Topics in Modal Analysis & Testing, Volume 8

Preface	6
Contents	7
1 Modal Analysis on a Wind Turbine Blade Based on Wind Tunnel Experiments	10
1.1 Introduction	10
1.2 Modal Analysis and Operational Calculus	11
1.3 Output Only Modal Parameters Estimation	12
1.4 Wind Turbine Blade	12
1.5 Wind Tunnel Experiment	14
1.6 Application of the Time Domain Identification Scheme	15
1.7 Conclusion	16
References	16
2 An Investigation of Vibrational Characteristics of Lap Joints Using Experimental and AnalyticalMethods	17
2.1 Introduction	17
2.2 Experimental Methods	18
2.3 Analytical Methods	19
2.3.1 Solid Structure FE Model	20
2.3.2 Welded Structure FE Model	20
2.3.3 Bolted Structure FE Model	20
2.3.4 Fractional Strain Energy Method	21
2.4 User Interface Development	22
2.5 Results and Discussion	24
2.5.1 Experimental Modal Comparisons	25
2.5.2 FE Model Comparisons	27
2.5.3 Strain-Energy Method Comparisons	29
2.6 Conclusions	31
References	32
3 Using Strain Gages as References to Calculate Free-Free Frequency Response Functions	33
3.1 Introduction	33
3.1.1 Calculation of Free-Free FRFs Using Interface Forces as References	33
3.1.2 Numerical Example	35
3.2 Summary	38
References	38
4 A Principle for Obtaining Pragmatic Uncertainty Bounds on Modal Parameters	39
4.1 Introduction	39
4.2 Theory	40
4.2.1 Multiple-Reference Ibrahim Time Domain (MITD) Method	40
4.2.2 Modified Multiple-Reference Ibrahim Time Domain (MMITD) Method	41
4.2.3 Low Order Versus High Order Method	42
4.2.4 Normalization to the Lowest or Highest Coefficient of the Matrix Polynomials	42
4.2.5 Calculating the System Matrix with Respect to Either the Original Hankel Matrix or the Time Shifted Hankel Matrix	43
4.3 Methodology	43
4.4 Results and Discussion	44
4.5 Conclusions	46
References	46
5 On Partitioning of an SHM Problem and Parallels with Transfer Learning	48
5.1 Introduction	48
5.2 Problem Description	49
5.3 Problem Splitting	51
5.4 Knowledge Transfer Between the Two Problems	52
5.5 Discussion and Conclusions	56
References	57
6 An Ontological Approach to Structural Health Monitoring	58
6.1 Introduction	58
6.2 Components of the Ontology	59
6.3 Main Ontology Structure	60
6.4 Connections	62
6.5 Aspects of the Ontology	63
6.6 Discussion and Conclusions	65
References	66
7 Passive Aeroelastic Tailored Wing Modal Test Using the Fixed Base Correction Method	67
Nomenclature	67
7.1 Introduction	68
7.2 Theory/Correction Methodology	69
7.3 Test Description	71
7.3.1 Test Article	71
7.3.2 Finite Element Model	72
7.3.3 Modal Test Setup	73
7.3.4 Modal Test Instrumentation	74
7.3.5 Modal Test Accelerometer Layout	74
7.3.6 Modal Test Shaker Layout	75
7.4 Results	80
7.4.1 Uncorrected Results	80
7.4.2 Fixed Base Corrected Results with 10 Shakers	81
7.4.3 Fixed Base Corrected Results with 12 Shakers	82
7.5 Fixed Base Corrected Results with 14 Shakers	83
7.6 Summary	88
References	88
8 Nonlinear Normal Mode Estimation with Near-Resonant Steady State Inputs	90
8.1 Overview of the Basic SNRM Algorithm	90
8.2 Nonlinear Resonant Steady State Response Analysis	91
8.3 Discussion on the SNRM Algorithm Extension	92
8.4 Conclusion and Future Work	93
References	93
9 Automatic Modal Parameter Identification with Methods of Artificial Intelligence	94
Nomenclature	94
9.1 Introduction	95
9.2 Background	95
9.3 Peak Descriptor	96
9.4 Generation of Training Data	97
9.5 Classification	98
