Showing papers on "High-dimensional model representation published in 2017"
TL;DR: This paper focuses on dimensionality reduction problem, and proposes a novel feature-selection algorithm, which is based on the method called high dimensional model representation, which provides both high classification accuracy and robust features with a satisfactory computational time.
Abstract: In hyperspectral image analysis, the classification task has generally been addressed jointly with dimensionality reduction due to both the high correlation between the spectral features and the noise present in spectral bands, which might significantly degrade classification performance. In supervised classification, limited training instances in proportion with the number of spectral features have negative impacts on the classification accuracy, which is known as Hughes effects or curse of dimensionality in the literature. In this paper, we focus on dimensionality reduction problem, and propose a novel feature-selection algorithm, which is based on the method called high dimensional model representation. The proposed algorithm is tested on some toy examples and hyperspectral datasets in comparison with conventional feature-selection algorithms in terms of classification accuracy, stability of the selected features and computational time. The results show that the proposed approach provides both high classification accuracy and robust features with a satisfactory computational time.
100 citations
TL;DR: A new kernel function derived from orthogonal polynomials is proposed for support vector regression (SVR), based on which the Sobol’ global sensitivity indices can be computed analytically by the coefficients of the surrogate model built by SVR.
81 citations
TL;DR: Results show that the proposed hybrid metamodel which combines Cut-HDMR with Co-kriging and kriging is very efficient in approximating high dimensional problems by using multi-fidelity samples, thus making it particularly suitable for high dimensional engineering design problems involving computationally expensive simulations.
Abstract: Multi-fidelity metamodeling provides an efficient way to approximate expensive black-box problems by utilizing the samples of multiple fidelities. While it still faces the challenge of "curse-of-dimensionality" when used in approximating high dimensional problems. On the other hand, the high dimensional model representation (HDMR) method, as an efficient tool to tackle high dimensional problems, can only handle single-fidelity samples in approximation. Therefore, a hybrid metamodel which combines Cut-HDMR with Co-kriging and kriging is proposed to improve the metamodeling efficiency for high dimensional problems. The developed HDMR, termed as MF-HDMR, can efficiently use multi-fidelity samples to approximate black-box problems by using a two stage metamodeling strategy. It can naturally explore and exploit the linearity/nonlinearity and correlations among variables of underlying problems, which are unknown or computationally expensive. Besides, to further improve the efficiency of MF-HDMR, an extended maximin distance sequential sampling method is proposed to add new sample points of different fidelities in the metamodeling process. Moreover, a mathematical function is used to illustrate the modeling theory and procedures of MF-HDMR. In order to validate the proposed method, it is tested by several numerical benchmark problems and successfully applied in the optimal design of a long cylinder pressure vessel. Moreover, an overall comparison between the proposed method and several other metamodeling methods has been made. Results show that the proposed method is very efficient in approximating high dimensional problems by using multi-fidelity samples, thus making it particularly suitable for high dimensional engineering design problems involving computationally expensive simulations.
42 citations
TL;DR: In this paper, a case study of Carpathian flysch rock-soil slopes is presented, and the efficiency of the reliability index calculation is estimated by comparing results with ones from neural network application.
18 citations
TL;DR: The efficiency and accuracy of the proposed approach in stochastic response analysis have been assessed by comparison with Monte Carlo simulation and excellent results in terms of accuracy and computational effort obtained makes the proposed methodology potential for further complex applications.
16 citations
TL;DR: In this paper, the authors developed an efficient hybrid reliability analysis method to handle both random and dependent interval input variables, which decomposes the nested double loops into sequential probability analysis (PA) loop and interval analysis (IA) loop.
Abstract: Random variables could be dependent, and so could interval variables. To accommodate dependent interval variables, this work develops an efficient hybrid reliability analysis method to handle both random and dependent interval input variables. Due to the dependent interval variables, the reliability analysis needs to perform the probability analysis for every combination of dependent interval variables. This involves a nested double-loop procedure and dramatically decreases the efficiency. The proposed method decomposes the nested double loops into sequential probability analysis (PA) loop and interval analysis (IA) loop. An efficient IA algorithm based on the cut-HDMR (High Dimensional Model Representation) expansion is developed and a sampling strategy with the leave-one-out technique without extra calls of the limit-state function is proposed. The proposed method has good accuracy and efficiency as demonstrated by two engineering examples.
