Fangyi Li^*, Dachang Zhu^*, Huimin Shi

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1981-1999, 2024, DOI:10.32604/cmes.2023.031332

Abstract In time-variant reliability problems, there are a lot of uncertain variables from different sources. Therefore, it is important to consider these uncertainties in engineering. In addition, time-variant reliability problems typically involve a complex multilevel nested optimization problem, which can result in an enormous amount of computation. To this end, this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model. In this method, the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a time-independent reliability problem. Further, to solve the… More >

Jiaqi He¹, Yangjun Luo^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.2, pp. 777-800, 2020, DOI:10.32604/cmes.2020.010688

Abstract For structures that only the predicted bounds of uncertainties are available, this study proposes a Bayesian method to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data. According to the given interval ranges of uncertainties, we determine the initial characteristic parameters of a multi-ellipsoid convex set. Moreover, to update the plausibility of characteristic parameters, a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed. Then, an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved. The credible non-probabilistic reliability… More >

Fangyi Li^1,2, Zhen Luo³, Jianhua Rong¹, Lin Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.6, pp. 453-482, 2013, DOI:10.3970/cmes.2013.095.453

Abstract This paper aims to propose a non-probabilistic reliability-based multiobjective optimization method for structures with uncertain-but-bounded parameters. A combination of the interval and ellipsoid convex models is used to account for the different groups of uncertain parameters, in which the interval model accounts for uncorrelated parameters, while the ellipsoid model is applied to correlated parameters. The design is then formulated as a nested double-loop optimization problem. A multi-objective genetic algorithm is used in the out loop optimization to optimize the design vector for evaluating the objectives, and the Sequential Quadratic Programming (SQP) algorithm is applied in the inner loop to evaluate… More >

Zichun Yang^1,2,3, Wencai Sun²

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.2, pp. 193-212, 2013, DOI:10.3970/cmes.2013.092.193

Abstract The set-based structural eigenvalue problem is defined, by expressing the uncertainties of the structural parameters in terms of various convex sets. A new method based on Kriging model and Particle Swarm Optimization (PSO) is proposed for solving this problem. The introduction of the Kriging model into this approach can effectively reduce the computational burden especially for largescale structures. The solutions of the non-linear and non-monotonic problems are more accurate than those obtained by other methods in the literature with the PSO algorithm. The experimental points for Kriging model are sampled according to Latin hypercube sampling method. Two approaches of imposing… More >

C. Jiang^1,2, Q.F. Zhang¹, X. Han¹, D. Li³, J. Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.1, pp. 65-82, 2011, DOI:10.3970/cmes.2011.074.065

Abstract In this paper, an interval optimization method is developed to deal with a class of problems that there exists dependence between the interval parameters. An ellipsoidal convex model is used to model the uncertainty domain, in which the parameter dependence can be well reflected through the shape of a multi-dimensional ellipsoid. Based on an order relation and a reliability-based possibility degree of interval, the uncertain optimization can be transformed to a deterministic nesting optimization. An efficient algorithm is then constructed to solve the created nesting optimization, in which a sequence of approximate interval optimizations are created and the optimal design… More >