Error Analysis with Applications in Engineering [electronic resource] / by Zbigniew A. Kotulski, Wojciech Szczepinski.Material type: TextLanguage: English Series: Solid Mechanics and Its Applications: 169Publisher: Dordrecht : Springer Netherlands, 2010Description: X, 270p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9789048135707Subject(s): Engineering | Distribution (Probability theory) | Mechanical engineering | Engineering | Structural Mechanics | Machinery and Machine Elements | Probability Theory and Stochastic Processes | Control, Robotics, MechatronicsAdditional physical formats: Printed edition:: No titleDDC classification: 620.1 LOC classification: TA349-359Online resources: Click here to access online
Basic Characteristics of Error Distribution; Histograms -- Random Variables and Probability; Normal Distribution -- Probability Distributions and Their Characterizations -- Functions of Independent Random Variables -- Two-dimensional Distributions -- Two-dimensional Functions of Independent Random Variables -- Three-dimensional Distributions -- Three-dimensional Functions of Independent Random Variables -- Problems Described by Implicit Equations -- Useful Definitions and Facts of Probability Theory for Further Reading.
This book presents, in the simplest possible manner, those branches of error analysis which find direct applications in solving various problems in engineering. Chapters I, II, III, and IV contain a presentation of the fundamentals of error calculus: basic characteristics of error distributions, histograms and their various applications, basic continuous distributions of errors and functions of independent random variables. In Chapter V, two-dimensional distributions of errors are discussed with applications. Fundamentals of the theory of two-dimensional continuous independent and dependent random variables are also discussed in that chapter. Then the methods of determination of the ellipses of probability concentration for the two-dimensional continuous normal distribution are given. Chapter VI deals with two-dimensional vectorial functions of independent random variables along with practical applications to the analysis of the positioning accuracy of mechanisms with two-dimensional movements. The procedure of determination of ellipses of probability concentration is also described. In Chapter VII, three-dimensional distributions of errors are considered, while Chapter VIII deals with the three-dimensional vectorial functions of independent random variables. The theory is illustrated by examples of the analysis of the positioning accuracy of robot manipulators. The examples of determining the ellipsoids of probability concentration are presented. Chapter IX contains error analysis-inspired problems that are described by implicit equations and Chapter X presents useful definitions and facts of probability theory for future readings. This book has been written for readers whose main interests are applications of error calculus in various problems of engineering. In all ten chapters much attention is paid to the practical significance of error analysis.