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Doubly weighted moving least squares and its application to structural reliability analysis

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Abstract

In this paper, we proposed a two-stage hybrid reliability analysis framework based on the surrogate model, which combines the first-order reliability method and Monte Carlo simulation with a doubly-weighted moving least squares (DWMLS) method. The first stage consists of constructing a surrogate model based on DWMLS. The weight system of DWMLS considers not only the normal weight factor of moving least squares, but also the distance from the most probable failure point (MPFP), which accounts for reliability problems. An adaptive experimental design scheme is proposed, during which the MPFP is progressively updated. The approximate values and sensitivity information of DWMLS are chosen to determine the number and location of the experimental design points in the next iteration, until a convergence criterion is satisfied. In the second stage, MCS on the surrogate model is then used to calculate the probability of failure. The proposed method is applied to five benchmark examples to validate its accuracy and efficiency. Results show that the proposed surrogate model with DWMLS can estimate the failure probability accurately, while requiring fewer original model simulations.

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Abbreviations

n :

number of input random variables

N:

number of experimental points

x :

vector of input random variables

β :

reliability index

β HL :

reliability index by Hasofer–Lind algorithm

μ :

mean

σ :

standard deviation

g(X):

limit state function

\(\hat{{g}}({\rm {\bf X}})\) :

approximate limit state function/ response surface function

X add :

new added experimental points in any iteration

MLS:

moving least square

DWMLS:

doubly weighted moving least square

SVR:

support vector regression

ANN:

artificial neural networks

MPFP:

most probable failure point

MCS:

Monte Carlo Simulation

FORM:

first order reliability method

SORM:

second order reliability method

H–L:

Hasofer–Lind algorithm

RSM:

response surface method

LHD:

Latin hypercube design

FEA:

finite element analysis

CFD:

computational fluid dynamics

COV:

coefficient of variation

UDR:

Univariate Dimension-Reduction

MPP-UDR:

Most probable point based UDR

SGI:

Sparse Grid Interpolation

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Acknowledgments

The study reported in this paper was funded by China Scholarship Council under support number 2010623114. The authors also thank Prof. Raphael T. Haftka and Dr Felipe A. C. Viana for their valuable comments.

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Authors and Affiliations

  1. School of Aeronautic and Astronautic, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jian Li & Hai Wang

  2. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611, USA

    Jian Li & Nam H. Kim

Authors
  1. Jian Li
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  2. Hai Wang
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  3. Nam H. Kim
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Correspondence to Nam H. Kim.

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Li, J., Wang, H. & Kim, N.H. Doubly weighted moving least squares and its application to structural reliability analysis. Struct Multidisc Optim 46, 69–82 (2012). https://doi.org/10.1007/s00158-011-0748-2

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  • DOI: https://doi.org/10.1007/s00158-011-0748-2

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