Download or read book Machine Learning for Model Uncertainties in Turbulence Models and Monte Carlo Integral Approximation written by Brendan D. Tracey and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: While computational fluid dynamics (CFD) is playing an ever-increasing role in the design process, physical experiments are still required for final verification. There is a demand for certification through simulation, but there is a gap in predictive quality. Reynolds-averaged Navier-Stokes flow simulations have known deficiencies, especially for high Reynolds number flows with turbulent transition and separation, and higher fidelity Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) are not generally affordable. Quantification and reduction of uncertainty in simulation results is necessary, and yet it is rare for error bounds to be returned by a simulation, and progress towards more accurate turbulent closures in RANS models seems to have stalled. Today, however, the community is better equipped than ever to address this challenge. The rise in data science has driven the creation of tools and techniques to analyze and synthesize massive data sets. Most importantly, the data needed for statistical inference is available; computational budgets allow for RANS calculations on a number of input conditions and design settings, LES advances to increasingly complex geometries, and DNS continues to expand its Reynolds-number range. This dissertation harnesses data-driven approaches to address issues of uncertainty in predictive tools. First, the dissertation explores creating accurate models from data by replicating the behavior of a known model. Computational data is collected from the Spalart-Allmaras turbulence model, a neural network algorithm is trained on this data, and the learned model is re-embedded within a CFD flow solver. The robustness and accuracy of this procedure is explored as influenced by loss function choice, feature selection, and training data. Next, the dissertation considers model uncertainty in low-fidelity models. High-fidelity data from DNS of combustion (using finite-rate chemistry) are used to augment the low-fidelity flamelet progress variable-based RANS approach (FPVA). Supervised learning approaches are used to construct two error models, one for the local inaccuracies in the model and a second addressing the spatial correlation of these errors. These uncertainty models are combined to estimate the uncertainty in the FPVA model. Finally, a methodology is presented for quantifying the effects of input uncertainty on an output variable of interest. This is done by constructing an approximate model of the system using available data samples, and then using this as a control variate to reduced the squared estimation error in the output. Results are presented which demonstrate improved accuracy for a wide range of problem dimensions, function types, and sampling types. Taken together, these approaches indicate the potential of data-driven techniques to identify and reduce uncertainties in complex flow simulations.

Download or read book Data driven and Physics constrained Uncertainty Quantification for Turbulence Models written by Jan Felix Heyse and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulations are an important tool for prediction of turbulent flows. Today, most simulations in real-world applications are Reynolds-averaged Navier-Stokes (RANS) simulations, which average the governing equations to solve for the mean flow quantities. RANS simulations require modeling of an unknown quantity, the Reynolds stress tensor, using turbulence models. These models are limited in their accuracy for many complex flows, such as those involving strong stream-line curvature or adverse pressure gradients, making RANS predictions less reliable for design decisions. For RANS predictions to be useful in engineering design practice, it is therefore important to quantify the uncertainty in the predictions. More specifically, in this dissertation the focus is on quantifying the model-form uncertainty associated with the turbulence model. A data-free eigenperturbation framework introduced in the past few years, allows to make quantitative uncertainty estimates for all quantities of interest. It relies on a linear mapping from the eigenvalues of the Reynolds stress into the barycentric domain. In this framework, perturbations are added to the eigenvalues in that barycentric domain by perturbing them towards limiting states of 1 component, 2 component, and 3 component turbulence. Eigenvectors are permuted to find the extreme states of the turbulence kinetic energy production term. These eigenperturbations allow to explore a range of shapes and alignments of the Reynolds stress tensor within constraints of physical realizability of the resulting Reynolds stresses. However, this framework is limited by the introduction of a uniform amount of perturbation throughout the domain and by the need to specify a parameter governing the amount of perturbation. Data-driven eigenvalue perturbations are therefore introduced in this work to address those limitations. They are built on the eigenperturbation framework, but use a data-driven approach to determine how much perturbation to impose locally at every cell. The target amount of perturbation is the expected distance between the RANS prediction and the true solution in the barycentric domain. A general set of features is introduced, computed from the RANS mean flow quantities. The periodic flow over a wavy wall (for which also a detailed high-fidelity simulation dataset is available) serves as training case. A random forest machine learning model is trained to predict the target distance from the features. A hyperparameter study is carried out to find the most appropriate hyperparameters for the random forest. Random forest feature importance estimates confirm general expectations from physical intuition. The framework is applied to two test cases, the flow over a backward-facing step and the flow in an asymmetric diffuser. Both test cases and the training case exhibit a flow separation where the cross sectional area increases. The distribution of key features is studied for these cases and compared against the one from the training case. It is found that the random forest is not extrapolating. The results on the two test cases show uncertainty estimates that are characteristic of the true error in the predictions and give more representative bounds than the data-free framework does. The sets of eigenvectors from the RANS prediction and the true solution can be connected through a rotation. The idea of data-driven eigenvector rotations as a data-driven extension to the eigenvectors is studied. However, continuousness of the prediction targets is not generally achievable because of the ambiguity of the eigenvector direction. The lack of smoothness prevents the machine learning models from learning the relationship between the features and the targets, making data-driven eigenvector rotations in the discussed setup not practical. The last chapter of this dissertation introduces a data-driven baseline simulation, which corresponds to the expected value in the data-driven eigenvalue perturbation framework. The Reynolds stress is a weighted sum of the Reynolds stresses from the extreme states. A random classification forest trained to predict which extreme state is closest to the true Reynolds stress is used to compute these weights. It does so by giving a probabilistic meaning to the raw predictions of the constituent decision trees. On the test cases, the data-driven baseline predictions are similar but not equal to the data-free baseline. They complement the uncertainty estimates from the data-driven eigenvalue perturbations.

