Research on Experimental Tools for Infrastructure Health Monitoring

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1 SAMCO SUMMER WORKSHOP September 6-9, 2005 Research on Experimental Tools for Infrastructure Health Monitoring Emin Aktan, K. Grimmelsman, K. Ciloglu,, Q. Pan, J. Prader Drexel University, Philadelphia, PA, USA

2 Contents Motivations Field: The Seymour Bridge Study Theory/Lab: Cantilever beam and physical phenomenological model with uncertainty Field: Ambient vibration testing of the Henry Hudson and Brooklyn Bridges Summary of lessons learned

3 The Engineer of 2020: Visions of Engineering in the New Century, National Academy of Engineering The engineer of 2020 will need to be conversant with and embrace a whole realm of new technologies, but some old problems are not going to go away. They will demand new attention and, perhaps, new technologies. In some cases their continuing neglect will move them from problems to crises. Physical Infrastructures in Urban Settings: without a sufficient focus on environmental impact and sustainability victims of pollution, traffic and transportation infrastructure concerns, decreasing greenery, poor biodiversity, and disparate educational services. infrastructures are in serious decline, aging water treatment, waste disposal, transportation, and energy facilities are among the top concerns for public officials and citizens alike.

4 Challenges and Opportunities for Civil Engineers Challenges: Civil (and Environmental) Engineering is slipping in its image, worth and societal standing Civil engineers have not been very successful as stewards of infrastructures and constructed systems for safe, effective, sustainable operation, preservation, protection, maintenance, repair, retrofit and replacement Civil engineers should transform systems engineering and associated tools to more effectively address large infrastructure systems problems. We need to re-learn civil engineering by scientific observation, identification, simulation and control of actual operating infrastructure systems by developing and using the proper tools! Opportunity: Properly educated/trained Civil and Environmental Engineers remain essential for leading and coordinating the multi-disciplinary teams and integrating technology and knowledge essential for effective engineering and management of large infrastructure systems.

5 The Health Monitoring Paradigm for Large Infrastructure Systems Health Monitoring: Define and track health by data and analytical simulation so current and expected performance can be described in a proactive manner Health Monitoring paradigm offers great advantages: Objective characterization of health Proactive management of maintenance Enabler of performance-based engineering, intelligent infrastructures and asset management paradigms Reality of lifecycle of constructed infrastructures Requires integrating a spectrum of experimental, analytical, and information technologies System Identification approach offers rational framework for optimum integration of these technologies

6 Classification of Experimental Tools Local NDE Geometry Measure- ment Short-Term (Hours) Structural Testing Load Testing (Static or Quasi-Static Testing) Vibration Analysis (Dynamic Testing) Material Testing Thermal Magnetic Ultrasonic Acoustic Electrical Forced- Vibration by Exciter Electro- Chem Optical Nuclear Surveying GPS Laser Remote Sensing Photo Methods Controlled Measure Input & Outputs Static Trucks Crawling Trucks Special Loading Devices Uncontrolled Measure Outputs Only Input by Traffic Measure Input by WIM & Outputs Input by Traffic Controlled Measure Input & Outputs Impact Uncontrolled Measure Outputs Only Input by Traffic, Wind, Seismic

7 Classification of Experimental Tools Long-Term Monitoring (Months Decades) Low-Bandwidth Measurements Construction Effects Wind/Ambient Weather Conditions Temperature Movements or Displacements Mechanical Variables (Force, Stress, Strain, etc) Deterioration/Damage Effects Changes in: Geometry, Electro-chemical chemical Properties High-Bandwidth Measurements Vibrations Traffic Loads Operations Incidents or Accidents Impacts Earthquake Security Monitoring

13 Parameter Estimation for MIMO Modal Analysis of Large Structures F. Necati Catbas 1 ; David L. Brown 2 ; and A. Emin Aktan 3 Abstract: EMA Writers were challenged in their attempts to measure the dynamic properties of an aged bridge by EMA due to inconsistencies within the data set due to short-term variations in ambient conditions. A complex interaction was observed between the dynamic properties of the bridge, hour-to-hour temp changes, and controlled damages applied to the bridge. Inconsistencies in the data set made curve fitting difficult for some common parameter estimation algorithms that have been designed to handle consistent data sets. Although the quality of measurements within the entire data set was affected by time variance and nonlinearity, increasing the number of reference measurements significantly improved the reliability of the information which could be extracted. In conjunction with the MIMO technique, a parameter estimation method using CMIF was developed and implemented in this study to determine the modal properties with proper scaling to obtain modal flexibility. This method proved to be successful with the data acquired from the aged and deteriorated highway bridge. Journal of Engineering Mechanics, Vol. 130, No. 8, August 1, 2004.

