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Author: Zhanlin Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 103
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Book Description
Uncertainties exist in both physics-based and data-driven models of systems. Understanding how system inputs affect a system output's uncertainty is essential to improve system outputs such as quality and productivity. Variance-based sensitivity analysis, which is widely used for uncertainty quantification, characterizes how the output variance is propagated from inputs. To estimate the variance-based sensitivity indices of the output with respect to inputs, polynomial chaos expansions (PCEs) are widely used. However, a majority of existing PCEs impose parametric distributional assumptions on inputs. Furthermore, existing sensitivity indices for dependent inputs impose strong assumptions on the dependence structure of the inputs or lack interpretability. Although recent studies proposed fully data-driven PCEs without strong assumptions on inputs, these PCEs are generally inefficient because the minimally required number of observations increases exponentially in the number of the inputs. To address these challenges, three data-driven PCEs are proposed in this dissertation. We first propose the sparse network PCE (SN-PCE) model for a broad class of systems whose input-output relationships are expressed as directed acyclic graphs. The proposed SN-PCE model accurately estimates variance-based sensitivity indices with far fewer observations than state-of-the-art black-box methods. Next, we propose data-driven sensitivity indices by constructing ordered partitions of linearly independent polynomials of dependent inputs for PCEs. The proposed sensitivity indices provide intuitive interpretations of how the dependent inputs affect the variance of the output without a priori knowledge of the dependence structure of the inputs. Finally, we propose a data-driven algorithm to build sparse PCEs for models with dependent inputs. The proposed algorithm not only reduces the number of minimally required observations but also improves upon the numerical stability and estimation accuracy of a state-of-the-art sparse PCE.
Author: Zhanlin Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 103
Get Book Here
Book Description
Uncertainties exist in both physics-based and data-driven models of systems. Understanding how system inputs affect a system output's uncertainty is essential to improve system outputs such as quality and productivity. Variance-based sensitivity analysis, which is widely used for uncertainty quantification, characterizes how the output variance is propagated from inputs. To estimate the variance-based sensitivity indices of the output with respect to inputs, polynomial chaos expansions (PCEs) are widely used. However, a majority of existing PCEs impose parametric distributional assumptions on inputs. Furthermore, existing sensitivity indices for dependent inputs impose strong assumptions on the dependence structure of the inputs or lack interpretability. Although recent studies proposed fully data-driven PCEs without strong assumptions on inputs, these PCEs are generally inefficient because the minimally required number of observations increases exponentially in the number of the inputs. To address these challenges, three data-driven PCEs are proposed in this dissertation. We first propose the sparse network PCE (SN-PCE) model for a broad class of systems whose input-output relationships are expressed as directed acyclic graphs. The proposed SN-PCE model accurately estimates variance-based sensitivity indices with far fewer observations than state-of-the-art black-box methods. Next, we propose data-driven sensitivity indices by constructing ordered partitions of linearly independent polynomials of dependent inputs for PCEs. The proposed sensitivity indices provide intuitive interpretations of how the dependent inputs affect the variance of the output without a priori knowledge of the dependence structure of the inputs. Finally, we propose a data-driven algorithm to build sparse PCEs for models with dependent inputs. The proposed algorithm not only reduces the number of minimally required observations but also improves upon the numerical stability and estimation accuracy of a state-of-the-art sparse PCE.
Author: Osama Alkhateeb
Publisher:
ISBN:
Category : Detectors
Languages : en
Pages : 95
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Book Description
In the last two decades, polynomial chaos expansion (PCE) methods have received considerable attention due to their efficiency and accuracy in modelling stochastic processes. However, implementing these methods require specifying the input distributions of a model a priori. This might not be feasible in data-driven applications in which the inputs are represented as data samples obtained from real-time measurements. Further, fitting the data with parametric distributions may introduce undesirable errors. The arbitrary polynomial chaos (aPC) method overcomes this limitation by constructing a chaos expansion based on the statistical moments rather than the probability distributions. The first objective of this dissertation is to develop a procedure based on aPC for data-driven uncertainty quantification (UQ) in applications of electromagnetics and wireless communication. Although the aPC method is considered to be simple and effective, it becomes numerically unstable when high-order expansions are sought. Alternatively, the multi-element arbitrary polynomial chaos (ME-aPC) alleviates this drawback by replacing the aPC expansion with a piecewise reduced order one. The second objective of this dissertation is to develop a procedure based on ME-aPC, and to demonstrate its efficiency in data-driven UQ. The proposed procedures are implemented with several model problems of electromagnetics such as filters and sensors, and with model problems of wireless communications addressing uncertainties in lunar radio links. The accuracy of the procedures is validated with plots of relative error, and in some examples, with results obtained via the classical Monte Carlo (MC) method.
