, experimental data is assumed to be concentrated on an unknown subset of Euclidean space and can be treated as the sampling of random vector to be determined. Meanwhile, experimental is solved in the framework of matrix and the scaling transformation is conducted on the datasets of PBX9502 with multi-physics attributes. Then the principal component analysis is utilized to normalize the scaling matrix, and the normalization matrix is labeled as training sets. Moreover, the altered multi-dimensional Gaussian kernel density estimation is utilized for estimating the probability distribution of training set. Furthermore, diffusion map is used to discover and characterize the geometry and structure of dataset. In other words, nonlinear manifold based on the training set is constructed trough diffusion map. To specifically, the first eigenvalue and corresponding eigenvector is related to the construction of diffusion basis and diffusion maps. To make it further, Itô-MCMC sampler is associated with dissipative Hamilton systems driven by Wiener process, for which the initial condition is set to be training set and prior probability is conceived as invariant measure. Störmer-Verlet scheme is used for solving the stochastic dissipative Hamilton equations. At last, additional realizations of learning dataset are fulfilled through the inversion transformation. The result shows that random number generated from PLoM satisfies the requirement of industrial and high fidelity simulation. The 95% confidence interval of density is included in the range calibrated by Los Alamos National Laboratory. And value of detonation velocity calibrated by Prof. Chengwei Sun also falls into 95% confidence interval of detonation velocity generated by PLoM. It is also deduced from the learning set that density and detonation velocity satisfies the affine transformation. Furthermore, detonation pressure has nonlinear relationship with density. Tiny variation of density can lead to magnificent fluctuation of detonation pressure and detonation velocity. Detonation pressure has the largest discreetness among all the physical quantities through the comparison of variation coefficients of learning set, which coincides with the assertion of experts such as Prof. Chengwei Sun. The methodology used is sufficiently general and can be extended to other detonation systems.
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Keywords:
- Probabilistic learning on manifold /
- diffusion map /
- stochastic dissipative Hamilton equations /
- small datasets /
- detonation /
- uncertainty quantification
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[1] Sun C W, Wei Y Z, Zhou Z K 2000Applied detonation physics(Beijing:National Defense Industry Press)[孙承纬,卫玉章,周之奎2000应用爆轰物理(北京:国防工业出版社)]
[2] Mader C 1979Numerical Modeling of Detonations(Berkeley:University of California)
[3] Liang X, Wang R L, Hu Z X, Chen J T 2023Explos. Shock. Waves. 43 71(In Chinese)[梁霄,王瑞利,胡星志,陈江涛2023爆炸与冲击43 71]
[4] Liang X, Wang R L 2024Acta. Arma. 45 1673(In Chinese)[梁霄,王瑞利2024兵工学报45 1673]
[5] Liang X, Wang R L 2020Int. J. Uncertainty. Quantif. 10 83
[6] Bratton R N, Avramova M, Ivanov K 2014 Nucl. Eng. Technol. 46313
[7] Sandia National Laboratory 2016Direct electron-beam-injection experiments for validation of air-chemistry models
[8] Los Alamos National Laboratory 2022Advanced simulation and computing (ASC) principal investigators Meeting, Los Alamos, New Mexico.
[9] Hu Z H, Ye T, Liu X G, Wang J 2017Acta. Phys. Sin. 66 012801(In Chinese)[胡泽华,叶涛,刘雄国,王佳2017 , 66 012801]
[10] AIAA 1998Guide for the verification and validation of computational fluid dynamics simulations
[11] Air Force Research Laboratory 2013Strategy Report, Ohio
[12] Hu X Z, Duan Y H, Wang R L, Liang X, Chen J T 2019J. Verif. Valid. Uncert. 4 021006.
[13] Zhang S Q, Yang H T 2023Acta. Phys. Sin. 72 110303(In Chinese)[张诗琪,杨化通2023 72110303]
[14] Wishart J, Como S, Forgione U, Weast J, Weston L, Smart A, Nicols G, Ramesh S 2020SAE. Int. J. CAV 3 267
[15] Department of Energy 2005Holistic, hierarchical VVUQ as the scientific method for PSAAP
[16] Department of Defense 2019Modeling and simulation (M&S) verification, validation, and accreditation (VV&A), recommended practices guide (RPG):Introduction
[17] Dahm W 2010Technology horizons a vision for Air Force Science& Technology During 2010-2030, USAF HQ
[18] Balci O 1994Ann. Oper. Res 53 121
[19] Metzger E J, Barton N P, Smedstad O M, Ruston B C, Wallcraft A J, Whitcomb T R, Ridout J A, Franklin D S, Zamudio L, Posey P G, Reynolds C A, Phelps M 2016Verification and validation of a Navy ESPC hindcast with loosely coupled data assimilation, American Geophysical Union
[20] American Society of Mechanical Engineers 2022Verification, validation, and uncertainty quantification terminology in computational modeling and simulation
[21] Oberkampf W, Roy C 2010Verification and Validation in Scientific Computing(Cambridge:Cambridge University Press)
[22] Liang X, Wang R L 2019Def. Technol. 15 398
[23] Wang Y J, Zhang S D, Li H, Zhou H B 2016Acta. Phys. Sin. 65106401[王言金,张树道,李华,周海兵2016 , 65 106401]
[24] Park C, Nili S, Mathew J T, Ouellet F, Koneru R, Kim N, Balachandar S, Haftka R 2021 J. Verif. Valid. Uncert 6119007
[25] Liang X, Wang R L 2017 Acta. Phys. Sin. 6616401[梁霄,王瑞利2017 , 66 116401]
[26] Soize C, Ghanem R 2016J. Comput. Phys 321 242
[27] Ghanem R, Soize C, Safta C, Huan X, Lacaze G, Oefelein J C, Najm H N 2019J. Comput. Phys 399 108930
[28] Capiez-Lernout E, Ezvan O, Soize C 2024J. Comput. Inf. Sci. Eng. 24 061006
[29] Nespoulous J, Perrin G, Funfschilling C, Soize C 2024Phy. D. 457 133977
[30] Capiez-Lernout E, Soize C 2022Int. J. Non. Linear. Mech. 143104023
[31] Metropolis N, Ulam S 1949J. Am. Stat. Assoc. 44335
[32] Hastings W 1970Biometrika. 10957
[33] Geman S, Geman D 1984IEEE Trans. Pattern. Anal. Mach. Intell. 6 721
[34] Campbell A 1984Pyrotechnics. 9 183
[35] Peterson P, Idar D 2005 Propell. Explos. Pyrot. 30 88
[36] Davis W, Joints L 2002Cracks 200212th International Symposium Detonation, San Diego, 2002
[37] Handley C, Lambourn B, Whitworth N, James H, Belfield W 2018 Appl. Phys. Rev. 5 011303
[38] Coifman R, Lafon S, Lee A, Maggioni M, Nadler B, Warner F 2005Proc. Natl. Acad. Sci. USA. 1027426
[39] Hairer E, Lubich C, Wanner G 2002Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations(Heidelberg:Springer-Verlag)
[40] Soize C 2008Int. J. Numer. Methods Eng. 76 1583
[41] Shannon C 1948Bell. Syst. Tech. J. 27623
[42] Gustavsen R, Sheffield S, Alcon R 2006J. Appl. Phys. 99 114907
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