Development of stochastic isogeometric analysis (SIGA) method for uncertainty in shape

In this paper, a new method is proposed that extend the classical deterministic isogeometric analysis (IGA) into a probabilistic analytical framework in order to evaluate the uncertainty in shape and aim to investigate a possible extension of IGA in the field of computational stochastic mechanics. Stochastic IGA (SIGA) method for uncertainty in shape is developed by employing the geometric characteristics of the non-uniform rational basis spline and the probability characteristics of polynomial chaos expansions (PCE). The proposed method can accurately and freely evaluate problems of uncertainty in shape caused by deformation of the structural model. Additionally, we use the intrusive formulation approach to incorporate PCE into the IGA framework, and the C++ programming language to implement this analysis procedure. To verify the validity and applicability of the proposed method, two numerical examples are presented. The validity and accuracy of the results are assessed by comparing them to the results obtained by Monte Carlo simulation based on the IGA algorithm.     

Sounding of finite solid bodies by way of topological derivative

This paper is concerned with an application of the concept of topological derivative to elastic‐wave imaging of finite solid bodies containing cavities. Building on the approach originally proposed in the (elastostatic) theory of shape optimization, the topological derivative, which quantifies the sensitivity of a featured cost functional due to the creation of an infinitesimal hole in the cavity‐free (reference) body, is used as a void indicator through an assembly of sampling points where it attains negative values. The computation of topological derivative is shown to involve an elastodynamic solution to a set of supplementary boundary‐value problems for the reference body, which are here formulated as boundary integral equations. For a comprehensive treatment of the subject, formulas for topological sensitivity are obtained using three alternative methodologies, namely (i) direct differentiation approach, (ii) adjoint field method, and (iii) limiting form of the shape sensitivity analysis. The competing techniques are further shown to lead to distinct computational procedures. Methodologies (i) and (ii) are implemented within a BEM‐based platform and validated against an analytical solution. A set of numerical results is included to illustrate the utility of topological derivative for 3D elastic‐wave sounding of solid bodies; an approach that may perform best when used as a pre‐conditioning tool for more accurate, gradient‐based imaging algorithms. Despite the fact that the formulation and results presented in this investigation are established on the basis of a boundary integral solution, the proposed methodology is readily applicable to other computational platforms such as the finite element and finite difference techniques. Copyright © 2004 John Wiley & Sons, Ltd.     

Evaluation of a simple finite element method for the calculation of effective electrical conductivity of compression moulded polymer–graphite composites

Finite element (FE) techniques can be used for the calculation of the effective properties of random heterogeneous materials, the required input simply consisting of phase properties and representative three-dimensional models of material microstructure. This approach has been widely exploited in recent years, although limited by the considerable amount of computational power required to obtain statistically accurate results. By using simple microstructural models of compression moulded polymer–graphite composites and a FE code modified for execution on graphical processing units, we show that reliable predictions of electrical properties for these materials can now be obtained in a reasonable computational time and with acceptable accuracy and precision. By using an approach based on design of experiments, we also perform a set of simulations aimed at determining the microstructural details which are most significant for the effective properties of these materials.     

Shape-Based Approach for Full Field Displacement Calculation of Cellular Materials

In this paper, we propose a new approach of optical full-field measurement for displacement calculation on the surface of a cellular solid. Cell boundary points are sampled as nodes in the analysis. To find the nodal values of displacements the nodes are to be mapped onto their corresponding points in the deformed cell boundary by shape based point matching. A thin plate spline based robust point matching (TPS-RPM) approach is used instead of correlation of intensity pattern between two regions in traditional displacement measurement methods. The proposed approach involves multiple-step image processing including cell region segmentation, cell region matching and node matching. Consequently displacements at a given node can be found easily. Two numerical examples of cellular solids under compressive loading are considered for assessing the effectiveness and accuracy of the proposed algorithm. The results show that local displacements around cell boundaries on the surfaces of the specimen can be effectively determined with the shape based method, thus it appears that the proposed methods is promising for predicting displacements of complex cellular materials.     

