概率盒全局灵敏度和活跃子空间跨层降维

doi:10.7527/S1000-6893.2020.24582

Abstract

Abstract: Uncertainties in aerospace simulation systems are usually multi-sourced and mixed, with a high dimension of system parameters. To address the problem of mixed uncertainty quantification of high-dimension parameters, a cross-layer dimension reduction method combining the global sensitivity analysis of the probability box and the active subspace method is proposed. Based on the probability box characterization for aleatory and epistemic uncertainties, the pinching method is used to analyze the global sensitivity of parameters for parameter selection. The active subspace method is adopted for dimension reduction according to the eigen-decomposition of the output gradient covariance matrix. A cross-layer method based on the parameter selection and dimension reduction with the probability box analysis is then constructed. Finally, the NASA multidisciplinary uncertainty quantification challenge problem is taken as an example. The first-level parameter selection is performed through the global sensitivity analysis of the probability box, and the dimension of the input parameters is reduced from the original 21 to 13. Then the active subspace method is used for the second-level dimension reduction, with the dimension of parameters further reduced to one. The results demonstrate that the proposed method can perform sensitivity ranking for parameters with mixed uncertainties and effectively reduce the dimension of the model input parameters, laying a foundation for further mixed uncertainty quantification and optimization of high-dimension systems.

Key words: probability box, global sensitivity, pinching method, active subspace, dimension reduction, cross-layer

CLC Number:

V215

HU Zhengwen, ZHANG Baoqiang, DENG Zhenhong. Cross-layer dimension reduction based on probability box global sensitivity analysis and active subspace method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(9): 224582-224582.

