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E-raamat: Structural Reliability: Approaches from Perspectives of Statistical Moments

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  • Ilmumisaeg: 13-Apr-2021
  • Kirjastus: Wiley-Blackwell
  • Keel: eng
  • ISBN-13: 9781119620693
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Structural Reliability: Approaches from Perspectives of Statistical MomentsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 13-Apr-2021
  • Kirjastus: Wiley-Blackwell
  • Keel: eng
  • ISBN-13: 9781119620693
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"The aim of this book is to deliver a unified presentation of the theory and techniques with the emphases on the applications of the moment information of random variables for structural reliability. The contents of the book will be useful for post-graduate students, researchers and engineers in the field of civil, mechanical, aerospace and aeronautical and ship engineering, and so forth. Structural reliability deals with the safety evaluation and risk assessment of engineering structures. The structuresinclude the buildings, bridges, aircrafts, etc., refer to those bodies or systems consisting of some materials in a certain way and having the function of bearing loads and actions. One of the principal aims of structural design is the assurance of structural performance within the constraint of economy. The reliability of a structure can therefore be defined as its ability to fulfill its design purpose for a specified reference period. Since the deterministic approach failed to provide a quantitative measure of safety, probabilistic measure of safety, i.e., the structural reliability theory, has to be used. The use of the first few moments of random variables and the performance function, in original form or in its first/second order approximation, formthe basic content of the book. The methods, being easy to be implemented, can avoid the shortcomings of FORM, such as the design points, derivative-based iterative computation, and thus are expected to be conveniently applied to structural reliability analysis and reliability based design"--

The aim of this book is to deliver a unified presentation of the theory and techniques with the emphases on the applications of the moment information of random variables for structural reliability. The contents of the book will be useful for post-graduate students, researchers and engineers in the field of civil, mechanical, aerospace and aeronautical and ship engineering, and so forth.

Structural reliability deals with the safety evaluation and risk assessment of engineering structures. The structures include the buildings, bridges, aircrafts, etc., refer to those bodies or systems consisting of some materials in a certain way and having the function of bearing loads and actions. One of the principal aims of structural design is the assurance of structural performance within the constraint of economy. The reliability of a structure can therefore be defined as its ability to fulfill its design purpose for a specified reference period. Since the deterministic approach failed to provide a quantitative measure of safety, probabilistic measure of safety, i.e., the structural reliability theory, has to be used.

The use of the first few moments of random variables and the performance function, in original form or in its first/second order approximation, form the basic content of the book. The methods, being easy to be implemented, can avoid the shortcomings of FORM, such as the design points, derivative-based iterative computation, and thus are expected to be conveniently applied to structural reliability analysis and reliability based design.
Preface xi
Acknowledgements xv
1 Measures of Structural Safety 1(10)
