Affine Arithmetic Based Solution Of Uncertain Static And Dynamic Problems

Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches.

Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches.

This book meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of soft computing on the other. Soft computing is the recent development about the computing methods which include fuzzy set theory/logic, evolutionary computation (EC), probabilistic reasoning, artificial neural networks, machine learning, expert systems, etc. Soft computing refers to a partnership of computational techniques in computer science, artificial intelligence, machine learning, and some other engineering disciplines, which attempt to study, model, and analyze complex problems from different interdisciplinary problems. This, as opposed to traditional computing, deals with approximate models and gives solutions to complex real-life problems. Unlike hard computing, soft computing is tolerant of imprecision, uncertainty, partial truth, and approximations. Interdisciplinary sciences include various challenging problems of science and engineering. Recent developments in soft computing are the bridge to handle different interdisciplinary science and engineering problems. In recent years, the correspondingly increased dialog between these disciplines has led to this new book. This is done, firstly, by encouraging the ways that soft computing may be applied in traditional areas, as well as point towards new and innovative areas of applications and secondly, by encouraging other scientific disciplines to engage in a dialog with the above computation algorithms outlining their problems to both access new methods as well as to suggest innovative developments within itself.

Explore the applications of range analysis to power systems under conditions of uncertainty In Interval Methods for Uncertain Power System Analysis, accomplished engineer Dr. Alfredo Vaccaro delivers a comprehensive discussion of the mathematical foundations of range analysis and its application to solving traditional power system operation problems in the presence of strong and correlated uncertainties. The book explores highly relevant topics in the area, from interval methods for uncertainty representation and management to a variety of application examples. The author offers readers the latest methodological breakthroughs and roadmaps to implementing the mathematics discussed within, as well as best practices commonly employed across the industry. Interval Methods for Uncertain Power System Analysis includes examinations of linear and non-linear equations, as well as: A thorough introduction to reliable computing, including discussions of interval arithmetic and interval-based operators Comprehensive explorations of uncertain power flow analysis, including discussions of problem formulation and sources of uncertainty in power flow analysis In-depth examinations of uncertain optimal power flow analysis Fulsome discussions of uncertain small signal stability analysis, including treatments of how to compute eigenvalues of uncertain matrices Perfect for engineers working in power flow and optimal power flow analyses, optimization theory, and computer aided simulation, Interval Methods for Uncertain Power System Analysis will also earn a place in the libraries of researchers and graduate students studying decision making under uncertainty in power systems operation.

Affine Arithmetic-Based Methods for Uncertain Power System Analysis presents the unique properties and representative applications of Affine Arithmetic in power systems analysis, particularly as they are deployed for reliability optimization. The work provides a comprehensive foundation in Affine Arithmetic necessary to understand the central computing paradigms that can be adopted for uncertain power flow and optimal power flow analyses. These paradigms are adapted and applied to case studies, which integrate benchmark test systems and full step-by-step procedure for implementation so that readers are able to replicate and modify. The work is presented with illustrative numerical examples and MATLAB computations. Provides a uniquely comprehensive review of affine arithmetic in both its core theoretical underpinnings and their developed applications to power system analysis Details the exemplary benefits derived by the deployment of affine arithmetic methods for uncertainty handling in decision-making processes Clarifies arithmetical complexity and eases the understanding of illustrative methodologies for researchers in both power system and decision-making fields

A problem factory consists of a traditional mathematical analysis of a type of problem that describes many, ideally all, ways that the problems of that type can be cast in a fashion that allows teachers or parents to generate problems for enrichment exercises, tests, and classwork. Some problem factories are easier than others for a teacher or parent to apply, so we also include banks of example problems for users. This text goes through the definition of a problem factory in detail and works through many examples of problem factories. It gives banks of questions generated using each of the examples of problem factories, both the easy ones and the hard ones. This text looks at sequence extension problems (what number comes next?), basic analytic geometry, problems on whole numbers, diagrammatic representations of systems of equations, domino tiling puzzles, and puzzles based on combinatorial graphs. The final chapter previews other possible problem factories.

The contents of this brief Lecture Note are devoted to modeling, simulations, and applications with the aim of proposing a unified multiscale approach accounting for the physics and the psychology of people in crowds. The modeling approach is based on the mathematical theory of active particles, with the goal of contributing to safety problems of interest for the well-being of our society, for instance, by supporting crisis management in critical situations such as sudden evacuation dynamics induced through complex venues by incidents.