References

[1] YAO W, CHEN X Q, LUO W C, et al. Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles[J]. Progress in Aerospace Sciences, 2011, 47(6):450-479.
[2] ZANG T, HEMSCH M, HILBURGER M, et al. Needs and opportunities for uncertainty-based multidisciplinary design methods for aerospace vehicles:NASA/TM-2002-211462[R]. Washington, D.C.:NASA, 2002.
[3] 徐明, 李建波, 彭名华, 等. 基于不确定性的旋翼转速优化直升机参数设计[J]. 航空学报, 2016, 37(7):2170-2179. XU M, LI J B, PENG M H, et al. Parameter design of helicopter with optimum speed rotor based on uncertainty optimization[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(7):2170-2179(in Chinese).
[4] NANNAPANENI S, MAHADEVAN S. Probability-space surrogate modeling for fast multidisciplinary optimization under uncertainty[J]. Reliability Engineering & System Safety, 2020, 198:106896.
[5] HORA S C. Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management[J]. Reliability Engineering & System Safety, 1996, 54(2-3):217-223.
[6] SRIVASTAVA A, SUBRAMANIYAN A K, WANG L P. Hybrid Bayesian solution to NASA langley research center multidisciplinary uncertainty quantification challenge[J]. Journal of Aerospace Information Systems, 2014, 12(1):114-139.
[7] NAGEL J B, SUDRET B. A unified framework for multilevel uncertainty quantification in Bayesian inverse problems[J]. Probabilistic Engineering Mechanics, 2016, 43:68-84.
[8] SONG J W, WEI P F, VALDEBENITO M, et al. Generalization of non-intrusive imprecise stochastic simulation for mixed uncertain variables[J]. Mechanical Systems and Signal Processing, 2019, 134:106316.
[9] WILLIAMSON R C, DOWNS T. Probabilistic arithmetic.I.Numerical methods for calculating convolutions and dependency bounds[J]. International Journal of Approximate Reasoning, 1990, 4(2):89-158.
[10] SIMON C, BICKING F. Hybrid computation of uncertainty in reliability analysis with p-box and evidential networks[J]. Reliability Engineering & System Safety, 2017, 167:629-638.
[11] KARANKI D R, KUSHWAHA H S, VERMA A K, et al. Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment[J]. Risk Analysis, 2009, 29(5):662-675.
[12] SUN S A, FU G T, DJORDJEVIĆ S, et al. Separating aleatory and epistemic uncertainties:Probabilistic sewer flooding evaluation using probability box[J]. Journal of Hydrology, 2012, 420-421:360-372.
[13] 黄心, 王清心, 丁家满. 基于概率盒理论的电网规划方案中指标不确定性建模[J]. 信息与控制, 2016, 45(3):272-277. HUANG X, WANG Q X, DING J M. Index uncertainty modeling in grid planning based on probability box theory[J]. Information and Control, 2016, 45(3):272-277(in Chinese).
[14] BENNER P, SORENSEN D C, MEHRMANN V. Dimension reduction of large-scale systems[M]. Berlin, Heidelberg:Springer, 2005.
[15] LI L, WAN H, GAO W J, et al. Reliability based multidisciplinary design optimization of cooling turbine blade considering uncertainty data statistics[J]. Structural and Multidisciplinary Optimization, 2019, 59(2):659-673.
[16] CHU J, ZHANG C, FU G, et al. Improving multi-objective reservoir operation optimization with sensitivity-informed dimension reduction[J]. Hydrology and Earth System Sciences, 2015, 19(8):3557-3570.
[17] CARREIRA-PERPINÀN M A. A review of dimension reduction techniques:CS-96-09[R]. Sheffield:University of Sheffield, 1997.
[18] BRIGGS A, SCULPHER M, BUXTON M. Uncertainty in the economic evaluation of health care technologies:The role of sensitivity analysis[J]. Health Economics, 1994, 3(2):95-104.
[19] 邬晓敬, 张伟伟, 宋述芳, 等. 翼型跨声速气动特性的不确定性及全局灵敏度分析[J]. 力学学报, 2015, 47(4):587-595. WU X J, ZHANG W W, SONG S F, et al. Uncertainty quantification and global sensitivity analysis of transonic aerodynamics about airfoil[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4):587-595(in Chinese).
[20] 冯凯旋, 吕震宙, 蒋献. 基于偏导数的全局灵敏度指标的高效求解方法[J]. 航空学报, 2018, 39(3):221699. FENG K X, LYU Z Z, JIANG X. Efficient algorithm for estimating derivative-based global sensitivity index[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(3):221699(in Chinese).
[21] BORGONOVO E, PLISCHKE E. Sensitivity analysis:A review of recent advances[J]. European Journal of Operational Research, 2016, 248(3):869-887.
[22] ZHOU C C, ZHANG Z, LIU F C, et al. Sensitivity analysis for probabilistic anti-resonance design of aeronautical hydraulic pipelines[J]. Chinese Journal of Aeronautics, 2019, 32(4):948-953.
[23] LIANG C, MAHADEVAN S. Bayesian sensitivity analysis and uncertainty integration for robust optimization[J]. Journal of Aerospace Information Systems,2014, 12(1):189-203.
[24] OBERGUGGENBERGER M, KING J, SCHMELZER B. Classical and imprecise probability methods for sensitivity analysis in engineering:A case study[J]. International Journal of Approximate Reasoning, 2009, 50(4):680-693.
[25] FERSON S, TROY TUCKER W. Sensitivity analysis using probability bounding[J]. Reliability Engineering & System Safety, 2006, 91(10-11):1435-1442.
[26] SONG J W, LU Z Z, WEI P F, et al. Global sensitivity analysis for model with random inputs characterized by probability-box[J]. Proceedings of the Institution of Mechanical Engineers, Part O:Journal of Risk and Reliability, 2015, 229(3):237-253.
[27] BI S F, BROGGI M, WEI P F, et al. The Bhattacharyya distance:Enriching the P-box in stochastic sensitivity analysis[J]. Mechanical Systems and Signal Processing, 2019, 129:265-281.
[28] PEDRONI N, ZIO E. Hybrid uncertainty and sensitivity analysis of the model of a twin-jet aircraft[J]. Journal of Aerospace Information Systems, 2015, 12(1):73-96.
[29] FODOR I K. A survey of dimension reduction techniques[DB/OL]. arXiv preprint:1403.2877, 2002.
[30] WOLD S, ESBENSEN K, GELADI P. Principal component analysis[J]. Chemometrics andIntelligent Laboratory Systems, 1987, 2(1-3):37-52.
[31] MA Y Y, ZHU L P. A review on dimension reduction[J]. International Statistical Review, 2013, 81(1):134-150.
[32] 陈鑫, 刘莉, 岳振江. 基于本征正交分解和代理模型的高超声速气动热模型降阶研究[J]. 航空学报, 2015, 36(2):462-472. CHEN X, LIU L,YUE Z J. Reduced order aerothermodynamic modeling research for hypersonic vehicles based on proper orthogonal decomposition and surrogate method[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(2):462-472(in Chinese).
[33] JACKSON J E. A user's guide to principal components[M]. New York:John Wiley & Sons, 1991:26-62.
[34] CONSTANTINE P G, DOW E, WANG Q Q. Active subspace methods in theory and practice:Applications to kriging surfaces[J]. SIAM Journal on Scientific Computing, 2014, 36(4):A1500-A1524.
[35] CONSTANTINE P G. Active subspaces:Emerging ideas for dimension reduction in parameter studies[M]. Philadelphia:SIAM, 2015:21-88.
[36] LUKACZYK T W, CONSTANTINE P, PALACIOS F, et al. Active subspaces for shape optimization[C]//10th AIAAMultidisciplinary Design Optimization Conference. Reston:AIAA, 2014:1171.
[37] JEFFERSON J L, GILBERT J M, CONSTANTINE P G, et al. Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model[J]. Computers & Geosciences, 2015, 83:127-138.
[38] HU X Z, CHEN X Q, LATTARULO V, et al. Multidisciplinary optimization under high-dimensional uncertainty for small satellite system design[J]. AIAA Journal, 2016, 54(5):1732-1741.
[39] JOLLIFFE I T. Discarding variables in a principal component analysis. I:Artificial data[J]. Applied Statistics, 1972, 21(2):160.
[40] CRESPO L G, KENNY S P, GIESY D P. The NASA langley multidisciplinary uncertainty quantification challenge[C]//16th AIAA Non-Deterministic Approaches Conference. Reston:AIAA, 2014

