Uncertainty Quantification Analysis of Solid Rocket Motor Grain Ignition at Low Temperature Based on Improved PolynomialChaos Expansion

doi:10.3969/j.issn.1000-1093.2020.01.005

Abstract

Abstract: In the process of computing the polynomial chaos expansion (PCE) coefficients based on projection method, an improper PCE order and Gauss point number may lead to overfitting and underfitting problems, which impacts the computing accuracy of PCE surrogate model seriously. An improved PCE method is presented to avoid overfitting and underfitting. In the improved PCE method, the adaptive PCE order P^* is determined, the adaptive uniform grid (N^*)^d is determined to compute the sensitivity indices of each input variable, and then an adaptive non-uniform grid is constructed based on obtained sensitivity indices to compute PCE coefficients. The proposed method is adopted to analyze an example of solid rocket motor ignition at low temperature, in which the effect of material parameter randomness on grain output response are studied and the probability distribution of output response is obtained. A more accurate result can be obtained by the proposed method, and the accuracy and efficiency of the proposed method are verified through comparing with traditional methods. Key

Key words: solidrocketmotorgrain, uncertaintyquantification, improvedPCEmetamodel, globalsensitivityanalysis, non-uniformgrid

CLC Number:

V435⁺.21

LI Yangtian， LI Haibin， WEI Guangmei， WENG Jiexin. Uncertainty Quantification Analysis of Solid Rocket Motor Grain Ignition at Low Temperature Based on Improved PolynomialChaos Expansion[J]. Acta Armamentarii, 2020, 41(1): 40-48.

References

［1］陈小前, 姚雯, 欧阳琦. 飞行器不确定性多学科设计优化理论与应用［M］. 北京:科学出版社, 2013.
CHEN X Q, YAO W, OUYANG Q. Aircraft uncertainty multidisciplinary design optimization theory and application［M］. Beijing:Science Press, 2013.(in Chinese)
［2］何琨, 徐潇源, 严正, 等. 基于稀疏多项式混沌展开的孤岛微电网概率潮流计算［J］. 电力系统自动化, 2019, 43(2): 67-79.
HE K, XU X Y, YAN Z, et al. Island micro power grid based on sparse polynomial chaos expansion probabilistic power flow calculation［J］. Automation of Electric Power Systems, 2019, 43(2): 67-79. (in Chinese)
［3］ NI P H, XIA Y, LI J, et al. Using polynomial chaos expansion for uncertainty and sensitivity analysis of bridge structures［J］. Mechanical Systems and Signal Processing, 2019, 119: 293-311.
［4］ PENG X, LI D H, WU H P, et al. Uncertainty analysis of composite laminated plate with data-driven polynomial chaos expansion method under insufficient input data of uncertain parameters［J］. Composite Structures, 2019, 209: 625-633.
［5］ NGUYEN B T, SAMIMI A, VERGARA S E W, et al. Analysis of electromagnetic wave propagation in variable magnetized plasma via polynomial chaos expansion［J］. IEEE Transactions on Antennas and Propagation, 2019, 67(1): 438-449.
［6］ CHYUAN S W. Nonlinear thermoviscoelastic analysis of solid propellant grains subjected to temperature loading［J］. Finite Elements in Analysis and Design, 2002, 38(7): 613-630.
［7］ CHYUAN S W. Dynamic analysis of solid propellant grains subjected to ignition pressurization loading［J］. Journal of Sound and Vibration, 2003, 268(3): 465-483.
［8］刘中兵, 张兵, 周艳青. 固体发动机低温点火适应性模拟试验技术［J］. 固体火箭技术, 2015, 38(2): 203-207.
LIU Z B, ZHANG B, ZHOU Y Q. Simulation experiment technology for low temperature ignition adaptability of solid rocket motor ［J］. Journal of Solid Rocket Technology, 2015, 38(2): 203-207. (in Chinese)
［9］邓康清, 张路, 庞爱民, 等. 自由装填式固体火箭发动机药柱低温点火结构完整性分析［J］. 固体火箭技术, 2018, 41(4): 428-434.
DENG K Q, ZHANG L, PANG A M, et al. Analysis on structural integrity of a free loading solid propellant grains under ignition loading at low temperature［J］. Journal of Solid Rocket Technology, 2018, 41(4): 428-434.(in Chinese)

