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

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. KeywordsDoubly weighted moving least squares · Surrogate model · Two-stage hybrid method · Adaptive experimental design · Structural reliability analysis · Latin hypercube design Nomenclature n number of input random variables N number of experimental points x vector of input random variables β reliability index β H L reliability index by Hasofer-Lind algorithm μ mean σ standard deviation g(X) limit state function g(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 70 J. Li et al.

Robust optimization of composite cylindrical shell by a trigonometric mixed response surface method

“…The Gaussian function was considered a useful form with the weight coefficient 𝛼 = 2 for the weighted functions by Li and Wang. 43 In this paper, the weighted matrix W(x) can be constructed by Gaussian functions in diagonal terms.…”

A Novel Progressive Response Surface Method for High-order polynomial Metamodel

“…Wx be defined as: (11) In Equation ( 10 is the coefficient of the Gaussian weight function. Among these weight functions, for MLSM, it has been thought most effective weight function using the Gaussian function by most scholars [21,22].In particular, the coefficient value of this Gaussian weight function can be taken as 2.5  = [22]. Analogously, the minimum of the residual error under weight functions can also be obtained by this partial derivative Equation:…”

“…A weighted RSM had been implemented for structural reliability analysis using MLSM by Kaymaz and McMahon [8]. To accurately predict the failure probability, Li, Wang and Kim [9] proposed a doubly-weighted moving least squares (DWMLS) method. It is obvious that the MLSM is another effective method to improve the accuracy of the RSM model.…”

Robust Design Optimization for Crashworthiness of Vehicle Side Impact

“…Second, the process of uncertainty quantification is computationally intensive and often requires a tradeoff between efficiency and accuracy. Even the popular methods for uncertainty quantification such as perturbation method [27,28], Kriging [29][30][31][32][33][34], polynomial chaos expansion (PCE) [35][36][37][38][39][40][41][42], moving least square method [43][44][45][46], collocation-based approaches [47], tensor product-based approach [48], and radial basis function [49][50][51][52][53] often yields erroneous results when coupled into the framework of RDO. In this context, there is a need of efficient uncertainty quantification tool that can be utilized for solving RDO problems.…”