Fast characterization of aluminum plates with TV-holography measurements of the frequency spectrum of multimode, quasi- monochromatic Lamb waves

We introduce a novel approach for measuring the frequency spectrum of Lamb waves and, subsequently, for obtaining the thickness and the bulk wave velocities of isotropic, homogeneous plates. It is based on Fourier transforming a set of spatial and temporal samples of the acoustic displacement but, in contrast to the traditional approach that employs dense temporal sampling and a reduced set of spatial sampling locations, our data set is a sequence of 2-D high-resolution maps of the instantaneous out-of-plane displacement obtained with TV holography. We have devised three variants to obtain a set of points of the wavenumber-frequency space, based, respectively, on the spatial (1-D or 2-D) and on the spatio-temporal (3-D) Fourier transforms. The whole process to obtain these points can be easily automated and substantial time savings can be achieved, compared with other full-field techniques that require human intervention or with pointwise scanned probes. Experimental demonstration of the three variants with quasimonochromatic multimode Lamb waves in aluminum plates is presented. The characteristic parameters of the plates are calculated by fitting the theoretical model to the experimental points of the frequency spectrum. The analysis of the uncertainties shows that the accuracy of the method is only slightly lower than the accuracy of a previously reported method based on measuring the wavelength of single-modes, for which the data acquisition procedure is much slower.     

Spatial analysis of time of flight-secondary ion mass spectrometric images by ordinary kriging and inverse distance weighted interpolation techniques

Ordinary kriging and inverse distance weighted (IDW) are two interpolation methods for spatial analysis of data and are commonly used to analyze macroscopic spatial data in the fields of remote sensing, geography, and geology. In this study, these two interpolation techniques were compared and used to analyze microscopic chemical images created from time of flight-secondary ion mass spectrometry images from a patterned polymer sample of fluorocarbon (C(x)F(y)) and poly(aminopropyl siloxane) (APS, a.k.a. siloxane). Data was eliminated from the original high-resolution data set by successive random removal, and the image file was interpolated and reconstructed with a random subset of points using both methods. The statistical validity of the reconstructed image was determined by both standard geographic information system (GIS) validation statistics and evaluating the resolution across an image boundary using ASTM depth and image resolution methodology. The results show that both ordinary kriging and IDW techniques can be used to accurately reconstruct an image using substantially fewer sample points than the original data set. Ordinary kriging performed better than the IDW technique, resulting in fewer errors in predicted intensities and greater retention of original image features. The size of the data set required for the most accurate reconstruction of the original image is directly related to the autocorrelation present within the data set. When 10% of the original siloxane data set was used for an ordinary kriging interpolation, the resulting image still retained the characteristic gridlike pattern. The C(x)F(y) data set exhibited stronger spatial correlation, resulting in reconstruction of the image with only 1% of the original data set. The removal of data points does result in a loss of image resolution; however, the resolution loss is not directly related to the percentage of sample points removed.     

Agent-based project scheduling: computational study of large problems

We present in this paper the results of a computational study for project scheduling based on new ideas for project representation taken from digital circuit technology (Knotts et al. , 1998a) and a solution approach based on the artificial intelligence notion of agent technology. We experimented with projects with up to 10 000 stochastic duration activities which can be executed in a number of modes requiring renewable, nonrenewable, and periodically renewable resources. This study is about agent implementation in a project scheduling domain. It compares agent types and priority rules with respect to their impact on project schedule duration and computational performance. This work demonstrates: (i) that artificial intelligence concepts of agent technology can be successfully implemented for project scheduling; and (ii) in conducting project scheduling studies we can experiment successfully with large project networks. Both points made in this research are new.     

Karhunen–Loève expansion for multi-correlated stochastic processes

We propose two different approaches generalizing the Karhunen–Loève series expansion to model and simulate multi-correlated non-stationary stochastic processes. The first approach (muKL) is based on the spectral analysis of a suitable assembled stochastic process and yields series expansions in terms of an identical set of uncorrelated random variables. The second approach (mcKL) relies on expansions in terms of correlated sets of random variables reflecting the cross-covariance structure of the processes. The effectiveness and the computational efficiency of both muKL and mcKL is demonstrated through numerical examples involving Gaussian processes with exponential and Gaussian covariances as well as fractional Brownian motion and Brownian bridge processes. In particular, we study accuracy and convergence rates of our series expansions and compare the results against other statistical techniques such as mixtures of probabilistic principal component analysis. We found that muKL and mcKL provide an effective representation of the multi-correlated process that can be readily employed in stochastic simulation and dimension reduction data-driven problems.     

