ANALYSIS OF GLOBAL RELIABILITY AND SENSITIVITY OF STRUCTURES BASED ON MLS-SVM
-
摘要: 作为一种有效的代理模型，支持向量机(SVM)以统计学习中的结构风险最小化原则为基本原理，在具有隐式极限状态函数的结构可靠度分析中得到了广泛的应用。然而，传统的支持向量机在核函数的选择、全局基本变量空间建模、计算效率等方面还存在许多不足。针对这些不足，该文提出一种新的基于移动最小二乘(MLS)技术的支持向量机模型(MLS-SVM)，可以在全局基本变量空间中具备自适应能力。该文将MLS-SVM应用于复杂结构的整体可靠度和全局灵敏度分析，并将该模型与基于再生核函数的支持向量机(RPK-SVM)及基于最小二乘的支持向量机(LS-SVM)进行比较分析，结果表明：该文提出的模型相较其他两种模型具有更高的精度和计算效率。Abstract: As one of efficient surrogate models, the support vector machine (SVM), which is based on the principle of structural risk minimization in statistical learning, has been widely used in structural reliability analysis with implicit limit state functions. However, the traditional support vector machines still have many shortcomings, such as the selection of kernel function, global basic variable space modeling, computational efficiency, etc. In order to overcome these shortcomings, this paper proposes a new support vector machine model based on moving least squares (MLS) technology named MLS-SVM. With this model, the training sample sets can be adaptive in the global basic variable space. Then this model is applied to global reliability and sensitivity analysis of reinforced concrete (RC) frame structures, and then is compared with the support vector machines based on the regenerative kernel function (RK-SVM) and the least square technique (LS-SVM). It is shown by the numerical results that, compared with the two comparative models, the MLS-SVM model has higher accuracy and better computational efficiency.
-
图 1 F3各结构可靠度指标随变异系数的变化
Figure 1. Changes of structural reliability indexes with variation coefficient on F3 structure
表 1 结构不确定性因素
Table 1. Structural uncertainty factors
不确定性来源 随机变量 平均值 变异系数 相关性系数 分布类型 C30 混凝土 ${X_1}( { {f_{\rm c0,core} } })$ 28.99 N/mm2 0.20 0.3 对数正态 ${X_2}( { {f_{\rm cu,core} } } )$ 17.91 N/mm2 0.20 0.3 ${X_3}( { {\varepsilon _{\rm c0,core} } } )$ 0.0023 0.20 0.3 ${X_4}( { {\varepsilon _{\rm cu,core} } } )$ 0.0143 0.20 0.3 ${X_5}( { {f_{\rm c0,cover }} } )$ 25.57 N/mm2 0.20 0.3 ${X_6}( { {\varepsilon _{\rm cu,cover} } } )$ 0.0040 0.20 0.3 C35 混凝土 ${X_1}( { {f_{\rm c0,core} } })$ 32.57 N/mm2 0.20 0.3 对数正态 ${X_2}( { {f_{\rm cu,core} } } )$ 20.76 N/mm2 0.20 0.3 ${X_3}( { {\varepsilon _{\rm c0,core} } } )$ 0.0022 0.20 0.3 ${X_4}( { {\varepsilon _{\rm cu,core} } })$ 0.0124 0.20 0.3 ${X_5}( { {f_{\rm c0,cover} } } )$ 29.76 N/mm2 0.20 0.3 ${X_6}( { {\varepsilon _{\rm cu,cover} } })$ 0.0040 0.20 0.3 HRB335 钢筋/(N/mm2) ${X_7}( { {f_{\rm y} }})$ 378 0.10 0.4 对数正态 ${X_8}( { {E_0} } )$ 200000 0.05 0.4 恒荷载/kN/m3) ${X_9}( \gamma )$ 26.50 0.10 − 正态 活荷载/(kN/m) ${X_{10} }( q )$ 0.98 0.45 − Gamma 
下载: 导出CSV
表 2 总水平地震作用及统计信息
Table 2. General earthquake level and statistical information
结构类型 标准值 平均值 变异系数 分布类型 F3 487.67 548.01 0.3 极值Ⅰ型 F6 506.85 665.81 F9 613.28 727.79
下载: 导出CSV
表 3 考虑水平地震作用变异性的结构整体可靠度指标
Table 3. The global reliability index of the structure considering the variability of horizontal earthquake action
可靠度指标 变异系数 0.2 0.4 0.6 0.8 1.0 Kriging F3 0.7527 0.5154 0.4190 0.3327 0.3021 F6 0.5225 0.4227 0.4061 0.3166 0.2434 F9 0.6417 0.4609 0.3825 0.2883 0.2848 SVR(RBF) F3 0.8141 0.5747 0.4228 0.4106 0.3758 F6 0.5569 0.4689 0.4154 0.3311 0.2502 F9 0.6888 0.5200 0.4346 0.4003 0.3876 SVR(RPK) F3 0.7910 0.5666 0.4507 0.4105 0.3569 F6 0.5576 0.4552 0.4150 0.3276 0.2582 F9 0.8343 0.6302 0.5390 0.5301 0.5111 MLS-SVM F3 0.7501 0.5135 0.4278 0.3540 0.2970 F6 0.5429 0.4420 0.4007 0.3205 0.2460 F9 0.6125 0.4564 0.35686 0.31469 0.2881 FORM F3 0.7763 0.5037 0.4048 0.3644 0.3144 F6 0.5145 0.4529 0.3933 0.3042 0.2400 F9 0.6571 0.4755 0.4029 0.3221 0.2753
