空间分割全局灵敏度方法研究及其在风机叶片极限载荷工况中的应用

马远卓; 赵翔; 李洪双; 赵振宙; 许波峰

doi:10.6052/j.issn.1000-4750.2022.05.0398

空间分割全局灵敏度方法研究及其在风机叶片极限载荷工况中的应用

马远卓^1, ,,
赵翔^2,,
李洪双^3,,
赵振宙^1,,
许波峰^1,

1.
河海大学能源与电气学院，南京 211100
2.
中国飞行试验研究院飞机所，西安 710089
3.
南京航空航天大学航空学院，南京 210016

基金项目: 国家自然科学基金项目(12102125，52376179)；江苏省自然科学基金项目(BK20200512)；中国博士后科学基金项目(2021M690868)；装备预先研究领域基金项目(80910010103)；中央高校基本科研业务费项目(B230201050)

详细信息

作者简介:
赵　翔(1992−)，女，陕西人，工程师，硕士，主要从事飞机结构设计研究(E-mail: zhaoxiang@nuaa.edu.cn)

李洪双(1978−)，男，黑龙江人，教授，博士，博导，主要从事结构可靠性及结构优化研究(E-mail: hongshuangli@nuaa.edu.cn)

赵振宙(1982−)，男，内蒙古人，教授，博士，博导，主要从事风力机空气动力学、涡流发生器研究(E-mail: joephy@163.com)

许波峰(1985−)，男，江苏人，副教授，博士，硕导，主要从事风力机空气动力学、叶片设计研究(E-mail: bfxu1985@hhu.edu.cn)

通讯作者:
马远卓(1989−)，男，安徽人，讲师，博士，硕导，主要从事结构可靠性及结构优化研究(E-mail: 20200007@hhu.edu.cn)

中图分类号: TK83
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出版历程
- 收稿日期: 2022-05-03
- 修回日期: 2022-11-03
- 网络出版日期: 2022-12-16
- 刊出日期: 2024-05-24

RESEARCH ON SPACE PARTITION GLOBAL SENSITIVITY AND ITS APPLICATION IN WIND TURBINE BLADE UNDER ULTIMATE LOAD

1.
College of Energy and Electrical Engineering, Hohai University, Nanjing 211100, China
2.
Department of Aircraft, China Flight Test Establishment, Xi’an 710089, China
3.
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要:
全局灵敏度分析，旨在考量结构系统中各输入随机变量对输出响应不确定性及风险水平影响的重要度。它能为后续的可靠度评估、故障诊断、系统设计、预测及优化等提供重要参考。尽管各类全局灵敏度分析方法不断涌现，但高维复杂结构(如风机叶片结构)灵敏度分析仍是目前的难题。该文针对空间分割全局灵敏度分析方法的三种可能计算形式及最优分割方案展开研究，通过标准算例分析和误差理论推导，提出能充分利用样本信息、有效减轻计算负担的求解形式及分割方案，并将其应用于风机叶片极限载荷工况下的全局灵敏度分析中，同时为未来设计更为高效、经济和可靠的风机结构提供参考。
- 全局灵敏度分析 /
- Sobol指标 /
- 空间分割 /
- 误差分析 /
- 极限载荷
Abstract:
Estimating the importance measure of a structural system by global sensitivity analysis methods can figure out the importance ranking of the input random variables that affect the uncertainty of the output response and the risk level, which provides a basis for the subsequent research on reliability evaluation, on fault diagnosis and system design, on prediction and optimization. A variety of global sensitivity methods has been developed. However, the global sensitivity analysis on high dimensional and complex structures such as wind turbine blade is still a problem to be solved. Three possible calculation forms of space partition global sensitivity analysis methods and the optimal partition scheme are thusly studied. The optimal calculation form and partition scheme, being able to utilize the information of samples and to reduce computational burden as fully as possible, are presented via the analysis of the standard example and by reasoning of the errors. The method is applied to the global sensitivity analysis of wind turbine blade under the ultimate load condition. The method has demonstrated its significance in improving the efficiency on future design of the wind turbine blade, on saving design cost and improving product quality.
- global sensitivity analysis /
- Sobol index /
- space partition /
- error analysis /
- ultimate load

HTML全文

图 1 计算流程示意图

Figure 1. Flowchart of the calculation process

下载: 全尺寸图片幻灯片

图 2 各变量一阶灵敏度指标-G 函数

Figure 2. S_i for Sobol’s G function

下载: 全尺寸图片幻灯片

图 3 简化叶片结构^[27-28]

Figure 3. Simplified structural model^[27-28]

下载: 全尺寸图片幻灯片

图 4 各参数一阶灵敏度均值(S_i)及标准差(STD)

