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Author:
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Languages : en
Pages : 58
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Author: Brian A. Lockwood
Publisher:
ISBN: 9781267323378
Category : Aerodynamics, Hypersonic
Languages : en
Pages : 195
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Book Description
With the proliferation of simulation within the design and analysis of engineering systems, uncertainty quantification and sensitivity analysis have taken on increased importance, providing valuable information for assessing the reliability of simulation outputs and a means for improving these results. In this work, uncertainty quantification and sensitivity analysis within the context of hypersonic computational fluid dynamics is examined. The simulation of hypersonic relies on numerous constitutive relations to account for chemical reactions, internal energy modes and molecular transport. Within these constitutive relations are hundreds of constants and parameters, which are often the result of experimental measurements. The goal of sensitivity analysis is determining the simulation parameters most affecting an output of interest, while the goal of uncertainty quantification is determining the variability of simulation outputs resulting from the uncertainty associated with model parameters. Traditional methods for uncertainty quantification and sensitivity analysis typically rely on exhaustive sampling, where hundreds to thousands of simulations are performed and relevant statistics are computed. For complex simulations, these exhaustive approaches are prohibitively expensive and well beyond the computational budget of most projects. For this work, gradient-based methods are used to reduce the expense of uncertainty quantification and sensitivity analysis. Using an adjoint-based approach, the derivative of an output with respect to simulation parameters can be computed in a constant amount of work, providing more information about the simulation output without a significant increase in cost. This additional information can then be leveraged in novel ways, such as surrogate models or optimization, to accelerate the process of uncertainty quantification or sensitivity analysis. This dissertation demonstrates these gradient-based methods for sensitivity analysis and uncertainty quantification in hypersonic flow simulations and assesses the performance of these methods in terms of cost and accuracy.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309256348
Category : Mathematics
Languages : en
Pages : 144
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Book Description
Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.
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Languages : en
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Abstract : Uncertainty is inherent to real-world engineering systems, and reliability analysis aims at quantitatively measuring the probability that engineering systems successfully perform the intended functionalities under various sources of uncertainties. In this dissertation, heterogeneous uncertainties including input variation, data uncertainty, simulation model uncertainty, and time-dependent uncertainty have been taken into account in reliability analysis and reliability-based design optimization (RBDO). The input variation inherently exists in practical engineering system and can be characterized by statistical modeling methods. Data uncertainty occurs when surrogate models are constructed to replace the simulations or experiments based on a set of training data, while simulation model uncertainty is introduced when high-fidelity simulation models are built through idealizations and simplifications of real physical processes or systems. Time-dependent uncertainty is involved when considering system or component aging and deterioration. Ensuring a high level of system reliability is one of the critical targets for engineering design, and this dissertation studies effective reliability analysis and reliability-based design optimization (RBDO) techniques to address the challenges of heterogeneous uncertainties. First of all, a novel reliability analysis method is proposed to deal with input randomness and time-dependent uncertainty. An ensemble learning framework is designed by integrating the Long short-term memory (LSTM) and feedforward neural network. Time-series data is utilized to construct a surrogate model for capturing the time-dependent responses with respect to input variables and stochastic processes. Moreover, a RBDO framework with Kriging technique is presented to address the time-dependent uncertainty in design optimization. Limit state functions are transformed into time-independent domain by converting the stochastic processes and time parameter to random variables, and Kriging surrogate models are then built and enhanced by a design-driven adaptive sampling scheme to accurately identify potential instantaneous failure events. Secondly, an equivalent reliability index (ERI) method is proposed for handling both input variations and surrogate model uncertainty in RBDO. To account for the surrogate model uncertainty, a Gaussian mixture model is constructed based on Gaussian process model predictions. To propagate both input variations and surrogate model uncertainty into reliability analysis, the statistical moments of the GMM is utilized for calculating an equivalent reliability index. The sensitivity of ERI with respect to design variables is analytically derived to facilitate the surrogate model-based product design process, lead to reliable optimum solutions. Thirdly, different effective methods are developed to handle the simulation model uncertainty as well as the surrogate model uncertainty. An active resource allocation framework is proposed for accurate reliability analysis using both simulation and experimental data, where a two-phase updating strategy is developed for reducing the computational costs. The framework is further extended for RBDO problems, where multi-fidelity design algorithm is presented to ensure accurate optimum designs while minimizing the computational costs. To account for both the bias terms and unknown parameters in the simulation model, Bayesian inference method is adopted for building a validated surrogate model, and a Bayesian-based mixture modeling method is developed to ensure reliable system designs with the consideration of heterogeneous uncertainties.
Author: Roger Ghanem
Publisher: Springer
ISBN: 9783319123844
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.
Author:
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ISBN:
Category :
Languages : en
Pages : 75
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Author:
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ISBN:
Category :
Languages : en
Pages : 73
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Author: Anirban Basudhar
Publisher:
ISBN:
Category :
Languages : en
Pages : 464
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This dissertation presents a sampling-based method that can be used for uncertainty quantification and deterministic or probabilistic optimization. The objective is to simultaneously address several difficulties faced by classical techniques based on response values and their gradients. In particular, this research addresses issues with discontinuous and binary (pass or fail) responses, and multiple failure modes. All methods in this research are developed with the aim of addressing problems that have limited data due to high cost of computation or experiment, e.g. vehicle crashworthiness, fluid-structure interaction etc. The core idea of this research is to construct an explicit boundary separating allowable and unallowable behaviors, based on classification information of responses instead of their actual values. As a result, the proposed method is naturally suited to handle discontinuities and binary states. A machine learning technique referred to as support vector machines (SVMs) is used to construct the explicit boundaries. SVM boundaries can be highly nonlinear, which allows one to use a single SVM for representing multiple failure modes. One of the major concerns in the design and uncertainty quantification communities is to reduce computational costs. To address this issue, several adaptive sampling methods have been developed as part of this dissertation. Specific sampling methods have been developed for reliability assessment, deterministic optimization, and reliability-based design optimization. Adaptive sampling allows the construction of accurate SVMs with limited samples. However, like any approximation method, construction of SVM is subject to errors. A new method to quantify the prediction error of SVMs, based on probabilistic support vector machines (PSVMs) is also developed. It is used to provide a relatively conservative probability of failure to mitigate some of the adverse effects of an inaccurate SVM. In the context of reliability assessment, the proposed method is presented for uncertainties represented by random variables as well as spatially varying random fields. In order to validate the developed methods, analytical problems with known solutions are used. In addition, the approach is applied to some application problems, such as structural impact and tolerance optimization, to demonstrate its strengths in the context of discontinuous responses and multiple failure modes.
Author: Yan Wang
Publisher: Woodhead Publishing Limited
ISBN: 0081029411
Category : Materials science
Languages : en
Pages : 604
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Book Description
Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.
Author: Cornelius Lanczos
Publisher: SIAM
ISBN: 9781611971187
Category : Mathematics
Languages : en
Pages : 581
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Book Description
Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field."
