J.L. Sereno¹, J.C.F. Pereira¹

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.1, pp. 23-44, 2011, DOI:10.3970/cmes.2011.073.023

Abstract The evolution of a two-dimensional vortex pair in ground effect was studied under the influence of random initial inputs comprising vortex strength (circulation) or initial vortex position. The paper addresses the questions of how do variations and uncertainties of initial conditions translate to the variability of vortex pair evolution. The stochastic solutions were obtained recurring to the Polynomial Chaos Expansion method of random processes applied to the Navier-Stokes equations for a laminar flow. The method quantifies the extent, dependence and propagation of uncertainty through the model system and, in particular, a methodology for the calculation More >

Fangyi Li¹, Guangyao Li^2,3, Guangyong Sun², Zhen Luo⁴, Zheng Zhang²

CMC-Computers, Materials & Continua, Vol.19, No.1, pp. 37-56, 2010, DOI:10.3970/cmc.2010.019.037

Abstract The focus of this paper is concentrated on multi-disciplinary and multi-objective optimization for thin walled beam systems considering safety, normal mode, static loading-bearing and weight, in which the uncertainties of the parameters are described via intervals. The size and shape of the cross-section are treated as design parameters during optimization. Considering the lightweight and safety, the design problem is formulated with two individual objectives to measure structural weight and maximum energy absorption, respectively, constrained by the average force, normal mode and maximum stress. The optimization problem with uncertainties is further transformed into a deterministic optimization More >

C. Jiang¹, Y.C. Bai¹, X. Han^1,2, H.M. Ning¹

CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 21-42, 2010, DOI:10.3970/cmc.2010.018.021

Abstract In this paper, an efficient interval optimization method based on a reliability-based possibility degree of interval (RPDI) is suggested for the design of uncertain structures. A general nonlinear interval optimization problem is studied in which the objective function and constraints are both nonlinear and uncertain. Through an interval order relation and a reliability-based possibility degree of interval, the uncertain optimization problem is transformed into a deterministic one. A sequence of approximate optimization problems are constructed based on the linear approximation technique. Each approximate optimization problem can be changed to a traditional linear programming problem, which More >

S. Turrin¹, M. Hanss¹, A.P.S. Selvadurai²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.3, pp. 237-258, 2009, DOI:10.3970/cmes.2009.052.237

Abstract Despite the continuing advances in rockfall analysis, the mathematical modeling and simulation of rockfall phenomena continues to be significantly influenced by a large amount of aleatory and epistemic uncertainty on significant number of model parameters. This paper focuses on the representation and quantification of epistemic uncertainties in rockfall modeling and simulation by fuzzy numbers. The propagation of the epistemic uncertainties considered is then calculated by the transformation method as a practical implementation of fuzzy arithmetic. Epistemic uncertainties on the material properties, on the boulder geometry and dimensions, on the kinematics of the impact and on More >

F. Fleissner¹, T. Haag², M. Hanss², P. Eberhard¹

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.2, pp. 181-196, 2009, DOI:10.3970/cmes.2009.052.181

Abstract In alpine regions human settlements and infrastructure are at risk to be hit by landslides or other types of geological flows. This paper presents a new approach that can aid the design of protective constructions. An uncertainty analysis of the flow around a debris barrier is carried out using a chute flow laboratory model of the actual debris flow. A series of discrete element simulations thereby serves to compare and assess two different barrier designs. In this study, the transformation method of fuzzy arithmetic is used to investigate the influence of epistemically uncertain model parameters. More >

G.J.A. Loeven^1,2, H. Bijl³

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.3, pp. 193-212, 2008, DOI:10.3970/cmes.2008.036.193

Abstract In this paper a Two-Step approach is presented for uncertainty quantification for expensive problems with multiple uncertain parameters. Both steps are performed using the Probabilistic Collocation method. The first step consists of a sensitivity analysis to identify the most important parameters of the problem. The sensitivity derivatives are obtained using a first or second order Probabilistic Collocation approximation. For the most important parameters the probability distribution functions are propagated using the Probabilistic Collocation method using higher order approximations. The Two-Step approach is demonstrated for flow around a NACA0012 airfoil with eight uncertain parameters in the More >

D. Moens¹, M. De Munck, D. Vandepitte

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.2, pp. 129-150, 2007, DOI:10.3970/cmes.2007.022.129

Abstract Recently, an interval finite element methodology has been developed to calculate envelope frequency response functions of uncertain structures with interval parameters. The methodology is based on a hybrid interval implementation of the modal superposition principle. This hybrid procedure consists of a preliminary optimization step, followed by an interval arithmetic procedure. The final envelope frequency response functions have been proved to give a very good approximation of the actual response range of the interval problem. Initially, this method was developed for undamped structures. Based on the theoretical principles of this approach, this paper introduces a new… More >

B. Amaziane¹, A. Naji², D. Ouazar³, A. H.-D. Cheng⁴

CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 85-96, 2005, DOI:10.3970/cmc.2005.002.085

Abstract In this paper the optimization of groundwater pumping in coastal aquifers under the threat of saltwater intrusion is investigated. The aquifer is inhomogeneous and contains several hydraulic conductivities zones. The aquifer data such as the hydraulic conductivities are uncertain, but with their expected mean and standard deviation values given. A stochastic boundary element method based on the perturbation technique is employed as the simulation tool. The stochastic optimization is handled by the chance-constrained programming. Genetic algorithm is selected as the optimization tool. Numerical examples of deterministic and stochastic problems are provided to demonstrate the feasibility More >