Topics in Model Validation and Uncertainty Quantification, Volume 5

Preface	6
Contents	8
Chapter 1: Optimal Inequalities to Bound a Performance Probability	10
1.1 Introduction	10
1.2 Concentration-of-Measure Inequalities of Probability Bounds	12
1.2.1 Upper Probability Bounds Based on Concentration-of-Measure Inequalities	12
1.2.2 Numerical Implementation of the Technique	13
1.3 Application to the 2D Rosenbrock Function	14
1.3.1 The Two-Dimensional Rosenbrock Function	14
1.3.2 Estimation of the McDiarmid Diameter and Upper Probability Bounds	15
1.3.3 Convergence Behavior of Sampling-Based Estimates	18
1.4 Application to the High-Fidelity Model of a Three-Story Frame	19
1.4.1 Description of the Three-Story Frame Structure	19
1.4.2 Upper Probability Bounds of the Three-Story Frame Structure	20
1.5 Conclusion	23
References	23
Chapter 2: Remaining Fatigue Life Predictions Considering Load and Model Parameters Uncertainty	25
2.1 Introduction	25
2.2 General Overview and Description of Proposed Framework for Remaining Fatigue Life Predictions	26
2.3 Application Example	27
2.4 Conclusions	31
References	32
Chapter 3: Fast Computing Techniques for Bayesian Uncertainty Quantification in Structural Dynamics	33
3.1 Introduction	33
3.2 Bayesian Uncertainty Quantification and Propagation Framework	34
3.3 Fast Computing Techniques for Large Order Finite Element Models	35
3.3.1 Component Model Synthesis for Parameter Estimation in Structural Dynamics	35
3.3.2 Surrogate Models	36
3.3.3 Parallel Computing Algorithms	37
3.4 Application on Finite Element Model Updating of a Bridge	37
3.5 Conclusions	39
References	39
Chapter 4: Bayesian Uncertainty Quantification and Propagation in Nonlinear Structural Dynamics	40
4.1 Introduction	40
4.2 Review of Bayesian Formulation for Parameter Estimation and Model Class Selection	41
4.3 Application to a Small Scale Laboratory Vehicle Model	42
4.4 Results	44
4.5 Conclusions	46
References	47
Chapter 5: Probabilistic Damage Identification of the Dowling Hall Footbridge Using Bayesian FE Model Updating	49
5.1 Introduction	49
5.2 The Dowling Hall Footbridge and Its Continuous Monitoring System	50
5.3 Simulation of Structural Damage on the Footbridge	51
5.4 Bayesian FE Model Updating	52
5.4.1 Bayesian Formulation and Sampling	53
5.4.2 Model Updating Results	54
5.5 Conclusions	56
References	57
Chapter 6: Considering Wave Passage Effects in Blind Identification of Long-Span Bridges	58
6.1 Introduction	59
6.2 Proposed Identification Technique	59
6.2.1 Time-Frequency Blind Source Separation	62
6.3 Application Examples	62
6.3.1 Synthetic Simulation	62
6.3.2 Experimental Data: The Prototype Viaduct Bridge	66
6.4 Conclusions	70
References	70
Chapter 7: Quantification of Parametric Model Uncertainties in Finite Element Model Updating Problem via Fuzzy Numbers	72
7.1 Introduction	72
7.2 Fuzzy Finite Element Model Updating	73
7.3 Gaussian Process Model for FFEMU	74
7.4 Numerical Verification	75
7.5 Conclusion	78
References	79
Chapter 8: Quantifying Maximum Achievable Accuracy of Identified Modal Parameters from Noise Contaminated Free Vibration Data	80
8.1 Introduction	80
8.2 Fisher Information	81
8.3 Cramer-Rao Lower Bound	81
8.4 Cramer-Rao Lower Bound for a SDoF	81
8.5 Fourier Domain Identification	82
8.6 Numerical Illustration	83
8.7 Conclusions	84
References	85
Chapter 9: Using P-Box and PiFE to Express Uncertainty in Model Updating	86
9.1 Introduction	86
9.2 Pseudo-inverse Finite Element (PiFE)	87
9.3 Interval Arithmetic and Associated Challenges	87
9.4 Validation Example	88
9.4.1 Modal Parameter Intervals	88
9.4.2 Application of PiFE and Naïve Method	89
9.4.3 Application of PiFE and All Possible Combination Method	91
9.5 Conclusions	91
References	92
Chapter 10: Robust Model Calibration with Load Uncertainties	94
10.1 Introduction	94
10.2 Robust Parameter Calibration	95
10.3 Application	96
10.3.1 SDOF System	96
10.3.2 Wind Turbine Power Train Model	99
10.4 Conclusion	101
References	102