14 citations
TL;DR: This work uses a recently developed approach based on a new derivation of the high dimensional model representation method for implementing a computationally efficient probabilistic analysis approach for re-entry.
14 citations
01 Jun 2017
TL;DR: Testing and comparison results show that the developed bisection-sampling-based support vector regression–high-dimensional model representation metamodeling technique can achieve high modeling accuracy with a smaller number of training sample evaluations.
Abstract: A major challenge of metamodeling in simulation-based engineering design optimization is to handle the "curse of dimensionality," i.e. the exponential growth of computational cost with increase of problem dimensionality. Encouragingly, it has been reported recently that a high-dimensional model representation assisted by a radial basis function is capable of deriving high-dimensional input-output relationships at dramatically reduced computational cost. In this article, support vector regression is employed as an alternative to be coupled with high-dimensional model representation for the metamodeling of high-dimensional problems. In particular, the bisection sampling method is proposed to be used in the metamodeling process to generate high-quality training samples. Testing and comparison results show that the developed bisection-sampling-based support vector regression-high-dimensional model representation metamodeling technique can achieve high modeling accuracy with a smaller number of training sample evaluations. For the problem examined in this study, the bisection-sampling-based support vector regression-high-dimensional model representation enables high modeling accuracy and linear computational complexity as the problem dimensionality increases. Analysis of this performance advantage shows that the use of bisection method enables the developed metamodeling technique to be more effective in dealing with high-dimensional problems.
13 citations
TL;DR: In this paper, the authors derived universal expressions of the variance contributions of correlated inputs to the uncertainty in a model output based on the high dimensional model representation (HDMR) of the model function.
Abstract: Sensitivity analysis is indispensable to structural design and optimization. This paper focuses on sensitivity analysis for models with correlated inputs. To explore the contributions of correlated inputs to the uncertainty in a model output, the universal expressions of the variance contributions of the correlated inputs are first derived in the paper based on the high dimensional model representation (HDMR) of the model function. Then by analyzing the composition of these variance contributions, the variance contributions by an individual correlated input to the model output are further decomposed into independent contribution by the individual input itself, independent contribution by interaction between the individual input and the others, contribution purely by correlation between the individual input and the others, and contribution by interaction associated with correlation between the individual input and the others. The general expressions of these components are also derived. Based on the characteristics of these general expressions, a universal framework for estimating the various variance contributions of the correlated inputs is developed by taking the efficient state dependent parameter (SDP) method as an illustration. Numerical and engineering tests show that this decomposition of the variance contributions of the correlated inputs can provide useful information for exploring the sources of the output uncertainty and identifying the structure of the model function for the complicated models with correlated inputs. The efficiency and accuracy of the SDP-based method for estimating the various variance contributions of the correlated inputs are also demonstrated by the examples.
13 citations
TL;DR: The svr-based HDMR method enables efficient construction of high dimensional models with satisfactory prediction accuracy from a modest number of samples, which also permits accurate computation of the sensitivity indices.
Abstract: High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing high dimensional input-output system behavior. In practice, the HDMR component functions are each approximated by an appropriate basis function expansion. This procedure often requires many input-output samples which can restrict the treatment of high dimensional systems. In order to address this problem we introduce svr-based HDMR to efficiently and effectively construct the HDMR expansion by support vector regression (SVR) for a function $$f(\mathbf{x})$$
. In this paper the results for independent variables sampled over known probability distributions are reported. The theoretical foundation of the new approach relies on the kernel used in SVR itself being an HDMR expansion (referred to as the HDMR kernel ), i.e., an ANOVA kernel whose component kernels are mutually orthogonal and all non-constant component kernels have zero expectation. Several HDMR kernels are constructed as illustrations. While preserving the characteristic properties of HDMR, the svr-based HDMR method enables efficient construction of high dimensional models with satisfactory prediction accuracy from a modest number of samples, which also permits accurate computation of the sensitivity indices. A genetic algorithm is employed to optimally determine all the parameters of the component HDMR kernels and in SVR. The svr-based HDMR introduces a new route to advance HDMR algorithms. Two examples are used to illustrate the capability of the method.