下载: 导出CSV
表 4 结构全局灵敏度指标
Table 4. Structural global sensitivity index
随机变量 变量编号 $ {S_i} $(F3) ${{S}_i^{\rm T}}$(F3) $ {S_i} $(F6) ${{S}_i^{\rm T}}$(F6) ${S_i}$(F9) ${{S}_i^{\rm T}}$(F9) $钢筋屈服强度{f_{\rm y}}$ 1 0.648700 0.667500 0.693500 0.70350 0.713100 0.72000 $约束混凝土极限应力{f_{\rm cu,core} }$ 2 0.003650 0.004840 0.005238 0.00374 0.000380 0.00420 $无约束混凝土峰值应力{f_{\rm c0,cover} }$ 3 0.005449 0.008500 0.008173 0.00880 0.005750 0.04576 $约束混凝土峰值应变{\varepsilon _{\rm c0,core} }$ 4 0.002653 0.004345 0.003200 0.00536 0.002490 0.00560 $约束混凝土极限应变 {\varepsilon _{\rm cu,core} }$ 5 0.005102 0.007121 0.004279 0.00580 0.003600 0.00739 $无约束混凝土极限应变{\varepsilon _{\rm cu,cover} }$ 6 0.000040 0.001440 0.000154 0.00238 0.000319 0.00291 $约束混凝土峰值应力 {f_{\rm c0,core} }$ 7 0.243000 0.253400 0.230700 0.24000 0.254000 0.27400 钢筋弹性模量E0 8 0.000259 0.002295 0.000058 0.00191 0.000390 0.00241 混凝土容重γ 9 0.042550 0.042950 0.045540 0.04286 0.023080 0.01529 楼面活荷载q 10 0.000008 0.003500 0.000136 0.00245 0.000030 0.00259
下载: 导出CSV
-
[1] 李国强, 李杰. 结构设计的发展方向——以整体结构可靠度为目标的结构设计 [C]. 南京: 中国土木工程学会工程结构可靠性全国第三届学术交流会议, 1992: 121 − 126.Li Guoqiang, Li Jie. Development Direction – structural design taking global structural reliability as target [C]. Nanjing: The 3rd Conference on Reliability of Engineering Structures, China Civil Engineering Society, 1992: 121 − 126. (in Chinese) [2] Li J, Chen J B, Fan W L. The equivalent extreme-value event and evaluation of the structural system reliability [J]. Structural Safety, 2007, 29: 112 − 131. doi: 10.1016/j.strusafe.2006.03.002 [3] 陈建兵, 李杰. 结构随机动力非线性反应的整体灵敏度分析[J]. 计算力学学报, 2008, 25(2): 169 − 176.Chen Jianbing, Li Jie. Global sensitivity in nonlinear stochastic dynamic response analysis of structures [J]. Chinese Journal of Computational Mechanics, 2008, 25(2): 169 − 176. (in Chinese) [4] 王涛, 李正良, 范文亮. 基于改进统计矩点估计法和最大熵原理的结构整体可靠度分析[J]. 工程力学, 2022, 39(3): 193 − 200. doi: 10.6052/j.issn.1000-4750.2021.01.0092Wang Tao, Li Zhengliang, Fan Wenliang. Global reliability analysis of structures based on improved statistical moment point estimation method and maximum entropy principle [J]. Engineering Mechanics, 2022, 39(3): 193 − 200. (in Chinese) doi: 10.6052/j.issn.1000-4750.2021.01.0092 [5] 宋鹏彦. 结构整体可靠度方法及RC框架非线性整体抗震可靠度分析[D]. 哈尔滨: 哈尔滨工业大学, 2012.Song Pengyan. Structural global reliability methods and nonlinear global seismic reliability analysis of RC frames [D]. Harbin: Harbin institute of Technology, 2012. (in Chinese) [6] 宋鹏彦, 陈建兵. 混凝土框架结构的随机地震反应与整体可靠度分析[C]. 哈尔滨: 第九届全国地震工程学术会议, 2014: 323 − 327.Song Pengyan, Chen Jianbing. Stochastic seismic response and global reliability analysis of concrete frame structures [C]. Harbin: The 9th National Conference on Earthquake Engineering, 2014: 323 − 327. (in Chinese) [7] 魏鹏飞. 结构系统可靠性及灵敏度分析研究 [D]. 西安: 西北工业大学, 2014.Wei Pengfei. Research on system reliability and global sensitivity of structures [D]. Xi’an: Northwestern Polytechnical University, 2014. (in Chinese) [8] 李攻博. 基于MLS-SVM代理模型的结构整体可靠度与全局灵敏度分析[D]. 