基于改进型多项式混沌展开的固体火箭发动机药柱低温点火不确定性量化分析

doi:10.3969/j.issn.1000-1093.2020.01.005

兵工学报 ›› 2020, Vol. 41 ›› Issue (1): 40-48.doi: 10.3969/j.issn.1000-1093.2020.01.005

基于改进型多项式混沌展开的固体火箭发动机药柱低温点火不确定性量化分析

李阳天^1，2，李海滨²，韦广梅²，翁洁鑫³

（1.内蒙古财经大学统计与数学学院，内蒙古呼和浩特 010070； 2.内蒙古工业大学理学院，内蒙古呼和浩特 010051； 3.内蒙古动力机械研究所，内蒙古呼和浩特 010010）

收稿日期:2019-04-08 修回日期:2019-04-08 上线日期:2020-02-22
作者简介:李阳天(1988—), 男, 博士研究生。E-mail: 2200173641@qq.com
基金资助:
国家自然科学基金项目（11962021、11262014）

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

LI Yangtian^1,2， LI Haibin²， WEI Guangmei²， WENG Jiexin³

(1.College of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, Inner Mongolia, China; 2.College of Science, Inner Mongolia University of Technology, Hohhot 010051, Inner Mongolia, China; 3.Inner Mongolia Dynamical Machine Academy, Hohhot 010010, Inner Mongolia, China)

Received:2019-04-08 Revised:2019-04-08 Online:2020-02-22

摘要/Abstract

摘要： 基于映射法求解多项式混沌展开(PCE)系数过程中，不恰当的PCE阶数与高斯节点数会引起过拟合与欠拟合现象，严重影响PCE代理模型的计算精度。为避免过拟合与欠拟合现象，提出了改进型PCE方法。确定自适应PCE阶数P^*和自适应均匀网格(N^*)^d，并通过P^*和(N^*)^d计算各输入变量的灵敏度指数；基于所得灵敏度指数建立自适应非均匀网格，求解PCE系数。采用所提方法对固体火箭发动机药柱低温点火算例进行分析，研究材料参数随机性对药柱输出响应的影响，获得输出响应的概率分布。研究结果表明，与传统方法对比，所提方法能够得到更加精确的不确定性量化分析结果，验证了所提方法的准确性与高效性。

关键词: 固体火箭发动机药柱, 不确定性量化, 改进型PCE模型, 全局灵敏度分析, 非均匀网格

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

中图分类号:

V435⁺.21

李阳天，李海滨，韦广梅，翁洁鑫. 基于改进型多项式混沌展开的固体火箭发动机药柱低温点火不确定性量化分析[J]. 兵工学报, 2020, 41(1): 40-48.

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.

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

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基于改进型多项式混沌展开的固体火箭发动机药柱低温点火不确定性量化分析

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

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