Cross-layer dimension reduction based on probability box global sensitivity analysis and active subspace method

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Bowen SHU, Jiangtao HUANG, Zhenghong GAO, Gang LIU, Chengjun HE, Lu XIA. Sensitivity analysis of vector performance of two⁃dimensional shock vector control nozzle [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(13): 127831-127831.
[2]	Wanying YUN, Zhenzhou LYU. An efficient surrogate method for analyzing parameter global reliability sensitivity [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(12): 227670-227670.
[3]	LI Hangxing, HU Dike, WU Shaoqing. Optimization design of dynamic vibration absorbers for vibration and noise reduction of composite fairing [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 225249-225249.
[4]	MA Zongzhan, XU Zhi, TANG Shuo, ZHANG Qian. Improved iterative guidance method for launch vehicles [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(2): 324218-324218.
[5]	WANG Nana, XIE Qing, SU Xingyu, REN Zhuyin. Active subspace methods for analysis and optimization of turbulent combustion [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(12): 625228-625228.
[6]	WANG Chen, ZUO Yanfei, JIANG Zhinong, HU Minghui, FENG Kun. A backstepping method of gas turbine unbalance vector based on dimension reduction and reconstruction of full speed coefficient matrix [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(11): 223670-223670.
[7]	ZHANG Wei, GAO Zhenghong, ZHOU Lin, XIA Lu. Adaptive parameterization method for surrogate-based global optimization [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(10): 123815-123815.
[8]	ZHANG Zhuxi, ZHU Xi, ZHU Shaochuan, ZHANG Mingyuan, DU Wenbo. Unsupervised evaluation of airspace complexity based on kernel principal component analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(8): 322969-322969.
[9]	FENG Kaixuan, LYU Zhenzhou, JIANG Xian. Efficient algorithm for estimating derivative-based global sensitivity index [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(3): 221699-221699.
[10]	LIU Fuchao, WEI Pengfei, ZHOU Changcong, ZHANG Zheng, YUE Zhufeng. Time-dependent reliability and sensitivity analysis for planar motion mechanisms with revolution joint clearances [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(11): 422133-422141.
[11]	WANG Rongqiao, LIU Fei, HU Dianyin, LI Da. Uncertainty quantification in low cycle fatigue life model based on Bayesian theory [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(9): 220832-220832.
[12]	QI Junwei, WANG Chunjie, DING Jianzhong. Precision analysis of deployable structures based on dimension reduction method and effective link length [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(6): 220590-220590.
[13]	ZHAO Hailong, YUE Zhufeng, LIU Wei. A Kriging surrogate model method for moment-independent importance analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(7): 2234-2241.
[14]	RUAN Wenbin, LIU Yang, XIONG Lei. Influence of side aerodynamic derivative uncertainty on side flight load based on global sensitivity analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(6): 1827-1832.
[15]	GONG Xiangrui, LYU Zhenzhou, ZUO Jianwei. Two improved methods for variance-based global sensitivity analysis' W-indices [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(6): 1888-1898.