Reliability Evaluation of Dynamic Systems Excited in Time Domain - Redset

Achintya Haldar - University of Arizona, Tucson, Arizona, USAHamoon Azizsoltani - North Carolina State University, Raleigh, North Carolina, USAJ. Ramon Gaxiola-Camacho - Autonomous University of Sinaloa, Culiacan, MexicoSayyed Mohsen Vazirizade - Vanderbilt University, Nashville, Tennessee, USAJungwon Huh - Chonnam National University, Gwangju, Korea

• 1 REDSET and Its Necessity 11.1 Introductory Comments 11.2 Reliability Evaluation Procedures Existed Around 2000 21.3 Improvements or Alternative to Stochastic Finite Element Method (SFEM) 21.4 Other Alternatives Besides SFEM 41.4.1 Random Vibration 41.4.2 Alternative to Basic Monte Carlo Simulation 51.4.3 Alternatives to Random Vibration Approach for Large Problems 51.4.4 Physics-Based Deterministic FEM Formulation 51.4.5 Multidisciplinary Activities to Study the Presence of Uncertainty in Large Engineering Systems 61.4.6 Laboratory Testing 71.5 Justification of a Novel Risk Estimation Concept REDSET Replacing SFEM 71.6 Notes for Instructors 81.7 Notes to Students 9Acknowledgments 92 Fundamentals of Reliability Assessment 112.1 Introductory Comments 112.2 Set Theory 122.3 Modeling of Uncertainty 142.3.1 Continuous Random Variables 152.3.2 Discrete Random Variables 162.3.3 Probability Distribution of a Random Variable 162.3.4 Modeling of Uncertainty for Multiple Random Variables 172.4 Commonly Used Probability Distributions 192.4.1 Commonly Used Continuous and Discrete Random Variables 192.4.2 Combination of Discrete and Continuous Random Variables 202.5 Extreme Value Distributions 202.6 Other Useful Distributions 212.7 Risk-Based Engineering Design Concept 212.8 Evolution of Reliability Estimation Methods 252.8.1 First-Order Second-Moment Method 252.8.2 Advanced First-Order Reliability Method (AFOSM) 262.8.3 Hasofer-Lind Method 262.9 AFOSM for Non-Normal Variables 312.9.1 Two-Parameter Equivalent Normal Transformation 312.9.2 Three-Parameter Equivalent Normal Transformation 332.10 Reliability Analysis with Correlated Random Variables 332.11 First-Order Reliability Method (FORM) 352.11.1 FORM Method 1 352.11.2 Correlated Non-Normal Variables 372.12 Probabilistic Sensitivity Indices 392.13 FORM Method 2 402.14 System Reliability Evaluation 402.15 Fundamentals of Monte Carlo Simulation Technique 412.15.1 Steps in Numerical Experimentations Using Simulation 422.15.2 Extracting Probabilistic Information from N Data Points 432.15.3 Accuracy and Efficiency of Simulation 432.16 Concluding Remarks 443 Implicit Performance or Limit State Functions 473.1 Introductory Comments 473.2 Implicit Limit State Functions – Alternatives 483.3 Response Surface Method 493.4 Limitations of Using the Original RSM Concept for the Structural Reliability Estimation 503.5 Generation of Improved Response Surfaces 513.5.1 Polynomial Representation of an Improved Response Surface 523.6 Experimental Region, Coded Variables, and Center Point 543.6.1 Experimental Region and Coded Variables 543.6.2 Experimental Design 553.6.3 Saturated Design 563.6.4 Central Composite Design 563.7 Analysis of Variance 563.8 Experimental Design for Second-Order Polynomial 583.8.1 Experimental Design – Model 1: SD with Second-Order Polynomial without Cross Terms 583.8.2 Experimental Design – Model 2: SD with Second-Order Polynomial with Cross Terms 593.8.3 Experimental Design – Model 3: CCD with Second-Order Polynomial with Cross Terms 613.9 Comparisons of the Three Basic Factorial Designs 613.10 Experimental Designs for Nonlinear Dynamic Problems Excited in the Time Domain 643.11 Selection of the Most Appropriate Experimental Design 643.12 Selection of Center Point 653.13 Generation of Limit State Functions for Routine Design 663.13.1 Serviceability Limit State 663.13.2 Strength Limit State Functions 673.13.3 Interaction Equations for the Strength Limit State Functions 673.13.4 Dynamic Effect in Interaction Equations 683.14 Concluding Remarks 694 Uncertainty Quantification of Dynamic Loadings Applied in the Time Domain 714.1 