14 10-6 Complex Mode Indicator Function (CMIF) 10-7 Log Mag Modal Filtering frequency, (Hz) 10-6 Enhanced Frequency Response Function (efrf) Enhanced Mode 10-7 Log Mag frequency, (Hz) CMIF and efrf Plots for Modal Analysis

15 1 kip/point Deflection, (in)x kip = 4.45 kn 1 inch = 2.54 cm 1 mode 5 modes 9 modes 10 modes 12 modes 13 modes Convergence of Girder Deflection by Including Mass-Normal Modes to Modal Flexibility

16 Flexibility Coefficients of Girder 3 Output point (sensor location) Input point (impact hammer) Driving point (input and output) Unit Load Vector on Girder Flexibility Coefficients for Inner Girders Measurement Points [Flexibility]= Coefficients Corresponding to Unmeasured Degrees of Freedom Bridge Girder Condition Indicator for Girder 3 [Defl.] = 0 0 =.... [F] 0 Zero Load On Other Girders Zero Deflection On Other Girders Reduced Flexibility Matrix from Abbreviated -MIMO Tests

17 Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz, Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz Frequency and Mode Shape Comparison for Seymour Bridge Tests: (a) Inner Girders only; (b) All 6 Girders

18 kips 30 kips N Girder Dynamic Test 2 Inner Girder Dynamic Test Truck Load Instrumentation Reading Deflection, in. 1 kip = 4.45 kn 1 inch = 2.54 cm Correlation of High and Low Spatial Resolution Modal Tests with Truck Load Test

19 1 kip/point Welding and Restoration of BCs ~10% ~50% ~65% After 1/2 Flange After 2/2 Flange After Web Cut After X-Brace Cut /4 Welding/Restoration of BC's 10/14 After 1/2 Flange Cut at Girder 4 at South Span 10/21 After 2/2 Flange Cut at Girder 4 at South Span 10/29 After Web Cut at Girder 4 at South Span 10/30 After X-Brace Cut at South Span ~10% ~50% ~65% Deflection (in) UNIT LOAD PATTERN M 1 kip/point Removed Bearing Flange/Web Cut Location (2" to the South of Point 4M) X-Bracing Cut Location Girder 4 N Damage Location 1 kip = 4.45 kn 1 inch = 2.54 cm Sensitivity of Bridge Girder Condition Indicator to Damage

20 1 kip/point Test Set 1 11% change at damage location Test Set Test Set 2 10% change at damage location Test Set 1 Deflection (in) 9/30 Before Flange Cut Damage (1) 10/4 Before Flange Cut Damage (2) Average Change, μ = 7.7% Standard Dev., σ = 5.4% Test Set 2 Test Set 1 Damage Location 10/14 After Flange Cut Damage (1) 10/14 After Flange Cut Damage (2) Average Change, μ = 4.3% Standard Dev., σ = 4.2% 1 kip = 4.45 kn 1 inch = 2.54 cm Variability of BGCI Deflections from Different Tests for the Same Condition

SUBJECTIVE vs OBJECTIVE RATING OF SEYMOUR AVE. BRIDGE As-Is Condition BARS RF FEM Description (ODOT) RF Operating Rating Level 1.185 3.

10 SUBJECTIVE ANALYSIS Fair Condition - Primary structural elements are sound, but have minor section loss.

Bridge Inspectors - Shut down the bridge. The damages need to be repaired immediately.

