Liming Yang¹, Yongping Gao², Qun Sun³

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.6, pp. 493-506, 2015, DOI:10.3970/cmes.2015.104.493

Abstract Minimax probability machine (MPM) has been recently proposed and shown its advantage in pattern recognition. In this paper, we present a new minimax probabilistic approach (MPA),which can provide an explicit lower bound on prediction accuracy. Applying the Chebyshev-Cantelli inequality, the MPA is posed as a second order cone program formulation and solved effectively. Following that, this method is exploited directly to recognize the purity of hybrid seeds using near-infrared spectroscopic data. Experimental results in different spectral regions show that the proposed MPA is competitive with the existing minimax probability machine and support vector machine in generalization, while requires less computational… More >

S. Chakraverty^1,2, Smita Tapaswini¹

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.2, pp. 71-90, 2014, DOI:10.3970/cmes.2014.103.071

Abstract Fractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain fractional Fornberg-Whitham equation. Using the single parametric form of fuzzy numbers, original fuzzy fractional Fornberg-Whitham equation is converted first to an interval based fuzzy differential… More >

Marcin Kamiński^1,2, Bernd Lauke²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.6, pp. 411-440, 2013, DOI:10.3970/cmes.2013.093.411

Abstract The main aim in this paper is a computational study devoted to the sensitivity gradients and probabilistic moments of the effective elastic parameters for the rubber-filled polymers. The methodology is based on least squares recovery of the polynomial functions relating the effective tensor components and the given input design/random parameters. All numerical experiments are provided with respect to Young’s moduli of the elastomer constituents. Computational analysis is possible thanks to the application of the Response Function Method, which is enriched in our approach with the weighting procedures implemented according to the Dirac-type distributions. The homogenized elasticity tensor components are derived… 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 free stream conditions and geometry.… More >

M.M. Kaminski

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.2, pp. 113-140, 2011, DOI:10.3970/cmes.2011.080.113

Abstract The main aim of this work is to demonstrate a solution to the transient problems for the statistically homogeneous media with random physical parameters. This is done with the use of the stochastic perturbation technique based on the general order Taylor series expansions and the additionally modified implementation of the Finite Element Method. Now, both the Direct Differentiation Method as well as the Response Function Method are employed to form and solve up to the nth order state equations. Computational implementation of both approaches is illustrated using two examples - by determination of the probabilistic moments of the temperature histories… More >

N. Liu,¹,W. Gao ¹, C.M. Song¹, N. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.2, pp. 79-102, 2011, DOI:10.3970/cmes.2011.072.079

Abstract This paper presents the probabilistic dynamic analysis of vehicle-bridge interaction systems. The bridge's and vehicle's parameters are considered as random variables as well as the road surface roughness is modeled as random process. A two-degree-of-freedom spring-mass system is used to represent a moving vehicle and the bridge is modeled as an Euler-Bernoulli beam. From the equation of motion for the vehicle-bridge coupling system, the expressions for mean value and standard deviation of bridge response are developed by using the random variable's functional moment method. The effects of the individual system parameters and the road surface roughness on the bridge response… More >

Wei Gao¹, Chongmin Song¹, Francis Tin-Loi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 151-190, 2009, DOI:10.3970/cmes.2009.046.151

Abstract Static response and reliability of structures with a mixture of random and interval parameters under uncertain loads are investigated in this paper. Structural stiffness matrix is a random interval matrix when some structural parameters are modeled as random variables and others are considered as intervals. The structural displacement and stress responses are also random interval variables. From the static finite element governing equations, the random interval structural responses are obtained using the random interval perturbation method based on the first- and second-order perturbations. The expressions for mean value and standard deviation of random interval structural displacement and stress responses are… More >

Yao Hsu¹, Chih-Yen Su², Wen-Fang Wu^3,4

CMC-Computers, Materials & Continua, Vol.36, No.2, pp. 155-176, 2013, DOI:10.3970/cmc.2013.036.155

Abstract To study the fatigue reliability of a flip-chip chip scale package (FCCSP) subject to thermal cyclic loading, a Monte Carlo simulation-based parametric study is carried out in the present study. A refined procedure as compared with the recently released Probabilistic Design System (PDS) of ANSYS is proposed and employed in particular. The thermal-cyclic fatigue life of the package is discussed in detail since it is related directly to the reliability of the package. In consideration of the analytical procedure as well as real manufacturing processes, a few geometric dimensions and material properties of the package are assumed random. The empirical… More >

K. C. Liu¹, S. M. Arnold²

CMC-Computers, Materials & Continua, Vol.35, No.1, pp. 35-65, 2013, DOI:10.3970/cmc.2013.035.035

Abstract It is well known that failure of a material is a locally driven event. In the case of ceramic matrix composites (CMCs), significant variations in the microstructure of the composite exist and their significance on both deformation and life response need to be assessed. Examples of these variations include changes in the fiber tow shape, tow shifting/nesting and voids within and between tows. In the present work, the influence of many of these scale specific architectural features of woven ceramic composite are examined stochastically at both the macroscale (woven repeating unit cell (RUC)) and structural scale (idealized using multiple RUCs).… More >

C. Wang¹, W. Gao¹, C.W. Yang¹, C.M. Song¹

CMC-Computers, Materials & Continua, Vol.25, No.1, pp. 19-46, 2011, DOI:10.3970/cmc.2011.025.019

Abstract The random interval response and probabilistic interval reliability of structures with a mixture of random and interval properties are studied in this paper. Structural stiffness matrix is a random interval matrix if some structural parameters and loads are modeled as random variables and the others are considered as interval variables. The perturbation-based stochastic finite element method and random interval moment method are employed to develop the expressions for the mean value and standard deviation of random interval structural displacement and stress responses. The lower bound and upper bound of the mean value and standard deviation of random interval structural responses… More >