Model Validation and Uncertainty Quantification, Volume 3

Preface	6
Contents	7
1 Variational Coupled Loads Analysis Using the Hybrid Parametric Variation Method	10
Acronyms	10
1.1 Introduction	11
1.2 Theory	12
1.3 Selection of Component Eigenvalue and Stiffness Matrix Dispersion Values	16
1.4 Nominal ICPS/LVSA Based on ISPE Configuration 3	17
1.5 Updated ICPS/LVSA Based on ISPE Configuration 3	18
1.6 Propagation of Uncertainty into Response to Buffet Loads	19
1.7 Conclusion	26
References	26
2 Bayesian Uncertainty Quantification in the Development of a New Vibration Absorber Technology	28
2.1 Introduction	28
2.2 Fluid Dynamic Vibration Absorber (FDVA)	29
2.3 Mathematical Modeling and Experimental Testing of FDVA	29
2.4 Model A	30
2.5 Model B	30
2.6 Model C	31
2.7 Experiment	31
2.8 Quantification of Uncertainty with Bayesian Interval Hypothesis-Based Method	31
2.9 Model Confidence for Model A, B and C	33
2.10 Conclusion	34
References	34
3 Comparison of Complexity Measures for Structural Health Monitoring	36
3.1 Introduction	37
3.2 Theoretical Background	38
3.2.1 Shannon, Rényi, and Spectral Entropy	38
3.2.2 Approximate and Sample Entropy	38
3.2.3 Permutation Entropy	39
3.2.4 Mutual Information	39
3.2.5 Naïve Bayes Classifier	40
3.2.6 K-Means Clustering	40
3.3 Experimental Design	40
3.3.1 Bearing Defects in a Rotating Machine	40
3.3.2 Four-Degree of Freedom Impact Oscillator	41
3.3.3 Impact Oscillator with Bearing Damage	41
3.4 Data Analysis	43
3.4.1 Applying Complexity Measures to Time Series Data	43
3.4.2 Performing K-Means Clustering on the Labeled Complexity Measurements and Calculating Error	43
3.5 Results and Discussions	43
3.5.1 Bearing Defects in Rotating Machine	43
3.5.2 Four-Degree of Freedom Impact Oscillator	44
3.5.3 Impact Oscillator with Bearing Damage	44
3.6 Discussion	46
3.7 Conclusion	47
References	47
4 Selection of an Adequate Model of a Piezo-Elastic Support for Structural Control in a Beam Truss Structure	49
4.1 Introduction	49
4.2 System Description	50
4.2.1 Mathematical Model of the Two-Dimensional Truss Structure	51
4.3 Piezo-Elastic Support for Structural Control	52
4.3.1 Piezo-Elastic Support Model 1	53
4.3.2 Piezo-Elastic Support Model 2	54
4.3.3 Transfer Function of the Two-Dimensional Truss Structure	55
4.4 Comparison of the Two Models	56
4.5 Conclusion	57
References	57
5 Impact Load Identification for the DROPBEAR Setup Using a Finite Input Covariance (FIC)Estimator	58
5.1 Introduction	58
5.2 Background	58
5.3 Analysis	59
5.4 Conclusion	60
References	61
6 Real-Time Digital Twin Updating Strategy Based on Structural Health Monitoring Systems	62
6.1 Introduction	62
6.2 Updating Strategy	63
6.3 Divergence Analysis	64
6.4 Synthetic Data Illustration	65
6.5 Divergence Analysis Based on Laboratory Data	68
6.6 Conclusion	69
References	71
7 On the Fusion of Test and Analysis	72
8 Design of an Actuation Controller for Physical Substructures in Stochastic Real-Time HybridSimulations	75
8.1 Introduction	75
8.2 Problem Definition	76
8.3 Dynamics of Control Plant and Actuation System	79
8.4 Model Predictive Control	81
8.5 Surrogate Modelling	82
8.6 Global Sensitivity Analysis	83
8.7 Results	84
8.8 Conclusion	87
References	87
9 Output-Only Nonlinear Finite Element Model Updating Using Autoregressive Process	89
9.1 Introduction	89
9.2 Proposed Method	89
9.3 Validation	90
9.3.1 Structure, FE Model and Measured Response	90
9.3.2 Estimation Results	91
9.4 Conclusions	91
References	92
10 Axle Box Accelerometer Signal Identification and Modelling	93
10.1 Introduction	93
10.2 Non-parametric Response Signal Identification	94
10.3 Parametric Response Signal Identification	96
10.4 Conclusions	97
References	98