［10］刘赟, 王浩, 陶如意, 等. 点火过程对小型固体火箭发动机内弹道影响［J］. 含能材料, 2013, 21(1): 75-79.
LIU Y, WANG H, TAO R Y, et al. Effect of ignition process on interior trajectory of small solid rocket motor［J］. Chinese Journal of Energetic Materials, 2013, 21(1): 75-79.(in Chinese)
［11］张海联, 周建平. 基于粘弹性随机有限元的固体推进剂药柱可靠性分析［J］. 固体火箭技术, 2003, 26(3): 21-24.
ZHANG H L, ZHOU J P. Reliability analysis of solid propellant grain based on viscoelastic stochastic finite element method［J］. Journal of Solid Rocket Technology, 2003, 26(3): 21-24. (in Chinese)
［12］ YAMAN H, ELIK V, DEAGˇU2IRMENCI E. Experimental investigation of the factors affecting the burning rate of solid rocket propellants［J］. Fuel, 2014, 115: 794-803.
［13］ GRIEGO C, YILMAZ N, ATMANLI A. Sensitivity analysis and uncertainty quantification on aluminum particle combustion for an upward burning solid rocket propellant［J］. Fuel, 2019, 237: 1177-1185.
［14］ SURYAWANSHI A, GHOSH D. Reliability based optimization in aeroelastic stability problems using polynomial chaos based metamodels［J］. Structural and Multidisciplinary Optimization, 2016, 53(5): 1069-1080.
［15］ LE MATRE O P, REAGAN M T, NAJM H N, et al. A stochastic projection method for fluid flow: II. Random process［J］. Journal of Computational Physics, 2002, 181(1): 9-44.
［16］ SUDRET B. Global sensitivity analysis using polynomial chaos expansions［J］. Reliability Engineering & System Safety, 2008, 93(7): 964-979.
［17］ AL-BITTAR T, SOUBRA A H. Efficient sparse polynomial chaos expansion methodology for the probabilistic analysis of computationally-expensive deterministic models［J］. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38(12): 1211-1230.
［18］ ABRAMOWITZ M, STEGUN I A, ROMAIN J E. Handbook of mathematical functions, with formulas, graphs, and mathematical tables［J］. Physics Today, 1966, 19(1): 120-121.
［19］ MOLLON G, DIAS D, SOUBRA A H. Probabilistic analysis of pressurized tunnels against face stability using collocation-based stochastic response surface method［J］. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 137(4): 385-397.
［20］ SUDRET B, BERVEILLER M, LEMAIRE M. A stochastic finite element procedure for moment and reliability analysis［J］. European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, 2006, 15(7/8): 825-866.
［21］ GARCIA-CABREJO O, VALOCCHI A. Global sensitivity analysis for multivariate output using polynomial chaos expansion［J］. Reliability Engineering & System Safety, 2014, 126: 25-36.
［22］ SURYAWANSHI A, GHOSH D. Reliability based optimization in aeroelastic stability problems using polynomial chaos based metamodels［J］. Structural and Multidisciplinary Optimization, 2016, 53(5): 1069-1080.
［23］ LEE S H, CHEN W. A comparative study of uncertainty propagation methods for black-box-type problems［J］. Structural and Multidisciplinary Optimization, 2009, 37(3): 239-253.
［24］ LI D Q, CHEN Y F, LU W B, et al. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables［J］. Computers and Geotechnics, 2011, 38(1): 58-68.
［25］ ZHAO H, GAO Z H, GAO Y, et al. Effective robust design of high lift NLF airfoil under multi-parameter uncertainty［J］. Aerospace Science and Technology, 2017, 68: 530-542.
［26］刘中兵, 周艳青, 张兵. 固体发动机低温点火条件下药柱结构完整性分析［J］. 固体火箭技术, 2015, 38(3): 351-355.
LIU Z B, ZHOU Y Q, ZHANG B. Structural integrity analysis on grains of solid rocket motor at low temperature ignition［J］. Journal of Solid Rocket Technology, 2015, 38(3): 351-355. (in Chinese)
［27］宋仕雄, 史宏斌, 刘中兵, 等. 低温状态点火瞬间固体发动机药柱结构响应分析［J］. 固体火箭技术, 2018, 41(3): 278-283.
SONG S X, SHI H B, LIU Z B, et al. Structural analysis of solid rocket motor grain at ignition transient under low temperature［J］. Journal of Solid Rocket Technology, 2018, 41(3): 278-283. (in Chinese)
［28］张书俊. 固体火箭发动机粘弹性药柱的动态可靠度分析［D］. 长沙: 国防科学技术大学, 2006.
ZHANG S J. Structure dynamic reliability analysis of solid rocket motor viscoelasticity grains［D］. Changsha:National University of Defense Technology, 2006. (in Chinese)
［29］高凤莲. 某型固体火箭发动机药柱结构完整性研究［D］. 长沙:国防科学技术大学, 2012.
GAO F L. Research of structural integrity for a certain solid rocket motor grain［D］. Changsha:National University of Defense Technology, 2012. (in Chinese)
［30］蒙上阳, 唐国金, 雷勇军. 材料性能对固体发动机结构完整性的影响［J］. 国防科技大学学报, 2002, 24(5): 10-15.
MENG S Y, TANG G J, LEI Y J. Effects of solid rocket motor material properties on the structure integrity［J］. Journal of National University of Defense Technology, 2002, 24(5): 10-15. (in Chinese)

第41卷第1期
2020 年1月兵工学报ACTA
ARMAMENTARIIVol.41No.1Jan.2020

[1]	LUO Zhongfeng, GUAN Xiaorong, XU Cheng. Global Sensitivity Analysis of a Self-propelled Gun's Structural Parameters for Position and Attitude of Projectile at Muzzle [J]. Acta Armamentarii, 2021, 42(2): 254-267.
[2]	LIANG Xiao, CHEN Jiangtao, WANG Ruili. Uncertainty Quantification of Detonation with High-dimensional Parameter Uncertainty [J]. Acta Armamentarii, 2020, 41(4): 692-701.