哈尔滨: 哈尔滨工业大学, 2016.Li Gongbo. Global reliability and sensitivity analysis of structures using MLS-SVM meta-model [D]. Harbin: Harbin Institute of Technology, 2016. (in Chinese) [9] 宋彦. 基于随机响应面法的结构整体可靠度与全局灵敏度分析[D]. 哈尔滨: 哈尔滨工业大学, 2016.Song Yan. Global reliability and sensitivity analysis of structures based on stochastic response surface methods [D]. Harbin: Harbin Institute of Technology, 2016. (in Chinese) [10] 宋彦, 吕大刚. 采用随机响应面法钢筋混凝土框架抗震全局灵敏度分析[J]. 福州大学学报( 自然科学版), 2017, 45(4): 493 − 500.Song Yan, Lu Dagang. Seismic global sensitivity analysis of RC frame structures through stochastic response surface methods [J]. Journal of Fuzhou University (Natural Science Edition), 2017, 45(4): 493 − 500. (in Chinese) [11] 陈力波, 黄才贵, 谷音. 基于改进响应面法的公路简支梁桥地震易损性分析[J]. 工程力学, 2018, 35(4): 208 − 218. doi: 10.6052/j.issn.1000-4750.2017.06.0512Chen Libo, Huang Caigui, Gu Yin. Seismic vulnerability analysis of simply supported highway bridges based on an improved response surface method [J]. Engineering Mechanics, 2018, 35(4): 208 − 218. (in Chinese) doi: 10.6052/j.issn.1000-4750.2017.06.0512 [12] 张书颖, 陈适之, 韩万水, 等. 基于集成学习的FRP加固混凝土梁抗弯承载力预测研究[J]. 工程力学. doi: 10.6052/j.issn.1000-4750.2021.06.0422.Zhang Shuying, Chen Shizhi, Han Wanshui, et al. Study on prediction of FRP strengthened reinforced concrete beam’s moment bearing capacity based on ensemble learning algorithm[J]. Engineering Mechanics. doi: 10.6052/j.issn.1000-4750.2021.06.0422. (in Chinese) [13] 李正良, 王成, 王涛, 等. 基于主动学习Kriging模型的直立锁缝屋面系统抗风揭可靠度分析[J]. 工程力学. doi: 10.6052/j.issn.1000-4750.2021.06.0430.Li Zhengliang, Wang Cheng, Wang Tao, et al. Reliability analysis of wind-resistance of standing seam roof system based on active learning kriging model[J]. Engineering Mechanics. doi: 10.6052/j.issn.1000-4750.2021.06.0430. (in Chinese) [14] Wang P, Lu Z, Tang Z. An application of the Kriging method in global sensitivity analysis with parameter uncertainty [J]. Applied Mathematical Modelling, 2013, 37: 6543 − 6555. doi: 10.1016/j.apm.2013.01.019 [15] Hurtado J E. An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory [J]. Structural Safety, 2004, 26: 271 − 293. doi: 10.1016/j.strusafe.2003.05.002 [16] 金伟良, 袁雪霞. 基于LS-SVM的结构可靠度响应面分析方法[J]. 浙江大学学报: 工学版, 2007, 41(1): 44 − 47.Jin Weiliang. Yuan Xuexia. Response surface method based on LS SVM for structural reliability analysis [J]. Journal of Zhejiang University (Engineering Science), 2007, 41(1): 44 − 47. (in Chinese) [17] Lu D G, Li G B. Reproducing kernel-based support vector machine for structural reliability analysis. [C]. Vancouver, Canada: 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12, 2015: 614 − 615. [18] Vapink V. Statistical learning theory [M]. New York: Wiley, 1998. [19] Clarke S M, Griebsch J H, Simpson T W. Analysis of support vector regression for approximation of complex engineering analyses [J]. Journal of Mechanical Design, 2005, 127: 1077 − 1087. doi: 10.1115/1.1897403 [20] Belytschko T, Krongauz Y, Organ D, et al. Meshless methods: An overview and recent developments [J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1/2/3/4): 3 − 47. [21] Saltelli A, Homma T. Importance measures in global sensitivity analysis of model output [J]. Reliability Engineering and System Safety, 1996, 52(1): 1 − 17. doi: 10.1016/0951-8320(96)00002-6 -
点击查看大图
图(3) / 表(4)
计量
- 文章访问数: 46
- HTML全文浏览量: 13
- PDF下载量: 26
- 被引次数: 0
