EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

P-CS不确定性量化模型与其性能数据驱动更新方法

何佳琦 贾晓璇 吴伟达 钟杰华 罗阳军

何佳琦, 贾晓璇, 吴伟达, 钟杰华, 罗阳军. P-CS不确定性量化模型与其性能数据驱动更新方法. 力学学报, 2022, 54(10): 1-17 doi: 10.6052/0459-1879-22-173
引用本文: 何佳琦, 贾晓璇, 吴伟达, 钟杰华, 罗阳军. P-CS不确定性量化模型与其性能数据驱动更新方法. 力学学报, 2022, 54(10): 1-17 doi: 10.6052/0459-1879-22-173
He Jiaqi, Jia Xiaoxuan, Wu Weida, Zhong Jiehua, Luo Yangjun. P-cs uncertainty quantification model and its performance data-driven updating method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 1-17 doi: 10.6052/0459-1879-22-173
Citation: He Jiaqi, Jia Xiaoxuan, Wu Weida, Zhong Jiehua, Luo Yangjun. P-cs uncertainty quantification model and its performance data-driven updating method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 1-17 doi: 10.6052/0459-1879-22-173

P-CS不确定性量化模型与其性能数据驱动更新方法

doi: 10.6052/0459-1879-22-173
基金项目: 基础研究项目群项目(514010103-303)和国家自然科学基金(11972104)资助
详细信息
    作者简介:

    罗阳军, 教授, 研究方向: 多源不确定性分析、多场耦合拓扑优化理论与方法研究. E-mail: yangjunluo@dlut.edu.cn

    通讯作者:

  • 中图分类号: O224, TU311.4

P-CS UNCERTAINTY QUANTIFICATION MODEL AND ITS PERFORMANCE DATA-DRIVEN UPDATING METHOD

  • 摘要: 在实际工程中, 广泛存在大量的不确定性信息, 直接或间接影响着工程结构形式设计、结构性能评估与预测以及在役结构损伤识别等工作的开展与决策. 这些多源不确定性信息往往需要用多种不同的不确定性量化模型加以描述; 与此同时, 不确定性变量在使用过程中可能随时间变化且难以直接测量, 需要间接根据性能测试信息在使用工程中更新不确定性量化模型. 为兼顾上述两个问题, 本文基于等概率变换原则提出了一种P-CS (Probability-Convex Set) 不确定性量化模型, 该模型将不确定性变量用概率随机变量与非概率凸集变量组合表征, 可统一表达概率模型、非概率模型以及非精确概率模型, 实现多源、多类型不确定性的统一量化. 本文进一步基于贝叶斯理论提出了一种针对该P-CS不确定性量化模型的性能数据驱动更新方法. 该更新方法根据性能测试数据信息更新P-CS不确定性量化模型参数取值的信度分布, 从而根据后验信度分布计算得出当前P-CS不确定性量化模型参数集合. 通过数值算例详述了P-CS不确定性量化模型的构建方法与其概率、非概率特性, 并验证了性能数据驱动更新P-CS模型方法的适用性.

     

  • 图  1  非精确概率模型示意图

    Figure  1.  Schematic illustration of imprecise probabilistic model

    图  2  椭球模型旋转角度示意图

    Figure  2.  Schematic illustration of the rotation angle of ellipsoidal model

    图  3  二维焦元示意图

    Figure  3.  Schematic illustration of 2-dimensional focus elements

    图  4  更新计算方法流程图

    Figure  4.  A flow chart of the updating method.

    图  5  概率密度累积函数族

    Figure  5.  Family of probability density cumulative functions

    图  6  概率密度累积函数族的边界

    Figure  6.  Boundaries for the family of probability density cumulative functions

    图  7  等概率水平条件下不确定性变量变化范围验证

    Figure  7.  Validation of the variation range of uncertainties under equal probability levels

    图  8  二维 P-CS模型示意图

    Figure  8.  Schematic illustration of the 2-dimensional P-CS model

    图  9  等概率水平下椭圆模型包络性验证

    Figure  9.  Validation of elliptic model envelope under equal probability levels

    图  10  多源不确定性P-CS模型示意图

    Figure  10.  Schematic illustration of the multidimensional P-CS model

    图  11  悬臂梁结构

    Figure  11.  A cantilevered beam structure

    图  12  第一次更新计算后参数后验信度分布

    Figure  12.  Posterior credibility distributions after the first updating

    图  13  第二次更新计算后参数后验信度分布

    Figure  13.  Posterior credibility distributions after the second updating

    图  14  第三次更新计算后参数后验信度分布

    Figure  14.  Posterior credibility distributions after the third updating

    图  15  悬臂梁结构算例最终参数后验信度分布

    Figure  15.  Final posterior credibility distributions of the example of a cantilevered beam structure