Download or read book Machine Learning Methods for Modeling Turbulence in Large Eddy Simulations written by Marius Kurz and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reliable prediction of turbulent flows is of crucial importance since turbulence is prevalent in the majority of flows found in science and engineering. Turbulence is a multi-scale phenomenon, for which flow features can span several orders of magnitude in size. This results in enormous resolution requirements in numerical simulations of turbulent flow. The framework of large eddy simulation relaxes these resolution demands by resolving only the largest, most energetic features of the flow and approximating the dynamics of the smaller, unresolved scales with turbulence models. The goal of this thesis is to leverage the recent advances in machine learning methods to formulate data-driven modeling strategies for implicitly filtered large eddy simulation. To this end, two modeling strategies are devised based on the supervised and the reinforcement learning paradigms. First, artificial neural networks are trained using supervised learning to recover the unknown closure terms from the filtered flow field. It is demonstrated that recurrent neural networks can predict the unknown closure terms with excellent accuracy. The second modeling strategy is based on the reinforcement learning paradigm. For this, Relexi is introduced as a novel reinforcement learning framework that allows to employ legacy flow solvers as training environments at scale. With Relexi, artificial neural networks are trained within forced homogeneous isotropic turbulence to adapt the parameters of traditional turbulence models dynamically in space and time. The trained models provide accurate and stable simulations and generalize well to other resolutions and higher Reynolds numbers. It is demonstrated within this thesis that machine learning methods can be applied to derive data-driven turbulence models for implicitly filtered large eddy simulation and that these models can be trained and incorporated efficiently into practical simulations on high-performance computing systems.

Download or read book Uncertainty Modelling and Analysis written by Bilal M. Ayyub and published by Elsevier Publishing Company. This book was released on 1994 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vital information on machine intelligence and pattern recognition is provided by this publication. In particular, the 31 papers discuss the ways in which uncertainty modelling and analysis are becoming an integral part of system definition and modelling in many fields. Contributions are sourced from an international base of researchers, scientists and engineers working on theoretical developments and diversified applications in engineering systems. The book is divided into two main parts. The first, Uncertainty Models and Measures, includes chapters on theoretical studies and developments carried out on uncertainty (including cognitive uncertainty and how it relates to information and intelligence), information, fuzzy logic, expert systems and neural networks. There are also chapters on modelling uncertainty in the reliability assessment of complex systems, linguistic connectives, the principle of maximum buoyancy, uncertain evidence, inductive learning, convex modelling, new uncertainty measures and information and uncertainty.The larger second part, Applications to Engineering Systems, contains application-oriented studies in fields related to civil, electrical, energy and general engineering systems. The papers cover studies on general uncertainty types in structural engineering, bridges, transmission structures, structural reliability, structural identification, system life cycle analysis, control, construction activities, decision analysis, signal detection, risk management, product quality, military command and control, data bases, long-term projections and predictions and assessment of insurance indices.The book conveys the excitement, advances and promises that all these fields offer to our expanding information-based technological society. It also hopes to stimulate the interest of other researchers around the world who are facing the challenge of new theoretical studies and innovative technological changes.