1.1 Introduction
1(1)
1.2 Uncertainties in Structural Design
1(8)
1.2.1 Uncertainties in the Properties of Structures and Their Environment
1(3)
1.2.2 Sources and Types of Uncertainties
4(1)
1.2.3 Treatment of Uncertainties
5(4)
1.2.4 Design and Decision Making with Uncertainties
9(1)
1.3 Deterministic Measures of Safety
9(1)
1.4 Probabilistic Measure of Safety
10(1)
1.5 Summary
10(1)
2 Fundamentals of Structural Reliability Theory 11(26)
2.1 The Fundamental Case
11(5)
2.2 Performance Function and Probability of Failure
16(8)
2.2.1 Performance Function
16(1)
2.2.2 Probability of Failure
17(2)
2.2.3 Reliability Index
19(5)
2.3 Monte Carlo Simulation
24(9)
2.3.1 Formulation of the Probability of Failure
24(1)
2.3.2 Generation of Random Numbers
25(3)
2.3.3 Direct Sampling for Structural Reliability Evaluation
28(5)
2.4 A Brief Review on Structural Reliability Theory
33(2)
2.5 Summary
35(2)
3 Moment Evaluation for Performance Functions 37(62)
3.1 Introduction
37(2)
3.2 Moment Computation for some Simple Functions
39(14)
3.2.1 Moment Computation for Linear Sum of Random Variables
39(3)
3.2.2 Moment Computation for Products of Random Variables
42(3)
3.2.3 Moment Computation for Power of a Lognormally Distributed Random Variable
45(5)
3.2.4 Moment Computation for Power of an Arbitrarily Distributed Random Variable
50(2)
3.2.5 Moment Computation for Reciprocal of an Arbitrary Distributed Random Variable
52(1)
3.3 Point Estimates for a Function with One Random Variable
53(7)
3.3.1 Rosenblueth's Two-Point Estimate
53(2)
3.3.2 Gorman's Three-Point Estimate
55(5)
3.4 Point Estimates in Standardised Normal Space
60(16)
3.4.1 Formulae of Moment of Functions with Single Random Variable
60(3)
3.4.2 Two- and Three-Point Estimates in the Standard Normal Space
63(1)
3.4.3 Five-Point Estimate in Standard Normal Space
64(1)
3.4.4 Seven-Point Estimate in Standard Normal Space
65(3)
3.4.5 General Expression of Estimating Points and Their Corresponding Weights
68(2)
3.4.6 Accuracy of the Point Estimate
70(6)
3.5 Point Estimates for a Function of Multiple Variables
76(13)
3.5.1 General Expression of Point Estimates for a Function of n Variables
76(2)
3.5.2 Approximate Point Estimates for a Function of n Variables
78(5)
3.5.3 Dimension Reduction Integration
83(6)
3.6 Point Estimates for a Function of Correlated Random Variables
89(5)
3.7 Hybrid Dimension-Reduction Based Point Estimate Method
94(2)
3.8 Summary
96(3)
4 Direct Methods of Moment 99(40)
4.1 Basic Concept of Methods of Moment
99(5)
4.1.1 Integral Expression of Probability of Failure
99(1)
4.1.2 The Second-Moment Method
100(2)
4.1.3 General Expressions for Methods of Moment
102(2)
4.2 Third-Moment Reliability Method
104(18)
4.2.1 General Formulation of the Third-Moment Reliability Index
104(2)
4.2.2 Third-Moment Reliability Indices
106(4)
4.2.3 Empirical Applicable Range of Third-Moment Method
110(3)
4.2.4 Simplification of Third-Moment Reliability Index
113(4)
4.2.5 Applicable Range of the Second-Moment Method
117(5)
4.3 Fourth-Moment Reliability Method
122(16)
4.3.1 General Formulation of the Fourth-Moment Reliability Index
122(2)
4.3.2 Fourth-Moment Reliability Index on the Basis of the Pearson System
124(3)
4.3.3 Fourth-Moment Reliability Index Based on Third-Order Polynomial Transformation
127(3)
4.3.4 Applicable Range of Fourth-Moment Method
130(6)
4.3.5 Simplification of Fourth-Moment Reliability Index
136(2)
4.4 Summary
138(1)
5 Methods of Moment Based on First- and Second-Order Transformation 139(54)
5.1 Introduction
139(1)
5.2 First-Order Reliability Method
139(17)
5.2.1 The Hasofer-Lind Reliability Index
139(2)
5.2.2 First-Order Reliability Method
141(6)
5.2.3 Numerical Solution for FORM
147(6)
5.2.4 The Weakness of FORM
153(3)
5.3 Second-Order Reliability Method
156(35)
