分享鲁汶大学Bart Peeters的博士论文，是随机子空间算法的典范之作！                              下载链接：http://vibration.shef.ac.uk/doc/1211.pdf                                                                                                       

 

SYSTEM IDENTIFICATION AND

DAMAGE DETECTION IN CIVIL 

ENGINEERING

土木工程中的系统辨识和损伤检测

 

Jury: Prof. dr. ir. E. Aernoudt, voorzitter Prof. dr. ir. G. De Roeck, promotor Prof. dr. ir. A. Cunha (University of Porto) Prof. dr. ir. G. Degrande Prof. dr. ir. B. De Moor Prof. dr. ir. W. Heylen Dr. ir. H. Van der Auweraer (LMS International) Prof. dr. ir. G. Vermeir

Proefschrift voorgedragen tot het behalen van het doctoraat in de toegepaste wetenschappen   door   Bart PEETERS

 

UDC 534.32:624                   December 2000

 

ABSTRACT摘要

This thesis addresses two key issues of a real-life vibration-based structural health monitoring system. The first issue is the determination of an experimental model of a vibrating structure from output-only data. The use of freely available ambient excitation sources reduces significantly the cost of testing. Besides, there is no alternative in a continuous monitoring system. By applying advanced subspace methods to acceleration measurements, a high-quality experimental model can be identified. This is verified by many simulation, laboratory and real-life experiments.

对现实中基于振动的结构健康监测系统的两个关键问题进行研究。

1：仅从响应数据中确定振动结构的试验模型。无需付费、唾手可得的环境激励源极大地降低了测试费用。在连续监测系统中，除此之外，别无选择。针对加速度测量结果，利用先进的子空间方法，可辨识出高质量的试验模型。籍由大量仿真，实验室和真实试验所验证之。

 The second issue is the detection of damage under varying environmental conditions. The problem is that both damage and temperature are affecting the experimental model of a structure. A statistical system identification solution is developed to separate these influences. A thorough analysis of bridge vibration test data is presented. The tests were unique in that they combined long-term monitoring with the application of realistic damage scenarios. The conclusion is that damage can successfully be detected under varying environmental conditions.

2：不同环境条件下的损伤检测。损伤和温度二者都影响结构试验模型。提出了一种统计系统辨识解决方法来分离这些影响。全面分析了桥梁振动测试数据。本测试的独特之处在于：其既是长期监测的结果，并且施加了真实的损伤情形。结论是，在不同环境条件下可以成功检测损伤。

 

CONTENTS目录

 