    图  16  悬臂梁结构算例更新过程图

    Figure  16.  The updating process of the example of a cantilevered beam structure

    图  17  框架结构

    Figure  17.  A frame structure

    图  18  框架结构算例最终参数后验信度分布

    Figure  18.  Final posterior credibility distributions of the example of a frame structure

    图  19  框架结构算例更新过程图

    Figure  19.  The updating process of the example of a frame structure

    表  1  多源不确定性变量的P-CS量化模型

    Table  1.   P-CS models for multi-source uncertainty

    Types of uncertaintiesPrior informationP-CS model
    Aleatory uncertaintiesPrecise probability distributions$ {\boldsymbol{X}} = {\tilde{\boldsymbol X}} \sim {\varphi _0}\left( {{\tilde{\boldsymbol X}}} \right) $
    Aleatory uncertaintiesPossible probability distributions$ {\boldsymbol{X}} = {\tilde{\boldsymbol X}} \oplus \Omega $
    Aleatory uncertaintiesBounds for uncertainties$ {\boldsymbol{X}} \in \Omega $
    Epistemic uncertaintiesBounds for uncertainties$ {\boldsymbol{X}} \in \Omega $
    下载: 导出CSV

    表  2  悬臂梁结构算例性能测试样本$ \left( {1 \times {{10}^{ - 4}}{\text{Rad}}} \right) $

    Table  2.   Performance test samples of the example of a cantilevered beam structure$ \left( {1 \times {{10}^{ - 4}}{\text{Rad}}} \right) $

    3.192.933.113.052.952.963.032.923.123.15
    2.052.132.162.172.152.172.252.132.202.19
    2.552.612.682.522.572.562.602.462.542.62
    下载: 导出CSV

    表  3  框架结构算例性能测试样本$ \left( {1 \times {{10}^{ - 4}}{\text{Rad}}} \right) $

    Table  3.   Performance test samples of the example of a frame structure$ \left( {1 \times {{10}^{ - 4}}{\text{Rad}}} \right) $

    10.059.989.889.869.7810.069.9510.0810.059.97
    13.7913.8313.9913.9014.0213.9113.8813.9213.9513.94
    下载: 导出CSV
  • [1] 王栋. 载荷作用位置不确定条件下结构动态稳健性拓扑优化设计. 力学学报, 2021, 53(5): 1439-1448 doi: 10.6052/0459-1879-21-009

    Wang Dong. Robust dynamic topology optimization of continuum structure subjected to harmonic excitation of loading position uncertainty. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1439-1448 (in Chinese) doi: 10.6052/0459-1879-21-009
    [2] Frangopol DM. Life-cycle performance, management, and optimization of structural systems under uncertainty: accomplishments and challenges. Structure and Infrastructure Engineering:Maintenance, 2011, 7(6): 389-413 doi: 10.1080/15732471003594427
    [3] Huang Y, Shao C, Wu B, et al. State-of-the-art review on Bayesian inference in structural system identification and damage assessment. Advances in Structural Engineering, 2018, 22(6): 1329-1351
    [4] 许灿, 朱平, 刘钊, 陶威. 平纹机织碳纤维复合材料的多尺度随机力学性能预测研究. 力学学报, 2020, 52(3): 763-773 doi: 10.6052/0459-1879-20-002

    Xu Can, Zhu Ping, Liu Zhao, Tao Wei. Research on multiscale stochastic mechanical properties prediction of plain woven carbon fiber composites. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(3): 763-773(in Chinese) doi: 10.6052/0459-1879-20-002
    [5] 万志强, 陈建兵, Michael Beer. 随机参数系统不确定性量化的泛函观点与整体灵敏度分析. 力学学报, 2021, 53(3): 837-854 doi: 10.6052/0459-1879-20-336

    Wan Zhiqiang, Chen Jianbing, Michael Beer. Functional perspective of uncertainty quantification for stochastic parametric systems and global sensitivity analysis. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 837-854(in Chinese) doi: 10.6052/0459-1879-20-336
    [6] 唐新姿, 王效禹, 袁可人, 彭锐涛. 风速不确定性对风力机气动力影响量化研究. 力学学报, 2020, 52(1): 51-59 doi: 10.6052/0459-1879-19-214

