Xinxin Yue¹, Jian Zhang^2,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.4, pp. 1-2, 2024, DOI:10.32604/icces.2024.011344

Abstract The "curse of dimensionality" faced by high-dimensional complex engineering problems can be tackled by a set of quantitative model evaluation and analysis tools named high-dimensional model representation (HDMR) [1,2], which has attracted much attention from researchers in various fields, such as global sensitivity analysis (GSA) [3], structural reliability analysis (SRA) [4], CFD uncertainty quantification [5] and so on [6]. In this paper, a new method for uncertainty quantification is proposed. Firstly, PCE-HDMR for SRA is developed by taking advantage of the accuracy and efficiency of PCE-HDMR for modeling high-dimensional problems [7]. Secondly, the formulas for… More >

Haojie Lian¹, Jiaqi Wang¹, Leilei Chen^2,*, Shengze Li³, Ruochen Cao⁴, Qingyuan Hu⁵, Peiyun Zhao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.1, pp. 1143-1163, 2024, DOI:10.32604/cmes.2024.048549 - 16 April 2024

Abstract This paper presents a novel framework aimed at quantifying uncertainties associated with the 3D reconstruction of smoke from 2D images. This approach reconstructs color and density fields from 2D images using Neural Radiance Field (NeRF) and improves image quality using frequency regularization. The NeRF model is obtained via joint training of multiple artificial neural networks, whereby the expectation and standard deviation of density fields and RGB values can be evaluated for each pixel. In addition, customized physics-informed neural network (PINN) with residual blocks and two-layer activation functions are utilized to input the density fields of More >

Liang Zhang^1,*, Zigang He¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.2, pp. 1-1, 2023, DOI:10.32604/icces.2023.09713

Abstract The different elastic properties of tension and compression are obvious in many engineering materials, especially new materials. Materials with this characteristic, such as graphite, ceramics, and composite materials, are called bi-modulus materials. Their mechanical properties such as Young’s modulus have randomness in tension and compression due to different porosity, microstructure, etc. To calibrate the mechanical properties of bi-modulus materials by bridging FEM simulation results and scarce experimental data, the paper presents a data-fusion computational method. The FEM simulation is implemented based on Parametric Variational Principle (PVP), while the experimental result is obtained by Digital Image… More >

Yong Li^1,*, Joel P. Conte², Philip E. Gill³

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.3, pp. 517-543, 2019, DOI:10.32604/cmes.2019.06269

Abstract In the field of earthquake engineering, the advent of the performance-based design philosophy, together with the highly uncertain nature of earthquake ground excitations to structures, has brought probabilistic performance-based design to the forefront of seismic design. In order to design structures that explicitly satisfy probabilistic performance criteria, a probabilistic performance-based optimum seismic design (PPBOSD) framework is proposed in this paper by extending the state-of-the-art performance-based earthquake engineering (PBEE) methodology. PBEE is traditionally used for risk evaluation of existing or newly designed structural systems, thus referred to herein as forward PBEE analysis. In contrast, its use… More >

Ryan Weisman³, Manoranjan Majji⁴, Kyle T. Alfriend⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.3, pp. 269-304, 2016, DOI:10.3970/cmes.2016.111.269

Abstract This paper presents a closed form solution to Liouville's equation governing the evolution of the probability density function associated with the motion of a body in a central force field and subject to J2. It is shown that the application of transformation of variables formula for mapping uncertainties is equivalent to the method of characteristics for computing the time evolution of the probability density function that forms the solution of the Liouville's partial differential equation. The insights derived from the nature of the solution to Liouville's equation are used to reduce the dimensionality of uncertainties More >

V. Vittaldev¹, R. P. Russell²

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 83-117, 2016, DOI:10.3970/cmes.2016.111.083

Abstract Monte Carlo simulations are an accurate but computationally expensive procedure for approximating the resultant non-Gaussian probability density function (PDF) after propagation of an initial Gaussian PDF through a nonlinear function. Univariate splitting libraries for Gaussian Mixture Models (GMMs) exist with up to five elements in the literature. The number of splits are extended in the present work by generating three homoscedastic univariate splitting libraries with up to 39 elements. Mulitvariate GMMs are typically handled with splits along a single direction. Instead, we generate a regular multidirectional grid over the initial multivariate Gaussian distribution by recursively… More >

A.R.Ervilha^1,2, F.A.Sousa¹, J.M.C.Pereira¹, J.C.F.Pereira¹

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.5, pp. 361-387, 2012, DOI:10.3970/cmes.2012.089.361

Abstract Faster than real time stochastic fire spread predictions are reported using a Non-Intrusive Spectral Projection (NISP) method based on Polynomial Chaos expansion and Graphic Processing Units (GPUs). The fireLib BEHAVE model together with a raster surface fire growth algorithm was implemented using the Compute Unified Device Architecture (CUDA) programming language. The uncertainty generated by the four random variables considered (wind speed, wind direction, fuel moisture, and fuel load) is quantified in the stochastic solution. Stochastic simulation of an idealized vegetation fire in a realistic complex terrain is obtained with speed-ups as high as 176 when More >

W. Zhang¹, X. Han^1,2, J. Liu¹, R. Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.5, pp. 385-408, 2012, DOI:10.3970/cmes.2012.086.385

Abstract A novel inverse technique is presented for quantifying the uncertainty of the identified the results in an encounter condition identification problem. In this technique, the polynomial response surface method based on the structure-selection technique is first adopted to construct the approximation model of the projectile/target system, so as to reduce the computational cost. The Markov Chain Monte Carlo method is then used to identify the encounter condition parameters and their confidence intervals based on this cheap approximation model with Bayesian perspective. The results are demonstrated through the simulated test cases, which show the utility and More >

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 >

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 >