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Wei Chen - One of the best experts on this subject based on the ideXlab platform.
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A New Weighted Stochastic Response Surface Method for Uncertainty Propagation
13th AIAA ISSMO Multidisciplinary Analysis Optimization Conference, 2010Co-Authors: Fenfen Xiong, Ying Xiong, Wei Chen, Shuxing YangAbstract:Conventional stochastic response surface method (SRSM) based on polynomial chaos expansion (PCE) for Uncertainty Propagation treats every sample points equally during the regression process and may produce inaccurate coefficient estimations in PCE. A new weighted stochastic response surface method (WSRSM) to overcome such limitation by considering the sample probabilistic weights in regression is studied in this work. Techniques that associate sample probabilistic weights to different sampling approaches such as Gaussian Quadrature point (GQ), Monomial Cubature Rule (MCR) and Latin Hypercube Design (LHD) are developed. The proposed method is demonstrated by several mathematical and engineering examples. Results show that for various sampling techniques, WSRSM can consistently improve the accuracy of Uncertainty Propagation compared to the conventional SRSM without adding extra computational cost. Insights into the relative accuracy and efficiency of using various sampling techniques in implementation are provided.
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A new sparse grid based method for Uncertainty Propagation
Structural and Multidisciplinary Optimization, 2009Co-Authors: Fenfen Xiong, M. Steven Greene, Ying Xiong, Wei Chen, Shuxing YangAbstract:Current methods for Uncertainty Propagation suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. The sparse grid technique, originally invented for numerical integration and interpolation, is extended to Uncertainty Propagation in this work to overcome the difficulty. The concept of Sparse Grid Numerical Integration (SGNI) is extended for estimating the first two moments of performance in robust design, while the Sparse Grid Interpolation (SGI) is employed to determine failure probability by interpolating the limit-state function at the Most Probable Point (MPP) in reliability analysis. The proposed methods are demonstrated by high-dimension mathematical examples with notable variate interactions and one multidisciplinary rocket design problem. Results show that the use of sparse grid methods works better than popular counterparts. Furthermore, the automatic sampling, special interpolation process, and dimension-adaptivity feature make SGI more flexible and efficient than using the uniform sample based metamodeling techniques.
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Analytical Uncertainty Propagation via Metamodels in Simulation-Based Design under Uncertainty
10th AIAA ISSMO Multidisciplinary Analysis and Optimization Conference, 2004Co-Authors: Wei Chen, Ruichen Jin, Agus SudjiantoAbstract:In spite of the benefits, one of the most challenging issues for implementing optimization under Uncertainty, such as the use of robust design approach, is associated with the intensive computational demand of Uncertainty Propagation, especially when the simulation programs are computationally expensive. In this paper, an efficient approach to Uncertainty Propagation via the use of metamodels is presented. Metamodels, created through computer simulations to replace expensive simulation programs, are widely used in simulation-based design. Different from existing techniques that apply sample-based methods to metamodels for Uncertainty Propagation, our method utilizes analytical derivations to eliminate the random errors as well as to reduce the computational expenses of sampling. In this paper, we provide analytical formulations for mean and variance evaluations via a variety of metamodels commonly used in engineering design applications. The benefits of our proposed techniques are demonstrated through the robust design for improving vehicle handling. In addition to the improved accuracy and efficiency, our proposed analytical approach can greatly improve the convergence behavior of optimization under Uncertainty.
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Analytical Metamodel-Based Global Sensitivity Analysis and Uncertainty Propagation for Robust Design
SAE Technical Paper Series, 2004Co-Authors: Ruichen Jin, Wei Chen, Agus SudjiantoAbstract:Metamodeling approach has been widely used due to the high computational cost of using high-fidelity simulations in engineering design. Interpretation of metamodels for the purpose of design, especially design under Uncertainty, becomes important. The computational expenses associated with metamodels and the random errors introduced by sample-based methods require the development of analytical methods, such as those for global sensitivity analysis and Uncertainty Propagation to facilitate a robust design process. In this work, we develop generalized analytical formulations that can provide efficient as well as accurate global sensitivity analysis and Uncertainty Propagation for a variety of metamodels. The benefits of our proposed techniques are demonstrated through vehicle related robust design applications.
