吉林大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (1): 174-179.doi: 10.13229/j.cnki.jdxbgxb201701026

• Orginal Article • Previous Articles     Next Articles

Structural reliability analysis based on dimension reduction algorithm

MENG Guang-wei, FENG Xin-yu, ZHOU Li-ming, Li Feng   

  1. College of Mechanical Science and Engineering,Jilin University,Changchun 130022,China
  • Received:2015-11-06 Online:2017-01-20 Published:2017-01-20

Abstract:

Considering the high-dimensional non-linear performance functions of complex structures, a new structural reliability analysis method based on dimension reduction algorithm was proposed. The n one-dimensional approximate functions were established to substitute the n dimensional performance function by using dimension reduction algorithm. With the help of Taylor series and statistical moment theory, the first four order moments of the performance function were solved. The cumulative distribution function of the performance function was fitted by Edgeworth series and the failure probability of the structure was obtained based on the reliability theory. Compared with the traditional methods, the new method does not need to use integral method to solve the statistical moments of the performance function, and not need to search the most possible failure point iteratively. Numerical results indicate that the proposed method has high precision and good adaptability.

Key words: engineering mechanics, reliability analysis, dimension reduction method, Taylor series, Edgeworth series, moment method

CLC Number: 

  • TB114.3
[1] 张鹏军,王惠源,李强,等.弹药精确装填可靠性分析及测试[J].光学精密工程,2014,22(7):1787-1793.
Zhang Peng-jun,Wang Hui-yuan,Li Qiang,et al.Analysis and test of reliability for ammunition accurate ramming[J].Optics and Precision Engineering,2014,22(7):1787-1793.
[2] 陈传海,杨兆军,孟广伟,等.考虑多种误差影响的数控机床载荷谱编制[J].光学精密工程,2015,23(10z):355-360.
Chen Chuan-hai,Yang Zhao-jun,Meng Guang-wei,et al.Load spectra of NC machine tools considering multiple influence factors[J]. Optics and Precision Engineering,2015,23(10z):355-360.
[3] Tang X S, Li D Q, Zhou C B, et al. Copula-based approaches for evaluating slope reliability under incomplete probability information[J]. Structural Safety, 2015, 52: 90-99.
[4] Balu A S, Rao B N. Multicut-High Dimensional Model Representation for Reliability Bounds Estimation[M]. New York: Springer International Publishing, 2015: 499-510.
[5] 周志国, 卢江跃. 弯曲振动下压电陶瓷复合圆盘的可靠性分析[J]. 吉林大学学报:工学版, 2013,43(增刊1):138-142.
Zhou Zhi-guo,Lu Jiang-yue. Reliability analysis of piezoceramics composite plate under bending vibration model[J]. Journal of Jilin University (Engineering and Technology Edition), 2013,43(Sup.1):138-142.
[6] 王保群, 张强勇, 李术才, 等. 盐岩地下储气库体积收敛失效概率分析与模型试验验证[J]. 吉林大学学报:地球科学版, 2014, 44(3): 954-960.
Wang Bao-qun, Zhang Qiang-yong, Li Shu-cai,et al. Analysis of failure probability and verification of model test underground uas storage's volume convergence in salt rock[J]. Journal of Jilin University(Earth Science Edition), 2014, 44(3): 954-960.
[7] Alibrandi U, Alani A M, Ricciardi G. A new sampling strategy for SVM-based response surface for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2015, 41: 1-12.
[8] Arastu M, Datta T K. Reliability analysis using genetic algorithm under seismic load[J]. Research Journal of Science and Technology, 2015, 7(1): 9-13.
[9] Dai H, Zhang H, Wang W. A multiwavelet neural network‐based response surface method for structural reliability analysis[J]. Computer-Aided Civil and Infrastructure Engineering, 2015, 30(2): 151-162.
[10] Rahman S, Wei D. A univariate approximation at most probable point for higher-order reliability analysis[J]. International Journal of Solids and Structures, 2006, 43(9): 2820-2839.
[11] Kong C, Sun Z, Niu X, et al. Moment methods for C/SiC woven composite components reliability and sensitivity analysis[J]. Science and Engineering of Composite Materials, 2014, 21(1): 121-128.
[12] Vrbik J. Moments of AR( k ) parameter estimators[J]. Communications in Statistics-Simulation and Computation, 2014, 44(5):1239-1252.
[13] Rivlin Y, Pinchas M. Edgeworth expansion based model for the convolutional noise pdf[J]. Mathematical Problems in Engineering, 2014,2014(4):1-19.
[14] Kah D, Emre O, Tran Q H, et al. High order moment method for polydisperse evaporating sprays with mesh movement: application to internal combustion engines[J]. International Journal of Multiphase Flow, 2015,71:38-65.
