Ambient Vibration Monitoring

Ambient Vibration Monitoring is the backbone of such structural assessment monitoring and control. It provides the possibility to gain useful data under ambient conditions for the assessment of structures and components.

Written by a widely respected authority in this area, Ambient Vibration Monitoring describes the current practice of ambient vibration methodologies illustrated by a number of practical examples.  Designed to aid the practical engineer with their understanding of the topic, it is the culmination of many years of practical research and includes numerous ‘real world’ examples.  It also provides information on applicable solutions.

This book will enable not only practitioners (in civil, mechanical and aerospace engineering), but also researchers and students, to learn more about the theory and practical applications of this subject.

PREFACE xi

ACKNOWLEDGEMENTS xiii

SUMMARY xv

1 INTRODUCTION 1

1.1 Scope of Applications 1

1.2 Laws and Regulations 2

1.3 Theories on the Development of the AVM 4

2 OBJECTIVES OF APPLICATIONS 7

2.1 System Identification 7

2.1.1 Eigenfrequencies and Mode Shapes 8

2.1.2 Damping 11

2.1.3 Deformations and Displacements 11

2.1.4 Vibration Intensity 12

2.1.5 Trend Cards 13

2.2 Stress Test 13

2.2.1 Determination of Static and Dynamic Stresses 14

2.2.2 Determination of the Vibration Elements 14

2.2.3 Stress of Individual Structural Members 15

2.2.4 Determination of Forces in Tendons and Cables 15

2.3 Assessment of Stresses 17

2.3.1 Structural Safety 17

2.3.2 Structural Member Safety 19

2.3.3 Maintenance Requirements and Intervals 19

2.3.4 Remaining Operational Lifetime 21

2.4 Load Observation (Determination of External Influences) 21

2.4.1 Load Collective 21

2.4.2 Stress Characteristic 21

2.4.3 Verification of Load Models 23

2.4.4 Determination of Environmental Influences 24

2.4.5 Determination of Specific Measures 24

2.4.6 Check on the Success of Rehabilitation Measures 25

2.4.7 Dynamic Effects on Cables and Tendons 25

2.4.8 Parametric Excitation 27

2.5 Monitoring of the Condition of Structures 28

2.5.1 Assessment of Individual Objects 29

2.5.2 Periodic Monitoring 31

2.5.3 BRIMOS_ Recorder 31

2.5.4 Permanent Monitoring 34

2.5.5 Subsequent Measures 35

2.6 Application of Ambient Vibration Testing to Structures for Railways 35

2.6.1 Sleepers 36

2.6.2 Noise and Vibration Problems 39

2.7 Limitations 49

2.7.1 Limits of Measuring Technology 49

2.7.2 Limits of Application 51

2.7.3 Limits of Analysis 52

2.7.4 Perspectives 53

References 54

3 FEEDBACK FROM MONITORING TO BRIDGE DESIGN 55

3.1 Economic Background 55

3.2 Lessons Learned 56

3.2.1 Conservative Design 56

3.2.2 External versus Internal Pre-stressing 57

3.2.3 Influence of Temperature 57

3.2.4 Displacement 61

3.2.5 Large Bridges versus Small Bridges 64

3.2.6 Vibration Intensities 66

3.2.7 Damping Values of New Composite Bridges 68

3.2.8 Value of Patterns 68

3.2.9 Understanding of Behaviour 72

3.2.10 Dynamic Factors 72

References 75

4 PRACTICAL MEASURING METHODS 77

4.1 Execution of Measuring 78

4.1.1 Test Planning 83

4.1.2 Levelling of the Sensors 83

4.1.3 Measuring the Structure 84

4.2 Dynamic Analysis 84

4.2.1 Calculation Models 84

4.2.2 State of the Art 88

4.3 Measuring System 89

4.3.1 BRIMOS_ 89

4.3.2 Sensors 90

4.3.3 Data-Logger 91

4.3.4 Additional Measuring Devices and Methods 92

4.4 Environmental Influence 93

4.5 Calibration and Reliability 96

4.6 Remaining Operational Lifetime 97

4.6.1 Rainflow Algorithm 98

4.6.2 Calculation of Stresses by FEM 101

4.6.3 S–N Approach and Damage Accumulation 104

4.6.4 Remaining Service Lifetime by Means of Existing Traffic Data and Additional Forward and Backward Extrapolation 105

4.6.5 Conclusions and Future Work 106

References 109

5 PRACTICAL EVALUATION METHODS 111

5.1 Plausibility of Raw Data 111

5.2 AVM Analysis 112

5.2.1 Recording 112

5.2.2 Data Reduction 114

