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System analysis --- Sensitivity theory (Mathematics) --- 519.71 --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Sensitivity (Mathematics) --- System sensitivity theory (Mathematics) --- Control theory --- Control systems theory: mathematical aspects --- System analysis. --- 519.71 Control systems theory: mathematical aspects --- Sensitivity theory (Mathematics). --- Network analysis --- Network science

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"This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties" [Publisher]

Sensitivity theory (Mathematics) --- Sensibilité, Théorie de la (mathématiques) --- Global analysis (Mathematics) --- Analyse globale (mathématiques) --- R (Computer program language) --- R

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This book presents a comprehensive introduction to design sensitivity analysis theory as applied to electromagnetic systems. It treats the subject in a unified manner, providing numerical methods and design examples. The specific focus is on continuum design sensitivity analysis, which offers significant advantages over discrete design sensitivity methods. Continuum design sensitivity formulas are derived from the material derivative in continuum mechanics and the variational form of the governing equation. Continuum sensitivity analysis is applied to Maxwell equations of electrostatic, magnetostatic and eddy-current systems, and then the sensitivity formulas for each system are derived in a closed form; an integration along the design interface. The book also introduces the recent breakthrough of the topology optimization method, which is accomplished by coupling the level set method and continuum design sensitivity. This topology optimization method enhances the possibility of the global minimum with minimised computational time, and in addition the evolving shapes during the iterative design process are easily captured in the level set equation. Moreover, since the optimization algorithm is transformed into a well-known transient analysis algorithm for differential equations, its numerical implementation becomes very simple and convenient. Despite the complex derivation processes and mathematical expressions, the obtained sensitivity formulas are very straightforward for numerical implementation. This book provides detailed explanation of the background theory and the derivation process, which will help readers understand the design method and will set the foundation for advanced research in the future.

Electromagnetic devices --- Sensitivity theory (Mathematics) --- Mathematical models. --- Electronics. --- Production of electric energy or. --- Electronics and Microelectronics, Instrumentation. --- Continuous Optimization. --- Power Electronics, Electrical Machines and Networks. --- Electrical engineering --- Physical sciences

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Evolutionary computation. --- Architecture --- Sensitivity theory (Mathematics) --- Structural optimization. --- Réseaux neuronaux à structure évolutive --- Théorie de la sensibilité (Mathématiques) --- Optimisation des structures --- Technological innovations. --- Computer-aided design. --- Innovations --- Conception assistée par ordinateur --- Sasaki, Mutsuro --- Réseaux neuronaux à structure évolutive --- Théorie de la sensibilité (Mathématiques) --- Conception assistée par ordinateur

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The computational models of physical systems comprise parameters, independent and dependent variables. Since the physical processes themselves are seldom known precisely and since most of the model parameters stem from experimental procedures which are also subject to imprecisions, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model. The functional derivatives (also called "sensitivities") of results (also called "responses") produced by mathematical/computational models are needed for many purposes, including: (i) understanding the model by ranking the importance of the various model parameters; (ii) performing "reduced-order modeling" by eliminating unimportant parameters and/or processes; (iii) quantifying the uncertainties induced in a model response due to model parameter uncertainties; (iv) performing "model validation," by comparing computations to experiments to address the question "does the model represent reality?" (v) prioritizing improvements in the model; (vi) performing data assimilation and model calibration as part of forward "predictive modeling" to obtain best-estimate predicted results with reduced predicted uncertainties; (vii) performing inverse "predictive modeling"; (viii) designing and optimizing the system. This 3-Volume monograph describes a comprehensive adjoint sensitivity analysis methodology, developed by the author, which enables the efficient and exact computation of arbitrarily high-order sensitivities of model responses in large-scale systems comprising many model parameters. The qualifier "comprehensive" is employed to highlight that the model parameters considered within the framework of this methodology also include the system's uncertain boundaries and internal interfaces in phase-space. The model's responses can be either scalar-valued functionals of the model's parameters and state variables (e.g., as customarily encountered in optimization problems) or general function-valued responses. Since linear operators admit bona-fide adjoint operators, responses of models that are linear in the state functions (i.e., dependent variables) can depend simultaneously on both the forward and the adjoint state functions. Hence, the sensitivity analysis of such responses warrants the treatment of linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward state functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator may admit an adjoint operator). Thus, Volume 1 of this book presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as "nth-CASAM-L"), which is conceived for the most efficient computation of exactly obtained mathematical expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters underlying the respective forward/adjoint systems. Volume 2 of this book presents the application of the nth-CASAM-L to perform a fourth-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark which is representative of a large-scale model comprises many (21,976) uncertain parameters, thereby amply illustrating the unique potential of the nth-CASAM-L to enable the exact and efficient computation of chosen high-order response sensitivities to model parameters. Volume 3 of this book presents the "nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems" (abbreviation: nth-CASAM-N) for the practical, efficient, and exact computation of arbitrarily-high order sensitivities of responses to model parameters for systems that are also nonlinear in their underlying state functions. Such computations are not feasible with any other methodology. The application of the nth-CASAM-L and the nth-CASAM-N overcomes the so-called "curse of dimensionality" in sensitivity and uncertainty analysis, thus revolutionizing all of the fields of activities which require accurate computation of response sensitivities. Since this monograph includes many illustrative, fully worked-out, paradigm problems, it can serve as a textbook or as supplementary reading for graduate courses in academic departments in the natural sciences and engineering.

Statistical science --- Mathematics --- Mathematical physics --- Nuclear physics --- Relation between energy and economics --- Applied physical engineering --- Engineering sciences. Technology --- Planning (firm) --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- energiebeheer (technologie) --- energiemanagement (economie) --- ICT (informatie- en communicatietechnieken) --- energiebeleid --- energie-economie --- economie --- mathematische modellen --- statistiek --- mineralen (chemie) --- mijnbouw --- wiskunde --- ingenieurswetenschappen --- fysica --- atoomfysica --- statistisch onderzoek --- Sensitivity theory (Mathematics) --- Linear systems --- Mathematical models.