Author: Sergio Daniel Marques Amaral
Publisher:
ISBN:
Category :
Languages : en
Pages : 175
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Book Description
To support effective decision making, engineers should comprehend and manage various uncertainties throughout the design process. In today's modern systems, quantifying uncertainty can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprised of a large number of components. In many cases, these components may be developed by different groups and even run on different computational platforms, making it challenging or even impossible to achieve tight integration of the various models. This thesis presents an approach for overcoming this challenge by establishing a divide-and-conquer methodology, inspired by the decomposition-based approaches used in multidisciplinary analysis and optimization. Specifically, this research focuses on uncertainty analysis, also known as forward propagation of uncertainties, and sensitivity analysis. We present an approach for decomposing the uncertainty analysis task amongst the various components comprising a feed-forward system and synthesizing the local uncertainty analyses into a system uncertainty analysis. Our proposed decomposition-based multicomponent uncertainty analysis approach is shown to converge in distribution to the traditional all-at-once Monte Carlo uncertainty analysis under certain conditions. Our decomposition-based sensitivity analysis approach, which is founded on our decomposition-based uncertainty analysis algorithm, apportions the system output variance among the system inputs. The proposed decomposition-based uncertainty quantification approach is demonstrated on a multidisciplinary gas turbine system and is compared to the traditional all-at-once Monte Carlo uncertainty quantification approach. To extend the decomposition-based uncertainty quantification approach to high dimensions, this thesis proposes a novel optimization formulation to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program and can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem yields importance weights that are shown to result in convergence in the Ll-norm of the weighted proposal empirical distribution function to the target distribution function, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches. The proposed approaches presented herein are demonstrated on a realistic application; environmental impacts of aviation technologies and operations. The results demonstrate that the decomposition-based uncertainty quantification approach can effectively quantify the uncertainty of a multicomponent system for which the models are housed in different locations and owned by different groups.
Author: Charles Hirsch
Publisher: Springer
ISBN: 331977767X
Category : Technology & Engineering
Languages : en
Pages : 799
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Book Description
This book covers cutting-edge findings related to uncertainty quantification and optimization under uncertainties (i.e. robust and reliable optimization), with a special emphasis on aeronautics and turbomachinery, although not limited to these fields. It describes new methods for uncertainty quantification, such as non-intrusive polynomial chaos, collocation methods, perturbation methods, as well as adjoint based and multi-level Monte Carlo methods. It includes methods for characterization of most influential uncertainties, as well as formulations for robust and reliable design optimization. A distinctive element of the book is the unique collection of test cases with prescribed uncertainties, which are representative of the current engineering practice of the industrial consortium partners involved in UMRIDA, a level 1 collaborative project within the European Commission's Seventh Framework Programme (FP7). All developed methods are benchmarked against these industrial challenges. Moreover, the book includes a section dedicated to Best Practice Guidelines for uncertainty quantification and robust design optimization, summarizing the findings obtained by the consortium members within the UMRIDA project. All in all, the book offers a authoritative guide to cutting-edge methodologies for uncertainty management in engineering design, covers a wide range of applications and discusses new ideas for future research and interdisciplinary collaborations.
Author: Loïc Brevault
Publisher: Springer Nature
ISBN: 3030391264
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Spotlighting the field of Multidisciplinary Design Optimization (MDO), this book illustrates and implements state-of-the-art methodologies within the complex process of aerospace system design under uncertainties. The book provides approaches to integrating a multitude of components and constraints with the ultimate goal of reducing design cycles. Insights on a vast assortment of problems are provided, including discipline modeling, sensitivity analysis, uncertainty propagation, reliability analysis, and global multidisciplinary optimization. The extensive range of topics covered include areas of current open research. This Work is destined to become a fundamental reference for aerospace systems engineers, researchers, as well as for practitioners and engineers working in areas of optimization and uncertainty. Part I is largely comprised of fundamentals. Part II presents methodologies for single discipline problems with a review of existing uncertainty propagation, reliability analysis, and optimization techniques. Part III is dedicated to the uncertainty-based MDO and related issues. Part IV deals with three MDO related issues: the multifidelity, the multi-objective optimization and the mixed continuous/discrete optimization and Part V is devoted to test cases for aerospace vehicle design.
