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Structural Reliability: Approaches from Perspectives of Statistical Moments

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The subject of structural reliability, which deals with the problems of evaluating the safety and risk posed by a wide variety of structures, has grown rapidly over the last four decades. And while the First-Order Reliability Method is principally used by most textbooks on this subject, other approaches have identified some of the limitations of that method.


Características

  • ISBN: 9781119620815
  • Páginas: 656
  • Tamaño: 17x24
  • Edición:
  • Idioma: Español
  • Año: 2021

Disponibilidad: 24 horas

Contenido Structural Reliability: Approaches from Perspectives of Statistical Moments


Discover a new and innovative approach to structural reliability from two authoritative and accomplished authors

The subject of structural reliability, which deals with the problems of evaluating the safety and risk posed by a wide variety of structures, has grown rapidly over the last four decades. And while the First-Order Reliability Method is principally used by most textbooks on this subject, other approaches have identified some of the limitations of that method.

In Structural Reliability: Approaches from Perspectives of Statistical Moments, accomplished engineers and authors Yan-Gang Zhao and Dr. Zhao-Hui Lu, deliver a concise and insightful exploration of an alternative and innovative approach to structural reliability. Called the Methods of Moment, the authors’ approach is based on the information of statistical moments of basic random variables and the performance function. The Methods of Moment approach facilitates ­structural reliability analysis and reliability-based design and can be extended to other engineering disciplines, yielding further insights into challenging problems involving ­randomness.

Readers will also benefit from the inclusion of:

    A thorough introduction to the measures of structural safety, including uncertainties in structural design, deterministic measures of safety, and probabilistic measures of safety
    An exploration of the fundamentals of structural reliability theory, including the performance function and failure probability
    A practical discussion of moment evaluation for performance functions, including moment computation for both explicit and implicit performance functions
    A concise treatment of direct methods of moment, including the third- and fourth-moment reliability methods

Perfect for professors, researchers, and graduate students in civil engineering, Structural Reliability: Approaches from Perspectives of Statistical Moments will also earn a place in the libraries of professionals and students working or studying in mechanical engineering, aerospace and aeronautics engineering, marine and offshore engineering, ship engineering, and applied mechanics.



Table of contents

Preface

1 Measures of Structural Safety


1.1 Introduction
1.2 Uncertainties in Structural Design
  1.2.1 Uncertainties in the Properties of Structures and Their Environment
  1.2.2 Sources and Types of Uncertainty
  1.2.3 Treatment of Uncertainties
  1.2.4 Design and Decision Making Under Uncertainties
1.3 Deterministic Measures of Safety
1.4 Probabilistic Measure of Safety
1.5 Summary

2 Fundamentals of Structural Reliability Theory

2.1 The Fundamental Case
2.2 Performance Function and Failure Probability
   2.2.1 Performance Function   
   2.2.2 Probability of Failure
   2.2.3 Reliability Index
2.3 Monte Carlo Simulation
   2.3.1 Introduction
   2.3.2 Generation of Random Numbers
   2.3.3 Direct Sampling
2.4 A Brief Review on Structural Reliability Theory
2.5 Summary

3 Moment Evaluation for Performance Functions

3.1 Introduction
3.2 Moment Computation for Some Simple Functions
   3.2.1 Moment Computation for Linear Sum of Random Variables
   3.2.2 Moment Computation for Multiply of Random Variables
   3.2.3 Moment Computation for Power of a Lognormally Distributed Random Variable
   3.2.4 Moment Computation for Power of an Arbitrarily Distributed Random Variable
   3.2.5 Moment Computation for Reciprocal of an Arbitrary Distributed Random Variable
3.3 Point Estimate for a Function of One Random Variable
   3.3.1 Rosenblueth’s Two-Point Estimate
   3.3.2 Gorman’s Three-Point Estimate
3.4 Point Estimates in Standardized Normal Space
   3.4.1 Basic ideas
   3.4.2 Two- and Three-point Estimates in the Standard Normal Space
   3.4.3 Five-Point Estimate in Standard Normal Space
   3.4.4 Seven-Point Estimate in Standard Normal Space
   3.4.5 General Expression of Estimating Points and Their Corresponding Weights
   3.4.6 Accuracy of the Point Estimate
3.5 Point Estimates for a Function of Multiple Variables
   3.5.1 General Expression of Point Estimate for a Function of n Variables
   3.5.2 Approximate Point Estimate for a Function of n Variables
   3.5.3 Dimension Reduction Integration
3.6 Point Estimates for a Function of Correlative Random Variables
3.7 Hybrid Dimension-Reduction Based Point Estimate Method
3.8 Summary