5.3.1 Necessity of Second-Order Reliability Method
156(1)
5.3.2 Second-Order Approximation of the Performance Function
157(13)
5.3.3 Failure Probability for Second-Order Performance Function
170(5)
5.3.4 Methods of Moment for Second-Order Approximation
175(12)
5.3.5 Applicable Range of FORM
187(4)
5.4 Summary
191(2)
6 Structural Reliability Assessment Based on the Information of Moments of Random Variables 193(60)
6.1 Introduction
193(2)
6.2 Direct Methods of Moment without Using Probability Distribution
195(2)
6.2.1 Second-Moment Formulation
195(1)
6.2.2 Third-Moment Formulation
196(1)
6.2.3 Fourth-Moment Formulation
196(1)
6.3 First-Order Second-Moment Method
197(6)
6.4 First-Order Third-Moment Method
203(16)
6.4.1 First-Order Third-Moment Method in Reduced Space
203(1)
6.4.2 First-Order Third-Moment Method in Third-Moment Pseudo Standard Normal Space
204(15)
6.5 First-Order Fourth-Moment Method
219(14)
6.5.1 First-Order Fourth-Moment Method in Reduced Space
219(1)
6.5.2 First-Order Fourth-Moment Method in Fourth-Moment Pseudo Standard Normal Space
220(13)
6.6 Monte Carlo Simulation Using Statistical Moments of Random Variables
233(13)
6.7 Subset Simulation Using Statistical Moments of Random Variables
246(6)
6.8 Summary
252(1)
7 Transformation of Non-Normal Variables to Independent Normal Variables 253(54)
7.1 Introduction
253(1)
7.2 The Normal Transformation for a Single Random Variable
253(1)
7.3 The Normal Transformation for Correlated Random Variables
254(11)
7.3.1 Rosenblatt Transformation
254(1)
7.3.2 Nataf Transformation
255(10)
7.4 Pseudo Normal Transformations for a Single Random Variable
265(28)
7.4.1 Concept of Pseudo Normal Transformation
265(2)
7.4.2 Third-Moment Pseudo Normal Transformation
267(7)
7.4.3 Fourth-Moment Pseudo Normal Transformation
274(19)
7.5 Pseudo Normal Transformations of Correlated Random Variables
293(13)
7.5.1 Introduction
293(2)
7.5.2 Third-Moment Pseudo Normal Transformation for Correlated Random Variables
295(3)
7.5.3 Fourth-Moment Pseudo Normal Transformation for Correlated Random Variables
298(8)
7.6 Summary
306(1)
8 System Reliability Assessment by the Methods of Moment 307(58)
8.1 Introduction
307(1)
8.2 Basic Concepts of System Reliability
307(11)
8.2.1 Multiple Failure Modes
307(1)
8.2.2 Series Systems
308(3)
8.2.3 Parallel Systems
311(7)
8.3 System Reliability Bounds
318(20)
8.3.1 Uni-Modal Bounds
318(2)
8.3.2 Bi-Modal Bounds
320(2)
8.3.3 Correlation Between a Pair of Failure Modes
322(2)
8.3.4 Bound Estimation of the Joint Failure Probability of a Pair of Failure Modes
324(3)
8.3.5 Point Estimation of the Joint Failure Probability of a Pair of Failure Modes
327(11)
8.4 Moment Approach for System Reliability
338(14)
8.4.1 Performance Function for a System
339(3)
8.4.2 Methods of Moment for System Reliability
342(10)
8.5 System Reliability Assessment of Ductile Frame Structures Using Methods of Moment
352(12)
8.5.1 Challenges on System Reliability of Ductile Frames
352(1)
8.5.2 Performance Function Independent of Failure Modes
353(2)
8.5.3 Limit Analysis
355(1)
8.5.4 Methods of Moment for System Reliability of Ductile Frames
356(8)
8.6 Summary
364(1)
9 Determination of Load and Resistance Factors by Methods of Moment 365(32)
9.1 Introduction
365(1)
9.2 Load and Resistance Factors
366(14)
9.2.1 Basic Concept
366(1)
9.2.2 Determination of LRFs by Second-Moment Method
366(3)
9.2.3 Determination of LRFs Under Lognormal Assumption
369(1)
9.2.4 Determination of LRFs Using FORM
370(8)
9.2.5 An Approximate Method for the Determination of LRFs
378(2)
9.3 Load and Resistance Factors by Third-Moment Method
380(8)
9.3.1 Determination of LRFs Using Third-Moment Method
380(2)
9.3.2 Estimation of the Mean Value of Resistance
382(6)
9.4 General Expressions of Load and Resistance Factors Using Methods of Moment
388(2)
