Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points

Qingqiu Zhou; Junjie Wang

doi:doi:10.11648/j.sd.20221005.11

| Peer-Reviewed

Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points

Qingqiu Zhou, Junjie Wang

Published in Science Discovery (Volume 10, Issue 5)

Received: 7 August 2022 Accepted: 1 September 2022 Published: 5 September 2022

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In the reliability theory, the moment method proposed by Zhao obtains the first fourth order moments of the structural function by the point estimation method based on Gauss-Emhart integral, assuming that the functional function satisfies a specific distribution or the approximate probability distribution function of the functional function is obtained by the Pearson system, so as to solve the reliability index and failure probability of the structure. For the elastic phase, the structural function is a smooth curve, and a large number of cases have proved that only 5-point estimation or 7-point estimation is required, and the moment method can achieve high accuracy, and the accuracy increases monotonically with the increase of the estimated number of points. In the case of structural elasto-plastic analysis, such as bridge ship impact analysis and structural static elasto-plastic analysis, the functional function will have folded points, and the accuracy and efficiency of the method of moments need to be studied. Comparing the calculation results of the method of moments and Monte-Carlo simulation, the accuracy of the method of moments does not increase monotonically with the increase of the estimated number of points in the case of the functional function with fold points, and when the number of estimated points is sufficient, generally 15-23, the calculation results of the method of moments are basically stable and have good accuracy. Under the same accuracy requirement, the calculation volume of the method of moments increases when the function function has fold points compared with the smooth function case, but the Monte-Carlo simulation still has higher calculation efficiency compared with the smooth function case.

Published in	Science Discovery (Volume 10, Issue 5)
DOI	10.11648/j.sd.20221005.11
Page(s)	279-285
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Method of Moments, Polygonal Line Force - Displacement Curve, Calculation Efficiency

References

[1]	Hasofer, A. M., and Lind, N. C. ‘Exact and invariant second moment code format. J. Engrg. Mech. Div., ASCE, 100 (1): 111-121. 1974.
[2]	Rackwitz, R. Practical probabilistic approach to design. First order reliability concepts for design codes, Bull. d’Information, No. 112, Comite European du Beton, Munich, Germany. 1976.
[3]	Breitung, K. Asymptotic approximation for multinormal integrals. J. Engrg. Mech., ASCE, 110 (3), 357–366. 1984.
[4]	Der Kiureghian, A., Lin, H. Z., and Hwang, S. J. Second-order reliability approximations. J. Engrg. Mech., ASCE, 113 (8), 1208–1225. 1987.
[5]	Cai, G. Q., and Elishakoff, I. Refined second-order reliability analysis. Struct. Safety, 14 (3), 267–276. 1994.
[6]	赵国藩，金伟良，贡金鑫.结构可靠度理论[M].中国建筑工业出版社，2000。
[7]	张明.结构可靠度理论-方法与程序[M].科学出版社，2009。
[8]	Zhao YG, Ono T. Moment methods for structural reliability. Structural Safety 2001; 23 (1): 47–75.
[9]	Zhao YG, Ono T. New point-estimates for probability moments. J Engrg, Mech, ASCE 2000; 126 (4): 433–6.
[10]	Tichy, M. First-order third-moment reliability method. Structural Safety. Vol. 16, 189-200, 1994.
[11]	SCHOPRA A K．Dynamics of Structures [M]. 2nd Edition，影印版．北京：清华大学出版社，2005。
[12]	孟德巍.船撞桥的简化动力分析[D]. 上海：同济大学土木工程学院，2010。
[13]	卜令涛.船舶对桥梁冲击作用的简化概率方法[D].上海：同济大学土木工程学院，2011。
[14]	Zhao, Y. and Ono, T. On the problems of the fourth moment method, Struct. Safety 26 (4): 343–347, 2004.
[15]	Sang Hoon Lee, Byung Man Kwak. Response surface augmented moment method for efficient reliability analysis, Structural Safety, 28: 261-272, 2006.
[16]	Fu T, Liu Y, Zhu Z. Research on Bridge Structure Reliability Evaluation due to Vessels Collison Based on a Statistical Moment Method [J]. Hindawi Limited, 2021.