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Model validation via Uncertainty Propagation and data transformations
AIAA Journal, 2004Co-Authors: Wei Chen, Lusine Baghdasaryan, Thaweepat Buranathiti, Jian CaoAbstract:Model validation has become a primary means to evaluate accuracy and reliability of computational simulations in engineering design. Because of uncertainties involved in modeling, manufacturing processes, and measurement systems, the assessment of the validity of a modeling approach must be conducted based on stochastic measurements to provide designers with confidence in using a model. A generic model validation methodology via Uncertainty Propagation and data transformations is presented. The approach reduces the number of physical tests at each design setting to one by shifting the evaluation effort to Uncertainty Propagation of the computational model. Response surface methodology is used to create metamodels as less costly approximations of simulation models for the Uncertainty Propagation. Methods for validating models with both normal and nonnormal response distributions are proposed. The methodology is illustrated with the examination of the validity of two finite element analysis models for predicting springback angles in a sample flanging process.
Gerard B.m. Heuvelink - One of the best experts on this subject based on the ideXlab platform.
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'spup' - An R package for Uncertainty Propagation in spatial environmental modelling
2016Co-Authors: Kasia Sawicka, Gerard B.m. HeuvelinkAbstract:Computer models are crucial tools in engineering and environmental sciences for simulating the behaviour of complex systems. While many models are deterministic, the Uncertainty in their predictions needs to be estimated before they are used for decision support. Advances in Uncertainty analysis have been paralleled by a growing number of software tools, but none has gained recognition for universal applicability, including case studies with spatial models and spatial model inputs. We develop an R package that facilitates Uncertainty Propagation analysis in spatial environmental modelling. The 'spup' package includes functions for Uncertainty model specification, Propagation of Uncertainty using Monte Carlo (MC) techniques, and Uncertainty visualization functions. Uncertain variables are represented as objects which Uncertainty is described by probability distributions. Spatial auto-correlation within a variable and crosscorrelation between variables is also accommodated for. The package has implemented the MC approach with efficient sampling algorithms, i.e. stratified random sampling and Latin hypercube sampling. The MC realizations may be used as an input to the environmental models called from R, or externally. Selected static and interactive visualization methods that are understandable by nonstatisticians can be used to visualize Uncertainty about the measured input, model parameters and output of the Uncertainty Propagation. Computer models are crucial tools in engineering and environmental sciences for simulating the behaviour of complex systems. While many models are deterministic, the Uncertainty in their predictions needs to be estimated before they are used for decision support. Advances in Uncertainty analysis have been paralleled by a growing number of software tools, but none has gained recognition for universal applicability, including case studies with spatial models and spatial model inputs. We develop an R package that facilitates Uncertainty Propagation analysis in spatial environmental modelling. The 'spup' package includes functions for Uncertainty model specification, Propagation of Uncertainty using Monte Carlo (MC) techniques, and Uncertainty visualization functions. Uncertain variables are represented as objects which Uncertainty is described by probability distributions. Spatial auto-correlation within a variable and crosscorrelation between variables is also accommodated for. The package has implemented the MC approach with efficient sampling algorithms, i.e. stratified random sampling and Latin hypercube sampling. The MC realizations may be used as an input to the environmental models called from R, or externally. Selected static and interactive visualization methods that are understandable by nonstatisticians can be used to visualize Uncertainty about the measured input, model parameters and output of the Uncertainty Propagation.