Leveraging the nugget parameter for efficient Gaussian process modeling

Gaussian process (GP) metamodels have been widely used as surrogates for computer simulations or physical experiments. The heart of GP modeling lies in optimizing the log‐likelihood function with respect to the hyperparameters to fit the model to a set of observations. The complexity of the log‐likelihood function, computational expense, and numerical instabilities challenge this process. These issues limit the applicability of GP models more when the size of the training data set and/or problem dimensionality increase. To address these issues, we develop a novel approach for fitting GP models that significantly improves computational expense and prediction accuracy. Our approach leverages the smoothing effect of the nugget parameter on the log‐likelihood profile to track the evolution of the optimal hyperparameter estimates as the nugget parameter is adaptively varied. The new approach is implemented in the R package GPM and compared to a popular GP modeling R package ( GPfit) for a set of benchmark problems. The effectiveness of the approach is also demonstrated using an engineering problem to learn the constitutive law of a hyperelastic composite where the required level of accuracy in estimating the response gradient necessitates a large training data set.     

Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring

Model reduction techniques such as the proper orthogonal decomposition (POD) method can be used to reduce the computational effort of simulations with a very large number of degrees-of-freedom. The reduction of finite element models including elastoplastic material behavior is still far from being trivial and inevitably leads to problems of efficiency and accuracy. One aim of the present paper is to combine the two methods—sub-structuring and POD-based model reduction—to overcome these difficulties. A typical field of application where plasticity dominates the material behavior are forming processes. The second aim of the paper is to investigate the applicability of the new approach in this context. The presented combined approach selective POD (SPOD) where the reduction is only applied in sub-domains with approximately elastic behavior shows higher accuracy than the general POD method. In this paper, the SPOD method is extended by an adaptive method of sub-structuring (A-SPOD) in which the sub-domain where model reduction is applied is determined automatically. While achieving errors of the same magnitude as by means of SPOD, the computational effort can be reduced significantly by using the A-SPOD approach.     

Generalized scattering-matrix method for the analysis of two-dimensional photonic bandgap devices

Development of accurate numerical methods for the analysis of photonic-bandgap-based devices is a relevant issue in optimizing existing devices and/or developing new design solutions. Within this framework, we present an innovative and general approach for the evaluation of the electromagnetic behavior of two-dimensional finite-extent photonic crystals made of a finite set of parallel rods. The proposed approach is a generalization of the scattering-matrix method introduced by Maystre and co-workers and of its improved version proposed by the present authors, which exploits a suitable aggregation into "macrocells" to achieve a reduction of the number of unknowns. As a matter of fact, both of these approaches can be exploited only in those cases in which particular modal expansions for the fields hold true. In order to overcome this limitation, we propose a suitable exploitation of the method of auxiliary sources to provide a general and reliable method for the numerical computation of the scattering matrix of an object of arbitrary shape. By taking advantage of this, we can then generalize our improved scattering matrix method to further increase its computational effectiveness. A numerical analysis of some square-lattice configurations is reported to confirm the accuracy of the proposed method and the remarkable computational benefit.     

Stabilized finite element methods with reduced integration techniques for miscible displacements in porous media

The objective of this work is to study some techniques to increase computational performance of stabilized finite element simulations of miscible displacements. We propose the use of a reduced integration technique for bilinear quadrilateral elements in the determination of the pressure and concentration fields. We also study the evaluation of pressure gradient (Darcy's velocity) by differentiation at super‐convergent points. Numerical examples are shown to validate our approach, accessing its efficiency and accuracy. Copyright © 2003 John Wiley & Sons, Ltd.     

Reusable intrinsic sample point (RISP) algorithm for the efficient numerical integration of three dimensional curved boundary elements

This paper presents an algorithm that provides an order of magnitude gain in the computational performance of the numerical integration of the boundary integral equations for three dimensional analysis. Existing algorithms for numerical integration have strategically clustered integration sample points based on the relative proximity of the load points to the boundary element being integrated using element subdivision or element co-ordinate transformation. The emphasis in these techniques has been on minimizing the number of sample points required to obtain a given level of accuracy. The present algorithm, while closely following the spirit of these earlier approaches, employs a discrete number of sets of predetermined, customized, near-optimum, sample point quantities associated with the intrinsic boundary element. The ability created by this approach to reuse sample point geometric information of the actual element allows for the realization of substantive computational economy. This algorithm provides accurate and efficient numerical results both when load points are far from, and when they are on the boundary element being integrated. Numerical results are provided to demonstrate the substantial economy achieved through the use of the present algorithm.     