Author: Christian Soize
Publisher: Springer
ISBN: 3319543393
Category : Computers
Languages : en
Pages : 344
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Book Description
This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.
Author: José Eduardo Souza De Cursi
Publisher: Springer Nature
ISBN: 3030536696
Category : Technology & Engineering
Languages : en
Pages : 472
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Book Description
This proceedings book discusses state-of-the-art research on uncertainty quantification in mechanical engineering, including statistical data concerning the entries and parameters of a system to produce statistical data on the outputs of the system. It is based on papers presented at Uncertainties 2020, a workshop organized on behalf of the Scientific Committee on Uncertainty in Mechanics (Mécanique et Incertain) of the AFM (French Society of Mechanical Sciences), the Scientific Committee on Stochastic Modeling and Uncertainty Quantification of the ABCM (Brazilian Society of Mechanical Sciences) and the SBMAC (Brazilian Society of Applied Mathematics).
Author: Liu Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 330
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Book Description
In the first part of the thesis, we develop a generalized polynomial chaos approach based stochastic Galerkin (gPC-SG) method for the linear semi-conductor Boltzmann equation with random inputs and diffusive scalings. The random inputs are due to uncertainties in the collision kernel or initial data. We study the regularity (uniform in the Knudsen number) of the solution in the random space, and prove the spectral accuracy of the gPC-SG method. We then use the asymptotic-preserving framework for the deterministic counterpart to come up with the stochastic asymptotic-preserving (sAP) gPC-SG method for the problem under study which is efficient in the diffusive regime. Numerical experiments are conducted to validate the accuracy and asymptotic properties of the method. In the second part, we study the linear transport equation under diffusive scaling and with random inputs. The method is based on the gPC-SG framework. Several theoretical aspects will be addressed. A uniform numerical stability with respect to the Knudsen number and a uniform error estimate is given. For temporal and spatial discretizations, we apply the implicit-explicit (IMEX) scheme under the micro-macro decomposition framework and the discontinuous Galerkin (DG) method. A rigorous proof of the sAP property is given. Extensive numerical experiments that validate the accuracy and sAP of the method are shown. In the last part, we study a class of highly oscillatory transport equations that arise in semiclassical modeling of non-adiabatic quantum dynamics. These models contain uncertainties, particularly in coefficients that correspond to the potentials of the molecular system. We first focus on a highly oscillatory scalar model with random uncertainty. Our method is built upon the nonlinear geometrical optics (NGO) based method for numerical approximations of deterministic equations, which can obtain accurate pointwise solution even without numerically resolving spatially and temporally the oscillations. With the random uncertainty, we show that such a method has oscillatory higher order derivatives in the random space, thus requires a frequency dependent discretization in the random space. We modify this method by introducing a new "time" variable based on the phase, which is shown to be non-oscillatory in the random space, based on which we develop a gPC-SG method that can capture oscillations with the frequency-independent time step, mesh size as well as the degree of polynomial chaos. A similar approach is then extended to a semiclassical surface hopping model system with a similar numerical conclusion. Various numerical examples attest that these methods indeed capture accurately the solution statistics pointwisely even though none of the numerical parameters resolve the high frequencies of the solution.
Author: Ralph C. Smith
Publisher: SIAM
ISBN: 161197321X
Category : Computers
Languages : en
Pages : 400
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Book Description
The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.
Author: T. J. Sullivan
Publisher:
ISBN: 9783919233943
Category :
Languages : en
Pages : 342
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Book Description
Author: Robert Barthorpe
Publisher: Springer
ISBN: 3319747932
Category : Technology & Engineering
Languages : en
Pages : 303
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Book Description
Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty
Author:
Publisher:
ISBN:
Category : Chemical engineering
Languages : en
Pages : 558
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Book Description