9.6 Measurement Setup	98
9.7 Conclusion	100
References	101
10 A Single Step Modal Parameter Estimation Algorithm: Computing Residues from Numerator Matrix Coefficients of Rational Fractions	102
10.1 Introduction	102
10.2 Theoretical Background	103
10.3 Analysis	107
10.4 Conclusions	110
References	111
11 Improved Expansion Results Using Regularized Solutions	112
11.1 Introduction	112
11.2 Theory	113
11.2.1 SEREP Expansion	113
11.2.2 Theory of Regularization in Direct Pseudo-Inverse Solutions	114
11.3 Models Used for Demonstrating Expansion Effects	115
11.3.1 Simple Model: Tuning Fork	115
11.3.2 Complicated Model: Coupled Components	116
11.4 Demonstration of the Effects of Gauge Location on Expansion Results	117
11.4.1 Case 1: Using Evenly Spaced Gauges to Expand the Response of Ten Modes	117
11.4.2 Case 2: Using Ten Gauges Placed with Effective Independence or Condition Number Optimization to Expand the Response of Ten Modes	118
11.4.3 Case 3: Using Forty Gauges on the Base Beam to Expand the Response of Ten Modes to the Top Beam	120
11.5 Demonstration of the Effects of Noise on Expansion Results	122
11.5.1 Model Configuration (Active Degrees of Freedom)	122
11.5.2 Noise Demonstration Test Matrix	123
11.5.3 Noise Contaminated Expansion Results	124
Mode Shape Expansion	124
Time Domain Expansion	125
11.6 Using Regularization to Improve Expansion Results	129
11.6.1 Mode Shape Expansion Improvement	129
11.6.2 Time Domain Expansion Improvement	131
11.6.3 Additional Considerations	132
11.7 Conclusions	134
References	135
12 Expansion of Coupled Structural-Acoustic Systems	136
12.1 Motivation and Theory	136
12.2 Modal Expansion of a Coupled Structure	137
12.3 Coupled Expansion of a Transient Response	141
12.4 Discussion and Conclusions	145
References	145
13 Expansion Methods Applied to Internal Acoustic Problems	146
13.1 Introduction	146
13.2 Theory	147
13.3 SEREP Expansion for Acoustic DOF in a Small Domain Model	148
13.4 Transmissibility Expansion for Acoustic DOF in a Large Domain Model	151
13.5 Discussion and Conclusions	154
References	154
14 Scaling an OMA Modal Model of a Wood Building Using OMAH and a Small Shaker	155
14.1 Introduction	155
14.2 OMAH Theory	156
14.3 Structure and Instrumentation	156
14.4 Parameter Extraction by OMA	158
14.5 Mode Shape Scaling by OMAH	159
14.6 Verification of OMAH Result	160
14.7 Conclusion	160
References	161
15 Quantitative Study on the Modal Parameters Estimated Using the PLSCF and the MITD Methods and an Automated Modal Analysis Algorithm	162
15.1 Introduction	162
15.2 Theory	163
15.2.1 The Poly-reference Least Squares Complex Frequency (LSCF) Algorithm	164
15.2.2 The Multi-reference Ibrahim Time Domain (MITD) Algorithm	165
15.3 Methodology	165
15.4 Results	166
15.5 Discussion	168
15.6 Conclusions	170
References	170
16 Empirical Models for the Health Monitoring of High-Rise Buildings: The Case of Palazzo Lombardia	172
16.1 Introduction	172
16.2 Background	173
16.3 Empirical Model	174
16.4 The Prediction of the Eigenfrequency Values	177
16.5 Conclusion	177
References	178
17 Towards Population-Based Structural Health Monitoring, Part II: Heterogeneous Populations and Structures as Graphs	179
17.1 Introduction	179
17.2 Irreducible Element Representations of Structures	180
17.2.1 Geometry	181
17.2.2 Topology	183
Joints	183
17.2.3 Materials	183
17.3 Producing an Attributed Graph	185