13 citations
01 Jan 2017
TL;DR: In this paper, a generalized high dimensional model representation (HDMR) was used to obtain global sensitivity indices of uncorrelated model parameters in combustion systems, which are then used for model tuning.
Abstract: The High Dimensional Model Representation (HDMR) method has been applied in several previous studies to obtain global sensitivity indices of uncorrelated model parameters in combustion systems. However, the rate parameters of combustion models are intrinsically correlated and therefore uncertainty analysis methods are needed that can handle such parameters. A generalized HDMR method is presented here, which uses the Rosenblatt transformation on a correlated model parameter sample to obtain a sample of independent parameters. The method provides a full set of both correlated and marginal sensitivity indices. Ignition delay times predicted by an optimized hydrogen–air combustion model in stoichiometric mixtures near the three explosion limits are investigated with this new global sensitivity analysis tool. The sensitivity indices which account for all the correlated effects of the rate parameters are shown to dominate uncertainties in the model output. However, these correlated indices mask the individual influence of parameters. The final marginal uncorrelated sensitivity indices for individual parameters better indicate the change of importance of homogeneous gas phase and species wall-loss reactions as the pressure is increased from above the first explosion limit to above the third limit. However, these uncorrelated indices are small and whilst they provide insights into the dominant chemical and physical processes of the model over the range of conditions studied, the correlations between parameters have a very significant effect. The implications of this result on model tuning will be discussed.
TL;DR: It is shown that modified GMDH-NN algorithm can calculate coefficients of metamodel efficiently, so this paper aims at combining it with HDMR and proposes GM DH-HDMR method, which shows higher precision and faster convergence rate.
TL;DR: The representation introduced here is not based on the general EMPR but on a specific EMPR version constructed for bivariate function decomposition, called “Tridiagonal Kernel Enhanced Multivariance Products Representation (TKEMPR)”.
TL;DR: A new hybrid method is proposed to estimate the failure probability of a structure subject to random parameters, using the high dimensional model representation combined with artificial neural network (ANN) to approximate implicit limit state functions in structural reliability analysis.
Abstract: A new hybrid method is proposed to estimate the failure probability of a structure subject to random parameters. The high dimensional model representation (HDMR) combined with artificial neural network (ANN) is used to approximate implicit limit state functions in structural reliability analysis. HDMR facilitates the lower dimensional approximation of the original limit states function. For evaluating the failure probability, a first-order HDMR approximation is constructed by deploying sampling points along each random variable axis and hence obtaining the structural responses. To reduce the computational effort of the evaluation of limit state function, an ANN surrogate is trained based on the sampling points from HDMR. The component of the approximated function in HDMR can be regarded as the input of the ANN and the response of limit state function can be regarded as the target for training an ANN surrogate. This trained ANN surrogate is used to obtain structural outputs instead of directly calling the numerical model of a structure. After generating the ANN surrogate, Monte Carlo simulation (MCS) is performed to obtain the failure probability, based on the trained ANN surrogate. Three numerical examples are used to illustrate the accuracy and efficiency of the proposed method.
TL;DR: In this paper, a recursive method has been constructed on the Bivariate EMPR and the remainder term of each step therein has been expanded into EMPR from step to step until no remainder term appears in one of the consecutive steps.
Abstract: This work focuses on the utilization of a very recently developed decomposition method, weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) which can be equivalently used on continuous functions, and, multiway arrays after appropriate unfoldings. This recursive method has been constructed on the Bivariate EMPR and the remainder term of each step therein has been expanded into EMPR from step to step until no remainder term appears in one of the consecutive steps. The resulting expansion can also be expressed in a three factor product representation whose core factor is a tridiagonal matrix. The basic difference and novelty here is the non-constant weight utilization and the applications on certain chemical system data sets to show the efficiency of the WTMEMPR truncation approximants.
27 Jan 2017
TL;DR: A novel method with the help of High Dimensional Model Representation (HDMR) philosophy to achieve accurate image retrieval with high speed is developed and test the performance is obtained.