Cite This Article

Plain Text BibTeX RIS

APA Style

Qingqiu Zhou, Junjie Wang. (2022). Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points. Science Discovery, 10(5), 279-285. https://doi.org/10.11648/j.sd.20221005.11

Copy | Download

ACS Style

Qingqiu Zhou; Junjie Wang. Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points. Sci. Discov. 2022, 10(5), 279-285. doi: 10.11648/j.sd.20221005.11

Copy | Download

AMA Style

Qingqiu Zhou, Junjie Wang. Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points. Sci Discov. 2022;10(5):279-285. doi: 10.11648/j.sd.20221005.11

Copy | Download

@article{10.11648/j.sd.20221005.11,
  author = {Qingqiu Zhou and Junjie Wang},
  title = {Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points},
  journal = {Science Discovery},
  volume = {10},
  number = {5},
  pages = {279-285},
  doi = {10.11648/j.sd.20221005.11},
  url = {https://doi.org/10.11648/j.sd.20221005.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20221005.11},
  abstract = {In the reliability theory, the moment method proposed by Zhao obtains the first fourth order moments of the structural function by the point estimation method based on Gauss-Emhart integral, assuming that the functional function satisfies a specific distribution or the approximate probability distribution function of the functional function is obtained by the Pearson system, so as to solve the reliability index and failure probability of the structure. For the elastic phase, the structural function is a smooth curve, and a large number of cases have proved that only 5-point estimation or 7-point estimation is required, and the moment method can achieve high accuracy, and the accuracy increases monotonically with the increase of the estimated number of points. In the case of structural elasto-plastic analysis, such as bridge ship impact analysis and structural static elasto-plastic analysis, the functional function will have folded points, and the accuracy and efficiency of the method of moments need to be studied. Comparing the calculation results of the method of moments and Monte-Carlo simulation, the accuracy of the method of moments does not increase monotonically with the increase of the estimated number of points in the case of the functional function with fold points, and when the number of estimated points is sufficient, generally 15-23, the calculation results of the method of moments are basically stable and have good accuracy. Under the same accuracy requirement, the calculation volume of the method of moments increases when the function function has fold points compared with the smooth function case, but the Monte-Carlo simulation still has higher calculation efficiency compared with the smooth function case.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points
AU  - Qingqiu Zhou
AU  - Junjie Wang
Y1  - 2022/09/05
PY  - 2022
N1  - https://doi.org/10.11648/j.sd.20221005.11
DO  - 10.11648/j.sd.20221005.11
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 279
EP  - 285
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20221005.11
AB  - In the reliability theory, the moment method proposed by Zhao obtains the first fourth order moments of the structural function by the point estimation method based on Gauss-Emhart integral, assuming that the functional function satisfies a specific distribution or the approximate probability distribution function of the functional function is obtained by the Pearson system, so as to solve the reliability index and failure probability of the structure. For the elastic phase, the structural function is a smooth curve, and a large number of cases have proved that only 5-point estimation or 7-point estimation is required, and the moment method can achieve high accuracy, and the accuracy increases monotonically with the increase of the estimated number of points. In the case of structural elasto-plastic analysis, such as bridge ship impact analysis and structural static elasto-plastic analysis, the functional function will have folded points, and the accuracy and efficiency of the method of moments need to be studied. Comparing the calculation results of the method of moments and Monte-Carlo simulation, the accuracy of the method of moments does not increase monotonically with the increase of the estimated number of points in the case of the functional function with fold points, and when the number of estimated points is sufficient, generally 15-23, the calculation results of the method of moments are basically stable and have good accuracy. Under the same accuracy requirement, the calculation volume of the method of moments increases when the function function has fold points compared with the smooth function case, but the Monte-Carlo simulation still has higher calculation efficiency compared with the smooth function case.
VL  - 10
IS  - 5
ER  -