21 SUBJECTIVE vs OBJECTIVE RATING OF SEYMOUR AVE. BRIDGE As-Is Condition BARS RF FEM Description (ODOT) RF Operating Rating Level Steel Damage Description FEM RF Operating Rating Level 3.29 Concrete Damage Description FEM RF Operating Rating Level 3.10 SUBJECTIVE ANALYSIS Fair Condition - Primary structural elements are sound, but have minor section loss. Secondary elements have significant deterioration. Poor Condition - Advanced section loss, deterioration or spalling. Bridge Inspectors - Shut down the bridge. The damages need to be repaired immediately. Consulting Engineers - There really isn't an immediate concern, but the repair would have to be fixed. The bridge can still carry its required capacity. Bridge Inspectors - Not a problem. The bridge was not designed as a composite. Consulting Engineers - Not a problem. The bridge was not designed as composite.

22 Some Important Conclusions of the Seymour Bridge Study (95-97) 97) Modal analysis of the highly non-stationary constructed system were not successful until short-time time MIMO tests were executed during periods of near-constant temperature. Many modal parameter identification algorithms were unsuccessful due to non-stationarity and highly coupled and damped modes. Even after mitigating non-stationarity stationarity,, a mode (#3) critical for modal flexibility could not be identified until a new CMIF based parameter estimation method was devised. Modal flexibility proved successful as a damage index. Ambient monitoring was not reliable and could not lead to identifying parameters comparable to those from MIMO. The structure, environment, damage, experiment and post- processing proved to be a highly coupled system

23 Idealized Physical Model of a Cantilever Beam Accel: = Support Steel Tube Section 3 x 1.5 x Instrumented Cantilever Beam

24 Dynamic Testing of a Cantilever Beam Laboratory Testing: Simple structure under near ideal conditions Analytical and experimental characterization Excitation: (1) random base, (2) random taps on beam (spatially distributed excitation), (3) No input, and (4) MIMO impact Test Objectives: Calibration of different dynamic test and data processing methods Identify, characterize, and mitigate sources of uncertainty

25 Partial Differential Equation Solution Solution for cantilever with distributed mass and stiffness (ignoring shear force and rotary motion): (Basic Equation for Lateral Vibration of Beams) 2 x 2 EI 2 x y 2 = γs g 2 t y 2 κ 4 = 2 ω n γs EIg (Substitute) cosκl coshκl ω 4 d X 4 = κ X X = A sin κx A cosκx A sinh κx A cosh κx dx (After Applying B.C.s) n (Solving κ) = κ 2 n = 1 EIg γs ω1 = rad/s ω2 = rad/s ω3 = rad/s (Solution to Equation) ω4 = e+003 rad/s ω5 = e+003 rad/s f1 = Hz f2 = Hz f3 = Hz f4 = Hz f5 = Hz

26 Partial Differential Equation Solution Classical solution method for cantilever beam with distributed mass and stiffness (ignores shear force and rotary motion) Natural Frequencies: f1 = Hz f2 = Hz f3 = Hz f4 = Hz Amplitude Mode Shapes for Cantilever Beam with Distributed Properties Datum Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 f5 = Hz Distance from Fixed End (in)

27 Laboratory Testing Overview Experimental Testing Static Testing Dynamic Testing Controlled Input Controlled Input Controlled Initial Conditions Ambient Vibration Static Flexibility Impact Pull-Release Random Taps on Beam Random Base Excitation Pre-Processing Processing Pre-Processing Processing Time Domain Algorithms Frequency Domain Algorithms Time Domain Algorithms Frequency Domain Algorithms Frequencies, Mode Shapes, Damping & Modal Flexibility Frequencies, Mode Shapes & Damping

28 Cantilever Testing

29 Accelerometer Calibration

30 Time Domain Segments Modal Shape Estimation - DFT FFT 1 FFT 2 FFT 3 FFT 4 Magnitude Phase Magnitude Phase Magnitude Magnitude Phase Phase FFT n Magnitude Phase Average Magnitude Average Phase PHASE (deg) MAGNITUDE (g) 10 4 FFT MAGNITUDE - RMS, Record Length = 10 minutes Frequency (Hz) FFT PHASE, Record Length = 10 minutes No. of Averages = 118 Phase Information is Poor Ch01 Ch02 Ch03 Ch04 Ch05 Ch06 Ch01 Ch02 Ch03 Ch04 Ch05 Ch06 RMS Average: Magnitude & phase calculated for FFT of each segment. Magnitude and phase results are averaged for all segments. 1 Sensor channels Frequency (Hz)