Figure 4. S_i and STD of all the input random variables

下载: 全尺寸图片幻灯片

表 1 叶片随机参数分布特性

Table 1 Deterministic variables of the turbine blade

变量	均值	标准差	分布类型
最大强度σ_max/MPa	5.18×10²	5.18×10¹	正态分布
衰减系数x	1.054×10⁻¹	1×10⁻³	正态分布
梁帽宽度a/m	5×10⁻¹	5×10⁻³	正态分布
梁帽外边界b₁/m	2.28×10⁻¹	4.6×10⁻³	正态分布
梁帽内边界b₂/m	2.17×10⁻¹	4.4×10⁻⁴	正态分布
转子半径R/m	2.15×10¹	2×10⁻²	正态分布
叶根半径r/m	2×10⁰	3×10⁻³	正态分布
风速U₁₀	由k、A及u_c决定		上截断Weibull分布

下载: 导出CSV

参考文献(28)

[1]	WEI P F, LYU Z Z, HAO W R, et al. Efficient sampling methods for global reliability sensitivity analysis [J]. Computer Physics Communications, 2012, 183(8): 1728 − 1743. doi: 10.1016/j.cpc.2012.03.014
[2]	WEI P F, LU Z Z, YUAN X K. Monte Carlo simulation for moment-independent sensitivity analysis [J]. Reliability Engineering & System Safety, 2013, 110: 60 − 67.
[3]	CHEN J B, WAN Z Q, BEER M. A global sensitivity index based on Fréchet derivative and its efficient numerical analysis [J]. Probabilistic Engineering Mechanics, 2020, 62: 103096. doi: 10.1016/j.probengmech.2020.103096
[4]	SHANG X B, CHAO T, MA P, et al. Derivative-based global sensitivity measure using radial basis function [J]. Structural and Multidisciplinary Optimization, 2020, 62(1): 107 − 129. doi: 10.1007/s00158-019-02477-3
[5]	吕大刚, 李功博, 宋彦. 基于MLS-SVM的结构整体可靠度与全局灵敏度分析[J]. 工程力学, 2022, 39(增刊 1): 92 − 100. doi: 10.6052/j.issn.1000-4750.2021.05.S015 LYU Dagang, LI Gongbo, SONG Yan. Analysis of global reliability and sensitivity of structures based on MLS-SVM [J]. Engineering Mechanics, 2022, 39(Suppl 1): 92 − 100. (in Chinese) doi: 10.6052/j.issn.1000-4750.2021.05.S015
[6]	SOBOL I M. Sensitivity analysis for non-linear mathematical models [J]. Mathematical Modelling and Computational Experiment, 1993, 1: 407 − 414.
[7]	SALTELLI A, ANNONI P, AZZINI I, et al. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index [J]. Computer Physics Communications, 2010, 181(2): 259 − 270. doi: 10.1016/j.cpc.2009.09.018
[8]	BORGONOVO E. A new uncertainty importance measure [J]. Reliability Engineering & System Safety, 2007, 92(6): 771 − 784.
[9]	EHRE M, PAPAIOANNOU I, STRAUB D. A framework for global reliability sensitivity analysis in the presence of multi-uncertainty [J]. Reliability Engineering & System Safety, 2020, 195: 106726.
[10]	SARAZIN G, MORIO J, LAGNOUX A, et al. Reliability-oriented sensitivity analysis in presence of data-driven epistemic uncertainty [J]. Reliability Engineering & System Safety, 2021, 215: 107733.
[11]	ZHANG K C, LU Z Z, CHENG K, et al. Global sensitivity analysis for multivariate output model and dynamic models [J]. Reliability Engineering & System Safety, 2020, 204: 107195.
[12]	陈超, 吕震宙. 模糊分布参数的全局灵敏度分析新方法[J]. 工程力学, 2016, 33(2): 25 − 33. doi: 10.6052/j.issn.1000-4750.2014.07.0624 CHEN Chao, LYU Zhenzhou. A new method for global sensitivity analysis of fuzzy distribution parameters [J]. Engineering Mechanics, 2016, 33(2): 25 − 33. (in Chinese) doi: 10.6052/j.issn.1000-4750.2014.07.0624
[13]	CUI L J, LYU Z Z, ZHAO X P. Moment-independent importance measure of basic random variable and its probability density evolution solution [J]. Science China Technological Sciences, 2010, 53(4): 1138 − 1145. doi: 10.1007/s11431-009-0386-8
[14]	LI L Y, LYU Z Z, FENG J, et al. Moment-independent importance measure of basic variable and its state dependent parameter solution [J]. Structural Safety, 2012, 38: 40 − 47. doi: 10.1016/j.strusafe.2012.04.001