17.4 A Note on Boundary Conditions	187
17.5 Some Formal Definitions for PBSHM	188
17.6 Conclusions	188
References	189
18 Developing a Correlation Criterion (SpaceMAC) for Repeated and Pseudo-repeated Modes	190
18.1 Introduction	190
18.2 Background	191
18.2.1 Repeated Roots	191
18.2.2 Modal Vectors as Vector Spaces and Subspaces	191
18.2.3 Modal Vectors as Vector Spaces and Subspaces	192
18.2.4 Existing Correlation Methods	192
18.2.5 Extracting and Conditioning Modal Vector	193
18.3 Analysis	194
18.3.1 Implementing Existing Methods	194
18.3.2 SPACEMAC Implementation	195
18.3.3 Results	196
18.4 Conclusion	199
References	201
19 Subsecond Model Updating for High-Rate Structural Health Monitoring	202
19.1 Introduction	202
19.2 Background	203
19.3 Analysis	205
19.4 Conclusion	207
References	207
20 Phase Quadrature Backbone Curve for Nonlinear Modal Analysis of Nonconservative Systems	208
20.1 Introduction	208
20.2 Phase Quadrature Backbone Curve	208
20.3 Numerical Results	209
20.4 Conclusion	210
References	210
21 Preliminary Results of Vibration Measurements on a Wind Turbine Test Bench	211
21.1 Introduction	211
21.2 Pretest	212
21.2.1 Conclusion from Pretest	213
21.3 Experimental Measurements	213
21.3.1 Experimental Setup	214
21.3.2 Data Processing and Analysis	215
Operational Measurements	215
Impact Tests	216
21.3.3 Results and Discussion	216
Hammer Comparison from Impact Test	216
Sensor Comparison from Impact Test	216
Operational Measurements	218
Comparing Impact Test to Operational Measurements	218
21.4 Conclusion	219
References	220
22 Feasibility for Damage Identification in Offshore Wind Jacket Structures Through Numerical Modelling of Global Dynamics	221
22.1 Introduction	221
22.2 Background	222
22.3 Analysis	223
22.4 Results	223
22.5 Conclusion	225
References	225
23 Use of Operational Modal Analysis to Identify Systems with Oscillatory Masses	227
23.1 Introduction	227
23.2 Theoretical Background	228
23.2.1 Operational Modal Analysis	228
23.2.2 Tuned Liquid Damper	229
23.3 Experimental Model	229
23.4 Results	231
23.4.1 Identification of Modal Properties	232
23.4.2 Estimation of Sloshing Frequency and Damping Ratio	234
23.5 Conclusion	235
References	236
24 OMA-Based Modal Identification and Response Estimation of a Monopile Model Subjectedto Wave Load	237
24.1 Introduction	237
24.2 Theory	238
24.2.1 Operational Modal Analysis	238
24.2.2 Wave Simulation and System Response	239
24.3 Experimental Setup	240
24.4 Numerical Analysis	240
24.4.1 Finite Element Model	241
24.4.2 Loads and System Response	241
24.5 Modal Identification and FE Model Updating	241
24.6 Response Simulation Results	243
24.7 Conclusion	244
References	245
25 A Concept for the Estimation of Displacement Fields in Flexible Wind Turbine Structures	246
25.1 Introduction	246
25.2 System Analysis	247
25.3 Basic Framework	247
25.4 State Estimation	248
25.5 Sensor Concept	249
25.6 Application to a Flexible Multibody System	249
25.6.1 Load Case	250
25.6.2 Results	250
25.7 Conclusion and Outlook	252
References	252
26 Towards Population-Based Structural Health Monitoring, Part III: Graphs, Networksand Communities	254
26.1 Introduction	254
26.2 Matching Using the Attributed Graphs	255
26.2.1 Introduction to Graph-Matching Algorithms	256
Definition	256
Isomorphism	256
Subgraphs	257
The Modular Product Graph	257
26.2.2 Bron-Kerbosch Algorithm	258