    Tang Xinzi, Wang Xiaoyu, Yuan Keren, Peng Ruitao. Quantitation study of influence of wind speed uncertainty on aerodynamic forces of wind turbine. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 51-59 (in Chinese) doi: 10.6052/0459-1879-19-214
    [7] Ben-Haim Y. A non-probabilistic concept of reliability. Structural Safety, 1994, 14(4): 227-245 doi: 10.1016/0167-4730(94)90013-2
    [8] Ben-Haim Y. A non-probabilistic measure of reliability of linear systems based on expansion of convex models. Structural Safety, 1995, 17(2): 91-109 doi: 10.1016/0167-4730(95)00004-N
    [9] Hong LX, Li HC, Fu JF, et al. Hybrid active learning method for non-probabilistic reliability analysis with multi-super-ellipsoidal model. Reliability Engineering and System Safety, 2022, 222: 108414 doi: 10.1016/j.ress.2022.108414
    [10] Zhan JJ, Luo YJ, Zhang XP, et al. A general assessment index for non-probabilistic reliability of structures with bounded field and parametric uncertainties. Computer Methods in Applied Mechanics and Engineering, 2020, 366(12): 113046
    [11] Kang Z, Zhang W. Construction and application of an ellipsoidal convex model using a semi-definite programming formulation from measured data. Computer Methods in Applied Mechanics and Engineering, 2016, 300: 461-489 doi: 10.1016/j.cma.2015.11.025
    [12] Meng Z, Zhang ZH, Zhou HL. A novel experimental data-driven exponential convex model for reliability assessment with uncertain-but-bounded parameters. Applied Mathematical Modelling, 2020, 77: 773-787 doi: 10.1016/j.apm.2019.08.010
    [13] Dempster AP. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 1967, 38(2): 325-339 doi: 10.1214/aoms/1177698950
    [14] Limbourg P, Rocquigny ED. Uncertainty analysis using evidence theory-confronting level-1 and level-2 approaches with data availability and computational constraints. Reliability Engineering and System Safety, 2010, 95(5): 550-564 doi: 10.1016/j.ress.2010.01.005
    [15] Frank MJ, Nelsen RB, Schweizer B. Best-possible bounds for the distribution of a sum-a problem of Kolmogorov. Probability Theory and Related Fields, 1987, 74(2): 199-211 doi: 10.1007/BF00569989
    [16] Faes M, Daub M, Marelli S, et al. Engineering analysis with probability boxes: a review on computational methods. Structural Safety, 2021, 93: 102092 doi: 10.1016/j.strusafe.2021.102092
    [17] Zadeh L. Probability measure of fuzzy event. Journal of Mathematical Analysis and Application, 1968, 23: 421-427 doi: 10.1016/0022-247X(68)90078-4
    [18] 董玉革, 陈心昭, 赵显德, 权钟完. 基于模糊事件概率理论的模糊可靠性分析通用方法. 计算力学学报, 2005, 22(3): 281-286 doi: 10.3969/j.issn.1007-4708.2005.03.005

    Dong Yuge, Chen Xinzhao, Zhao Xiande, Quan Zhongwan. A general approach for fuzzy reliability analysis based. Chinese Journal of Computational Mechanics, 2005, 22(3): 281-286 (in Chinese) doi: 10.3969/j.issn.1007-4708.2005.03.005
    [19] Xiao FY. Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Information Fusion, 2018, 46: 23-32
    [20] Wu DD, Tang YC. An improved failure mode and effects analysis method based on uncertainty measure in the evidence theory. Quality and Reliability Engineering, 2020, 36(5): 1786-1807 doi: 10.1002/qre.2660
    [21] Zhang Z, Jiang C, Ruan, XX, et al. A novel evidence theory model dealing with correlated variables and the corresponding structural reliability analysis method. Structural and Multidisciplinary Optimization, 2018, 57(4): 1749-1764 doi: 10.1007/s00158-017-1843-9
    [22] Destercke S, Dubois D, Chojnacki E. Unifying practical uncertainty representations-I: Generalized p-boxes. International Journal of Approximate Reasoning, 2008, 49(3): 649-663 doi: 10.1016/j.ijar.2008.07.003
    [23] Alam J, Neves LAC, Zhang H, et al. Assessment of remaining service life of deteriorated concrete bridges under imprecise probabilistic information. Mechanical Systems and Signal Processing, 2022, 167: 108565 doi: 10.1016/j.ymssp.2021.108565
    [24] Zhang H, Mullen RL, Muhanna RL. Structural analysis with probability-boxes. International Journal of Reliability and Safety, 2012, 6(1-3): 110-129
    [25] 万越, 吕震宙, 袁修开. 对称抛物型模糊变量下的可靠性及灵敏度分析. 力学季刊, 2010, 31(01): 83-91 doi: 10.15959/j.cnki.0254-0053.2010.01.013

    Wan Yue, Lv Zhenzhou, Yuan Xiukai. Reliability and Reliability Sensitivity Analysis Including Fuzzy Variables with Symmetric Parabolic Membership Functions. Chinese quarterly of mechanics, 2010, 31(01): 83-91 (in Chinese) doi: 10.15959/j.cnki.0254-0053.2010.01.013
    [26] Li WX, Liu L, Dai LF. Fuzzy probability measures based non-symmetric membership function: engineering examples of ground subsidence due to underground mining. Engineering Applications of Artificial Intelligence, 2010, 23(3): 420-431 doi: 10.1016/j.engappai.2010.01.003
    [27] 孙 杰, 张 晓, 牟在根. 不同隶属函数对地下连续墙模糊可靠度影响的分析. 岩土力学, 2008, 29(3): 838-840 doi: 10.3969/j.issn.1000-7598.2008.03.049