[15] Pearson P B. The impact of school-level factors on minority students' performance in AP calculus[D]. Warsaw: Portland State University,2014.
[16] Kim S D, Hammond R K, Bickel J E. Improved mean and variance estimating formulas for PERT analyses[J]. IEEE Transactions on Engineering Management, 2014, 61(2): 362-369.
[17] Abelev B,Adam J,Adamová D,et al. Multiplicity dependence of pion, kaon, proton and lambda production in p-Pb collisions at s NN = 5.02 TeV mathContainer Loading Mathjax[J]. Physics Letters B, 2014, 728(1): 25-38.
[18] Risti c ' M, Kundu D. Marshall-Olkin generalized exponential distribution[J]. Metron, 2015,73(3): 1-17.
[19] Duncan J, Wu Q, Promislow K, et al. Biased gradient squared descent saddle point finding method[J]. Journal of Chemical Physics, 2014, 140(19): 194102.
[20] Plasencia M, Pedersen A, Arnaldsson A, et al. Geothermal model calibration using a global minimization algorithm based on finding saddle points and minima of the objective function[J]. Computers & Geosciences, 2014, 65: 110-117.
[21] Chao Z, Chen G. A note on semi-convergence of generalized parameterized inexact Uzawa method for singular saddle point problems[J]. Numerical Algorithms, 2015, 68(1): 95-105.
[22] Shi X, Teixeira A P, Zhang J, et al. Structural reliability analysis based on probabilistic response modelling using the maximum entropy method[J]. Engineering Structures, 2014, 70(9): 106-116.
[23] Peco C, Millán D, Rosolen A, et al. Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants[J]. Computers & Structures, 2015, 150: 52-62.
[24] 宋述芳, 吕震宙. 基于鞍点估计及其改进法的可靠性灵敏度分析[J]. 力学学报, 2011, 43(1): 162-168.
Song Shu-fang, Lyu Zhen-zhou. The reliability sensitivity analysis based on saddlepoint approximation and its improved method[J]. Chinese Journal of Theoretical and Applied Mechanics,2011, 43(1): 162-168.
[1] NI Ying-sheng,SUN Qi-xin,MA Ye,XU Dong,LIU Chao. Shear distribution of multi-cell corrugated steel web composite beams based on space grid analysis [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(6): 1735-1746.
[2] YAN Ya-bin, WANG Xiao-yuan, WAN Qiang. Low-cycle fatigue fracture behavior of nanoscale interface [J]. 吉林大学学报(工学版), 2017, 47(4): 1201-1206.
[3] CHEN Jiang-yi, LIU Bao-yuan. Influence of fiber fracture damage on dispersion characteristic of guided wave in composite plate [J]. 吉林大学学报(工学版), 2017, 47(1): 180-184.
[4] SI Wei, MA Biao, REN Jun-ping, WANG Hai-nian, GE-Sang Ze-ren. Analysis of asphalt pavement performance under freeze-thaw cycles using reliability method [J]. 吉林大学学报(工学版), 2016, 46(1): 126-132.
[5] YANG Hui-yan, HE Xiao-cong, ZHOU Sen. Simulation and calculation methods for clinched joint strength [J]. 吉林大学学报(工学版), 2015, 45(3): 864-871.
[6] ZHANG Qing,WANG Lei. Internal force analysis of multiple rows of piles based on differential equation set [J]. 吉林大学学报(工学版), 2014, 44(5): 1327-1333.
[7] ZHOU Zhi-guo, LU Jiang-yue. Reliability Analysis of piezoceramics composite plate under bending vibration model [J]. 吉林大学学报(工学版), 2013, 43(增刊1): 138-142.
[8] ZHAO Shi-jia, XU Tao, CHEN Wei, TAN Li-hui. Efficient approach for modal sensitivity analysis for near defective systems [J]. 吉林大学学报(工学版), 2013, 43(增刊1): 497-499.
[9] WANG Xiao-yan, SHEN Gui-xiang, ZHANG Ying-zhi, ZHENG Shan, NIU Xu-lei, LIANG Dong. Analysis about failure correlation of CNC equipment base on DEMATEL [J]. 吉林大学学报(工学版), 2012, 42(增刊1): 100-103.
[10] XU Tao, ZHAO Shi-jia, ZHANG Wei, TAN Li-hui, LV Gang, LI Heng. Perturbed origin shift combined approximation method of N repeated defective systems [J]. 吉林大学学报(工学版), 2012, 42(增刊1): 147-150.
[11] YAN Guang, FAN Zhou, LI Zhong-hai, CHENG Xiao-quan, LIU Ke-ge, ZUO Chun-cheng. Analysis and design of composite cylindrical shell with cover [J]. , 2012, (06): 1437-1441.
[12] JIANG Hao, GUO Xue-dong. Concrete bridge modal parameter identification under seismic excitations [J]. 吉林大学学报(工学版), 2011, 41(增刊2): 185-188.
[13] TIAN Wei, GUO Xue-dong, YIN Xin-sheng. Theoretical and experimental research on oblique cross-section cracking resistance of wall-beam by concrete hollow block [J]. 吉林大学学报(工学版), 2011, 41(增刊2): 189-193.
[14] ZHANG Ying-zhi, ZHENG Rui, SHEN Gui-xiang, WANG Zhi-qiong, LI Huai-yang, et al. Failure dependency of CNC equipment based on copula theory [J]. 吉林大学学报(工学版), 2011, 41(6): 1636-1640.
[15] LI Chun-liang, WANG Guo-qiang, LIU Fu-shou, ZHAO Kai-jun. Mechanical behavior analysis of shield segment structure [J]. 吉林大学学报(工学版), 2011, 41(6): 1669-1674.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!