[15]	SALTELLI A. Sensitivity analysis for importance assessment [J]. Risk Analysis, 2002, 22(3): 579 − 590. doi: 10.1111/0272-4332.00040
[16]	PLISCHKE E, BORGONOVO E, SMITH C L. Global sensitivity measures from given data [J]. European Journal of Operational Research, 2013, 226(3): 536 − 550. doi: 10.1016/j.ejor.2012.11.047
[17]	ZHAI Q Q, YANG J, ZHAO Y. Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study [J]. Reliability Engineering & System Safety, 2014, 131: 66 − 82.
[18]	赵翔, 李洪双. 基于交叉熵和空间分割的全局可靠性灵敏度分析[J]. 航空学报, 2018, 39(2): 179 − 189. ZHAO Xiang, LI Hongshuang. Global reliability sensitivity analysis using cross entropy method and space partition [J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(2): 179 − 189. (in Chinese)
[19]	VELARDE J, KRAMHØFT C, SØRENSEN J D. Global sensitivity analysis of offshore wind turbine foundation fatigue loads [J]. Renewable Energy, 2019, 140: 177 − 189. doi: 10.1016/j.renene.2019.03.055
[20]	DAMGAARD M, ANDERSEN L V, IBSEN L B. Dynamic response sensitivity of an offshore wind turbine for varying subsoil conditions [J]. Ocean Engineering, 2015, 101: 227 − 234. doi: 10.1016/j.oceaneng.2015.04.039
[21]	ZHOU S T, MÜLLER K, LI C, et al. Global sensitivity study on the semisubmersible substructure of a floating wind turbine: Manufacturing cost, structural properties and hydrodynamics [J]. Ocean Engineering, 2021, 221: 108585. doi: 10.1016/j.oceaneng.2021.108585
[22]	HOMMA T, SALTELLI A. Importance measures in global sensitivity analysis of nonlinear models [J]. Reliability Engineering & System Safety, 1996, 52(1): 1 − 17.
[23]	LI C Z, MAHADEVAN S. An efficient modularized sample-based method to estimate the first-order Sobol׳ index [J]. Reliability Engineering & System Safety, 2016, 153: 110 − 121.
[24]	RONOLD K O, LARSEN G C. Reliability-based design of wind-turbine rotor blades against failure in ultimate loading [J]. Engineering Structures, 2000, 22(6): 565 − 574. doi: 10.1016/S0141-0296(99)00014-0
[25]	HU Z, DU X P. Time-dependent reliability analysis for turbine blade in extreme wind loading [C]. Rolla, Missouri: Proceedings of the 5th Annual ISC Graduate Research Symposium, 2011.
[26]	DS 472, Dansk ingeniorforenings og ingeniør-sammenslutningens norm for last og sikkerhed for vindmøllekonstruktioner [S]. Denmark: Dansk Ingenioerforening, 1992.
[27]	陈安杰, 王策, 贾娅娅, 等. 基于BEM的风力机叶片气动性能计算分析[J]. 工程力学, 2021, 38(增刊 1): 264 − 268. doi: 10.6052/j.issn.1000-4750.2020.05.S035 CHEN Anjie, WANG Ce, JIA Yaya, et al. Computation and analysis of aerodynamic performance of wind turbine blade based on BEM [J]. Engineering Mechanics, 2021, 38(Suppl 1): 264 − 268. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.05.S035
[28]	杨阳, 曾攀, 雷丽萍. 大型水平轴风力机新型叶片结构设计思想和研究进展[J]. 工程力学, 2019, 36(10): 1 − 7. doi: 10.6052/j.issn.1000-4750.2018.06.ST04 YANG Yang, ZENG Pan, LEI Liping. Concept and development of novel blade structure of large horizontal-axis wind turbine [J]. Engineering Mechanics, 2019, 36(10): 1 − 7. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.06.ST04

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空间分割全局灵敏度方法研究及其在风机叶片极限载荷工况中的应用

通讯作者: 马远卓(1989−)，男，安徽人，讲师，博士，硕导，主要从事结构可靠性及结构优化研究(E-mail: 20200007@hhu.edu.cn)

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出版历程

RESEARCH ON SPACE PARTITION GLOBAL SENSITIVITY AND ITS APPLICATION IN WIND TURBINE BLADE UNDER ULTIMATE LOAD

计量

出版历程

目录

通讯作者:
马远卓(1989−)，男，安徽人，讲师，博士，硕导，主要从事结构可靠性及结构优化研究(E-mail: 20200007@hhu.edu.cn)