Statics and Influence Functions

Statics and Influence Functions PDF

Author: Friedel Hartmann

Publisher: Springer Nature

Published: 2020-11-25

Total Pages: 476

ISBN-13: 3030558894

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This extended and revised second edition is intended for engineering students and researchers working with finite element methods in structural and mechanical analysis. Discussing numerical structural analysis from first mechanical and mathematical principles, it establishes the central role of influence functions (Green's functions) in finite element analysis, reanalysis, sensitivity analysis, parameter identification and in optimization, with a particular focus on computational aspects and questions of accuracy. It also presents a one-click reanalysis, a new technique that allows instantaneous modifications to a structure to be made by clicking on single elements. Lastly, the book features four programs that can be downloaded for the solution of the Poisson equation, 2-D elasticity, plate-bending problems and planar frames.

Statics and Influence Functions - from a Modern Perspective

Statics and Influence Functions - from a Modern Perspective PDF

Author: Friedel Hartmann

Publisher: Springer

Published: 2017-03-04

Total Pages: 357

ISBN-13: 3319512226

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The book teaches engineers many new things about a classical topic which suddenly is again in the center of interest because of its relevance for finite element analysis, for the accuracy of computational methods. It shows that influence functions play a fundamental role in the finite element analysis of structures and practically all of linear computational mechanics. It also strives to add new and important insights into modern structural analysis and into computational mechanics by establishing the central role of influence functions for the numerical analysis and to lay a new foundation to the energy and variational principles.

Robust Statistics

Robust Statistics PDF

Author: Frank R. Hampel

Publisher: John Wiley & Sons

Published: 2011-09-20

Total Pages: 502

ISBN-13: 1118150686

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The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This is a nice book containing a wealth of information, much ofit due to the authors. . . . If an instructor designing such acourse wanted a textbook, this book would be the best choiceavailable. . . . There are many stimulating exercises, and the bookalso contains an excellent index and an extensive list ofreferences." —Technometrics "[This] book should be read carefully by anyone who isinterested in dealing with statistical models in a realisticfashion." —American Scientist Introducing concepts, theory, and applications, RobustStatistics is accessible to a broad audience, avoidingallusions to high-powered mathematics while emphasizing ideas,heuristics, and background. The text covers the approach based onthe influence function (the effect of an outlier on an estimater,for example) and related notions such as the breakdown point. Italso treats the change-of-variance function, fundamental conceptsand results in the framework of estimation of a single parameter,and applications to estimation of covariance matrices andregression parameters.

Inference for Misallocation Statistics Using Influence Functions

Inference for Misallocation Statistics Using Influence Functions PDF

Author: Alexandros Fakos

Publisher:

Published: 2023

Total Pages: 0

ISBN-13:

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I provide formulas for the influence function of two common misallocation statistics: TFP loss from misallocation and potential TFP gain from reallocation. I also show how to use a finite-difference approximation to Gateaux derivatives to obtain sample analogs to influence functions for calculating the asymptotic variance and standard errors of statistics. This approach applies to a wide range of statistics and is useful for conducting inference in a minimum-distance estimation procedure. This approximate approach is simpler to execute than analytical influence functions and is faster than the bootstrap when the estimation procedure is computationally challenging.

Robust Statistics

Robust Statistics PDF

Author: Frank R. Hampel

Publisher: Wiley-Interscience

Published: 2005-04-06

Total Pages: 542

ISBN-13:

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An introduction to the concepts, theory and applications of robust statistics, providing a comprehensive account of the infinitesimal approach and insight into the robustness properties of existing procedures.

Influence Function Approach

Influence Function Approach PDF

Author: Y.A. Melnikov

Publisher: WIT Press

Published: 2008-02-07

Total Pages: 401

ISBN-13: 1845641299

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Structural mechanics is the study of the effects that forces of different physical origin (mechanical, thermal, magnetic and so on) produce on elements of structures such as cables, pillars, beams, plates and shells. This text represents the first ever attempt to include in a book format a number of standard problems from structural mechanics, which are treated by means of a single mathematical approach that is novel in the field. The influence (Green's) function method constitutes the basis for this approach. The material in this volume is based on the implementation of two important notions taken from different sciences. One of them (the influence function of a point concentrated force) is brought from structural mechanics, while the other (the Green’s function of a boundary-value problem) is taken from mathematics. They are closely related to each other, and their relation represents the keystone in this text. Bringing these notions together allows us to create a single methodological approach to a variety of problems in structural mechanics, makes their analysis easier and builds up a solid foundation for some further developments in the field. In presenting the material in this text, it was presumed that the reader's background is equally solid in undergraduate mathematics and mechanics. The reader is assumed to be relatively fluent in differential and integral calculus and to possess, at the same time, workable knowledge of the fundamental principles of statics and dynamics. Each chapter contains extensive ‘end chapter exercises’ specifically developed for each chapter, with answers and comments available in the Appendix.

Interpretable Machine Learning

Interpretable Machine Learning PDF

Author: Christoph Molnar

Publisher: Lulu.com

Published: 2020

Total Pages: 320

ISBN-13: 0244768528

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This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.

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