31 Time Domain Segments Modal Shape Estimation - DFT FFT 1 FFT 2 FFT 3 FFT 4 Real Part Imag. Part Real Part Imag. Part Real Part Imag. Part Real Part Imag. Part FFT n Real Part Imag. Part Avg. Real Parts + Avg. Imaginary Parts MAGNITUDE (g) 10 2 FFT MAGNITUDE - VECTOR AVG, Record Length = 10 minutes No. of Averages = 118 Magnitude Spectra are Noisy Frequency (Hz) FFT PHASE - VECTOR AVG, Record Length = 10 minutes Ch01 Ch02 Ch03 Ch04 Ch05 Ch06 Magnitude & Phase Vector Average: Real and imaginary parts of each FFT segment are averaged separately. PHASE (deg) Phase Information is Good Ch01 Ch02 Ch03 Ch04 Ch05 Ch06 1 Sensor channels Frequency (Hz)

32 Modal Shape Estimation - DFT MAGNITUDE (g) 10 4 FFT MAGNITUDE - RMS, Record Length = 10 minutes No. of Averages = Frequency (Hz) Ch01 Ch02 Ch03 Ch04 Ch05 Ch06 Hybrid Approach: RMS Avg. of FFT for Amplitude and Vector Avg. of FFT for Phase FFT PHASE - VECTOR AVG, Record Length = 10 minutes PHASE (deg) Ch01 Ch02 Ch03 Ch04 Ch05 Ch06 1 Sensor channels Frequency (Hz)

33 Frequency Correlation Frequency Correlation 1.223% 1.223% 1.174% 1.174% 1.101% 1.101% 1.315% 1.315% 1.355% 1.355% % 2.483% % % % 0.212% % 0.550% % 0.429% % 0.295% % 0.397% % 3.230% % % % 0.798% % 1.248% % 1.248% % 1.097% % 1.251% % 3.832% 5.852% 5.852% % 0.376% % 0.927% % 0.927% % 0.576% % 0.987% % 4.257% 1.882% 1.882% % 0.100% 0.124% 0.124% 0.124% 0.124% % 2.977% % 0.889% % 4.532% 2.644% 2.644% DOF 320 DOF 5 DOF 5 DOF Freq Freq (Hz) (Hz) Mode Mode Random Random Exc Exc at at Base Base No No Special Special Input Input Random Random Impact Impact Impact Impact Best Best Practice Practice Impact Impact SAP 2000 SAP 2000 Closed Closed Form Form Experimental Experimental Theory Theory

34 Physical Model CONNECTIONS SUPPORTS

FEA and static FEA used as an indicator of number modes that need be identified by the impact

35 Dynamic Test Parameter Selection FEM used as a reference point to identify the bandwidth of interest for dynamic testing Convergence between the modal flexibility calculated from dynamic FEA and static FEA used as an indicator of number modes that need be identified by the impact test FEM of the Physical Model Selected Parameters: Sampling Frequency: 200Hz Data Length: 2048 (10.24 sec)

36 Impact Test Results Comparison PTD vs. CMIF with Nominal Boundary Conditions CMIF Mode# CMIF Freq CMIF Damp PTD Mode# PTD Freq PTD Damp MAC

37 Impact Test Mode Shapes Identified by CMIF Method Mode Hz Mode Hz Mode Hz MAC ptd =1.000 MAC ptd =1.000 MAC ptd =1.000 Mode Hz Mode Hz Mode Hz MAC ptd =0.999 MAC ptd =0.996 MAC ptd =NA

Ambient Input Application Random forcing function was applied in 0-100 Hz

38 Ambient Input Application Random forcing function was applied in Hz frequency band Shaker location

39 Modal Parameter Identification using Ambient Vibration Data

40 CMIF Plot & Resulting Modes with Nominal Boundary Conditions Nonparametric Approach Mode 2 Mode 3 Mode Hz MAC Impact = Hz MAC Impact =NA Hz MAC Impact =NA Only one out of first Four modes was found

41 Prony s Method for Conditioning RD Results Prony's method is a technique for extracting the sinusoid or exponential signals by solving a set of linear equations for the coefficients of the recurrence equation that the signals satisfy. Infinite impulse response (IIR) filter coefficients a and b may be calculated by Prony s method from time domain impulse response i.e. the result of random decrement process.