5.2.3 Data Selection 115

5.2.4 Frequency Analysis, ANPSD (Averaged Normalized Power Spectral Density) 115

5.2.5 Mode Shapes 120

5.2.6 Damping 121

5.2.7 Deformations 123

5.2.8 Vibration Coefficients 125

5.2.9 Counting of Events 126

5.3 Stochastic Subspace Identification Method 129

5.3.1 The Stochastic Subspace Identification (SSI) Method 129

5.3.2 Application to Bridge Z24 130

5.4 Use of Modal Data in Structural Health Monitoring 134

5.4.1 Finite Element Model Updating Method 134

5.4.2 Application to Bridge Z24 141

5.4.3 Conclusions 147

5.5 External Tendons and Stay Cables 149

5.5.1 General Information 149

5.5.2 Theoretical Bases 150

5.5.3 Practical Implementation 150

5.5.4 State of the Art 151

5.5.5 Rain–Wind Induced Vibrations of Stay Cables 152

5.5.6 Assessment 152

5.6 Damage Identification and Localization 153

5.6.1 Motivation for SHM 154

5.6.2 Current Practice 155

5.6.3 Condition and Damage Indices 157

5.6.4 Basic Philosophy of SHM 159

5.7 Damage Prognosis 161

5.7.1 Sensing Developments 162

5.7.2 Data Interrogation Procedure for Damage Prognosis 162

5.7.3 Predictive Modelling of Damage Evolution 163

5.8 Animation and the Modal Assurance Criterion (MAC) 164

5.8.1 Representation of the Calculated Mode Shapes 164

5.8.2 General Requirements 164

5.8.3 Correlation of Measurement and Calculation (MAC) 164

5.8.4 Varying Number of Eigenvectors 165

5.8.5 Complex Eigenvector Measurement 165

5.8.6 Selection of Suitable Check Points using the MAC 166

5.9 Ambient Vibration Derivatives (AVD_) 168

5.9.1 Aerodynamic Derivatives 168

5.9.2 Applications of the AVM 168

5.9.3 Practical Implementation 169

References 170

6 THEORETICAL BASES 173

6.1 General Survey on the Dynamic Calculation Method 174

6.2 Short Description of Analytical Modal Analysis 176

6.3 Equation of Motion of Linear Structures 178

6.3.1 SDOF System 178

6.3.2 MDOF System 179

6.3.3 Influence of Damping 181

6.4 Dynamic Calculation Method for the AVM 181

6.5 Practical Evaluation of Measurements 181

6.5.1 Eigenfrequencies 181

6.5.2 Mode Shapes 183

6.5.3 Damping 185

6.6 Theory on Cable Force Determination 185

6.6.1 Frequencies of Cables as a Function of the Inherent Tensile Force 185

6.6.2 Influence of the Bending Stiffness 190

6.6.3 Influence of the Support Conditions 192

6.6.4 Comparison of the Defined Cases with Experimental Results 193

6.6.5 Measurement Data Adjustment for Exact Cable Force Determination 197

6.7 Transfer Functions Analysis 199

6.7.1 Mathematical Backgrounds 199

6.7.2 Transfer Functions in the Vibration Analysis 205

6.7.3 Applications (Examples) 214

6.8 Stochastic Subspace Identification 222

6.8.1 Stochastic State-Space Models 223

6.8.2 Stochastic System Identification 226

References 232

7 OUTLOOK 235

7.1 Decision Support Systems 236

7.2 Sensor Technology and Sensor Networks 236

7.2.1 State-of-the-Art Sensor Technology 236

7.3 Research Gaps and Opportunities 237

7.4 International Collaboration 239

7.4.1 Collaboration Framework 239

7.4.2 Activities 243

8 EXAMPLES FOR APPLICATION 245

8.1 Aitertal Bridge, Post-tensional T-beam (1956) 245

8.2 Donaustadt Bridge, Cable-Stayed Bridge in Steel (1996) 248

8.3 F9 Viaduct Donnergraben, Continuous Box Girder (1979) 250

8.4 Europa Bridge, Continuous Steel Box Girder (1961) 252

8.5 Gasthofalm Bridge, Composite Bridge (1979) 256

8.6 Kao Ping Hsi Bridge, Cable-Stayed Bridge (2000) 258

8.7 Inn Bridge Roppen, Concrete Bridge (1936) 260

8.8 Slope Bridge Saag, Bridge Rehabilitation (1998) 263

8.9 Flyover St Marx, Permanent Monitoring 265

8.10 Mur Bridge in St Michael, Bridge Rehabilitation 270

8.11 Rosen Bridge in Tulln, Concrete Cable-Stayed Bridge (1995) 272

8.12 VOEST Bridge, Steel Cable-Stayed Bridge (1966) 275

8.13 Taichung Bridge, Cable-Stayed Bridge 279

APPENDIX 283

Nomenclature 283

INDEX 289

Dr Helmut Wenzel, Managing Director

Dieter Pichler, both of VCE Holding GmbH, Vienna, Austria