Introductory Comments 714.2 Uncertainty Quantification in Seismic Loadings Applied in the Time Domain 734.2.1 Background Information 744.3 Selection of a Suite of Acceleration Time Histories Using PEER Database – Alternative 1 754.3.1 Earthquake Time History Selection Methodology 784.4 Demonstration of the Selection of a Suite of Ground Motion Time Histories – Alternative 1 794.5 Simulated Ground Motions Using the Broadband Platform (BBP) – Alternative 2 844.5.1 Broadband Platform Developed by SCEC 844.6 Demonstration of Selection and Validation of a Suite of Ground Motion Time Histories Using BPP 864.7 Applications of BBP in Selecting Multiple Earthquake Acceleration Time Histories 884.8 Summary of Generating Multiple Earthquake Time Histories Using BPP 914.9 Uncertainty Quantification of Wind-Induced Wave Loadings Applied in the Time Domain 914.9.1 Introductory Comments 914.9.2 Fundamentals of Wave Loading 944.9.3 Morison Equation 954.10 Modeling of Wave Loading 964.10.1 Wave Modeling Using the New Wave Theory 974.10.2 Wheeler Stretching Effect 984.10.3 Three-Dimensional Directionality 984.10.4 Summary of Deterministic Modeling of Wave Loading 1004.11 Uncertainty Quantifications in Wave Loading Applied in the Time Domain 1004.11.1 Uncertainty Quantification in Wave Loading – Three-Dimensional Constrained New Wave (3D CNW) Concept 1004.11.2 Three-Dimensional Constrained New Wave (3D CNW) Concept 1024.11.3 Uncertainty in the Wave Height Estimation 1044.11.4 Uncertainty Quantification of Wave Loading 1054.11.5 Quantification of Uncertainty in Wave Loading 1064.12 Wave and Seismic Loadings – Comparisons 1074.13 Concluding Remarks 1085 Reliability Assessment of Dynamic Systems Excited in Time Domain – REDSET 1115.1 Introductory Comments 1115.2 A Novel Reliability Estimation Concept – REDSET 1135.2.1 Integration of Finite Element Method, Improved Response Surface Method, and FORM 1135.2.2 Increase Efficiency in Generating an IRS 1145.2.3 OptimumNumber of NDFEA Required for the Generation of an IRS 1155.2.4 Reduction of Random Variables 1155.3 Advanced Sampling Design Schemes 1165.4 Advanced Factorial Design Schemes 1165.5 Modified Advanced Factorial Design Schemes 1195.5.1 Modified Advanced Factorial Design Scheme 2 (MS2) 1195.5.2 Modified Advanced Factorial Design Scheme 3 1215.6 Optimum Number of TNDFEA Required to Implement REDSET 1225.7 Improve Accuracy of Scheme MS3 Further – Alternative to the Regression Analysis 1225.7.1 Moving Least Squares Method 1225.7.2 Concept of Moving Least Squares Method 1235.7.3 Improve Efficiency Further to the Moving Least Squares Method 1245.8 Generation of an IRS Using Kriging Method 1265.8.1 Simple Kriging 1275.8.2 Ordinary Kriging 1285.8.3 Universal Kriging 1285.8.4 Variogram Function 1315.8.5 Scheme S3 with Universal Kriging Method 1335.8.6 Scheme MS3 with Modified Universal Kriging Method 1335.9 Comparisons of All Proposed Schemes 1335.10 Development of Reliability Evaluation of Dynamical Engineering Systems Excited in Time Domain (REDSET) 1355.10.1 Required Steps in the Implementation of REDSET 1365.11 Concluding Remarks 1386 Verification of REDET for Earthquake Loading Applied in the Time Domain 1396.1 Introductory Comments 1396.2 Verification – Example 1: 3-Story Steel Moment Frame with W24 Columns 1406.2.1 Example 1: Accuracy Study of All 9 Schemes 1406.2.2 Verification – Example 2: 3-Story Steel Moment Frame with W14 Columns 1476.3 Case Study: 13-Story Steel Moment Frame 1516.4 Example 4: Site-Specific Seismic Safety Assessment of CDNES 1606.4.1 Location, Soil Condition, and Structures 1616.4.2 Uncertainty Quantifications 1626.4.3 Uncertainty Quantifications in Resistance-Related Design Variables 1626.4.3.1 Uncertainty Quantifications in Gravity Load-related Design Variables 1656.4.3.2 Selection of a Suite of Site-Specific Acceleration Time Histories 1656.5 Risk Evaluation of Three Structures using REDSET 1666.5.1 Selection of Limit State Functions 1666.5.2 Estimations of the Underlying Risk for the Three Structures 1666.6 Concluding Remarks 1727 Reliability