Window Applied CMIF Conditioned RD Application RD IRF.

42 Comparison of Raw RD & Conditioned RD Results with Nominal Boundary Conditions Standard RD-CMIF Application RD IRF. Exp. Window Applied CMIF Conditioned RD Application RD IRF. Prony s Method Time Dom. IIR Filter Parameters (a & b) Back Calculated IRF CMIF

43 CMIF Plot & Resulting Modes with Nominal Boundary Conditions Parametric Approach Mode 2 Mode 3 MAC Impact = Hz Mode 1 MAC Impact = Hz Mode Hz MAC Impact = Hz MAC Impact =0.981

44 Some Sources of Uncertainty in Vibration Testing INPUT Non-stationary Echoes/Reflections Bandwidth Directionality Select Harmonics Interference/Noise TEST DESIGN STRUCTURAL SYSTEM Non-stationarity due to changes in environment Nonlinearity Incomplete free body/appendage tests Lack of observability due to insufficient sensor density Scale-induced complexity OUTPUT (DATA) Asynchronous Filters Sensor calibration Noise & bias Spurious pulses Bandwidth Window length Freq. resolution DATA PROCESSING Data quality measures Error ID/Cleaning Filtering, averaging, and windowing Post-processing Access Excitation Sensor density and modality Diagnose/Mitigate malfunctions VERIFICATION Modality Independence PARAMETER ID Parameter grouping Sensitivity Bandwidth Modality Objective Function Optimization ANALYTICAL MODEL Completeness Material variability Geometry BC & CC Temporal/spatial Nonlinearity & nonstationarity MECH PROPERTIES Frequency band Modal order Spatial adequacy 3D vs. idealized Separation Amplitude & phase Damping

45 Types of Uncertainty Affecting Reliability of Field Measurements EU - LUP Human Errors (HE) Inattention/Thoughtlessness Inexperience Omission (Forgetfulness) Commission (Bad Design) HE RP EU - UP Random Phenomena (RP) Epistemic Uncertainty (EU) Less Understood Phenomena (LUP) Unknown Phenomena (UP)

46 Preliminary Conclusions Input, structure, output, experimental setup, data processing, and other systems such as environment act as one interconnected system in an experiment Each element above contributes many components of uncertainty to the experiment Even when we experiment in laboratory with idealized physical models, we observe some mechanisms of uncertainty that impact the reliability of the results obtained by different input/post-processing processing combinations We were able to identify all 5 frequencies and mode shapes of the cantilever with reasonable accuracy irrespective of test/processing; however, this was not the case when we tested a more complex model Uncertainty due to supports and excitation and human error/inexperience emerge as significant barriers

47 Dynamic Testing of Bridges Typical applications: System identification for FE model calibration (i.e. seismic retrofits, baseline for HM) Damage detection/diagnosis Two common implementations: (1) Forced- Excitation Test and (2) Ambient Vibration Test Forced-vibration testing is not always feasible Fundamental assumptions regarding structure under test: (1) linear, (2) stationary, and (3) observable

48 Ambient Vibration Testing Objective: Extract modal parameters (frequencies, mode shapes, and damping) from structure subject to random dynamic excitation Damping estimates not very reliable Dynamic excitation is not measurable Typical sources of excitation for bridges include traffic, wind, pedestrians and micro-tremors (ground motions) Excitation is assumed to be stationary and broad-band, band, Gaussian white noise

49 Henry Hudson Bridge South Approach South Viaduct South Tower Arch Span North Tower North Viaduct North Approach 94 m 91 m 256 m 91 m 82 m Manhattan EAST ELEVATION The Bronx