11 Kalman-Based Virtual Sensing for Improvement of Service Response Replicationin Environmental Tests	99
11.1 Introduction	99
11.2 The Boundary Conditions Challenge	100
11.2.1 The Box Assembly with Removable Component	100
11.3 Virtual Sensing for Environmental Tests on the BARC	102
11.3.1 BARC Reduced Order Model	102
11.3.2 Augmented Kalman Filter for Joint Input-State Estimation	103
11.3.3 Optimal Sensor Placement Strategy	104
11.4 Input-State Estimation: Simulated Data	105
11.5 Input-State Estimation: Measured Data	106
11.5.1 Measurement Campaign	107
11.5.2 Input-State Estimation Using the AKF	107
11.6 Conclusions	111
References	111
12 Virtual Sensing of Wheel Position in Ground-Steering Systems for Aircraft Using Digital Twins	113
12.1 Introduction	113
12.2 Digital Twin of the Ground-Steering System	114
12.3 Interval Uncertainty Propagation	115
12.4 State Estimation Algorithms	117
12.5 Results	121
12.6 Conclusion	123
References	123
13 Assessing Model Form Uncertainty in Fracture Models Using Digital Image Correlation	125
13.1 Introduction	125
13.2 Crack Simulations	126
13.2.1 Finite Element Method	126
13.2.2 Extended Finite Element Method	126
13.2.3 Phase Field Fracture Method	127
13.3 Application to Compact Tension Test	128
13.3.1 Compact Tension Model	128
13.3.2 XFEM Convergence Study	129
13.3.3 PPF Convergence Study	129
13.3.4 Comparison of XFEM and PFF	131
13.4 Parametric Model Updating	131
13.5 Model Validation	132
13.6 Conclusions	133
References	135
14 Identification of Lack of Knowledge Using Analytical Redundancy Applied to StructuralDynamic Systems	136
14.1 Introduction	136
14.2 Background	137
14.3 Method	138
14.4 Validation	138
14.5 Conclusion	143
14.6 Outlook	143
References	143
15 A Structural Fatigue Monitoring Concept for Wind Turbines by Means of Digital Twins	144
15.1 Introduction	144
15.2 Background	145
15.3 Analysis	145
15.4 Conclusion	146
References	146
16 Damage Identification of Structures Through Machine Learning Techniques with Updated Finite Element Models and Experimental Validations	148
16.1 Introduction	148
16.2 Frequency and Time Domain Response Residuals	150
16.3 Machine Learning with Neural Networks	151
16.4 Experimental Application	151
16.5 Analysis of a Small-Scale Pin-Jointed CFRP Structure Analysis	153
16.6 Damage Identification	155
16.7 Conclusions	157
References	158
17 Modal Analyses and Meta-Models for Fatigue Assessment of Automotive Steel Wheels	160
17.1 Introduction	160
17.2 Stress-Stiffening Effect	161
17.3 Experimental Modal Analysis	162
17.4 Polynomial Chaos Expansion Model	163
17.5 Fatigue Tests	164
17.6 Conclusion	166
References	167
18 Towards the Development of a Digital Twin for Structural Dynamics Applications	169
18.1 Introduction	169
18.2 Overview of the Digital Twin	170
18.2.1 Experimental Data	170
18.2.2 Initial Modelling	171
18.3 The Problem of Model Updating in a Digital Twin	172
18.4 Data-Augmented Modelling	175
18.5 Hybrid Testing	176
18.6 Impact on Control	180
18.7 Decisions in a Digital Twin	181
18.8 Conclusions	182
References	182
19 An Improved Optimal Sensor Placement Strategy for Kalman-Based Multiple-Input Estimation	184
19.1 Introduction	184
19.2 Virtual Measurement Uncertainty and Bandwidth Prediction for Optimal Sensor Placement	185
19.3 Results	186
References	187
20 Towards Population-Based Structural Health Monitoring, Part IV: Heterogeneous Populations, Transfer and Mapping	189
20.1 Introduction	189
20.2 Population-Based Structural Health Monitoring and Transfer Learning	190
20.2.1 Population Types	190
20.2.2 Transfer Learning	192
20.2.3 Mapping Scenarios	192
20.2.4 Negative Transfer	194
20.3 Domain Adaptation	195
20.3.1 Homogeneous Populations	196
20.3.2 Heterogeneous Populations	198
20.4 Discussion and Conclusions	199