Abstract: Image retrieval continues to hold an important place in today’s extremely fast growing technology. In this field, the accurate image retrieval with high speed is critical. In this study, to achieve this important issue we developed a novel method with the help of High Dimensional Model Representation (HDMR) philosophy. HDMR is a decomposition method used to solve different scientific problems. To test the performance of the new method we used Columbia Object Image Library (COIL100) and obtained the encouraging results. These results are given in the findings section.
13 Nov 2017
TL;DR: The investigation on the use of meta-modeling techniques to directly map a range of initial conditions and model uncertainties, as well as characteristics of the considered object, into the parameters of the skew-normal distribution that usually characterizes the re-entry time windows, is briefly described.
Abstract: This paper presents the work to characterize and propagate the uncertainties on the atmospheric re-entry time of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite done with the framework of an ESA ITT project. Non-intrusive techniques based on Chebyshev polynomial approximation, and the Adaptive High Dimensional Model Representation multi-surrogate adaptive sampling have been used to perform uncertainty propagation and multivariate sensitivity analyses when both 3 and 6 degrees-of-freedom models where considered, considering uncertain-ties on initial conditions, and atmospheric and shape parameters. Two different uncertainty quantification/characterization approaches have been also proposed during the project. The same interpolation techniques used for non-expensive non-intrusive methods for uncertainty propagation, allowed the development of two methods based on direct optimization approaches, the Boundary Set Approach and the Inverse Uncertainty Quantification. Moreover, an innovative approach to treat the empirical accelerations has been proposed, based on polynomial expansions in the state variables. The method has been tested and further developed to consider uncertainties in the initial conditions, leading to a statistical characterization of the coefficients and representation of the possible trajectories. Finally, the investigation on the use of meta-modeling techniques to directly map a range of initial conditions and model uncertainties, as well as characteristics of the considered object, into the parameters of the skew-normal distribution that usually characterizes the re-entry time windows, bringing to a very fast characterization of the output PDF not requiring any further propagation at all, is also briefly described.
TL;DR: In this article, a model updating approach based on high-dimensional model representation (HDMR) is proposed for finite element modeling, obtaining explicit relationships between structural responses and parameters using HDMR and minimization of objective function developed using structural responses obtained from HDMR approximation functions using genetic algorithm.
Abstract: This paper presents a practical approach of model updating based on high-dimensional model representation (HDMR). The proposed methodology involves integrated finite element modeling, obtaining explicit relationships between the structural responses and parameters using HDMR and minimization of objective function developed using structural responses obtained from HDMR approximation functions using genetic algorithm. First, the efficiency of the proposed method is demonstrated by considering a simply supported beam example. Later model updating of an existing bridge is considered to check the adequacy of the proposed method.
01 Jan 2017
TL;DR: Here, it is demonstrated the effectiveness of high-dimensional model representation (HDMR) methods, which are not only able to calculate sensitivity indices but also able to visualize the effect of each parameter on the model output over its whole uncertainty range.
Abstract: Models used in Systems Engineering and Earth System Science are continuously evolving to include more processes and interactions at higher resolutions. This increase in complexity can also lead to an increase in the number of uncertain parameters. Parameter optimization methods can be used to constrain model parameters against observations. However, in most cases the large number of uncertain parameters leads to an underdetermined and ill-posed problem. It is therefore crucial to first identify the most important parameters in complex modeling systems by applying global sensitivity analysis methods. Here, we demonstrate the effectiveness of high-dimensional model representation (HDMR) methods, which are not only able to calculate sensitivity indices but also able to visualize the effect of each parameter on the model output over its whole uncertainty range. We introduce the graphical user interface (GUI)-HDMR software package and highlight its capabilities. A number of case studies from a wide range of applications are presented to underline the usefulness of the GUI-HDMR software and its ability to identify the most important parameters and their interactions in highly nonlinear complex modeling systems.
TL;DR: The results show that a good trade-off between computational complexity and approximation accuracy can be achieved for stochastic unconfined flow problems by selecting a suitable number of the most important dimensions in the M-dimensional model of hybrid HDMR.
