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  • Open Access


    Time Domain Inverse Problems in Nonlinear Systems Using Collocation & Radial Basis Functions

    T.A. Elgohary1, L. Dong2, J.L. Junkins3, S.N. Atluri4

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 59-84, 2014, DOI:10.3970/cmes.2014.100.059

    Abstract In this study, we consider ill-posed time-domain inverse problems for dynamical systems with various boundary conditions and unknown controllers. Dynamical systems characterized by a system of second-order nonlinear ordinary differential equations (ODEs) are recast into a system of nonlinear first order ODEs in mixed variables. Radial Basis Functions (RBFs) are assumed as trial functions for the mixed variables in the time domain. A simple collocation method is developed in the time-domain, with Legendre-Gauss-Lobatto nodes as RBF source points as well as collocation points. The duffing optimal control problem with various prescribed initial and final conditions, as well as the orbital… More >

  • Open Access


    Application of the MLPG Mixed Collocation Method for Solving Inverse Problems of Linear Isotropic/Anisotropic Elasticity with Simply/Multiply-Connected Domains

    Tao Zhang1,2, Leiting Dong2,3, Abdullah Alotaibi4, Satya N. Atluri2,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 1-28, 2013, DOI:10.3970/cmes.2013.094.001

    Abstract In this paper, a novel Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed for solving the inverse Cauchy problem of linear elasticity, wherein both the tractions as well as displacements are prescribed/measured at a small portion of the boundary of an elastic body. The elastic body may be isotropic/anisotropic and simply connected or multiply-connected. In the MLPG mixed collocation method, the same meshless basis function is used to interpolate both the displacement as well as the stress fields. The nodal stresses are expressed in terms of nodal displacements by enforcing the constitutive relation between stress and the displacement gradient… More >

  • Open Access


    The Jordan Structure of Residual Dynamics Used to Solve Linear Inverse Problems

    Chein-Shan Liu1, Su-Ying Zhang2, Satya N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.1, pp. 29-48, 2012, DOI:10.3970/cmes.2012.088.029

    Abstract With a detailed investigation of n linear algebraic equations Bx=b, we find that the scaled residual dynamics for y∈Sn−1 is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm based on the Jordan structure. The algorithms preserving the length of y are developed as the structure preserving algorithms (SPAs), which can significantly accelerate the convergence speed and are robust enough against the noise in the numerical… More >

  • Open Access


    Identification of Cavities in a Three-Dimensional Layer by Minimization of an Optimal Cost Functional Expansion

    A.E. Martínez-Castro1, I.H. Faris1, R. Gallego1

    CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 177-206, 2012, DOI:10.3970/cmes.2012.087.177

    Abstract In this paper, the identification of hidden defects inside a three-dimen -sional layer is set as an Identification Inverse Problem. This problem is solved by minimizing a cost functional which is linearized with respect to the volume defects, leading to a procedure that requires only computations at the host domain free of defects. The cost functional is stated as the misfit between experimental and computed displacements and spherical and/or ellipsoidal cavities are the defects to locate. The identification of these cavities is based on the measured displacements at a set of points due to time-harmonic point loads at an array… More >

  • Open Access


    Self-Adaptive Differential Evolution Based on the Concept of Population Diversity Applied to Simultaneous Estimation of Anisotropic Scattering Phase Function, Albedo and Optical Thickness

    F. S. Lobato1, V. Steffen Jr2, A. J. Silva Neto3

    CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 1-18, 2010, DOI:10.3970/cmes.2010.069.001

    Abstract Differential Evolution Algorithm (DE) has shown to be a powerful evolutionary algorithm for global optimization in a variety of real world problems. DE differs from other evolutionary algorithms in the mutation and recombination phases. Unlike some other meta-heuristic techniques such as genetic algorithms and evolutionary strategies, where perturbation occurs in accordance with a random quantity, DE uses weighted differences between solution vectors to perturb the population. Although the efficiency of DE algorithm has been proven in the literature, studies indicate that the efficiency of the DE methods is sensitive to its control parameters (perturbation rate and crossover rate) and there… More >

  • Open Access


    Stable MFS Solution to Singular Direct and Inverse Problems Associated with the Laplace Equation Subjected to Noisy Data

    LiviuMarin 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 203-242, 2008, DOI:10.3970/cmes.2008.037.203

    Abstract In this paper, a meshless method for the stable solution of direct and inverse problems associated with the two-dimensional Laplace equation in the presence of boundary singularities and noisy boundary data is proposed. The governing equation and boundary conditions are discretized by the method of fundamental solutions (MFS), whilst the existence of the boundary singularity is taken into account by subtracting from the original MFS solution the corresponding singular solutions, as given by the asymptotic expansion of the solution near the singular point. However, even in the case when the boundary singularity is accounted for, the numerical solutions obtained by… More >

  • Open Access


    A Computational Inverse Technique for Uncertainty Quantification in an Encounter Condition Identification Problem

    W. Zhang1, X. Han1,2, 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 efficiency of the proposed technique.… More >

  • Open Access


    The Concept of Best Vector Used to Solve Ill-Posed Linear Inverse Problems

    Chein-Shan Liu

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.5, pp. 499-526, 2012, DOI:10.3970/cmes.2012.083.499

    Abstract The iterative algorithms based on the concept of best vector are proposed to solve an ill-conditioned linear system: Bx-b=0, which might be a discretization of linear inverse problem. In terms of r:=Bx-b and a monotonically increasing positive function Q(t) of a time-like variable t, we define a future cone in the Minkowski space, wherein the discrete dynamics of the proposed algorithm is evolved. We propose two methods to approximate the best vector B-1r, and obtain three iterative algorithms for solving x, which we label them as the steepest-descent and optimal vectors iterative algorithm (SOVIA), the mixed optimal iterative algorithm (MOIA),… More >

  • Open Access


    Radiative Properties Estimation with the Luus-Jaakola and the Particle Collision Algorithm

    D. C. Knupp1, A. J. Silva Neto2, W. F. Sacco3

    CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 121-146, 2009, DOI:10.3970/cmes.2009.054.121

    Abstract The inverse analysis of radiative transfer in participating media has several practical applications. In most cases, the inverse problem is formulated implicitly and the solution is given by the minimization of an objective function. Gradient based methods have largely been used for that purpose, but it has been observed in recent years an increasing interest in the use of stochastic methods. In this work, it is proposed the use of the Luus-Jaakola method and the Particle Collision Algorithm. The former is a random search optimization method that has been successfully employed mainly in chemical engineering, and the latter is a… More >

  • Open Access


    Inverse Solution of a Chromatography Model by means of Evolutionary Computation

    M. Irízar, L. D. Câmara, A. J. Silva Neto, O. Llanes

    CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 1-14, 2009, DOI:10.3970/cmes.2009.054.001

    Abstract Modeling of Chromatography allows a better understanding and development of new techniques to be applied at industrial level, although it's relatively complex. The models of this process are represented by systems of partial differential equations with non linear parameters difficult to estimate generally, which constitutes an inverse problem. In general there aren't analytical solutions and therefore numerical methods should be used for their direct solutions. Frequently typical boundary conditions are considered, but it's convenient to study different approaches for those. Evolutionary Computation has been used successfully in many problems of diverse areas for searching in complex spaces. Considering previous works… More >

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