26.2.3 C-Clique-Finding Algorithm	259
C-Edges	259
26.3 Similarity Scores	260
26.4 Communities	263
26.5 Conclusion	264
Appendix	264
References	266
27 Utilization of Experimental Data in Elastic Multibody Simulation: Case Study on the Ampair 600 Turbine Blade	267
27.1 Introduction	267
27.2 Theoretical Background	268
27.3 Wind Turbine Blade Case Study	270
27.3.1 Test Setup	271
27.3.2 Mass Properties	272
27.3.3 Multibody Model Build-Up	273
27.4 Conclusion and Outlook	274
References	275
28 On the Use of PVDF Sensors for Experimental Modal Analysis	277
28.1 Introduction	277
28.2 Piezoelectric Polyvinylidene Fluoride (PVDF) Sensor	277
28.3 Measurement Setup	278
28.3.1 Results	278
References	279
29 Predicting Tool Wear Using Linear Response Surface Methodology and Gaussian Process Regression	280
29.1 Introduction	280
29.2 Experimental Set-Up	281
29.3 Results	282
29.4 Conclusions	283
References	283
30 Computer Aided Measurement Uncertainty Calculation by Modern DAQs for Raw Acceleration and Force Data in Modal Analysis	284
30.1 Consideration of Measurement Deviations in the Overall Result	285
30.2 Model for a Measurement Uncertainty Budget for Vibration Transducers	285
30.3 Calculation of the Expanded Uncertainty, Urel (a), for the Acceleration Amplitude of an Accelerometer at a Single Frequency Point	287
30.4 Determination of the Measurement Uncertainty	288
30.5 Calculation of the Expanded Uncertainty, Urel (x), for the Acceleration Phase Shift of an Accelerometer at a Single Frequency Point	289
30.6 Example of an Automatic KiXact Measurement Uncertainty Calculation with the KiDAQ Data Acquisition System	290
30.6.1 Introduction To KiDAQ	290
30.6.2 Introduction To KiXact	290
30.7 Summary	292
References	292
31 Towards Population-Based Structural Health Monitoring, Part VII: EOV Fields – EnvironmentalMapping	293
31.1 Introduction	293
31.1.1 Lillgrund Wind Farm	295
31.2 Environmental Mapping	296
31.2.1 Motivation	296
31.2.2 Wake Pattern in Wind Farms	296
31.2.3 Data-Based Model	297
31.3 Wind Speed Predictions	297
31.4 Conclusions	299
References	299
32 Investigation of Resistive Forces in Variable Recruitment Fluidic Artificial Muscle Bundles	301
32.1 Introduction	301
32.2 Effect of Inactive Elements in a Variable Recruitment Bundle	302
32.3 Resistive Force Past Free Strain	303
32.4 Experimental Observation of Resistive Forces with Varying Pressure	304
32.5 Implications on Overall Performance of a Variable Recruitment Bundle	306
32.6 Conclusion	308
References	309
33 Numerical and Experimental Study on the Modal Characteristics of a Rotor Test Rig	310
33.1 Introduction	310
33.2 Experimental Setup	311
33.2.1 Mechanical Structure	311
33.2.2 Data Acquisition	311
33.2.3 Experimental Modal Analysis Software	312
33.2.4 Measurement Repeatability	313
33.3 Experimental Modal Analysis	313
33.3.1 Excitation Variation	313
33.3.2 Experimental Modal Analysis Results	314
33.4 Correlation with Numerical Model	315
33.4.1 Numerical model	315
33.4.2 Experimental and Numerical Model Comparison	315
33.5 Conclusion	316
References	316
34 A Comparison of Different Boundary Condition Correction Methods	317
Nomenclature	317
34.1 Introduction	317
34.2 Demonstration Test Article	318
34.3 Summary of Test and Free-Free Modes	318
34.4 Method 1: Fixed Base Correction Method	321
34.5 Method 2: Constraint Shape Applied Directly to Mode Shapes	323