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Uncertainty Propagation in urban hydrology water quality modelling
2016Co-Authors: Arturo Torres Matallana, Ulrich Leopold, Gerard B.m. HeuvelinkAbstract:Uncertainty is often ignored in urban hydrology modelling. Engineering practice typically ignores uncertainties and Uncertainty Propagation. This can have large impacts, such as the wrong dimensioning of urban drainage systems and the inaccurate estimation of pollution in the environment caused by combined sewer overflows. This paper presents an Uncertainty Propagation analysis in urban hydrology modelling. The case study was the Haute-Sure catchment in Luxembourg for one yearly time series measured in 2010, and 10 individual rainfall events measured in 2011. The selection of model input variables for Uncertainty quantification was based on their level of Uncertainty and model sensitivity. Probability distribution functions were defined to represent the Uncertainty of the input variables. We applied a Monte Carlo technique using a simplified model, EmiStatR, which simulates the volume and substance flows in urban drainage systems. We focus in loads and concentrations of chemical oxygen demand and ammonium, which are important variables for wastewater and surface water quality management. Uncertainty is often ignored in urban hydrology modelling. Engineering practice typically ignores uncertainties and Uncertainty Propagation. This can have large impacts, such as the wrong dimensioning of urban drainage systems and the inaccurate estimation of pollution in the environment caused by combined sewer overflows. This paper presents an Uncertainty Propagation analysis in urban hydrology modelling. The case study was the Haute-Sure catchment in Luxembourg for one yearly time series measured in 2010, and 10 individual rainfall events measured in 2011. The selection of model input variables for Uncertainty quantification was based on their level of Uncertainty and model sensitivity. Probability distribution functions were defined to represent the Uncertainty of the input variables. We applied a Monte Carlo technique using a simplified model, EmiStatR, which simulates the volume and substance flows in urban drainage systems. We focus in loads and concentrations of chemical oxygen demand and ammonium, which are important variables for wastewater and surface water quality management.
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Unit 098 - Uncertainty Propagation in GIS - eScholarship
2000Co-Authors: Cc In Giscience, Gerard B.m. HeuvelinkAbstract:This unit outlines an introduction to the problem of Uncertainty Propagation in GIS; the definition and identification of a stochastic error model for quantitative spatial attributes; a description of common error Propagation techniques; applications of the theory; and how the results of an Uncertainty analysis may be used to improve the accuracy of GIS products.
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Unit 098 - Uncertainty Propagation in GIS
2000Co-Authors: Cc In Giscience, Gerard B.m. HeuvelinkAbstract:Author(s): 098, CC in GIScience; Heuvelink, Gerard B.M. | Editor(s): Goodchild, Michael F.; Kemp, Karen K. | Abstract: This unit outlines an introduction to the problem of Uncertainty Propagation in GIS; the definition and identification of a stochastic error model for quantitative spatial attributes; a description of common error Propagation techniques; applications of the theory; and how the results of an Uncertainty analysis may be used to improve the accuracy of GIS products.
Fenfen Xiong - One of the best experts on this subject based on the ideXlab platform.
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An enhanced data-driven polynomial chaos method for Uncertainty Propagation
Engineering Optimization, 2017Co-Authors: Fenggang Wang, Fenfen Xiong, Huan Jiang, Jianmei SongAbstract:ABSTRACTAs a novel type of polynomial chaos expansion (PCE), the data-driven PCE (DD-PCE) approach has been developed to have a wide range of potential applications for Uncertainty Propagation. While the research on DD-PCE is still ongoing, its merits compared with the existing PCE approaches have yet to be understood and explored, and its limitations also need to be addressed. In this article, the Galerkin projection technique in conjunction with the moment-matching equations is employed in DD-PCE for higher-dimensional Uncertainty Propagation. The enhanced DD-PCE method is then compared with current PCE methods to fully investigate its relative merits through four numerical examples considering different cases of information for random inputs. It is found that the proposed method could improve the accuracy, or in some cases leads to comparable results, demonstrating its effectiveness and advantages. Its application in dealing with a Mars entry trajectory optimization problem further verifies its effecti...
