Xu Zhang¹, Jianchao Ni², Juxi Hu^3,*, Weisi Chen⁴

Computer Systems Science and Engineering, Vol.46, No.2, pp. 1947-1960, 2023, DOI:10.32604/csse.2023.035118

Abstract Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors. Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid. The uncertain parameters mainly exist in the form of intervals. This method requires a lot of calculation and is often difficult to achieve efficiently. In order to solve this problem, this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty. Based on the non-probabilistic… More >

Qiang Qin^1,2,*, Xiaolei Cao¹, Shengpeng Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1457-1480, 2023, DOI:10.32604/cmes.2023.022078

Abstract In this work, an improved active kriging method based on the AK-IS and truncated importance sampling (TIS) method is proposed to efficiently evaluate structural reliability. The novel method called AWK-TIS is inspired by AK-IS and RBF-GA previously published in the literature. The innovation of the AWK-TIS is that TIS is adopted to lessen the sample pool size significantly, and the whale optimization algorithm (WOA) is employed to acquire the optimal Kriging model and the most probable point (MPP). To verify the performance of the AWK-TIS method for structural reliability, four numerical cases which are utilized as benchmarks in literature and… More >

Wencai Sun^{1, ∗}, Zichun Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 309-332, 2020, DOI:10.32604/cmes.2020.08386

Abstract It is very difficult to know the exact boundaries of the variable domain for problems with small sample size, and the traditional convex set model is no longer applicable. In view of this, a novel reliability model was proposed on the basis of the fuzzy convex set (FCS) model. This new reliability model can account for different relations between the structural failure region and variable domain. Key computational algorithms were studied in detail. First, the optimization strategy for robust reliability is improved. Second, Monte Carlo algorithms (i.e., uniform sampling method) for hyper-ellipsoidal convex sets were studied in detail, and errors… More >

M. Q. Chau^1,2, X. Han¹, Y. C. Bai¹, C. Jiang¹

CMC-Computers, Materials & Continua, Vol.27, No.2, pp. 128-142, 2012, DOI:10.32604/cmc.2012.027.128

Abstract The first-order reliability method (FORM) is one of the most widely used structural reliability analysis techniques due to its simplicity and efficiency. However, direct using FORM seems disability to work well for complex problems, especially related to high-dimensional variables and computation intensive numerical models. To expand the applicability of the FORM for more practical engineering problems, a response surface (RS) approach based FORM is proposed for structural reliability analysis. The radial basis function (RBF) is employed to approximate the implicit limit-state functions combined with Latin Hypercube Sampling (LHS) strategy. To guarantee the numerical stability, the improved HL-RF (iHL-RF) algorithm is… More >

Zichun Yang^1,2,3, Kunfeng Li^1,4, Qi Cai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.2, pp. 143-171, 2013, DOI:10.3970/cmes.2013.095.143

Abstract The conventional probabilistic reliability model for structures is based on the “probability assumption” and “binary-state assumption”. These assumptions are often offset the reality of practical engineering and lead to a wrong conclusion. In fact, besides randomness, fuzziness which is different from randomness in nature is also a prevalent uncertainty factor and plays an important role in structural reliability assessment. In this paper, a novel structural reliability model with random variables and fuzzy variables is established by using the fuzzy set theory, possibility theory and probability measure for fuzzy events, based on the “mixed probability and possibility assumption” and “fuzzy state… More >

W. Zhao^1,2, J.K. Liu³, X.Y. Li², Q.W. Yang⁴, Y.Y. Chen⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.6, pp. 469-488, 2013, DOI:10.3970/cmes.2013.093.469

Abstract In order to obtain reliable structural design, it is of extreme importance to evaluate the failure probability, safety levels of structure (reliability analysis) and the effect of a change in a variable parameter on structural safety (sensitivity analysis) when uncertainties are considered. With a computationally cheaper approximation of the limit state function, various response surface methods (RSMs) have emerged as a convenient tool to solve this especially for complex problems. However, the traditional RSMs may produce large errors in some conditions especially for those highly non-linear limit state functions. Instead of the traditional least squares approximation, in the present paper,… More >

S.R. Santos¹, L.C. Matioli², A.T. Beck³

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.1, pp. 23-56, 2012, DOI:10.3970/cmes.2012.083.023

Abstract Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on… More >