Abstract: In this paper we present a stochastic model reduction method for efficiently solving nonlinear unconfined flow problems in heterogeneous random porous media. The input random fields of flow model are parameterized in a stochastic space for simulation. This often results in high stochastic dimensionality due to small correlation length of the covariance functions of the input fields. To efficiently treat the high-dimensional stochastic problem, we extend a recently proposed hybrid high-dimensional model representation (HDMR) technique to high-dimensional problems with multiple random input fields and integrate it with a sparse grid stochastic collocation method (SGSCM). Hybrid HDMR can decompose the high-dimensional model into a moderate M-dimensional model and a few one-dimensional models. The moderate dimensional model only depends on the most M important random dimensions, which are identified from the full stochastic space by sensitivity analysis. To extend the hybrid HDMR, we consider two different criteria for sensitivity test. Each of the derived low-dimensional stochastic models is solved by the SGSCM. This leads to a set of uncoupled deterministic problems at the collocation points, which can be solved by a deterministic solver. To demonstrate the efficiency and accuracy of the proposed method, a few numerical experiments are carried out for the unconfined flow problems in heterogeneous porous media with different correlation lengths. The results show that a good trade-off between computational complexity and approximation accuracy can be achieved for stochastic unconfined flow problems by selecting a suitable number of the most important dimensions in the M-dimensional model of hybrid HDMR.
TL;DR: A novel theoretical and numerical framework for the estimation of Sobol’ sensitivity indices for models in which inputs are confined to a non-rectangular domain is developed and MC/QMC estimators based on the acceptance-rejection sampling method are proposed.
Abstract: The variance-based method of global sensitivity analysis based on Sobol’ sensitivity indices has become very popular among practitioners due to its ease of interpretation. A novel theoretical and numerical framework for the estimation of Sobol’ sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. MC/QMC estimators based on the acceptance-rejection sampling method are proposed for the numerical estimation of Sobol’ sensitivity indices. Random Sampling - High Dimensional Model Representation metamodeling method is used to approximate models and constraints which significantly reduces the cost of evaluating Sobol’ sensitivity indices. Several model test functions with constraints are considered. The method is shown to be general and efficient.
01 Jan 2017
TL;DR: Three novel approaches have been developed for efficient stochastic computations by combining two available techniques, namely, high dimensional model representation and Kriging, which results in a twofold approximation tool.
Abstract: The computational effort associated with uncertainty quantification of engineering systems has been one of the prime concerns over the years. In order to alleviate this issue, three novel approaches have been developed for efficient stochastic computations. All of the approaches have been developed by combining two available techniques, namely, high dimensional model representation (HDMR) and Kriging, which results in a twofold approximation tool. Furthermore, efficient variable selection methods, such as least absolute shrinkage and selection operator, least angle regression and forward selection, have been effectively incorporated into the improved model for the determination of regression coefficients. Implementation of the proposed approaches has been demonstrated with three analytical and two finite element problems. Excellent results in terms of accuracy and computational effort obtained make the proposed methodologies potential for further complex applications.
05 Jun 2017
TL;DR: The proposed modified radial basis function based high dimensional model representation method using proportional sampling strategy (denoted as RBF-HDMR-PS) sequentially adds first order sample points with a predetermined proportion coefficient to effectively construct each component RBF, which avoids the stochastic influence of random sampling process inRBF- HDMR.
Abstract: To effectively tackling high dimensional, expensive, black-box (HEB) problems, this paper proposes a modified radial basis function based high dimensional model representation method using proportional sampling strategy (denoted as RBF-HDMR-PS). Different from the standard RBF-HDMR, the proposed RBF-HDMR-PS sequentially adds first order sample points with a predetermined proportion coefficient to effectively construct each component RBF, which avoids the stochastic influence of random sampling process in RBF-HDMR. The proposed RBF-HDMR-PS using different proportion coefficients is tested through two benchmark numerical problems with highly nonlinear first order components for comparing with RBF-HDMR. A best proportion coefficient is chosen and integrated into RBF-HDMR-PS. The comparison results show that RBF-HDMR-PS outperforms RBF-HDMR in terms of approximation accuracy.