References	200
21 Feasibility Study of Using Low-Cost Measurement Devices for System Identification Using Bayesian Approaches	202
21.1 Introduction	202
21.2 Background	203
21.2.1 Bayesian Spectral Density Approach for System Identification (BSDA)	203
21.3 Experimental Setup	204
21.3.1 Structure Description	204
21.3.2 Structure Instrumentation and Tests Description	204
21.4 Results	205
21.4.1 Probabilistic SID in Low-Cost Devices	205
21.4.2 Marginal Distributions and Correlations	206
21.5 Conclusions	208
References	209
22 Kernelised Bayesian Transfer Learning for Population-Based Structural Health Monitoring	210
22.1 Introduction	210
22.2 Kernel-Based Transfer Learning	211
22.3 Shear Building Case Study	212
22.4 Conclusions	214
References	216
23 Predicting System Response at Unmeasured Locations Using a Laboratory Pre-Test	217
23.1 Motivation and Approach	217
23.2 MATV Hardware, Instrumentation and Testing	218
23.3 Predictions of Acoustic Test Truth Responses	221
23.4 Conclusions	221
References	221
24 Robust Estimation of Truncation-Induced Numerical Uncertainty	222
24.1 Introduction	222
24.2 The Truncation Error Actually Behaves According to the Modified Equation of the Numerical Method	224
24.3 Numerical Predictions Should Always be Accompanied by Their Bounds of Truncation-Induced Uncertainty	225
24.4 The Proposed Path-Forward Is to Render Solution Uncertainty Robust to the Commonly-Practiced Assumptions	226
24.4.1 A Description of how Truncation Error Behaves Can Be Obtained through Simple Linear Algebra	227
24.4.2 The Bounds of Truncation-Induced Uncertainty Can Be Made Robust to Assumptions Present in the Analysis	228
24.5 Conclusion	229
References	230
25 Fatigue Crack Growth Diagnosis and Prognosis for Damage-Adaptive Operation of MechanicalSystems	232
25.1 Extended Abstract	232
References	235
26 An Evolutionary Approach to Learning Neural Networks for Structural Health Monitoring	236
26.1 Introduction-SHM Motivation	236
26.2 Neural Networks (NN) in SHM	236
26.3 Neuroevolution of Augmenting Topologies	237
26.4 Topology Optimisation Algorithm	237
26.5 Neural Network Encoding	238
26.5.1 Population Initialisation	239
26.5.2 Genome Evaluation and Fitness Function	239
26.5.3 Tracking Innovation of Topology	239
26.5.4 Genetic Operators	239
26.5.5 Speciation	239
26.5.6 Reproduction	240
26.6 Experimental Validation	240
26.6.1 Task 1: Damage Detection	240
26.6.2 Task 2: Damage Classification	242
26.7 Concluding Remarks	244
References	244
27 Bayesian Solutions to State-Space Structural Identification	246
27.1 Introduction	246
27.2 Bayesian Inference Over State-Space Models	247
27.2.1 Markov Chain Monte Carlo	248
27.2.2 Sequential Monte Carlo	248
27.3 Results	249
27.4 Conclusions	251
References	252
28 Analyzing Propagation of Model Form Uncertainty for Different Suspension Strut Models	253
28.1 Introduction	253
28.2 System Description	254
28.2.1 Mathematical Model	255
28.2.2 Model Candidates	256
28.2.3 System Inputs, Outputs and Test Data	256
28.3 Analysing Propagation of Model form Uncertainty	257
28.3.1 Quantification of Model form Uncertainty	257
28.3.2 Definition of a Case Study	258
Case 1: Analytically Derived Initial Condition Model	258
Case 2: Measured Initial Conditions	258
28.3.3 Analysing the Results for Case 1 and Case 2	259
28.4 Conclusion	259
References	261
29 Determining Interdependencies and Causation of Vibration in Aero Engines Using Multiscale Cross-Correlation Analysis	262
29.1 Introduction	262
29.2 Multiscale Detrended Cross Correlation Analysis	263
29.3 Analysis	264
29.4 Model Building Using IODMD	266
29.5 Conclusion	268
References	268
30 Dynamic Data Driven Modeling of Aero Engine Response	270
30.1 Introduction	270
30.2 Dynamic Mode Decomposition	271
