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New collocation method for stochastic response surface reliability analyses

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Abstract

The stochastic response surface method (SRSM) is widely used in engineering reliability analyses due to its efficiency and accuracy. The selection of collocation points in the SRSM has great significance, as it may strongly affect the computed results. This paper investigates the performance of different selection strategies in SRSM, and proposes a new collocation method. First, two commonly used collocation methods—the regression-based collocation method and the linearly independent collocation method—are briefly reviewed; and their limitations in application to reliability analysis are discussed. Then, an improved collocation method that achieves a better tradeoff between efficiency and accuracy is proposed. Four examples are employed to test the performance of the proposed collocation method; and a comparative study is conducted to demonstrate its advantages with respect to some other existing collocation methods.

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Abbreviations

p :

Order of PCE

X :

A vector of random variables in physical space

U :

A vector of uncorrelated standard normal random variables

y :

Random output of the model

Γp(·):

Multidimensional Hermite polynomials of order p

n :

Number of random variables in PCE

a :

A vector of unknown coefficients

T :

Hermite polynomial information matrix

T :

Transpose matrix operator

N a :

Number of unknown coefficients

P i :

Selected collocation point

P i :

Symmetric point of Pi with respect to the origin

ζ :

Asymmetrical ratio of the selected collocation points

Δ:

Relative error with respect to MCS or LHS

N p :

Number of selected collocation points or limit state function evaluations

COV:

Coefficient of variation

P f :

Probability of failure

μ :

Mean value

SD:

Standard deviation

σ t :

Applied support pressure at the tunnel face

σ c,partial :

Collapse pressure provided by partial collapse mechanism

σ c,global :

Collapse pressure provided by global collapse mechanism

σ c,max :

Maximum collapse pressure provided by partial collapse or global collapse

c :

Cohesion

φ :

Friction angle

ρ :

Correlation coefficient

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Project nos. 41602304 and 41772329), the Sichuan Science and Technology Program (Project No. 2019YJ0405), the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Project no. SKLGP2016Z003) and the Spanish Ministry of Economy and Competitiveness (Project no. BIA2015-69152-R). Their support is greatly appreciated.

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366_2019_793_MOESM1_ESM.rar

Supplementary material 1 (RAR 98 kb) Supplementary materials Supplementary data associated with the selected collocation points for LICM, RBCM and SFRCM (up to the 6th order PCE and up to 10 random variables)

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Zeng, P., Li, T., Chen, Y. et al. New collocation method for stochastic response surface reliability analyses. Engineering with Computers 36, 1751–1762 (2020). https://doi.org/10.1007/s00366-019-00793-2

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