impacts and mitigation of uncertainty shmii-2 · 2005-11-28 · impacts and mitigation of...
TRANSCRIPT
Impacts and Mitigation of Impacts and Mitigation of Uncertainty for Improving the Uncertainty for Improving the
Reliability of Field MeasurementsReliability of Field MeasurementsKirk A. Grimmelsman & A. Emin AktanKirk A. Grimmelsman & A. Emin Aktan
Drexel UniversityDrexel University
SHMIISHMII--2’ 20052’ 2005The Second International Conference on Structural Health MonitorThe Second International Conference on Structural Health Monitoring of ing of
Intelligent InfrastructureIntelligent InfrastructureNovember 16, 2005November 16, 2005
ContentsContents
Introduction and definitionsIntroduction and definitionsContinuous monitoring of a pin and Continuous monitoring of a pin and hanger retrofithanger retrofitShort term testing and continuous Short term testing and continuous monitoring to evaluate fatigue lifemonitoring to evaluate fatigue lifeAmbient vibration testing of the Brooklyn Ambient vibration testing of the Brooklyn Bridge TowersBridge TowersSummarySummary
Health Monitoring ParadigmHealth Monitoring Paradigm
Health Monitoring: track health by data and analytical Health Monitoring: track health by data and analytical simulation so current and expected performance can simulation so current and expected performance can be described in a proactive mannerbe described in a proactive mannerHealth Monitoring paradigm offers great advantages:Health Monitoring paradigm offers great advantages:
Objective characterization of healthObjective characterization of healthProactive management of maintenanceProactive management of maintenanceEnabler of performanceEnabler of performance--based engineeringbased engineering
Requires integration of experimental, analytical, and Requires integration of experimental, analytical, and information technologiesinformation technologiesSystem Identification approach offers rational System Identification approach offers rational framework for optimum integration of these framework for optimum integration of these technologiestechnologies
Current State of Practice: Field Testing Current State of Practice: Field Testing and Monitoringand Monitoring
Practical objectives are primary motivation:Practical objectives are primary motivation:Reduce or quantify the uncertainty related to some Reduce or quantify the uncertainty related to some observedobservedbehavior, performance or mechanism (Reactive)behavior, performance or mechanism (Reactive)Improve the reliability of traditional design or analysis approaImprove the reliability of traditional design or analysis approachesches
Proactive structural health monitoring rarely consideredProactive structural health monitoring rarely considered
Lack of knowledge regarding capabilities/limitations of Lack of knowledge regarding capabilities/limitations of experiments experiments –– education emphasis is design instead of education emphasis is design instead of maintenance or renewalmaintenance or renewalLack of standards or guidelines for field experiments (need is Lack of standards or guidelines for field experiments (need is recognized, question is how to get there)recognized, question is how to get there)
Limited or no scientific characterization of how the Limited or no scientific characterization of how the parametrsparametrs/uncertainty in stages of experiment affect the quality and reli/uncertainty in stages of experiment affect the quality and reliability ability of the resultof the resultDesign, execution, and interpretation rely significantly on heurDesign, execution, and interpretation rely significantly on heuristicsistics
Types of Uncertainty Affecting Types of Uncertainty Affecting Reliability of Field Measurements Reliability of Field Measurements
Human Errors (HE)•Inattention/Thoughtlessness•Inexperience•Omission (Forgetfulness)•Commission (Bad Design)
Random Phenomena (RP)
Epistemic Uncertainty (EU)•Less Understood Phenomena (LUP)•Unknown Phenomena (UP)
EU - LUP
HE
RP
EU - UP
INPUT• Non-stationary• Echoes/Reflections• Bandwidth• Directionality• Select Harmonics• Interference/Noise
STRUCTURAL SYSTEM• Non-stationarity due to changes in environment • Nonlinearity • Incomplete free body/Appendage tests• Lack of observabilitydue 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
MECH PROPERTIES• Frequency band• Modal order• Spatial adequacy• 3D vs. idealized• Separation• Amplitude & phase• Damping
ANALYTICAL MODEL• Completeness • Material variability• Geometry• BC & CC• Temporal/spatial Nonlinearity & non-stationarity
PARAMETER ID• Parameter grouping• Sensitivity• Bandwidth• Modality• Objective Function• Optimization
VERIFICATION• Modality • Independence
TEST DESIGN• Access• Excitation• Sensor density and modality• Diagnose/Mitigate malfunctions
Some Sources of Uncertainty in ExperimentsSome Sources of Uncertainty in Experiments
Suspended SpanCantilever Arm
Cantilever Arm
Anchor Span Anchor Span
822 ft 411 ft 822 ft 411 ft 822 ft
3,288 ftP.P. 27 P.P. 45
Fix.Exp. Fix.Fix.Exp. Exp.
822 ft 822 ft411 ft411 ft 822 ft
3,288 ft
Commodore Barry Bridge
Continuous Monitoring to Characterize a Pin & Continuous Monitoring to Characterize a Pin & Hanger RetrofitHanger Retrofit
1
2
1
3
4
Retrofitted Truss Hanger Locations
Each hanger is retrofitted with four 7.5-inch diameter stainless steel rodsThe rods are pre-tensioned to remove DL from the truss hangers.