30.3 Input Output Dynamic Mode Decomposition	272
30.4 Aeroengine Vibration Modeling Using ioDMD	273
30.5 Conclusions	273
References	274
31 Nonlinear Model Updating Using Recursive and Batch Bayesian Methods	276
31.1 Introduction	276
31.2 Recursive and Batch Bayesian Model Updating	277
31.2.1 Non-adaptive UKF	277
31.2.2 Forgetting Factor Adaptive UKF	277
31.2.3 Batch Bayesian Method	278
31.3 Numerical Application to a 3-Story 3-Bay Frame Structure	278
31.3.1 Structure Description and Simulation	278
31.3.2 Updating Models with Modeling Errors	279
31.3.3 Model Updating Results	280
31.4 Conclusions	282
References	282
32 Towards Population-Based Structural Health Monitoring, Part I: Homogeneous Populations and Forms	284
32.1 Population-Based SHM	284
32.2 Homogeneous Populations and Forms	285
32.2.1 Strongly-Homogeneous Populations	285
32.2.2 The Population Form	286
Gaussian Process Regression as a Functional Representation of the Form	286
32.3 Case Study I: Strongly-Homogeneous Populations	287
32.3.1 Simulating Strongly-Homogeneous Members	288
The Frequency Response Function (FRF) for Damage Detection	288
Dataset Summary	289
32.3.2 Gaussian Process Regression of the FRF as the Population Form	290
Novelty Detection via the Form	290
32.3.3 Results	291
32.3.4 Discussion	291
32.4 Case Study 2: Beyond Strongly-Homogeneous – Extending the Form	294
32.4.1 Wind Turbine Population Data	294
Population Variance in the Power Curve Data	294
32.4.2 OMGP Regression of the Power Curve as the Population Form	295
32.4.3 Results	297
32.5 Concluding Remarks	297
References	298
33 A Detailed Assessment of Model Form Uncertainty in a Load-Carrying Truss Structure	300
33.1 Introduction	300
33.2 System Description and Mathematical Models	301
33.2.1 Inputs and Outputs	301
33.2.2 Beam Model of Upper Truss Structure	302
33.2.3 Rod Model of Upper Truss Structure	303
33.3 Detection and Quantification of Model Form Uncertainty	304
33.3.1 Detection of Model Form Uncertainty via Optimal Design of Experiments	305
33.3.2 Area Validation Metric	307
33.3.3 Frequentist Approach	307
33.3.4 Gaussian Process Based Quantification of Model Form Uncertainty	309
33.4 Conclusion	310
References	311
34 Recursive Nonlinear Identification of a Negative Stiffness Device for Seismic Protection of Structures with Geometric and Material Nonlinearities	312
34.1 Introduction	312
34.2 Adaptive Negative Stiffness Device	313
34.3 Modified Structure Model	314
34.4 Identification of a Frame Structure Equipped with an ANSD	315
34.5 Conclusion	318
References	319
35 Adequate Mathematical Beam-Column Model for Active Buckling Control in a Tetrahedron Truss Structure	320
35.1 Introduction	320
35.2 System Description	321
35.2.1 Single Beam-Column System	321
35.2.2 Piezo-Elastic Supports	322
35.2.3 Tetrahedron Truss Structure	323
35.3 Mathematical Model of Active Beam-Column	323
35.3.1 FE Model of Beam-Column System	324
35.3.2 Beam-Column Transfer Function	325
35.4 Lateral Dynamic Behavior of Tetrahedron Truss Structure	325
35.4.1 Experimental Beam-Column Transfer Functions	325
35.4.2 Comparison of Numerical and Experimental Dynamic Behavior	326
35.5 Conclusion	328
References	328
36 Site Characterization Through Hierarchical Bayesian Model Updating Using Dispersion and H/V Data	330
36.1 Introduction	330
36.2 Analysis	331
36.3 Experimental Data	331
References	332
37 Bayesian Inference Based Parameter Calibration of a Mechanical Load-Bearing Structure's Mathematical Model	333
37.1 Introduction	333
37.2 Load-Bearing Structure Under Investigation	334
37.2.1 Mathematical Model of the Load-Bearing Structure	335
37.2.2 Model Parameters	337
37.3 Model Parameter Calibration Procedure	338
37.3.1 Sensitivity Analysis	338
