Synthesis of Path-Generating Mechanisms and Tolerance Allocation Using Information Theory

1987 ◽  
Vol 109 (3) ◽  
pp. 366-371 ◽  
Author(s):  
R. P. Sukhija ◽  
A. C. Rao
Keyword(s):  
Information Theory ◽  
Maximum Entropy ◽  
Random Variables ◽  
Entropy Function ◽  
Tolerance Allocation ◽  
Optimum Allocation ◽  
Design Parameters ◽  
Communication Engineering ◽  
Probability Concept ◽  
Measure Of Uncertainty

The information theory based on probability concept was developed for application in communication engineering. This theory utilizes the concept of “entropy,” a measure of uncertainty. The errors existing in the output of a path-generating linkage and desired path can be taken as random variables. The entropy function is formulated in terms of design parameters. Minimization of maximum entropy leads to the synthesis of a path-generating mechanism. Optimum allocation of tolerances on link lengths is also carried out.

Introduction to Information Theory

2014 ◽  
Author(s):  
M. Vidyasagar
Keyword(s):  
Information Theory ◽  
Probability Distribution ◽  
Relative Entropy ◽  
Probability Distributions ◽  
Random Variables ◽  
Conditional Entropy ◽  
Random Variable ◽  
Entropy Function ◽  
Concave Functions ◽  
Leibler Divergence

This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random variable (or more precisely, the probability distribution of the random variable). When there are two or more random variables, it is worthwhile to study the conditional entropy of one random variable with respect to another. The last concept is relative entropy, also known as the Kullback–Leibler divergence, which measures the “disparity” between two probability distributions. The chapter first considers convex and concave functions before discussing the properties of the entropy function, conditional entropy, uniqueness of the entropy function, and the Kullback–Leibler divergence.

scholarly journals The Evaluation Of Algorithms For Determination Of The Reliability Index

2015 ◽  
Vol 61 (3) ◽  
pp. 133-147 ◽  
Author(s):  
A. Dudzik ◽  
U. Radoń
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Numerical Procedure ◽  
Vertical Displacement ◽  
Design Parameters ◽  
State Function ◽  
Structural Failure

AbstractThe study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

An approach of robust reliability design for mechanical components

2005 ◽  
Vol 219 (3) ◽  
pp. 275-283 ◽  
Author(s):  
Y M Zhang ◽  
X D He ◽  
Q L Liu ◽  
B C Wen
Keyword(s):  
Robust Design ◽  
Design Method ◽  
Random Variables ◽  
Design Parameters ◽  
Theoretical Formula ◽  
Reliability Design ◽  
Reliability Sensitivity ◽  
Mechanical Components ◽  
Reliability Based Optimization ◽  
Robust Reliability

The reliability-based optimization, the reliability sensitivity technique, and the robust design are employed to present a practical and effective approach of robust reliability design for mechanical components on the condition of known probabilistic characteristics of original random variables. The theoretical formula of robust reliability design for mechanical components is obtained. The respective program can be used to obtain the robust reliability design parameters accurately and quickly. According to the numerical results, the method proposed is a convenient and practical robust reliability design method.

Spatial Incompatibility: Part Interaction and Tolerance Allocation in Configuration Design

1998 ◽  
Author(s):  
Rikard Söderberg ◽  
Hans L. Johannesson
Keyword(s):  
Cost Effective ◽  
Tolerance Allocation ◽  
Design Parameters ◽  
Functional Requirements ◽  
Early Design ◽  
Spatial Coupling ◽  
Assembly Design ◽  
Geometrical Features ◽  
Cad Models ◽  
Early Design Stages

Abstract This paper describes how function-means modeling techniques and spatial coupling analysis can be used in early design stages to increase robustness and knowledge about geometrical sensitivity of an assembly design. By incorporating spatial constraint decomposition in function-means modeling, overall spatial constraints may be broken down into nominal dimensions and tolerances for geometrical features. The analysis is carried out at the very early design stages, before CAD models are created and when only simple sketches exist. By documenting all information about functional requirements, design parameters and constraints in a hierarchically decomposed function-means structure, spatial couplings and overall sensitivities may be detected and alternative, less sensitive, concept solutions may be developed. Analyses of functional and constraint couplings increases the knowledge of and understanding for the geometrical sensitivity of a complex assembly design. This knowledge and understanding then serves as a base for tolerance allocation, where tolerances are to be allocated in the most functional and cost effective way.

A Note on the Residual Entropy Function

1993 ◽  
Vol 7 (3) ◽  
pp. 413-420 ◽  
Author(s):  
Pietro Muliere ◽  
Giovanni Parmigiani ◽  
Nicholas G. Polson
Keyword(s):  
Information Theory ◽  
Probability Distribution ◽  
Random Variable ◽  
Reliability Theory ◽  
Entropy Function ◽  
Informational Content ◽  
Residual Entropy ◽  
Regularity Conditions ◽  
Information Theoretic ◽  
Information Theoretic Measures

Interest in the informational content of truncation motivates the study of the residual entropy function, that is, the entropy of a right truncated random variable as a function of the truncation point. In this note we show that, under mild regularity conditions, the residual entropy function characterizes the probability distribution. We also derive relationships among residual entropy, monotonicity of the failure rate, and stochastic dominance. Information theoretic measures of distances between distributions are also revisited from a similar perspective. In particular, we study the residual divergence between two positive random variables and investigate some of its monotonicity properties. The results are relevant to information theory, reliability theory, search problems, and experimental design.

scholarly journals Results on Varextropy Measure of Random Variables

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 356
Author(s):  
Nastaran Marzban Vaselabadi ◽  
Saeid Tahmasebi ◽  
Mohammad Reza Kazemi ◽  
Francesco Buono
Keyword(s):  
Hazard Rate ◽  
Random Variables ◽  
Record Values ◽  
Comparison Method ◽  
Dispersion Measure ◽  
Stochastic Comparison ◽  
Alternative Measure ◽  
Proportional Hazard ◽  
Hazard Rate Models ◽  
Measure Of Uncertainty

In 2015, Lad, Sanfilippo and Agrò proposed an alternative measure of uncertainty dual to the entropy known as extropy. This paper provides some results on a dispersion measure of extropy of random variables which is called varextropy and studies several properties of this concept. Especially, the varextropy measure of residual and past lifetimes, order statistics, record values and proportional hazard rate models are discussed. Moreover, the conditional varextropy is considered and some properties of this measure are studied. Finally, a new stochastic comparison method, named varextropy ordering, is introduced and some of its properties are presented.

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