Chapter 11: Simulating the Dynamics of the CX-100 Wind Turbine Blade: Model Selection Using a Robustness Criterion	103
11.1 Introduction	103
11.1.1 Motivation	103
11.1.2 Related Literature	105
11.2 Model Development and Experimental Campaign	105
11.2.1 Development of the CX-100 FE Model	105
11.2.2 NREL Modal Testing of the CX-100 Wind Turbine Blade	106
11.2.3 Fixed-Free Model of the CX-100 Wind Turbine Blade	107
11.3 Model Development for the Mass-Added Configuration of the CX-100 Wind Turbine Blade	107
11.3.1 Development of the Point Mass Model	108
11.3.2 Development of the Solid Mass Model	109
11.4 Analysis of Robustness to Uncertainty Applied to Models of the CX-100 Wind Turbine Blade	111
11.4.1 Conceptual Demonstration of Robustness Analysis	111
11.4.2 Rationale for the Definition of Uncertainty	111
11.4.3 Selection of the Mass Added Models	113
11.5 Conclusion	115
References	115
Chapter 12: Defining Coverage of a Domain Using a Modified Nearest-Neighbor Metric	117
12.1 Introduction	117
12.2 Characteristics of Ideal Coverage Definition	118
12.3 Earlier Definitions of Coverage	119
12.3.1 Atamturktur et al. ch12:bib8	119
12.3.2 Hemez et al. ch12:bib4	120
12.3.3 Stull et al. ch12:bib7	120
12.4 Proposed Coverage Definition	122
12.4.1 Penalizing Extrapolation	122
12.4.2 Accounting for Experimental Uncertainty	123
12.4.3 Application to Predictive Maturity Index (PMI)	123
12.5 Application to Viscoplastic Self-Consistent (VPSC) Code	124
12.5.1 Batch Sequential Design (BSD)	124
12.5.2 Results and Discussion	124
12.6 Conclusion	125
References	126
Chapter 13: Orthogonality for Modal Vector Correlation: The Effects of Removing Degrees-of-Freedom	127
13.1 Introduction	128
13.2 Weighted Orthogonality of Modal Vectors	129
13.3 Test Analysis Models (TAM)	130
13.3.1 Guyan	131
13.3.2 Improved Reduced System (IRS)	131
13.3.3 System Equivalent Reduction/Expansion Process (SEREP)	131
13.3.4 Modal	132
13.3.5 Hybrid	132
13.4 Modal Assurance Criteria (MAC)	133
13.5 Orthogonality Using SEREP	133
13.6 Previous Work	134
13.7 Optimal DOF Selection and Decreasing DOF'S	134
13.7.1 Expected Results	134
13.7.2 Removing DOF's Using Effective Independence	134
13.8 Future Work	135
13.9 Conclusion	136
References	136
Chapter 14: CAE Model Correlation Metrics for Automotive Noise and Vibration Analysis	138
14.1 Introduction	138
14.2 Statistical Analysis Methods ch14:bib1,ch14:bib2	139
14.2.1 Principal Component Analysis	139
14.2.2 Canonical Correlation Analysis	140
14.3 Noise and Vibration Engineering Metrics	141
14.4 Correlation Analysis and Metrics	141
14.4.1 PCA Based Correlation Metrics	142
14.4.2 Canonical Correlation Analysis	144
14.5 Conclusion	145
References	145
Chapter 15: Damage Localization Using a Statistical Test on Residuals from the SDDLV Approach	146
15.1 Introduction	146
15.2 The SDDLV Approach	147
15.2.1 Dynamical Equation and State-Space Model	147
15.2.2 Damage Localization Procedure	147
15.3 Uncertainties on Damage Localization Residuals	148
15.3.1 Covariance of R	148
15.3.2 Covariance of Damage Localization Residuals	149
15.3.3 Hypothesis Testing for Damage Localization	149
15.4 Numerical Application	150
15.4.1 Truss Structure	150
15.4.2 Plate	151
15.5 Conclusion	154
References	154
Chapter 16: Robust Tolerance Design in Structural Dynamics	156
16.1 Introduction	156
16.2 Robust Tolerance Design Strategy	157
16.2.1 Robust Design Theory	157
16.2.2 Taguchi's Method	158
16.2.2.1 Orthogonal Array Experiment	158
16.2.2.2 Analysis of Variance (ANOVA)	158
16.2.2.3 The Application of Taguchi's Method	159
16.2.3 Multi-objective Optimization	159
16.2.3.1 Calculation Strategy	159
16.2.3.2 The Application of Multi-objective Optimization	160
16.2.4 Proposed Tolerance Design Strategy	161
16.3 Case Study: Joint Assembly of Two Aero-Engine Casings	161
16.3.1 Problem Definition	162
16.3.2 Determine the Nominal Design	162
16.3.3 Tolerance Design: Multi-objective Optimization	163
16.3.4 Optimization Verification	166
16.4 Conclusion	167
References	167