37.3.2 Bayesian Inference for Model Parameter Calibration	339
37.4 Comparison of the Non-calibrated and Calibrated Model Predictions	340
37.5 Conclusion	341
References	342
38 Uncertainty Propagation in a Hybrid Data-Driven and Physics-Based Submodeling Method for Refined Response Estimation	344
38.1 Introduction	344
38.2 Background	345
38.3 Analysis	346
38.4 Results and Discussion	350
38.5 Conclusion	353
References	353
39 Adaptive Process and Measurement Noise Identification for Recursive Bayesian Estimation	355
39.1 Introduction	355
39.2 Adaptive Estimation	355
39.3 Numerical Results	356
39.4 Conclusions	357
References	357
40 Effective Learning of Post-Seismic Building Damage with Sparse Observations	359
40.1 Introduction	359
40.2 Learning Model	360
40.2.1 Gaussian Process Regression (GPR)	360
40.2.2 Covariance Functions	360
40.3 Case Study	361
40.3.1 Building Models	361
40.3.2 Data	363
Building Attributes	363
Seismic Indices	363
Damage Labels	363
40.3.3 Prediction	364
Covariance Selection	364
Prediction Results	364
40.4 Conclusion	366
A.1 Appendix: List of all Used Features and Labels Along with Their Statistical Properties	366
References	367
41 Efficient Bayesian Inference of Miter Gates Using High-Fidelity Models	368
41.1 Introduction	368
41.2 Testbed Structure and Finite Element Modeling	369
41.2.1 Modeling Options for Gap Formation	370
41.3 Estimating Gap Length in Miter Gates Using Bayesian Inference	370
41.3.1 Batch Inference Using SMC	371
41.4 Three-Stage Approach	372
41.4.1 Stage 1: Same FE Model	372
41.4.2 Stage 2: Different FE Models	373
41.4.3 Stage 3: Real World Data	374
41.5 Conclusions and Further Work	374
References	374
42 Two-Stage Hierarchical Bayesian Framework for Finite Element Model Updating	376
42.1 Introduction	376
42.2 Methodology	377
42.3 Application	378
References	379
43 Bayesian Nonlinear Finite Element Model Updating of a Full-Scale Bridge-Column Using Sequential Monte Carlo	381
43.1 Introduction	381
43.2 Finite Element Model Updating Using Bayesian Inference	382
43.2.1 Sequential Monte Carlo	383
43.3 Full-Scale Reinforced-Concrete Bridge Column	384
43.3.1 Finite Element Model of the Column	385
43.3.2 FE Model Updating Setup	385
43.4 Results	387
43.5 Conclusions	389
References	389
44 Optimal Input Locations for Stiffness Parameter Identification	390
44.1 Introduction	390
44.2 Optimal Input Location Using the Fisher Information Matrix	391
44.3 Experimental Application	392
44.4 Conclusion	393
References	394
45 Modal Identification and Damage Detection of Railway Bridges Using Time-Varying Modes Identified from Train Induced Vibrations	395
45.1 Introduction	395
45.2 Modal Identification	396
45.3 Damage Detection	397
45.4 Experimental Application	397
45.5 Conclusion	399
References	401
46 Test-Analysis Modal Correlation of Rocket Engine Structures in Liquid Hydrogen – Phase II	402
Nomenclature	402
46.1 Introduction	403
46.2 Literature Survey	404
46.3 Cantilever Beam Tight Tip-Clearance Modal Test and Analysis	406
46.4 Sub-Scale Inducer Modal Test and Analysis in Air and Water	408
46.5 Sub-Scale Inducer Tight Tip-Clearance Modal Test and Analysis in Water	409
46.6 Sub-Scale Inducer Ping Test and Analysis in Lh2	409
46.7 Combined Results & Extrapolation of Techniques to SLS Full-Scale Inducer	417
46.8 Conclusions & Future Work	417
References	419
47 An Output-Only Bayesian Identification Approach for Nonlinear Structural and Mechanical Systems	420
47.1 Introduction	420
47.2 Bayesian Identification of Nonlinear Systems	421
47.3 Proposed Output-Only Bayesian Identification Approach	421
47.4 Experimental Validation	422
47.4.1 Structural Model	422
47.4.2 Identification Results	423
47.5 Conclusion	423
References	425

RkJQdWJsaXNoZXIy MTMzNzEzMQ==