对8个输入随机变量进行了抽样，分别选取7条地震动记录和El Centro地震动记录，利用有限元软件OpenSEES进行了动力非线性时程分析，得到了基底剪力、顶点位移、最大楼层加速度和最大层间位移角4种结构地震需求。将核密度估计用于结构地震需求信息熵重要性分析的求解中，并用方差重要性分析方法进行了对比。结果表明：采用的抽样方法在样本量为几百时即可得到较好的结果，这远远少于现有的抽样方法所需要的成千上万的样本数，是一种准确高效的抽样方法；基于核密度估计得到的各个输入随机变量的信息熵重要性排序与方差重要性分析方法得到的各个输入随机变量的重要性排序基本一致，可见基于信息熵的重要性测度分析方法是一种良好的重要性分析方法。
Abstract
8 input random variables including the selected 7 ground motion records and an El Centro one were sampled, respectively.The dynamic nonlinear time history analysis was conducted for a multi-floor building with the finite element software OpenSees.Its base shear, top point displacement, the maximum floor acceleration and the maximum interlayer displacement angle were obtained as the structure’s seismic demands.The kernel density estimation was used to do the structural seismic demand information entropy importance analysis, and the results were compared with those using the variance importance analysis method.The results showed that the used sampling method can get better results when the sample number is hundreds, and this number is far less than thousands required by the existing sampling method, so it is an accurate and efficient sampling method; the information entropy importance sequencing of each input random variable based on the kernel density estimation and that based on the variance importance analysis are basically consistent, so the importance measure analysis method based on information entropy is a good method of importance analysis.
关键词
信息熵 /
核密度估计 /
地震需求 /
重要性分析
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Key words
information entropy /
kernel density estimation /
seismic demand /
importance analysis
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参考文献
[1] Ratto M, Pagano A, Young P. State Dependent Parameter meta-modelling and sensitivity analysis[J]. Computer Physics Communications, 2007, 177(11):863-876.
[2] 钟祖良, 涂义亮, 刘新荣,等.浅埋双侧偏压小净距隧道衬砌荷载及其参数敏感性分析[J].土木工程学报, 2013, 46(1):119-125.
Zhong Z, Tu Y, Liu X, et al. Calculation of lining loading of shallow-buried bilateral bias twin tunnel and its parameter sensitivity analysis[J]. China Civil Engineering Journal, 2013, 46(1):119-125.
[3] 李思，孙克国，仇文革，等.寒区隧道温度场的围岩热学参数影响及敏感性分析[J].土木工程学报,2017,50(1):117-122.
Li Si,Sun Keguo,Qiu Wenge, et al.Influence and sensitivity analysis of surrounding rock thermal parameters on temperature field of cold region tunnel[J]. China Civil Engineering Journal, 2017,50(1):117-122.
[4] 叶继红, 李柯燃. 多点输入下基于响应敏感性的单层球面网壳冗余特性研究[J]. 土木工程学报, 2016,49(9):20-29.
Ye Jihong, Li Keran. Research on redundancy characteristics of single-layer spherical reticulated shell based on response sensitivity[J]. Journal of civil engineering, 2016,49(9): 20-29.
[5] Saltelli A.Sensitivity analysis for importance assessment.Risk Analysis,2002,22(3):579-590.
[6] 吕震宙，宋述芳，李洪双等，结构机构可靠性及可靠性灵敏度分析[M]. 北京：科学出版社，2009.
Lü Zhenzhou, Song Shufang, Li Hongshuang and so on. Structural reliability and reliability sensitivity analysis[M]. Science Press, Beijing, 2009.
[7] Tang Z, Lu Z, Jiang B, et al. Entropy-Based Importance Measure for Uncertain Model Inputs[J]. Aiaa Journal, 2013, 51(10):2319-2334.
[8] Qiao Liu, Toshimitsu Homma. A new computational method of a moment-independent uncertainty importance measure[J]. Reliability Engineering & System Safety, 2009, 94(7):1205-1211.
[9] Shannon C E. A mathematical theory of communication[M]. s.n.], 1948.
[10] Tang Zhangchun. Entropy-Based Importance Measure for Uncertain Model Inputs[J]. Aiaa Journal, 2013, 51 (10) : 2319-2334.
[11] KhosrowDehnad. Density Estimation for Statistics and Data Analysis[J]. Technometrics, 2012, 29(4):495-495.
[12] X.B. Li. A method for fitting probability distributions to engineering properties of rock masses using Legendre orthogonal polynomials[J]. Structural Safety, 2009, 31 (4): 335-343.
[13] Christian Soize.Maximum entropy approach for modeling random uncertainties in transient elastodynamics[J]. Journal of the Acoustical Society of America, 2001, 109 (1): 1979-1996.
[14] Zhang P. Nonparametric Importance Sampling[J]. Publications of the American Statistical Association, 1996, 91(435):1245-1253.
[15] Silverman B W. Density estimation for statistics and Data analysis[M]. CRC press,1986.
[16] GB50010-2010，钢筋混凝土结构设计规范[S].
GB 50010-2010，Code for design of reinforced concrete frame structure[S].
[17] Mirza S A,Macgregor J G.Variability of mechanical properties of reinforced bars[J]. Journal of Structural Division,1979,105(5):921-937.
[18] Porter K A, Beck J L, Shaikhutdinov R V. Sensitivity of Building Loss Estimates to Major Uncertain Variables[J]. Earthquake Spectra, 2002, 18(4):719-743.
[19] Mirza S A, Hatzinikolas M, Macgregor J G. Statistical Descriptions of Strength of Concrete[J]. Journal of the Structural Division, 1979, 105(6):1021-1037.
[20] 宋帅，钱永久，钱聪. 桥梁地震需求中随机参数的重要性分析方法研究[J]. 工程力学，2018，35(3): 106-114.
Song Shuai, Qian Yong-jiu, Qian Cong. Research on methods for importance analysis of random parameters in bridge seismic demand [J]. engineering mechanics, 2018, 35 (3): 106-114.
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