Chapter 17: Uncertainty Propagation in Floating Raft System by FRF-Based Substructuring Method for Elastic Coupling	168
17.1 Introduction	168
17.2 Derivation of FRF-Based Substructuring Method for Floating Raft System	169
17.3 Uncertainty Propagation in Floating Raft System by FRF-Based Substructuring Method	170
17.4 Numerical Simulation	171
17.4.1 Noisy Simulated Data	171
17.4.2 Verification of the Uncertainty Propagation Method	175
17.5 Conclusion	175
References	175
Chapter 18: Crossing and Veering Phenomena in Crank Mechanism Dynamics	177
18.1 Introduction	177
18.2 Crank Mechanism Modeling	178
18.3 Curve Veering and Mode Localization: Overview	180
18.4 From Components Dynamic Requirements to System Dynamic Properties	183
18.5 Identification of Local and Global Modes	185
18.6 Conclusions	187
References	188
Chapter 19: Validating Low-Level Footfall-Induced Vibration Predictions in Steel and Concrete Structures	190
19.1 Introduction	190
19.2 Overview of Prediction Methodologies	191
19.2.1 American Institute of Steel Construction Design Guide 11	191
19.2.2 Steel Construction Institute and Concrete Centre	191
19.3 Vibration Criteria	191
19.4 Predicted and Measured Floor Vibrations	192
19.4.1 Steel Structure #1	192
19.4.2 Steel Structure #2	194
19.4.3 Steel Structure #3	194
19.4.4 Concrete Structure	195
19.5 Discussion	195
19.6 Conclusions	198
References	199
Chapter 20: Finite Element Model Updating of an Assembled Aero-Engine Casing	200
20.1 Introduction	200
20.2 Methodology of the Two Step Updating Procedure	201
20.2.1 Planning of the Modal Test	201
20.2.2 Model Updating Process	202
20.2.3 Joint Modeling	203
20.3 Case Study: Model Updating of a Jointed Aero-Engine Casing	204
20.3.1 Aero-Engine Casings and Modal Test	204
20.3.2 Updating of the Casing Components Using Test Data	206
20.3.3 Updating of the Joint Assembly Using Test Data	210
20.4 Conclusions	212
References	213
Chapter 21: Experimental Modal Analysis and Modelling of an Agricultural Tire	214
21.1 Introduction	214
21.2 Numerical Model	215
21.2.1 Structure Model	215
21.2.2 Tread Model	215
21.2.3 Soil Model	216
21.2.4 Generalized Forces	216
21.3 Identification of Modal Parameters	218
21.4 Simulation Results	219
21.5 Conclusion	220
References	220
Chapter 22: International Space Station Modal Correlation Analysis	222
22.1 Introduction	222
22.2 Math Models and Dynamics	223
22.3 On-Orbit Flight Testing: Dtf s4-1A	223
22.4 On-Orbit Instrumentation Systems	226
22.4.1 Overview	226
22.4.2 External Wireless Instrumentation System (EWIS)	227
22.4.3 Internal Wireless Instrumentation System (IWIS)	227
22.4.4 Structural Dynamic Measurement System	228
22.4.5 Space Acceleration Measurement System (SAMS)	228
22.4.6 Russian Inertial Measurement Unit (IMU)	229
22.4.7 ISS Photogrammetric System	230
22.5 Modal Analysis	230
22.5.1 Overview	230
22.5.2 Modal Analysis Procedure	231
22.5.3 Sample Data Plots	231
22.6 Model Correlation and Validation	232
22.6.1 Overview	232
22.6.2 Mode Correlation and Modal Analysis	233
22.6.3 Stage ULF-4: Dedicated Thruster Firing S4-1A: Results	237
22.6.3.1 S4-1A Photogrammetry Results	237
22.6.3.2 S4-1A MTS Strut Strain Gage Analysis	241
22.6.3.3 S4-1A Model Correlation	241
22.7 Conclusions	242
References	242
Chapter 23: Numerical Modeling of Vibration Induced Atomization of Liquids	244
23.1 Introduction	244
23.2 Literature Review	245
23.3 Analytical Study	248
23.4 Results	250
23.4.1 Amplitude Variable	250
23.5 Discussion	252
23.6 Conclusions	253
References	254
Chapter 24: Dynamical Modeling and Verification of Underwater Acoustic System	255
24.1 Introduction	255
24.2 Design and Production	256
24.2.1 Underwater Transducer Type Selection	256
24.2.2 Underwater Acoustic System	257
24.3 Finite Element Model of Underwater Acoustic System	258
24.4 Validation of Finite Element Model By Experimental Techniques	260
24.4.1 Admittance Measurement	260
24.4.2 TVR and RVS Measurements	260
24.5 Discussion	261
References	263

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