50 Henry Hudson Bridge

51 Description of Experiment Ambient vibration testing of arch and viaduct spans conducted in two stages Fixed array of accelerometers used for both stages 36 accelerometers used for Stage 1 and 40 accelerometers used for Stage 2 9 accelerometer locations common to both stages Mix of ICP and capacitive accelerometers used Data sampled primarily at 200 Hz in 15 minute records Monitor for 1 week during each test stage

52 Instrumentation Plan Stage 2 Test Setup Stage 1 Test Setup Upper Level L L V CL Arch T T T L L T V T T T T V T L L V V V L L T T T Lower Level T T T V T V V T V T V T T South Viaduct Tower T T T T T T Tower North Viaduct East Elevation T East Side Transverse Accelerometer V East Side Vertical Accelerometer L East Side Longitudinal Accelerometer T West Side Transverse Accelerometer V West Side Vertical Accelerometer L West Side Longitudinal Accelerometer V T V T Sensors used in Stage 1 & Stage 2 Tests

53 Sensors and Data Acquisition

54 Raw Data with Errors Arch - Transverse Viaduct - Transverse

55 Raw Data with Bias Error Tower Longitudinal Tower Longitudinal Capacitive Accelerometers Tower Longitudinal

56 Data with Different Amplitudes High Amplitude Data Arch - Vertical Arch - Transverse Low Amplitude Data

57 Filtered Data Arch - Vertical Arch - Transverse

58 Conditioned Data for Vertical Channels No Window or Averaging Hanning Window & Ensemble Averaging

59 Ambient Test Results Mode Stage 1 Test Combination of Stage 1 & Stage 2 Tests Mode Description Hz Hz Transverse Hz Hz Vertical Hz Hz Vertical Hz Hz Transverse Hz Hz Vertical Hz Transverse Hz Hz Torsional Hz Vertical Hz Transverse Hz Transverse Hz Transverse Hz Hz Vertical Hz Torsional Hz Vertical

60 FE Model of Bridge in SAP2000

61 FEM & Experimental Results Mode Initial FE Model FE Model Modified CC & Joint Mass Ambient Test Mode Description Hz Hz Hz Transverse Hz Hz Hz Vertical Hz Hz Hz Vertical Hz Hz Hz Transverse Hz Hz Hz Vertical Hz Hz Hz Transverse Hz Hz Torsional Hz Hz Vertical Hz Hz Transverse Hz Transverse Hz Hz Transverse Hz Hz Hz Vertical Hz Hz Torsional Hz Hz Vertical

62 Mode Shape Comparison FE Mode 1 f = Hz Projection of Mode Shape Points Transverse Mode 1, Test = Hz, SAP=0.588 Hz SAP_ARC SAP _LL SAP_UL T_ARC T_LL T_UL Distance (ft)

63 Mode Shape Comparison FE Mode 2 f = Hz Projection of Mode Shape Points Vertical Mode 1, Test = Hz, SAP = Hz SAP TEST Distance (ft)

Mode Shape Comparison FE Mode 3 f = 0.973 Hz Projection of Mode Shape Points 0.80 Vertical Mode 2, Test = 0.

64 Mode Shape Comparison FE Mode 3 f = Hz Projection of Mode Shape Points 0.80 Vertical Mode 2, Test = Hz, SAP = Hz SAP TEST Distance (ft)

65 Mode Shape Comparison Mode 4 f = Hz Transverse Mode 2, Test = Hz, SAP = Hz SAP_ARC SAP _LL SAP_UL T_ARC T_LL 800 Distance (ft) T_UL

66 Conclusions Most uncertainty was associated with data errors a challenge not really faced in laboratory Most data errors can be removed by digital signal processing, provided test design is adequate Primary excitation was traffic and this was spatially distributed due to type of structure Uncertainty due to non-stationary structure painting equipment removed between stages and temperature effects on structure Reasonable correlation of experiment and model with modified boundary conditions

67 Ambient Vibration Testing of the Brooklyn Bridge

68 Scope and Objectives Ambient vibration testing a component of seismic evaluation and retrofit study Results used for system identification to improve reliability of FE models Focus on towers, but span responses also measured Identify frequencies, mode shapes and damping

69 Description of Experiment Wind speed and direction measured Ambient temperature measurements Dynamic range adjusted after observing actual responses minimum range utilized Over 100 data sets sampled at Hz with a fixed array of 43 accelerometers Long data records hours to days Measurements recorded over a month