4 Direct Methods of Moment

4.1 Basic Concept of Methods of Moment
   4.1.1 Introduction
   4.1.2 The Second-Moment Method
   4.1.3 General Expressions for Methods of Moment
4.2 Third-Moment Reliability Method
   4.2.1 Introduction
   4.2.2 Third-Moment Reliability Indices
   4.2.3 Empirical Applicable Range of Third-Moment Reliability Method
   4.2.4 Simplification of Third-Moment Reliability Method
   4.2.5 Applicable Range of the Second-Moment method
4.3 Fourth-Moment Reliability Method
   4.3.1 Introduction
   4.3.2 Fourth-Moment Reliability Index on the Basis of the Pearson System  
   4.3.3 Fourth-Moment Reliability Index Based on Third-Order Polynomial Transformation  
   4.3.4 Applicable range of Fourth-Moment method
   4.3.5 Simplification of Fourth-Moment reliability index

5 Methods of Moment Based on First/Second Order Transformation

5.1 Introduction
5.2 First-Order Reliability Method
  5.2.1 The Hasofer-Lind reliability index
 ,5.2.2 First Order Reliability Method
  5.2.3 Numerical Solution for FORM
  5.2.4 The Weakness of FORM
5.3 Second Order Reliability Method
  5.3.1 Introduction
  5.3.2 Second Order Approximation of the Performance Function
  5.3.3 Failure probability for Second Order Performance Function
  5.3.4 Methods of Moment for Second Order Approximation
  5.3.5 Applicable Range of FORM
5.4 Summary

6 Structural Reliability Assessment based on the Information of Moments of Random Variables

6.1 Introduction
6.2 Direct Methods of Moment Without Using Probability Distribution
   6.2.1 Second-Moment Formulation
   6.4.2 Third-Moment Formulation
   6.4.3 Fourth-Moment Formulation
6.3 First-Order Second-Moment Method
   6.4.1 First-Order Third-Moment Method in Reduced Space
   6.4.2 First-Order Third-Moment Method in Pseudo Standard Normal Space
6.5 First-Order Fourth-Moment Method
   6.5.1 First-Order Fourth-Moment Method in Reduced Space
   6.5.2 First-Order Fourth-Moment Method in Pseudo Standard Normal Space
6.6 Monte Carlo Simulation Using Moment of Random Variables
6.7 Subset Simulation Using Statistical Moments of Random Variables
6.8 Summary

7 Transformation of Non-Normal Variables to Independent Normal Variables

7.1 Introduction
7.2 The Normal Transformation for a Single Random Variable
7.3 The Normal Transformation for Correlated Random Variable
   7.3.1 Rosenblatt Transformation
   7.3.2 Nataf Transformation
7.4 Pseudo Normal Transformations for a Single Random Variable
  7.4.1 Concept of Pseudo Normal Transformation
  7.4.2 Third Moment Pseudo Normal Transformation
  7.4.3 Fourth Moment Pseudo Normal Transformation
7.5 Pseudo Normal Transformations of Correlated Random Variables
  7.5.1 Introduction
  7.5.2 Third Moment Pseudo Normal Transformation for Correlated Random Variables
  7.5.3 Fourth Moment Pseudo Normal Transformation for Correlated Random Variables
7.6 Summary

