Uncertainty quantification of cylindrical test through Wiener chaos with basis adaptation and projection

LIANG Xiao; WANG Ruili

doi:10.11883/bzycj-2018-0253

Volume 39 Issue 4

Mar. 2019

Turn off MathJax

Article Contents

Article Navigation > Explosion And Shock Waves > 2019 > 39(4): 041408

LIANG Xiao, WANG Ruili. Uncertainty quantification of cylindrical test through Wiener chaos with basis adaptation and projection[J]. Explosion And Shock Waves, 2019, 39(4): 041408. doi: 10.11883/bzycj-2018-0253

Citation:

LIANG Xiao, WANG Ruili. Uncertainty quantification of cylindrical test through Wiener chaos with basis adaptation and projection[J]. Explosion And Shock Waves, 2019, 39(4): 041408. doi: 10.11883/bzycj-2018-0253

Citation:

PDF( 1051 KB)

Uncertainty quantification of cylindrical test through Wiener chaos with basis adaptation and projection

doi: 10.11883/bzycj-2018-0253

LIANG Xiao^{1, 2
,},
WANG Ruili^{2
,
,}

1.
Department of Mathematics, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
2.
Institute of Applied Physics and Computational Mathematics, Beijing 100089, China

Received Date: 2018-07-10
Rev Recd Date: 2018-10-01

Available Online: 2019-04-25

Publish Date: 2019-04-01

Abstract

Abstract

The mathematical-physical model used to describe the detonation dynamics has many uncertain factors due to the complexity and lack of knowledge for detonation phenomenon. Quantifying and assessing the impact of input uncertainties on output of detonation systems has a direct influence on reducing the risk based on the numerical model and simulation results for detonation. The Wiener chaos based on adapted basis is used to deal with the uncertainty quantification of high-dimensional random variables for detonation simulation. The rotation transformation and projection method is used to reduce the length of truncation number. Rosenblatt transformation is used to transform the set of dependent random variables into independent random variables. The equality of probability principle is used to change the non-Gaussian random variables into standard random variables. Uncertainty quantifications of the cylinder test with high dimensional input uncertainties are studied. The statistical informations such as mean, standard deviations, and confidence intervals are presented. The simulation results coincide with the experimental data, and the accuracy of the model is validated.
- cylinder test,
- uncertainty quantification,
- adapted basis,
- JWL EOS,
- Rosenblatt transform

FullText(HTML)

References(16)

References

[1]	章冠人, 陈大年. 凝聚炸药起爆动力学[M]. 北京: 国防工业出版社, 1991.
[2]	孙锦山. 凝聚炸药非理想爆轰的数值模拟 [J]. 力学进展, 1995, 25(1): 127–133. DOI: 10.6052/1000-0992-1995-1-J1995-043 SUN Jinshan. Numerical modeling of non-ideal detonation in condensed explosives [J]. Advances in Mechanics, 1995, 25(1): 127–133. DOI: 10.6052/1000-0992-1995-1-J1995-043
[3]	王瑞利, 江松. 多物理耦合非线性偏微分方程与数值解不 [J]. 中国科学: 数学, 2015, 45(6): 723–738. DOI: 10.1360/N012014-00115 WANG Ruili, JIANG Song. Mathematical methods for uncertainty quantification in nonlinear multi-physics systems and their numerical simulations [J]. Scientia Sinica: Mathematica, 2015, 45(6): 723–738. DOI: 10.1360/N012014-00115
[4]	王成, SHU Chiwang. 爆炸力学高精度数值模拟研究进展 [J]. 科学通报, 2015, 60(10): 882–898. DOI: 10.1360/N972014-00936 WANG Cheng, SHU Chiwang. Progresses in high-resolution numerical simulation of explosion mechanics [J]. Chinese Science Bulletin, 2015, 60(10): 882–898. DOI: 10.1360/N972014-00936
[5]	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 Xiao, WANG Ruili. Sensitivity analysis and validation of detonation computational fluid dynamics model [J]. Acta Physica Sinica, 2017, 66(11): 116401. DOI: 10.7498/aps.66.116401
[6]	梁霄, 王瑞利. 混合不确定度量化方法及其在计算流体动力学迎风格式中的应用 [J]. 爆炸与冲击, 2016, 36(4): 505–519. DOI: 10.11883/1001-1455(2016)04-0509-07 LIANG Xiao, WANG Ruili. Mixed uncertainty quantification and its application in upwind scheme for computational fluid mechanics [J]. Explosion and Shock Waves, 2016, 36(4): 505–519. DOI: 10.11883/1001-1455(2016)04-0509-07
[7]	汤涛, 周涛. 不确定性量化的高精度数值方法和理论 [J]. 中国科学: 数学, 2015, 45(7): 891–928. DOI: 10.1360/N012014-00218 TANG Tao, ZHOU Tao. Recent developments in high order numerical methods for uncertainty quantification [J]. Scientia Sinica Mathematica, 2015, 45(7): 891–928. DOI: 10.1360/N012014-00218
[8]	GHANEM R, SPANOS R. Stochastic finite elements: A spectral approach[M]. New York: Springer, 1991.
[9]	梁霄, 王瑞利. 爆炸波中的混合不确定度量化方法 [J]. 计算物理, 2017, 34(5): 574–582. DOI: 1001-246X(2017)05-0574-09 LIANG Xiao, WANG Ruili. Mixed uncertainty quantification of blast wave problem [J]. Chinese Journal of Computational Physics, 2017, 34(5): 574–582. DOI: 1001-246X(2017)05-0574-09
[10]	HUAN X, GERACI G, SAFTA C, et al. Multifidelity statistical analysis of large eddy simulation in Scramjet computations[C]//AIAA non-deterministic Approaches Conference. 2018: 1−11. DOI: 10.2514/6.2017-1089.
[11]	HUAN X, SAFTA C, SARGSYAN K, et al. Compressive sensing with cross-validation and stop-sampling for sparse polynomial chaos expansions [J]. SIAM/ASA Journal on Uncertainty Quantification, 2018, 6(2): 907–936. DOI: 10.1137/17M1141096.
[12]	王瑞利, 林忠, 魏兰, 等. 利用前沿推进法计算复杂炸药结构的起爆时间 [J]. 高压物理学报, 2015, 29(4): 286–292. DOI: 10.11858/gywlxb.2015.04.008 WANG Ruili, LIN Zhong, WEI Lan, et al. Calculating the initiation time of the explosive with complex structure using the advancing front technique [J]. Chinese Journal of High Pressure Physics, 2015, 29(4): 286–292. DOI: 10.11858/gywlxb.2015.04.008
[13]	TIPIREDDY R, GHANEM R. Basis adaptation in homogeneous chaos spaces [J]. Journal of Computational Physics, 2014, 259(3): 304–317. DOI: 10.1016/j.jcp.2013.12.009.
[14]	TSILIFIS P, GHANEM R. Reduced Wiener chaos representation of random fields via basis adaptation and projection [J]. Journal of Computational Physics, 2017, 341: 102–120. DOI: 10.1016/j.jcp.2017.04.009.
[15]	CAMERON R, MARTIN W. The orthogonal development of nonlinear functional in series of Fourier-Hermite functional [J]. Annals Mathematics, 1947, 48(2): 385–392. DOI: 10.2307/1969178.
[16]	ROSENBLATT M. Remarks on a multivariate transformation [J]. Annals of Mathematical Statistics, 1952, 23: 470–472. DOI: 10.1007/978-l-4419-8339-8_8.