70 Level H Tower Instrumentation Scheme Level G Level F Level E Level C Level B Level D Level A Brooklyn Tower Elevation Manhattan Tower Elevation

71 Span Instrumentation Scheme V T V T V T Brooklyn Bound Traffic Lanes Side Span V V T Brooklyn Tower Main Span Manhattan Bound Traffic Lanes V V V Partial Plan

72 Accelerometer Layout for Spans Pedestrian Walkway Outer Truss Inner Truss Inner Truss Outer Truss Roadway Roadway V T V STIFFENING TRUSSES Cross Section T L Transverse Accelerometer Longitudinal Accelerometer

73 Accelerometer Installation

74 Uncertainty in Experiment Spurious spikes in data remove during preprocessing Quality of ambient excitation: Low level excitation Non-stationary excitation Ambient excitation primarily from traffic on spans transfer to tower only occurs through connections with deck, main cables, and stays Identification of critical tower modes Damping estimates

75 Comparison of Tower and Span Ambient Responses Acceleration (g) Filtered Time Domain Data for Several Span & Brooklyn Tower Top Sensors HNL N51V N59V S51T HST Time (s) Acceleration (g) Zoomed View of Filtered Time Domain Data for Several Span & Brooklyn Tower Top Sensors Tower Accelerations (Top) Span Accelerations HNL N51V N59V S51T HST Time (s)

76 Effect of Spurious Spikes x 10-4 Filtered Time Domain Data with Noise for Channel #13 Acceleration (g) Typ.. Spikes Time (sec) PSD for Channel #13 PSD (g 2 /Hz) With Noise Avg of Segements Segments Composite of Valid Segments Composite of All Segments Frequency (Hz)

77 N M S Non-Stationary Excitation Frequency Domain Tower Transverse Acceleration (22-NOV NOV-04 16:01 20:00) H G g 2 /Hz 10-6 Brooklyn Tower Transverse - 16:01 to 20:00 - Bandpass 0.3 to 10.0 Hz HST GMT FST EST CST BST FNT FMT GST Duration = 4 Hours F E C B g 2 /Hz Frequency (Hz) Hz Average Normalized PSD ANPSD-T Hz Hz, Hz Hz, Hz Hz Frequency (Hz)

78 Non-Stationary Excitation Time Domain Amplitude Tower Transverse Acceleration (22-NOV NOV-04 17:01 17:16) H G Acceleration (g) 5 x HST Acceleration (g) 5 x GMT F E C Acceleration (g) x 10-4 Time (s) 0 FST Acceleration (g) x 10-4 Time (s) 0 EST B Acceleration (g) x 10-4 Time (s) 0 CST Acceleration (g) x 10-4 Time (s) 0 BST Duration = 15 minutes Time (s) Time (s)

79 Non-Stationary Excitation Frequency Domain Tower Transverse Acceleration (22-NOV NOV-04 17:01 17:16) H G PSD (g 2 /Hz) HST PSD (g 2 /Hz) GMT F E C PSD (g 2 /Hz) Frequency (Hz) FST PSD (g 2 /Hz) Frequency (Hz) EST B Frequency (Hz) CST Frequency (Hz) BST PSD (g 2 /Hz) PSD (g 2 /Hz) Frequency (Hz) Frequency (Hz)

80 Non-Stationary Excitation Time Domain Amplitude Tower Transverse Acceleration (22-NOV NOV-04 18:31 18:46) H G F E Acceleration (g) Acceleration (g) 5 x HST x 10-4 Time (s) 0 FST Acceleration (g) Acceleration (g) 5 x GMT x 10-4 Time (s) 0 EST C B Acceleration (g) x 10-4 Time (s) 0 CST Acceleration (g) x 10-4 Time (s) 0 BST Duration = 15 minutes Time (s) Time (s)

81 Non-Stationary Excitation Frequency Domain Tower Transverse Acceleration (22-NOV NOV-04 18:31 18:46) H 10-6 HST 10-6 GMT G F PSD (g 2 /Hz) Frequency (Hz) FST PSD (g 2 /Hz) Frequency (Hz) EST E PSD (g 2 /Hz) PSD (g 2 /Hz) C B Frequency (Hz) CST Frequency (Hz) BST PSD (g 2 /Hz) PSD (g 2 /Hz) Frequency (Hz) Frequency (Hz)