    Sun Jie, Zhang Xiao, Mu Zaigen. Analysis of effect of different membership function on calculation of fuzzy reliability in underground continuous wall. Rock and Soil Mechanics, 2008, 29(3): 838-840 (in Chinese) doi: 10.3969/j.issn.1000-7598.2008.03.049
    [28] Purba, Hendry J. Fuzzy probability on reliability study of nuclear power plant probabilistic safety assessment: A review. Progress in Nuclear Energy, 2014, 76: 73-80 doi: 10.1016/j.pnucene.2014.05.010
    [29] Ling CY, Lu ZZ, Feng KX, et al. Efficient numerical simulation methods for estimating fuzzy failure probability based importance measure indices. Structural and Multidisciplinary Optimization, 2019, 59: 577-593 doi: 10.1007/s00158-018-2085-1
    [30] Kala Z. Fuzzy probability analysis of the fatigue resistance of steel structural members under bending. Journal of Civil Engineering and Management, 2008, 14(1): 67-72 doi: 10.3846/1392-3730.2008.14.67-72
    [31] Li JW, Jiang C. A novel imprecise stochastic process model for time-variant or dynamic uncertainty quantification. Chinese Journal of Aeronautics, 2022, In Press, https://doi.org/10.1016/j.cja.2022.01.004
    [32] Ping MH, Han X, Jiang C, et al. A time-variant uncertainty propagation analysis method based on a new technique for simulating non-Gaussian stochastic processes. Mechanical Systems and Signal Processing, 2021: 107299
    [33] Wang L, Wang XJ, Chen X, et al. Time-variant reliability model and its measure index of structures based on a non-probabilistic interval process. Acta Mechanica, 2015, 226: 3221-3241 doi: 10.1007/s00707-015-1379-2
    [34] Meng Z, Guo LB, Hao P, et al. On the use of probabilistic and non-probabilistic super parametric hybrid models for time-variant reliability analysis. Computer Methods in Applied Mechanics and Engineering, 2021, 386: 114113 doi: 10.1016/j.cma.2021.114113
    [35] Ling CY, Lu ZZ. Adaptive Kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis. Applied Mathematical Modelling, 2020, 77: 1820-1841
    [36] Zhao Z, Lu ZH, Zhao YG. An efficient extreme value moment method combining adaptive Kriging model for time-variant imprecise reliability analysis. Mechanical Systems and Signal Processing, 2022, 171: 108905 doi: 10.1016/j.ymssp.2022.108905
    [37] Bissiri PG, Holmes CC, Walker SG. A general framework for updating belief distributions. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2016, 78(5): 1103-1130 doi: 10.1111/rssb.12158
    [38] Wang RC. Analysis and improvement of combination rule in D-S theory. Applied Mechanics and Materials, 2014, 556-562: 3930-3934 doi: 10.4028/www.scientific.net/AMM.556-562.3930
    [39] Pan Y, Zhang LM, Li ZW, et al. Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and D-S evidence theory. IEEE Transactions on Fuzzy Systems, 2019, 28(9): 2063-2077
    [40] He JQ, Luo YJ. A Bayesian updating method for non-probabilistic reliability assessment of structures with performance test data. Computer Modeling in Engineering and Sciences, 2020, 125(2): 777-800 doi: 10.32604/cmes.2020.010688
    [41] Ben-Haim Y, Elishakoff I. Discussion on: A non-probabilistic concept of reliability. Structural Safety, 1995, 17(3): 195-199 doi: 10.1016/0167-4730(95)00010-2
    [42] Rosenblatt M. Remarks on a multivariate transformation. Annals of Mathematical Statistics, 1952, 23: 470-472 doi: 10.1214/aoms/1177729394
    [43] Kang Z, Luo YJ, Li A. On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters. Structural Safety, 2011, 33(3): 196-205 doi: 10.1016/j.strusafe.2011.03.002
    [44] Jiang C, Han X, Lu GY, et al. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Computer Methods in Applied Mechanics and Engineering, 2011, 200(33-36): 2528-2546 doi: 10.1016/j.cma.2011.04.007
  • 加载中
图(19) / 表(3)
计量
  • 文章访问数:  16
  • HTML全文浏览量:  8
  • PDF下载量:  4
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-04-24
  • 录用日期:  2022-07-26
  • 网络出版日期:  2022-07-26

目录

    /

    返回文章
    返回