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Uncertainty Propagation techniques in probabilistic design of multilevel systems
2011 International Conference on Quality Reliability Risk Maintenance and Safety Engineering, 2011Co-Authors: Fenfen Xiong, Kun Guo, Wei ZhouAbstract:In hierarchical multilevel systems, information (interrelated responses) is passed among levels following a bottom-up sequence. One of the primary challenges for multilevel system design optimization under Uncertainty is associated with the quantification of Uncertainty propagated across multiple levels. Two newly developed Uncertainty Propagation techniques, the full numerical factorial integration method and the univariate dimension reduction method, are compared through their employment in probabilistic design of multilevel system. The Probabilistic Analytical Target Cascading (PATC) approach is used for solving the probabilistic multilevel hierarchical problems as well as demonstrating the two Uncertainty Propagation techniques. Covariance among the interrelated responses between neighboring levels is considered to improve the accuracy of the statistics estimation of upper-level outputs. Linear transformation of the correlated interrelated responses is adopted to facilitate the application of the Uncertainty Propagation techniques in PATC. The Monte Carlo method is used as the benchmark to verify the accuracy of these techniques.
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A New Weighted Stochastic Response Surface Method for Uncertainty Propagation
13th AIAA ISSMO Multidisciplinary Analysis Optimization Conference, 2010Co-Authors: Fenfen Xiong, Ying Xiong, Wei Chen, Shuxing YangAbstract:Conventional stochastic response surface method (SRSM) based on polynomial chaos expansion (PCE) for Uncertainty Propagation treats every sample points equally during the regression process and may produce inaccurate coefficient estimations in PCE. A new weighted stochastic response surface method (WSRSM) to overcome such limitation by considering the sample probabilistic weights in regression is studied in this work. Techniques that associate sample probabilistic weights to different sampling approaches such as Gaussian Quadrature point (GQ), Monomial Cubature Rule (MCR) and Latin Hypercube Design (LHD) are developed. The proposed method is demonstrated by several mathematical and engineering examples. Results show that for various sampling techniques, WSRSM can consistently improve the accuracy of Uncertainty Propagation compared to the conventional SRSM without adding extra computational cost. Insights into the relative accuracy and efficiency of using various sampling techniques in implementation are provided.
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A new sparse grid based method for Uncertainty Propagation
Structural and Multidisciplinary Optimization, 2009Co-Authors: Fenfen Xiong, M. Steven Greene, Ying Xiong, Wei Chen, Shuxing YangAbstract:Current methods for Uncertainty Propagation suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. The sparse grid technique, originally invented for numerical integration and interpolation, is extended to Uncertainty Propagation in this work to overcome the difficulty. The concept of Sparse Grid Numerical Integration (SGNI) is extended for estimating the first two moments of performance in robust design, while the Sparse Grid Interpolation (SGI) is employed to determine failure probability by interpolating the limit-state function at the Most Probable Point (MPP) in reliability analysis. The proposed methods are demonstrated by high-dimension mathematical examples with notable variate interactions and one multidisciplinary rocket design problem. Results show that the use of sparse grid methods works better than popular counterparts. Furthermore, the automatic sampling, special interpolation process, and dimension-adaptivity feature make SGI more flexible and efficient than using the uniform sample based metamodeling techniques.
Shuxing Yang - One of the best experts on this subject based on the ideXlab platform.