82 Cross Spectral Density & Coherence Top and Bottom Level Transverse Accelerometers 10-5 CSD OUT=BST, REF=HST H Magnitude (g 2 /Hz) Frequency (Hz) Phase (radians) B Frequency (Hz) 1 COHERENCE Frequency (Hz)

83 Tower Excitation from Traffic Amplitude (g) 0 fmax Ideal Excitation f (Hz) Amplitude (g) 0 fmax More Probable Excitation f (Hz)

84 Analytical Model of Isolated Tower 3D Tower Cross-Sections of Different Tower Levels

85 Analytical Model Results for Tower Mode 1 1st Long Hz Mode 2 1st Tran Hz Mode 3 1st Tor Hz Mode 4 2nd Long Hz Mode 5 2nd Tran Hz Mode 6 2nd Tor Hz

86 Tower Longitudinal Mode Shapes Height Above Base (ft) Tower Top Bold shapes have best coherence & largest peak in frequency spectra Tower Base BROOKLYN TOWER LONGITUDINAL MODE SHAPES Normalized Amplitude

87 Tower Lateral Mode Shapes Middle Tower Leg Sensors at Level F and Level G BROOKLYN TOWER LATERAL MODE SHAPES Middle Leg Transverse Sensors at Level F and Level G Tower Top Height Above Base (ft) Bold shapes have best coherence & largest peak in frequency spectra Tower Base Normalized Amplitude

88 Tower Torsional Mode Shapes BROOKLYN TOWER TORSIONAL MODE SHAPES Tower Top Height Above Base (ft) Tower Base Normalized Amplitude Bold shapes have best coherence & largest peak in frequency spectra

89 Identified Tower Modes Mode Frequency (Hz) Description 1 st Longitudinal Mode 1 st Lateral Mode 1 st Torsional Mode 2 nd Longitudinal Mode 2 nd Lateral Mode Coupled lateral and longitudinal mode

90 Conclusions Uncertainty due to data quality and errors (bias error, spikes) corrected through digital signal processing and manual removal of spikes Uncertain excitation due to transfer of traffic excitation through structural connections to the towers Non-stationary excitation sample for longer time Tower modes coupled with span modes reflection of motions between the two components Uncertainty related to extracting the more critical tower modes from the coupled modes of the spans and towers Seismic evaluation requires identifying those modes that determine the tower demands during earthquake - tbd

91 Conclusions Dynamic testing and modal analysis of real structures are often driven by real engineering objectives A process oriented approach to taking data, processing, and identifying the modal properties may fail to satisfy the real engineering objectives The physics of the problem must be considered during each stage of experiment and analysis so that we may reach meaningful interpretations of the results we cannot simply present a large quantity of identified frequencies/mode shapes for the purpose of seismic retrofitting Although many peaks in PSD may correspond to mathematical normal modes, identifying the subset associated with resonant motion of the tower is essential and this represents a significant challenge in ambient vibration testing

92 Summary The mechanisms of uncertainty in dynamic testing of actual structures are abundant Explicit consideration and mitigation of uncertainty in test design, execution, processing, and interpretation is critical for providing real engineering benefits from the experiment Although some uncertainty can be mitigated through proper design and execution of a field experiment, we may have to accept that some level of uncertainty will always remain heuristics related to structure and test objectives an important component of interpretation and decision making based on experiment

93 Relationship Between Uncertainty and Risk Threat/ Hazard Vulnerability Consequences

EXPERIMENTAL MODAL AND AERODYNAMIC ANALYSIS OF A LARGE SPAN CABLE-STAYED BRIDGE

The Seventh Asia-Pacific Conference on Wind Engineering, November 82, 29, Taipei, Taiwan EXPERIMENTAL MODAL AND AERODYNAMIC ANALYSIS OF A LARGE SPAN CABLE-STAYED BRIDGE Chern-Hwa Chen, Jwo-Hua Chen 2,