9.5 Determination of Load and Resistance Factors Using Fourth-Moment Method
390(6)
9.5.1 Basic Formulas
390(1)
9.5.2 Determination of the Mean Value of Resistance
391(5)
9.6 Summary
396(1)
10 Methods of Moment for Time-Variant Reliability 397(38)
10.1 Introduction
397(1)
10.2 Simulating Stationary Non-Gaussian Process Using the Fourth-Moment Transformation
397(18)
10.2.1 Brief Review on Simulating Stationary Non-Gaussian Process
397(1)
10.2.2 Transformation for Marginal Probability Distributions
398(1)
10.2.3 Transformation for Correlation Functions
399(4)
10.2.4 Methods to Deal with the Incompatibility
403(1)
10.2.5 Scheme of Simulating Stationary Non-Gaussian Random Processes
404(11)
10.3 First Passage Probability Assessment of Stationary Non-Gaussian Processes Using the Fourth-Moment Transformation
415(4)
10.3.1 Brief Review on First Passage Probability
415(1)
10.3.2 Formulation of the First Passage Probability of Stationary Non-Gaussian Structural Responses
415(2)
10.3.3 Computational Procedure for the First Passage Probability of Stationary Non-Gaussian Structural Responses
417(2)
10.4 Time-Dependent Structural Reliability Analysis Considering Correlated Random Variables
419(15)
10.4.1 Brief Review on Time-Dependent Structural Reliability Methods
419(1)
10.4.2 Formulation of Time-Dependent Failure Probability
420(2)
10.4.3 Fast Integration Algorithms for the Time-Dependent Failure Probability
422(12)
10.5 Summary
434(1)
11 Methods of Moment for Structural Reliability with Hierarchical Modelling of Uncertainty 435(28)
11.1 Introduction
435(1)
11.2 Formulation Description of the Structural Reliability with Hierarchical Modelling of Uncertainty
436(2)
11.3 Overall Probability of Failure Due to Hierarchical Modelling of Uncertainty
438(9)
11.3.1 Evaluating Overall Probability of Failure Based on FORM
438(3)
11.3.2 Evaluating Overall Probability of Failure Based on Methods of Moment
441(1)
11.3.3 Evaluating Overall Probability of Failure Based on Direct Point Estimates Method
442(5)
11.4 The Quantile of the Conditional Failure Probability
447(9)
11.5 Application to Structural Dynamic Reliability Considering Parameters Uncertainties
456(6)
11.6 Summary
462(1)
12 Structural Reliability Analysis Based on Linear Moments 463(34)
12.1 Introduction
463(1)
12.2 Definition of L-Moments
463(2)
12.3 Structural Reliability Analysis Based on the First Three L-Moments
465(14)
12.3.1 Transformation for Independent Random Variables
465(3)
12.3.2 Transformation for Correlated Random Variables
468(3)
12.3.3 Reliability Analysis Using the First Three L-Moments and Correlation Matrix
471(8)
12.4 Structural Reliability Analysis Based on the First Four L-Moments
479(16)
12.4.1 Transformation for Independent Random Variables
479(7)
12.4.2 Transformation for Correlated Random Variables
486(5)
12.4.3 Reliability Analysis Using the First Four L-Moments and Correlation Matrix
491(4)
12.5 Summary
495(2)
13 Methods of Moment with Box-Cox Transformation 497(16)
13.1 Introduction
497(1)
13.2 Methods of Moment with Box-Cox Transformation
498(14)
13.2.1 Criterion for Determining the Box-Cox Transformation Parameter
498(1)
13.2.2 Procedure of the Methods of Moment with Box-Cox Transformation for Structural Reliability
499(13)
13.3 Summary
512(1)
Appendix A Basic Probability Theory 513(48)
Appendix B Three-Parameter Distributions 561(18)
Appendix C Four-Parameter Distributions 579(26)
Appendix D Basic Theory of Stochastic Process 605(10)
References 615(16)
Index 631
Yan-Gang Zhao, Dr. Eng., is Professor at Kanagawa University, Japan and a Foreign Associate of the Engineering Academy of Japan.

Zhao-Hui Lu, Dr. Eng., is Professor at Beijing University of Technology and former Professor at Central South University, China.
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