VOORWOORD ...................................................... i

ABSTRACT ........................................................ iii

NOMENCLATURA ...................................................v

CONTENTS ........................................................ xi

1 INTRODUCTION ................................................1

  1.1 VIBRATION-BASED HEALTH MONITORING .....................2

  1.2 FOCUS OF THE THESIS ........................................5

  1.3 ORGANIZATION OF THE TEXT .................................7

2 MODELS OF VIBRATING STRUCTURES ..........................11

  2.1 INTRODUCTION .............................................12

  2.2 FINITE ELEMENT MODELS ...................................12

       2.2.1 The undamped eigenvalue problem .........................13

       2.2.2 Proportional damping ...................................14

       2.2.3 General viscous damping .................................16

  2.3 CONTINUOUS-TIME STATE-SPACE MODELS ....................19

       2.3.1 A state-space model of a vibrating structure ..................19

       2.3.2 Modal parameters and model reduction ......................21

       2.3.3 The special case of proportional damping ....................25

  2.4 DISCRETE-TIME STATE-SPACE MODELS .......................27

       2.4.1 About sampling ........................................27

       2.4.2 Modal parameters and model reduction ......................28

       2.4.3 Impulse responses ......................................29

  2.5 STOCHASTIC STATE-SPACE MODELS ..........................32

       2.5.1 The stochastic components ...............................32

       2.5.2 Properties of stochastic systems ............................33

       2.5.3 The forward innovation model .............................34

  2.6 ARMA MODELS .............................................36

       2.6.1 Obtaining the ARMA model ..............................36

       2.6.2 Modal parameters of an ARMA model ......................37

  2.7 CONTINUOUS-TIME FREQUENCY-DOMAIN MODELS ............40

       2.7.1 The Laplace transform ...................................40

       2.7.2 The transfer function ....................................41

       2.7.3 The spectrum ..........................................42

  2.8 DISCRETE-TIME FREQUENCY-DOMAIN MODELS ...............44

       2.8.1 The z-transform ........................................44

       2.8.2 The spectrum of a stochastic state-space model ...............45

       2.8.3 The spectrum of a forward innovation model .................46

  2.9 CONCLUSIONS ..............................................48

3 STOCHASTIC SYSTEM IDENTIFICATION ........................49

  3.1 INTRODUCTION .............................................50

  3.2 DATA TYPES ................................................50

        3.2.1 Time data .............................................50

       3.2.2 Covariance estimates ....................................52

       3.2.3 Spectrum estimates .....................................53

  3.3 FREQUENCY-DOMAIN SPECTRUM-DRIVEN METHODS ..........57

       3.3.1 Peak picking (PP) ......................................57

       3.3.2 Complex mode indication function (CMIF) ..................62

       3.3.3 Other spectrum-driven methods ...........................65

  3.4 TIME-DOMAIN COVARIANCE-DRIVEN METHODS ...............66

       3.4.1 The instrumental variable (IV) method ......................66

       3.4.2 Covariance-driven stochastic subspace identification (SSI-COV) . 73

       3.4.3 Other covariance-driven methods ..........................79

  3.5 TIME-DOMAIN DATA-DRIVEN METHODS ......................80

       3.5.1 Data-driven stochastic subspace identification (SSI-DATA) .....80

       3.5.2 Other data-driven methods ...............................89

  3.6 COVARIANCE-DRIVEN VS. DATA-DRIVEN SUBSPACE ...........90

  3.7 POSTPROCESSING ...........................................91

       3.7.1 Spectrum analysis ......................................91

       3.7.2 Modal response and prediction errors .......................94

  3.8 EXPERIMENTAL COMPARISON OF SYSTEM IDENTIFICATION

METHODS ..................................................96

  3.9 CONCLUSIONS .............................................103

4 IMPLEMENTATION ...........................................105

  4.1 MACEC, A GRAPHICAL USER INTERFACE FOR OUTPUT-ONLY MODAL

ANALYSIS .................................................106

       4.1.1 Introduction ..........................................106

       4.1.2 Development of MACEC ...............................107

       4.1.3 Functions of MACEC ..................................108

  4.2 AUTOMATIC MODAL ANALYSIS .............................114

  4.3 CONCLUSIONS .............................................115

5 APPLICATIONS ...............................................117

  5.1 REINFORCED CONCRETE BEAMS ............................118

       5.1.1 Introduction ..........................................118

       5.1.2 Data acquisition .......................................118

       5.1.3 System identification ...................................123

       5.1.4 Evolution of the modal parameters ........................129

  5.2 STEEL MAST ...............................................135

       5.2.1 Introduction ..........................................135

       5.2.2 Data acquisition .......................................136

       5.2.3 System identification ...................................138

  5.3 CONCLUSIONS .............................................144

6 ENVIRONMENTAL MODELS OF VIBRATING STRUCTURES ......145

  6.1 INTRODUCTION ............................................146

       6.1.1 Motivation ...........................................146

       6.1.2 A system identification approach ..........................147

  6.2 IDENTIFYING THE MODEL ..................................149

       6.2.1 ARX models ..........................................149

       6.2.2 ARX models and least squares (LS) .......................151

       6.2.3 Quality assessment .....................................153

  6.3 USING THE MODEL FOR SIMULATIONS .......................154

       6.3.1 The simulation error and its statistical properties .............154

       6.3.2 The ARX case ........................................157

  6.4 SYNTHESIS ................................................159

  6.5 CONCLUSIONS .............................................161

7 THE Z24-BRIDGE ..............................................163

  7.1 INTRODUCTION ............................................164

  7.2 EXCITATION SOURCES ......................................166

       7.2.1 Introduction ..........................................166

       7.2.2 Excitation sources applied to the Z24-Bridge ................166

       7.2.3 System identification results .............................169

       7.2.4 Conclusions ..........................................173

  7.3 PROGRESSIVE DAMAGE TESTS ..............................175

       7.3.1 The scenarios .........................................175

       7.3.2 Evolution of the modal parameters ........................178

  7.4 CONTINUOUS MONITORING AND DAMAGE DETECTION .......182

       7.4.1 The monitoring system .................................182

       7.4.2 System identification ...................................184

       7.4.3 Damage detection .....................................190

       7.4.4 Conclusions and recommendations ........................195

  7.5 CONCLUSIONS .............................................196

8 CONCLUSIONS AND FUTURE RESEARCH .......................197

  8.1 CONCLUSIONS .............................................197

  8.2 FUTURE RESEARCH ........................................198

A FREQUENCY-DOMAIN MODAL MODELS .......................201

A.1TRANSFER FUNCTIONS .....................................201

       A.1.1 From forces to displacements ............................201

       A.1.2 From forces to accelerations .............................202

A.2 SPECTRA ..................................................203

       A.2.1 The displacement spectrum ..............................203

       A.2.2 The acceleration spectrum ...............................205

B STATE-SPACE MODEL OF THE SIMULATION EXAMPLE .........207

C DEFERRED Z24-BRIDGE RESULTS .............................209

  C.1 EVOLUTION OF THE DAMPING RATIOS .......................209

  C.2 ENVIRONMENTAL MODEL OF THE Z24-BRIDGE ...............209

REFERENCES .....................................................213

NEDERLANDSE SAMENVATTING ..................................225

CURRICULUM VITAE .............................................235