Copy | Download

Author Information

Qingqiu Zhou

College of Civil Engineering, Tongji University, Shanghai, China
Junjie Wang

College of Civil Engineering, Tongji University, Shanghai, China

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Qingqiu Zhou, Junjie Wang. (2022). Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points. Science Discovery, 10(5), 279-285. https://doi.org/10.11648/j.sd.20221005.11

Copy | Download

ACS Style

Qingqiu Zhou; Junjie Wang. Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points. Sci. Discov. 2022, 10(5), 279-285. doi: 10.11648/j.sd.20221005.11

Copy | Download

AMA Style

Qingqiu Zhou, Junjie Wang. Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points. Sci Discov. 2022;10(5):279-285. doi: 10.11648/j.sd.20221005.11

Copy | Download

@article{10.11648/j.sd.20221005.11,
  author = {Qingqiu Zhou and Junjie Wang},
  title = {Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points},
  journal = {Science Discovery},
  volume = {10},
  number = {5},
  pages = {279-285},
  doi = {10.11648/j.sd.20221005.11},
  url = {https://doi.org/10.11648/j.sd.20221005.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20221005.11},
  abstract = {In the reliability theory, the moment method proposed by Zhao obtains the first fourth order moments of the structural function by the point estimation method based on Gauss-Emhart integral, assuming that the functional function satisfies a specific distribution or the approximate probability distribution function of the functional function is obtained by the Pearson system, so as to solve the reliability index and failure probability of the structure. For the elastic phase, the structural function is a smooth curve, and a large number of cases have proved that only 5-point estimation or 7-point estimation is required, and the moment method can achieve high accuracy, and the accuracy increases monotonically with the increase of the estimated number of points. In the case of structural elasto-plastic analysis, such as bridge ship impact analysis and structural static elasto-plastic analysis, the functional function will have folded points, and the accuracy and efficiency of the method of moments need to be studied. Comparing the calculation results of the method of moments and Monte-Carlo simulation, the accuracy of the method of moments does not increase monotonically with the increase of the estimated number of points in the case of the functional function with fold points, and when the number of estimated points is sufficient, generally 15-23, the calculation results of the method of moments are basically stable and have good accuracy. Under the same accuracy requirement, the calculation volume of the method of moments increases when the function function has fold points compared with the smooth function case, but the Monte-Carlo simulation still has higher calculation efficiency compared with the smooth function case.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Precision and Efficiency of the Method of Moments Applied to the Functional Functions with Fold Points
AU  - Qingqiu Zhou
AU  - Junjie Wang
Y1  - 2022/09/05
PY  - 2022
N1  - https://doi.org/10.11648/j.sd.20221005.11
DO  - 10.11648/j.sd.20221005.11
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 279
EP  - 285
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20221005.11
AB  - In the reliability theory, the moment method proposed by Zhao obtains the first fourth order moments of the structural function by the point estimation method based on Gauss-Emhart integral, assuming that the functional function satisfies a specific distribution or the approximate probability distribution function of the functional function is obtained by the Pearson system, so as to solve the reliability index and failure probability of the structure. For the elastic phase, the structural function is a smooth curve, and a large number of cases have proved that only 5-point estimation or 7-point estimation is required, and the moment method can achieve high accuracy, and the accuracy increases monotonically with the increase of the estimated number of points. In the case of structural elasto-plastic analysis, such as bridge ship impact analysis and structural static elasto-plastic analysis, the functional function will have folded points, and the accuracy and efficiency of the method of moments need to be studied. Comparing the calculation results of the method of moments and Monte-Carlo simulation, the accuracy of the method of moments does not increase monotonically with the increase of the estimated number of points in the case of the functional function with fold points, and when the number of estimated points is sufficient, generally 15-23, the calculation results of the method of moments are basically stable and have good accuracy. Under the same accuracy requirement, the calculation volume of the method of moments increases when the function function has fold points compared with the smooth function case, but the Monte-Carlo simulation still has higher calculation efficiency compared with the smooth function case.
VL  - 10
IS  - 5
ER  -

Copy | Download