基本解方法解水下刚性目标三维Helmholtz外散射问题

运用基本解方法求解水下刚性目标三维Helmholtz外散射问题。研究了源点位置分布和数目对基本解方法计算结果的影响,比较了最小二乘配点法和等额配点法的计算精度。结果表明,当源点构成的形状与目标边界的形状差异大时,计算精度差,增加源点的数量可提高计算精度,运用较少的源点也可获得令人满意的精度,从而提高计算效率,但源点不宜距离目标边界过远;最小二乘配点法的计算精度较等额配点法高些。     

Combining discrete and continuous optimization to solve kinodynamic motion planning problems

A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamic constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of intermediate points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the intermediate points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost.     

Direct evaluation of singular boundary integrals in two-dimensional biharmonic analysis

Development of techniques to provide rapid and accurate evaluation of the integrations required in boundary element method (BEM) formulations are receiving more attention in the literature. In this work, a series of direct expressions for surface integrals, required for a boundary element solution of the non-homogeneous biharmonic over a general two-dimensional curvilinear surface, are presented. The concept of an isoparametric representation, usually applied to the variation of the field variables and the geometry, is extended to the parametric mapping of the curvilinear geometry. The result renders the typically complicated Jacobian function into a series of polynomial expressions based on the shape function set and several discrete Jacobian values. An application of the isoparametric approximation of the Jacobian for a quadratic element representation is developed. Implementation of this approximation significantly improves the accuracy of the boundary integral solution by eliminating error associated with numerical quadrature. Overall computational efficiency is improved by reducing the time necessary to calculate individual surface integrals and evaluate field variables at internal points. A numerical solution of the boundary integral equations of phenomena governed by the biharmonic equation is presented and compared with an exact analysis.     

Solving an eigenvalue problem with a periodic domain using radial basis functions

A meshless method based on radial basis functions (RBFs) is proposed for solving an eigenvalue problem with a periodic domain. We compare Wendland's and Wu's compactly supported RBFs. The computational experiments examine the accuracy of the method as a result of variation in the number and layout of the original points and in addition, the shape factor. The results obtained from the method are in good agreement with the analytical solutions of the problem.     

Face modeling and editing with statistical local feature control models

This article presents a novel method based on statistical facial feature control models for generating realistic controllable face models. The local feature control models are constructed based on the exemplar 3D face scans. We use a three‐step model fitting approach for the 3D registration problem. Once we have a common surface representation for examples, we form feature shape spaces by applying a principal component analysis (PCA) to the data sets of facial feature shapes. We compute a set of anthropometric measurements to parameterize the exemplar shapes of each facial feature in a measurement space. Using PCA coefficients as a compact shape representation, we approach the shape synthesis problem by forming scattered data interpolation functions that are devoted to the generation of desired shape by taking the anthropometric parameters as input. The correspondence among all exemplar face textures is obtained by parameterizing a 3D generic mesh over a 2D image domain. The new feature texture with desired attributes is synthesized by interpolating the exemplar textures. With the exception of an initial tuning of feature point positions and assignment of texture attribute values, our method is fully automated. In the resulting system, users are assisted in automatically generating or editing a face model by controlling the high‐level parameters. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 341–358, 2007     

A fast and robust hybrid method for block‐structured mesh deformation with emphasis on FSI‐LES applications

The present work introduces an efficient technique for the deformation of block‐structured grids occurring in simulations of fluid–structure interaction (FSI) problems relying on large‐eddy simulation (LES). The proposed hybrid approach combines the advantages of the inverse distance weighting (IDW) interpolation with the simplicity and low computational effort of transfinite interpolation (TFI), while preserving the mesh quality in boundary layers. It is an improvement over the state‐of‐the‐art currently in use. To reach this objective, in a first step, three elementary mesh deformation methods (TFI, IDW, and radial basis functions) are investigated based on several test cases of different complexities analyzing not only their capabilities but also their computational costs. That not only allows to point out the advantages of each method but also demonstrates their drawbacks. Based on these specific properties of the different methods, a hybrid methodology is suggested that splits the entire grid deformation into two steps: first, the movement of the block‐boundaries of the block‐structured grid and second, the deformation of each block of the grid. Both steps rely on different methodologies, which allows to work out the most appropriate method for each step leading to a reasonable compromise between the grid quality achieved and the computational effort required. Finally, a hybrid IDW‐TFI methodology is suggested that best fits to the specific requirements of coupled FSI‐LES applications. This hybrid procedure is then applied to a real‐life FSI‐LES case. Copyright © 2016 John Wiley & Sons, Ltd.