34.6 Method 3: Hybrid Approach	325
34.7 Summary	327
References	329
35 Deflection Shape Balancing: An Alternative to Modal Balancing	330
35.1 Introduction	330
35.2 Background	330
35.3 Analysis	331
35.3.1 5 Weight Planes	331
35.3.2 10 Weight Planes	333
35.3.3 15 Weight Planes	333
35.3.4 20 Weight Planes	333
35.3.5 28 Weight Planes	338
35.3.6 Impact of the Number of Weight Planes	338
35.4 Conclusion	341
36 Real-Time Theoretical and Experimental Dynamic Mode Shapes for Structural Analysis Using Augmented Reality	344
36.1 Introduction	344
36.2 Experiment	345
36.2.1 Specimen	345
36.2.2 Theoretical Analysis	345
36.2.3 Experimental Analysis	346
36.3 Software Application Framework	347
36.4 Results	347
36.5 Ongoing Work	348
36.6 Conclusion	349
References	349
37 A Bottom-Up Approach to FE Model Updating of Industrial Structures	350
37.1 Project Motivation and Scope	350
37.2 Theoretical Background	351
37.3 Measurement of the Test Model	353
37.3.1 Test I	354
37.3.2 Test II	354
37.3.3 Test III	355
37.4 FE Modeling and Updating	356
37.4.1 Model I	356
37.4.2 Model II	361
37.4.3 Model III	366
37.5 Conclusions and Further Work	368
References	370
38 Shaft Bending to Zero Nodal Diameter Disc Coupling Effects in Rotating Structures Due to Asymmetric Bearing Supports	371
38.1 Introduction	371
38.2 Model Description	372
38.3 Numerical Results	372
38.4 Conclusions	374
References	374
39 Dynamic Characterization of a Pop-Up Folding Flat Explorer Robot (PUFFER) for PlanetaryExploration	375
39.1 Introduction	375
39.2 Background	376
39.3 Initial Puffer Finite Element Model	377
39.4 Modal Test Process Validation	379
39.5 Test Procedure	380
39.6 Test Results	381
39.7 Updated Puffer Finite Element Model	382
References	383
40 A Framework for the Design of Rotating Multiple Tuned Mass Damper	384
40.1 Introduction	384
40.2 Optimization of a Multiple Tuned Mass Damper Adapted to Rotating Frame	385
40.3 Conclusion	387
References	387
41 Operational Modal Analysis of Wind Turbine Drivetrain with Focus on Damping Extraction	389
41.1 Introduction	389
41.2 Methodology and Theoretical Background	390
41.2.1 Reduction of the Influence of Harmonic Content	390
41.2.2 Modal Parameter Estimation	391
PolyMax (p-LSCF)	391
PolyMax Plus	391
Stochastic Subspace Identification	392
41.3 Simulations	392
41.3.1 Comparison Between the Different Modal Parameter Estimators	392
41.3.2 Comparison Between the Different Lifter Types	393
41.4 Wind Turbine Application	394
41.5 Conclusions	395
References	395
42 Investigation of Viscous and Friction Damping Mechanisms in a Cantilever Beam and Hanger System	396
42.1 Introduction	396
42.2 Background	397
42.3 Procedure	398
42.4 Results	399
42.5 Analysis	401
42.6 Conclusion and Future Work	402
Reference	402
43 Detecting Nonsynchronous Heart Cells from Video – An Unsupervised Machine Learning Approach	403
43.1 Background	403
43.2 Motivation	404
43.3 Methodology	404
43.3.1 Video/Data Collection	404
43.3.2 Signal Processing	406
Non-negative Matrix Factorization	406
Sparse and Low-Rank Matrix Decompositions	406
43.4 Results	406
43.4.1 Non-negative Matrix Factorization on Videos	407
43.4.2 Sparse and Low-Rank Matrix Decompositions on Videos	408
43.4.3 Non-negative Matrix Factorization on Low-Rank Components	408
43.4.4 Mutual Information	409
43.5 Conclusion	412
References	412

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