Dedication
Preface
Acknowledgments
Nomenclature
List of Figures
List of Tables
1 Introduction
1.1 Structural Reliability Analysis
1.2 Non-deterministic Reliability Analysis Methods
1.2.1 Monte Carlo Simulation （MCS） Method
1.2.2 FORM （First-order Reliability Method）
1.2.3 Interval Analysis
1.2.4 Fuzzy Analysis
1.2.5 Response Surface Method （RSM）
1.2.6 Summary
1.3 Uncertainty Analysis of Dynamic Systems
1.3.1 Background
1.3.2 Literature Review of Analytical Approaches to Dynamic Systems
1.3.3 Summary
1.4 Scope of the Present Work
1.5 Overview of the Book
2.Technical Background
2.1 Definition of Structural Reliability
2.2 Technical Basis of the Monte Carlo Simulation Method
2.3 Theory of the First-order Reliability Method （FORM）
2.4 Response Surface Method
2.4.1 Response Surface Models and Fitting Techniques
2.4.2 Sampling Design Methods
2.5 Problems of Applying FORM and RSM Methods to Dynamic Systems
2.5.1 Problematic Failure Surfaces for FORM Applications
2.5.2 Inaccuracy of RSM in Predicting the Dynamic Response
2.6 Optimization Solution Through Modal Analysis
3.Theoretical Fundamentals of the Perturbation Approach
3.1 Definition of the New Parameters and Safety Margin
3.2 Derivation of the Two Moments of the New Parameters
3.2.1 Derivation of the Covariance Matrix of the Modal Parameter w2
3.2.2 Derivation of the Covariance Matrix of the Defined Parameter dr
3.2.3 Derivation of the Covariance Matrix of the Modal Parameter [□]
3.2.4 Derivation of the Covariance Matrix of the Defined Parameter rjk，r
3.2.5 Derivation of the Covariance Matrix of the Combined Parameter T
3.2.6 Derivation of the Mean Values of the Defined Parameters dr and rik，r
3.3 Application Procedure of the New Approach
3.4 Discussion
3.5 Summary
4.Application to a 2D System
4.1 Finite Element Model of a 2D Dynamic System
4.2 Applying the Combined Approach： Preliminary Analysis
4.2.1 Response Analysis
4.2.2 Safety Margin Contour
4.3 Perturbation Approach + FORM Method
4.3.1 Evaluating the Probability of Failure and In-depth Analysis
4.3.2 Solution 1： Second-order Approximation of d2
4.3.3 Solution 2： New Variable e2 to Replace d2
4.3.4 Solution 3： Variable □ to Replace e2
4.4 Solution 4： Monte Carlo Simulation Replacing FORM
4.4.1 Perturbation + Monte Carlo Simulation on r2 and w□
4.4.2 Reliability Analysis of the Updated Combined Approach
4.5 Summary
5.Application to a 3D Helicopter Model
5.1 Background of Helicopter Vibration'Control
5.2 A 3D Helicopter EE Model
5.2.1 System Details
5.2.2 Dynamic Characteristics of the Model
5.3 Response Analysis
5.4 Reliability Analysis of the Combined Approach
5.4.1 Probability vs. Excitation Frequencies
5.4.2 Probability vs. Maximum Displacement and Variation Coefficient
5.5 Efficiency Analysis
5.6 Summary
6.Complete Combined Approach
6.1 Response Surface Techniques in Obtaining Ck
6.1.1 Direct RS Model Fitting of the Stiffness Matrix K
6.1.2 Alternative Fitting Approach
6.1.3 Analytical Approach to Obtain the Covariance Matrix of K
6.1.4 Complete Combined Approach
6.2 Complete Application to 2D Frame Model
6.2.1 Type I RS Model Fitting with Koshal Design
6.2.2 Complete Combined Approach
6.3 Complete Application to 3D Helicopter Model
6.4 Summary
7.Conclusions and Future Work
7.1 Achievements and Conclusions
7.2 Future Work
7.2.1 Application of an Enhanced FORM Method
7.2.2 Further Simplification of Perturbation/Analytical Algorithms
7.2.3 Development for Non-Probabilistic Methods
Appendix Ⅰ：Transforming Random Variables from Correlated to Uncorrelated
Appendix Ⅱ：Analytical Solution of HL Safety Index
Appendix Ⅲ：Modal Analysis of Dynamic Systems
Appendix Ⅳ：Multiple Force Analysis
Appendix Ⅴ：Summary of the Defined Parameters
Appendix Ⅵ：Nodal Coordinates of the Helicopter Model
Appendix Ⅶ：Element Connectivity and Properties of the
Helicopter Model
References
Index
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