8 System Reliability Assessment by the Method of Moments

8.1 Introduction
8.2 Basic Concepts of System Reliability
   8.2.1 Multiple Failure Modes
   8.2.2 Series and Parallel Systems
8.3 System Reliability Bounds
   8.3.1 Uni-Modal Bounds
   8.3.2 Bi-Modal Bounds
   8.3.3 Correlation Between a Pair of Failure Modes
   8.3.4 Bound Estimation of the Joint Failure Probability of a Pair of Failure Modes
   8.3.5 Point Estimation of the Joint Failure Probability of a Pair of Failure Modes
8.4 Moment Approach for System Reliability
   8.4.1 Performance Function for a system
   8.4.2 Method of Moments for System Reliability
8.5 Methods of Moment for System Reliability Assessment of Ductile Frame Structure
   8.5.1 Introduction
   8.5.2 Performance Function Independent of Failure Modes
   8.5.3 Limit Analysis
   8.5.4 Methods of Moment for System Reliability of Ductile Frames

9 Determination of Load and Resistance Factors by Methods of Moment

9.1 Introduction
9.2 Basic Concept of Load and Resistance Factors
   9.2.1 Basic Concept
   9.2.2 Determination of LRFs by Second-Moment Method
   9.2.3 Determination of LRFs under Lognormal Assumption
   9.2.4 Determination of LRFs by FORM
   9.2.5 Practical Method for the Determination of LRFs
9.3 Load and Resistance Factors by Third-Moment Method
   9.3.1 Determination of LRFs using Third-Moment Method
   9.3.2 Estimation of the Mean Value of Resistance
9.4 General Expressions of Load and Resistance Factors using Method of Moments
9.5 Determination of Load and Resistance Factors Using Fourth-Moment Method
   9.5.1 Basic Formulas
   9.5.2 Determination of the Mean Value of Resistance
9.6 Summary

10 Methods of Moment for Time-Variant Reliability

10.1 Introduction
10.2 Simulating Stationary Non-Gaussian Process using The Fourth-Moment Transformation
    10.2.1 Introduction
    10.2.2 Transformation for Marginal Probability Distributions
    10.2.3 Transformation for Correlation Functions
    10.2.4 Methods to Deal with the Incompatibility
    10.2.5 Scheme of Simulating Stationary Non-Gaussian Random Processes
10.3 First Passage Probability Assessment of Stationary Non-Gaussian Processes Using Fourth-Moment Transformation
    10.3.1 Introduction
    10.3.2 Formulation of the First Passage Probability of Stationary Non-Gaussian Structural Responses
    10.3.4 Computational Procedure for the First Passage Probability of Stationary Non-Gaussian Structural Responses
10.4 Fast Integration Algorithms for Time-Dependent Structural Reliability Analysis Considering Correlated Random Variables
    10.4.1 Introduction
    10.4.2 Formulation of Time-Dependent Failure Probability
    10.4.3 Fast Integration Algorithms for the Time-Dependent Failure Probability
10.5 Summary

11 Methods of Moment for Structural Reliability with Hierarchical Modeling of Uncertainty

11.1 Introduction
11.2 Formulation Description of the Structural Reliability with Hierarchical Modeling of Uncertainty
11.3 Overall Probability of Failure Due to Hierarchical Modeling of Uncertainty    
   11.3.1 Evaluating Overall Probability of Failure Based on FORM
   11.3.2 Evaluating Overall Probability of Failure Based on Methods of Moment
   11.3.3 Evaluating Overall Probability of Failure Based on Direct Point Estimate Method
11.4 The Quantile of the Conditional Failure Probabilit
11.5 Application to Structural Dynamic Reliability Considering Parameters Uncertainties
11.6 Summary