Download or read book Bayesian Reinforcement Learning written by Mohammad Ghavamzadeh and published by . This book was released on 2015-11-18 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian methods for machine learning have been widely investigated, yielding principled methods for incorporating prior information into inference algorithms. This monograph provides the reader with an in-depth review of the role of Bayesian methods for the reinforcement learning (RL) paradigm. The major incentives for incorporating Bayesian reasoning in RL are that it provides an elegant approach to action-selection (exploration/exploitation) as a function of the uncertainty in learning, and it provides a machinery to incorporate prior knowledge into the algorithms. Bayesian Reinforcement Learning: A Survey first discusses models and methods for Bayesian inference in the simple single-step Bandit model. It then reviews the extensive recent literature on Bayesian methods for model-based RL, where prior information can be expressed on the parameters of the Markov model. It also presents Bayesian methods for model-free RL, where priors are expressed over the value function or policy class. Bayesian Reinforcement Learning: A Survey is a comprehensive reference for students and researchers with an interest in Bayesian RL algorithms and their theoretical and empirical properties.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Prediction of Flow Heat Transfer Turbulence and Combustion written by D. Brian Spalding and published by Elsevier. This book was released on 2015-07-14 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion: Selected Works of Professor D. Brian Spalding focuses on the many contributions of Professor Spalding on thermodynamics. This compilation of his works is done to honor the professor on the occasion of his 60th birthday. Relatively, the works contained in this book are selected to highlight the genius of Professor Spalding in this field of interest. The book presents various research on combustion, heat transfer, turbulence, and flows. His thinking on separated flows paved the way for the multi-dimensional modeling of turbulence. Arguments on the universality of the models of turbulence and the problems that are associated with combustion engineering are clarified. The text notes the importance of combustion science as well as the problems associated with it. Mathematical computations are also presented in determining turbulent flows in different environments, including on curved pipes, curved ducts, and rotating ducts. These calculations are presented to further strengthen the claims of Professor Spalding in this discipline. The book is a great find for those who are interested in studying thermodynamics.

Download or read book Process Modelling and Simulation written by César de Prada and published by MDPI. This book was released on 2019-09-23 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since process models are nowadays ubiquitous in many applications, the challenges and alternatives related to their development, validation, and efficient use have become more apparent. In addition, the massive amounts of both offline and online data available today open the door for new applications and solutions. However, transforming data into useful models and information in the context of the process industry or of bio-systems requires specific approaches and considerations such as new modelling methodologies incorporating the complex, stochastic, hybrid and distributed nature of many processes in particular. The same can be said about the tools and software environments used to describe, code, and solve such models for their further exploitation. Going well beyond mere simulation tools, these advanced tools offer a software suite built around the models, facilitating tasks such as experiment design, parameter estimation, model initialization, validation, analysis, size reduction, discretization, optimization, distributed computation, co-simulation, etc. This Special Issue collects novel developments in these topics in order to address the challenges brought by the use of models in their different facets, and to reflect state of the art developments in methods, tools and industrial applications.

Download or read book Computer Age Statistical Inference written by Bradley Efron and published by Cambridge University Press. This book was released on 2016-07-21 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.