Author: Frederica Darema
Publisher: Springer Nature
ISBN: 3031279867
Category : Computers
Languages : en
Pages : 937
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Book Description
This Second Volume in the series Handbook of Dynamic Data Driven Applications Systems (DDDAS) expands the scope of the methods and the application areas presented in the first Volume and aims to provide additional and extended content of the increasing set of science and engineering advances for new capabilities enabled through DDDAS. The methods and examples of breakthroughs presented in the book series capture the DDDAS paradigm and its scientific and technological impact and benefits. The DDDAS paradigm and the ensuing DDDAS-based frameworks for systems’ analysis and design have been shown to engender new and advanced capabilities for understanding, analysis, and management of engineered, natural, and societal systems (“applications systems”), and for the commensurate wide set of scientific and engineering fields and applications, as well as foundational areas. The DDDAS book series aims to be a reference source of many of the important research and development efforts conducted under the rubric of DDDAS, and to also inspire the broader communities of researchers and developers about the potential in their respective areas of interest, of the application and the exploitation of the DDDAS paradigm and the ensuing frameworks, through the examples and case studies presented, either within their own field or other fields of study. As in the first volume, the chapters in this book reflect research work conducted over the years starting in the 1990’s to the present. Here, the theory and application content are considered for: Foundational Methods Materials Systems Structural Systems Energy Systems Environmental Systems: Domain Assessment & Adverse Conditions/Wildfires Surveillance Systems Space Awareness Systems Healthcare Systems Decision Support Systems Cyber Security Systems Design of Computer Systems The readers of this book series will benefit from DDDAS theory advances such as object estimation, information fusion, and sensor management. The increased interest in Artificial Intelligence (AI), Machine Learning and Neural Networks (NN) provides opportunities for DDDAS-based methods to show the key role DDDAS plays in enabling AI capabilities; address challenges that ML-alone does not, and also show how ML in combination with DDDAS-based methods can deliver the advanced capabilities sought; likewise, infusion of DDDAS-like approaches in NN-methods strengthens such methods. Moreover, the “DDDAS-based Digital Twin” or “Dynamic Digital Twin”, goes beyond the traditional DT notion where the model and the physical system are viewed side-by-side in a static way, to a paradigm where the model dynamically interacts with the physical system through its instrumentation, (per the DDDAS feed-back control loop between model and instrumentation).
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: Jan Peter Hessling
Publisher: BoD – Books on Demand
ISBN: 9535132792
Category : Computers
Languages : en
Pages : 228
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Book Description
Uncertainty quantification may appear daunting for practitioners due to its inherent complexity but can be intriguing and rewarding for anyone with mathematical ambitions and genuine concern for modeling quality. Uncertainty quantification is what remains to be done when too much credibility has been invested in deterministic analyses and unwarranted assumptions. Model calibration describes the inverse operation targeting optimal prediction and refers to inference of best uncertain model estimates from experimental calibration data. The limited applicability of most state-of-the-art approaches to many of the large and complex calculations made today makes uncertainty quantification and model calibration major topics open for debate, with rapidly growing interest from both science and technology, addressing subtle questions such as credible predictions of climate heating.
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: Olivier Le Maitre
Publisher: Springer Science & Business Media
ISBN: 9048135206
Category : Science
Languages : en
Pages : 542
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Book Description
This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.
Author: Catherine Forbes
Publisher: John Wiley & Sons
ISBN: 1118097823
Category : Mathematics
Languages : en
Pages : 206
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Book Description
A new edition of the trusted guide on commonly used statistical distributions Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis. Following a basic introduction, forty popular distributions are outlined in individual chapters that are complete with related facts and formulas. Reflecting the latest changes and trends in statistical distribution theory, the Fourth Edition features: A new chapter on queuing formulas that discusses standard formulas that often arise from simple queuing systems Methods for extending independent modeling schemes to the dependent case, covering techniques for generating complex distributions from simple distributions New coverage of conditional probability, including conditional expectations and joint and marginal distributions Commonly used tables associated with the normal (Gaussian), student-t, F and chi-square distributions Additional reviewing methods for the estimation of unknown parameters, such as the method of percentiles, the method of moments, maximum likelihood inference, and Bayesian inference Statistical Distributions, Fourth Edition is an excellent supplement for upper-undergraduate and graduate level courses on the topic. It is also a valuable reference for researchers and practitioners in the fields of engineering, economics, operations research, and the social sciences who conduct statistical analyses.
Author: Francesco Montomoli
Publisher: Springer
ISBN: 3319929437
Category : Technology & Engineering
Languages : en
Pages : 204
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Book Description
This book introduces design techniques developed to increase the safety of aircraft engines, and demonstrates how the application of stochastic methods can overcome problems in the accurate prediction of engine lift caused by manufacturing error. This in turn addresses the issue of achieving required safety margins when hampered by limits in current design and manufacturing methods. The authors show that avoiding the potential catastrophe generated by the failure of an aircraft engine relies on the prediction of the correct behaviour of microscopic imperfections. This book shows how to quantify the possibility of such failure, and that it is possible to design components that are inherently less risky and more reliable. This new, updated and significantly expanded edition gives an introduction to engine reliability and safety to contextualise this important issue, evaluates newly-proposed methods for uncertainty quantification as applied to jet engines. Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines will be of use to gas turbine manufacturers and designers as well as CFD practitioners, specialists and researchers. Graduate and final year undergraduate students in aerospace or mathematical engineering may also find it of interest.
Author: Richard Askey
Publisher: American Mathematical Soc.
ISBN: 0821823213
Category : Jacobi polynomials
Languages : en
Pages : 63
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Book Description
A very general set of orthogonal polynomials in one variable that extends the classical polynomials is a set we called the q-Racah polynomials. In an earlier paper we gave the orthogonality relation for these polynomials when the orthogonality is purely discrete. We now give the weight function in the general case and a number of other properties of these very interesting orthogonal polynomials.