Assessment of Jacket-Type Offshore Platforms Using REDSET for Wave and Seismic Loadings 1757.1 Introductory Comments 1757.2 Reliability Estimation of a Typical Jacket-Type Offshore Platform 1767.3 Uncertainty Quantifications of a Jacket-Type Offshore Platform 1777.3.1 Uncertainty in Structures 1787.3.2 Uncertainty in Wave Loadings in the Time Domain 1797.4 Performance Functions 1807.4.1 LSF of Total Drift at the Top of the Platform 1807.4.2 Strength Performance Functions 1807.5 Reliability Evaluation of JTPs 1817.6 Risk Estimations of JTPs Excited by the Wave and Seismic Loadings – Comparison 1837.7 Comparison of Results for the Wave and Earthquake Loadings 1907.8 Concluding Remarks 1938 Reliability Assessment of Engineering Systems Using REDSET for Seismic Excitations and Implementation of PBSD 1958.1 Introductory Comments 1958.2 Assumed Stress-Based Finite Element Method for Nonlinear Dynamic Problems 1968.2.1 Nonlinear Deterministic Seismic Analysis of Structures 1968.2.2 Seismic Analysis of Steel Structures 1968.2.3 Dynamic Governing Equation and Solution Strategy 1978.2.4 Flexibility of Beam-to-Column Connection Models by Satisfying Underlying Physics – Partially Restrained Connections for Steel Structures 2008.2.5 Incorporation of Connection Rigidities in the FE Formulation Using Richard Four-Parameter Model 2028.3 Pre- and Post-Northridge Steel Connections 2048.4 Performance-Based Seismic Design 2078.4.1 Background Information and Motivation 2078.4.2 Professional Perception of PBSD 2088.4.3 Building Codes, Recommendations, and Guidelines 2108.4.4 Performance Levels 2108.4.5 Target Reliability Requirements to Satisfy Different Performance Levels 2118.4.6 Elements of PBSD and Their Sequences 2128.4.7 Explore Suitability of REDSET in Implementing PBSD 2128.5 Showcasing the Implementation of PBSD 2138.5.1 Verification of REDSET – Reliability Estimation of a 2-Story Steel Frame 2148.6 Implementation Potential of PBSD – 3-, 9-, and 20-Story Steel Buildings 2198.6.1 Description of the Three Buildings 2198.6.2 Post-Northridge PR Connections 2198.6.3 Quantification of Uncertainties in Resistance-Related Variables 2198.6.4 Uncertainties in Gravity Loads 2198.6.5 Uncertainties in PR Beam-to-Column Connections 2208.6.6 Uncertainties in Seismic Loading 2258.6.7 Serviceability Performance Functions – Overall and Inter-Story Drifts 2268.7 Structural Reliability Evaluations of the Three Buildings for the Performance Levels of CP, LS, and IO Using REDSET 2278.7.1 Observations for the Three Performance Levels 2288.8 Implementation of PBSD for Different Soil Conditions 2378.9 Illustrative Example of Reliability Estimation for Different Soil Conditions 2398.9.1 Quantifications of Uncertainties for Resistance-Related Variables and Gravity Loads 2408.9.2 Generation of Multiple Design Earthquake Time Histories for Different Soil Conditions 2408.9.3 Implementation of PBSD for Different Soil Conditions 2408.10 Concluding Remarks 2449 Reliability Assessment of Lead-Free Solders in Electronic Packaging Using REDSET for Thermomechanical Loadings 2479.1 Introductory Comments 2479.2 Background Information 2499.3 Deterministic Modelling of a Solder Ball 2519.3.1 Solder Ball Represented by Finite Elements 2519.3.2 Material Modeling of SAC Alloy 2519.3.2.1 HISS Plasticity Model 2529.3.2.2 Disturbed State Concept 2549.3.2.3 Creep Modeling 2549.3.2.4 Rate-Dependent Elasto-Viscoplastic Model 2559.3.3 Temperature-Dependent Modeling 2559.3.4 Constitutive Modeling Calibration 2559.3.5 Thermomechanical Loading Experienced by Solder Balls 2569.4 Uncertainty Quantification 2579.4.1 Uncertainty in all the Parameters in a Solder Ball 2589.4.2 Uncertainty Associated with Thermomechanical Loading 2609.5 The Limit State Function for the Reliability Estimation 2609.6 Reliability Assessment of Lead-Free Solders in Electronic Packaging 2619.7 Numerical Verification Using Monte Carlo Simulation 2629.8 Verification Using Laboratory Test Results 2639.9 Concluding Remarks 264Concluding Remarks for the Book - REDSET 266References 267Index 281