Download or read book Engineering Turbulence Modelling and Experiments 4 written by D. Laurence and published by Elsevier. This book was released on 1999-04-14 with total page 975 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain the papers presented at the 4th International Symposium on Engineering Turbulence Modelling and Measurements held at Ajaccio, Corsica, France from 24-26 May 1999. It follows three previous conferences on the topic of engineering turbulence modelling and measurements. The purpose of this series of symposia is to provide a forum for presenting and discussing new developments in the area of turbulence modelling and measurements, with particular emphasis on engineering-related problems. Turbulence is still one of the key issues in tackling engineering flow problems. As powerful computers and accurate numerical methods are now available for solving the flow equations, and since engineering applications nearly always involve turbulence effects, the reliability of CFD analysis depends more and more on the performance of the turbulence models. Successful simulation of turbulence requires the understanding of the complex physical phenomena involved and suitable models for describing the turbulent momentum, heat and mass transfer. For the understanding of turbulence phenomena, experiments are indispensable, but they are equally important for providing data for the development and testing of turbulence models and hence for CFD software validation.

Download or read book Handbook of Uncertainty Quantification written by Roger Ghanem and published by Springer. This book was released on 2016-05-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Model Reduction and Approximation written by Peter Benner and published by SIAM. This book was released on 2017-07-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Download or read book Worlds of Flow written by Olivier Darrigol and published by Oxford University Press. This book was released on 2005-09 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first fully-fledged history of hydrodynamics, including lively accounts of the concrete problems of hydraulics, navigation, blood circulation, meteorology, and aeronautics that motivated the main conceptual innovations. Richly illustrated, technically competent, and philosophically sensitive, it should attract a broad audience and become a standard reference for any one interested in fluid mechanics.

Download or read book Modeling Design and Optimization of Multiphase Systems in Minerals Processing written by Luis A. Cisternas and published by MDPI. This book was released on 2020-03-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mineral processing deals with complex particle systems with two-, three- and more phases. The modeling and understanding of these systems are a challenge for research groups and a need for the industrial sector. This Special Issue aims to present new advances, methodologies, applications, and case studies of computer-aided analysis applied to multiphase systems in mineral processing. This includes aspects such as modeling, design, operation, optimization, uncertainty analysis, among other topics. The special issue contains a review article and eleven articles that cover different methodologies of modeling, design, optimization, and analysis in problems of adsorption, leaching, flotation, and magnetic separation, among others. Consequently, the topics covered are of interest to readers from academia and industry.

Download or read book Turbulence written by Uriel Frisch and published by Cambridge University Press. This book was released on 1995-11-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.

Download or read book Frontiers in Massive Data Analysis written by National Research Council and published by National Academies Press. This book was released on 2013-09-03 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data mining of massive data sets is transforming the way we think about crisis response, marketing, entertainment, cybersecurity and national intelligence. Collections of documents, images, videos, and networks are being thought of not merely as bit strings to be stored, indexed, and retrieved, but as potential sources of discovery and knowledge, requiring sophisticated analysis techniques that go far beyond classical indexing and keyword counting, aiming to find relational and semantic interpretations of the phenomena underlying the data. Frontiers in Massive Data Analysis examines the frontier of analyzing massive amounts of data, whether in a static database or streaming through a system. Data at that scale-terabytes and petabytes-is increasingly common in science (e.g., particle physics, remote sensing, genomics), Internet commerce, business analytics, national security, communications, and elsewhere. The tools that work to infer knowledge from data at smaller scales do not necessarily work, or work well, at such massive scale. New tools, skills, and approaches are necessary, and this report identifies many of them, plus promising research directions to explore. Frontiers in Massive Data Analysis discusses pitfalls in trying to infer knowledge from massive data, and it characterizes seven major classes of computation that are common in the analysis of massive data. Overall, this report illustrates the cross-disciplinary knowledge-from computer science, statistics, machine learning, and application disciplines-that must be brought to bear to make useful inferences from massive data.

Download or read book Machine Learning Control Taming Nonlinear Dynamics and Turbulence written by Thomas Duriez and published by Springer. This book was released on 2016-11-02 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading researchers in turbulence control (S. Bagheri, B. Batten, M. Glauser, D. Williams) and machine learning (M. Schoenauer) for a broader perspective. All chapters have exercises and supplemental videos will be available through YouTube.