12 Structural Reliability Analysis Based on the First Few L-Moments

12.1 Introduction
12.2 Definition of L-moments 3
12.3 Structural Reliability Analysis Based on the First Three L-Moments
    12.3.1 Transformation for Independent Random Variables
    12.3.2 Transformation for Correlated Random Variables
    12.3.3 Reliability Analysis Using the First Three L-moments and Correlation Matrix
12.4 Structural Reliability Analysis Based on the First Four L-Moments
    12.4.1 Transformation for Independent Random Variables
    12.4.2 Transformation for Correlated Random Variables
    12.4.3 Reliability Analysis using the First Four L-Moments and Correlation Matrix
12.5 Summary

13 Methods of Moment with Box-Cox Transformation

13.1 Introduction
13.2 Methods of Moment with Box-Cox Transformation
    13.2.1 Criterion for Determining the Box-Cox Transformation Parameter
    13.2.2 Procedure of the Methods of Moment with Box-Cox Transformation for Structural Reliability
13.3 Summary

Appendix A Basic probability theory

A.1 Events and Probability
A.1.1 Introduction
A.1.2 Events and Their Combinations
A.1.3 Mathematical Operations of Sets
A.2 Random Variables and Their Distributions
A.3 Main Descriptors of a Random Variable
A.3.1 Measures of Location
A.3.2 Measures of Dispersion
A.3.3 Measures of Asymmetry
A.3.4 Measures of Sharpness
A.4 Moments and Cumulants
A.4.1 Moments
A.4.2 Moment and Cumulant Generating Functions
A.5 Normal and Lognormal Distributions
A.5.1 The Normal Distribution
A.5.2 The Logarithmic Normal Distribution
A.6 Commonly Used Distributions
A.6.1 Introduction
A.6.2 Rectangular Distribution
A.6.3 Bernoulli Sequences and the Binomial Distribution
A.6.4 The Geometric Distribution
A.6.5 The Poisson Process and Poisson Distribution
A.6.6 The Exponential Distribution
A.6.7 The Gamma Distribution
A.7 Extreme Value Distributions
A.7.1 Introduction
A.7.2 The Asymptotic Distributions
A.7.3 The Gumbel Distribution
A.7.4 The Frechet Distribution
A.7.5 The Weibull Distribution
A.8 Multiple Random Variables
A.8.1 Joint and Conditional Probability Distribution
A.8.2 Covariance and Correlation
A.9 Functions of Random Variables
A.9.1 Function of a Single Random Variable
A.9.2 Function of Multiple Random Variables
A.10 Summary

Appendix B Three-Parameter Distributions

B.1 Introduction
B.2 The 3P Lognormal Distribution
B.2.1 Definition of the Distribution
B.2.2 Simplification of the Distribution
B.3 Square Normal Distribution
B.3.1 Definition of the Distribution
B.3.2 Simplification of the Distribution
B.4 Comparison of the 3P Distributions
B.5 Applications of the 3P Distributions
B.5.1 Statistical Data Analysis
B.5.2 Representations of One and Two-Parameter Distributions
B.5.3 Distributions of Some Random Variables used in Structural Reliability
B.6 Summary

Appendix C Four-Parameter Distributions

C.1 Introduction
C.2 The Pearson System
C.2.1 Definition of the system
C.2.2 Various types of the PDF in Pearson system
C.3 Cubic Normal Distribution
C.3.1 Definition of the distribution
C.3.2 Representative PDFs of the distribution
C.3.3 Application in data analysis
C.3.5 Simplification of the distribution
C.4 Summary

Appendix D Basic Theory of Stochastic Process

D.1 General Concept of Stochastic Process
D.2 Time Domain Description of Stochastic Processes
D.2.1 Probability Distributions of Stochastic Processes
D.2.2 Moment Functions of Stochastic Processes
D.2.3 Stationary and Nonstationary Process
D.2.4 Ergodicity of a Stochastic Process
D.3 Frequency Domain Description of Stochastic Processes
D.3.2 Wide-and Narrow-Band Processes
D.4 Special Processes
D.4.1 White Noise Process
D.4.2 Markov Process
D.4.3 Poisson Process
D.4.4 Gaussian Process
D.5 Spectral Representation Method
D.6 Summary 5
References

 

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