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A New Weighted Stochastic Response Surface Method for Uncertainty Propagation
13th AIAA ISSMO Multidisciplinary Analysis Optimization Conference, 2010Co-Authors: Fenfen Xiong, Ying Xiong, Wei Chen, Shuxing YangAbstract:Conventional stochastic response surface method (SRSM) based on polynomial chaos expansion (PCE) for Uncertainty Propagation treats every sample points equally during the regression process and may produce inaccurate coefficient estimations in PCE. A new weighted stochastic response surface method (WSRSM) to overcome such limitation by considering the sample probabilistic weights in regression is studied in this work. Techniques that associate sample probabilistic weights to different sampling approaches such as Gaussian Quadrature point (GQ), Monomial Cubature Rule (MCR) and Latin Hypercube Design (LHD) are developed. The proposed method is demonstrated by several mathematical and engineering examples. Results show that for various sampling techniques, WSRSM can consistently improve the accuracy of Uncertainty Propagation compared to the conventional SRSM without adding extra computational cost. Insights into the relative accuracy and efficiency of using various sampling techniques in implementation are provided.
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A new sparse grid based method for Uncertainty Propagation
Structural and Multidisciplinary Optimization, 2009Co-Authors: Fenfen Xiong, M. Steven Greene, Ying Xiong, Wei Chen, Shuxing YangAbstract:Current methods for Uncertainty Propagation suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. The sparse grid technique, originally invented for numerical integration and interpolation, is extended to Uncertainty Propagation in this work to overcome the difficulty. The concept of Sparse Grid Numerical Integration (SGNI) is extended for estimating the first two moments of performance in robust design, while the Sparse Grid Interpolation (SGI) is employed to determine failure probability by interpolating the limit-state function at the Most Probable Point (MPP) in reliability analysis. The proposed methods are demonstrated by high-dimension mathematical examples with notable variate interactions and one multidisciplinary rocket design problem. Results show that the use of sparse grid methods works better than popular counterparts. Furthermore, the automatic sampling, special interpolation process, and dimension-adaptivity feature make SGI more flexible and efficient than using the uniform sample based metamodeling techniques.
Inseok Hwang - One of the best experts on this subject based on the ideXlab platform.
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Analytical Uncertainty Propagation for Satellite Relative Motion Along Elliptic Orbits
Journal of Guidance Control and Dynamics, 2016Co-Authors: Sangjin Lee, Hao Lyu, Inseok HwangAbstract:For satellites flying in close proximity, monitoring the uncertainties of neighboring satellites’ states is a crucial task because the Uncertainty information is used to compute the collision probability between satellites with the objective of collision avoidance. In this study, an analytical closed-form solution is developed for Uncertainty Propagation in the satellite relative motion near general elliptic orbits. The Tschauner–Hempel equations are used to describe the linearized relative motion of the deputy satellite where the chief orbit is eccentric. Under the assumption of the linearized relative motion and white Gaussian process noise, the Uncertainty Propagation problem is defined to compute the mean and covariance matrix of the relative states of the deputy satellite. The evolution of the mean and covariance matrix is governed by a linear time-varying differential equation, for which the solution requires the integration of the quadratic function of the inverse of the fundamental matrix associat...
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Analytical Solutions to Uncertainty Propagation in Satellite Relative Motion
AIAA Guidance Navigation and Control (GNC) Conference, 2013Co-Authors: Sangjin Lee, Inseok HwangAbstract:As satellites in a formation are required to fly in close proximity, computing collision probabilities which is based on Uncertainty Propagation of satellites’ relative position has become important. In this paper, we develop general analytical solutions to Uncertainty Propagation in linearized satellite relative motion. Various linear dynamic equations are used to describe the linearized relative motions. Under the assumption of the white Gaussian process noise, the Uncertainty Propagation problem is defined to compute the covariance matrix of the states of the deputy satellite at any given time. The evolution of the covariance matrix is governed by a linear time-varying differential equation, whose solution requires the integration of the quadratic function of the inverse of the fundamental matrix associated to the linear relative motion dynamics. The difficulty of the integration and finding the inverse of the fundamental matrix is addressed by introducing an adjoint system to the linear relative motion dynamics. From the analytical solution, we can evaluate the Uncertainty of the states of the deputy satellite at any time of interest without time consuming numerical integration.