Suspended Span Hanger RetrofitSuspended Span Hanger Retrofit
Typical Pin and Hanger MemberTypical Pin and Hanger Member
Top Joint Suspended SpanCantilever Arm
Han
ger
Pin
Pin
Pin
Hanger
Top and bottom pins prevent bending moments due to longitudinal expansion/contraction of the truss or live loads
from developing on the hanger cross section30
m
Auxiliary Support SystemAuxiliary Support System
The 4 pin and hanger members are The 4 pin and hanger members are retrofitted with an auxiliary support system retrofitted with an auxiliary support system to provide added redundancyto provide added redundancySupport system consists of:Support system consists of:
4 large diameter stainless steel rods4 large diameter stainless steel rodsfour spreader beams located at the upper and four spreader beams located at the upper and lower truss chordslower truss chordssplice couplers, nuts, and washerssplice couplers, nuts, and washers
Rods extend vertically from the upper chord Rods extend vertically from the upper chord of the cantilever arm to the lower chord of of the cantilever arm to the lower chord of the suspended span the suspended span
Auxiliary Support SystemAuxiliary Support System
Spreader Beam @ U.C.
Spreader Beam @ L.C
Splice Coupler
7.5” Diameter SS Rod
Hanger Sensors
Scope and Objectives of the MonitoringScope and Objectives of the MonitoringScope: uncontrolled testing before, during, and Scope: uncontrolled testing before, during, and after installation of the auxiliary support systemafter installation of the auxiliary support systemObjectives: ImmediateObjectives: Immediate
Axial force change for each hangerAxial force change for each hangerAxial forces in rodsAxial forces in rodsIdentify if bending of hangers occursIdentify if bending of hangers occursEvaluate consistency of tensioning at 4 Evaluate consistency of tensioning at 4 hanger locationshanger locationsAre any significant stresses induced in other Are any significant stresses induced in other membersmembers
Objectives: LongObjectives: Long--TermTermMonitor performance of systemMonitor performance of system
Typical Instrumentation SchemeTypical Instrumentation Scheme
Geokon VSM 4050 Vibrating Wire Strain Gage Hanger Elevation View
A
Hanger
Hanger Rod (Typ.)
A
C.L. Pin
B B
Section A-A Section B-B
6’-0”
Hanger Rod (Typ.)
22’-0”
Sensor Installation on RodsSensor Installation on Rods
Covers to minimize temperature effects on sensor readings
Strain gages bonded to S.S. rod with epoxy
VW Strain Gage
Results Results –– Strain Response of Hanger Strain Response of Hanger
Results Results –– Strain Response of RodsStrain Response of Rods
Observations from Raw DataObservations from Raw Data
Consistent behavior observed at all 4 Consistent behavior observed at all 4 hanger locations as rods were tensionedhanger locations as rods were tensionedMagnitudes of residual strains in rods and Magnitudes of residual strains in rods and hangers after tensioning slightly different hangers after tensioning slightly different at each hanger locationat each hanger locationAverage strains on rod and hanger cross Average strains on rod and hanger cross sections used for subsequent analysessections used for subsequent analyses
Uncertainty Uncertainty -- Data AnalysisData Analysis
Axial forces on rods and hanger calculatedAxial forces on rods and hanger calculatedHooke’sHooke’s Law (F = Law (F = ε ε xx E x A) E x A) Isolated free body assumptionIsolated free body assumption
Nominal material properties used to Nominal material properties used to calculate forces from strain measurementscalculate forces from strain measurementsSignificant difference in total force on rods Significant difference in total force on rods and change in force in hangerand change in force in hanger
Difference was 1760 Difference was 1760 kNkN in one casein one case
Further analyses required to interpret the Further analyses required to interpret the measurement results measurement results
Force Discrepancy AnalysisForce Discrepancy Analysis
Verify all measurement data validVerify all measurement data validDefine normalized parameters for use in Define normalized parameters for use in further analysis (Structural Identification)further analysis (Structural Identification)
Strain Ratio (SR): Absolute value of the ratio Strain Ratio (SR): Absolute value of the ratio of the average rod strains to the average of the average rod strains to the average hanger strain. hanger strain. Force Ratio (FR): Absolute value of the ratio Force Ratio (FR): Absolute value of the ratio of the change in hanger axial force to the sum of the change in hanger axial force to the sum of the rod forces of the rod forces
3D FEM Analyses3D FEM AnalysesComponents added 3D Components added 3D FEM of bridgeFEM of bridge
Rod postRod post--tensioning tensioning simulated with simulated with temperature loads temperature loads
Temperature loads Temperature loads modified until model rod modified until model rod and hanger strains and hanger strains converged to measured converged to measured strainsstrains
3D FEM of Hanger Region
ResultsResultsSR and FR from analysis were correlated with SR and FR from analysis were correlated with experimental counterpartsexperimental counterparts
Analytical SR & measured SR correlate closely when Analytical SR & measured SR correlate closely when modular ratio of the hanger steel to the rod steel is 1.30 modular ratio of the hanger steel to the rod steel is 1.30 (actual modular ratio not available (actual modular ratio not available –– nominal ratio ~ nominal ratio ~ 1.01)1.01)
Nominal and calibrated FEM give FR of 0.94 (6% of sum Nominal and calibrated FEM give FR of 0.94 (6% of sum of rod forces lost to 3D effects) if modular ratio is of rod forces lost to 3D effects) if modular ratio is assumed 1.30assumed 1.30
Uncertainty due to incomplete information for calculating Uncertainty due to incomplete information for calculating forces (material test results)forces (material test results)
Uncertainty only identified in trying to reconcile forces Uncertainty only identified in trying to reconcile forces from the rods and hangersfrom the rods and hangers
ShortShort--Term Structural Load Testing: Term Structural Load Testing: Remaining Fatigue Life EvaluationRemaining Fatigue Life Evaluation
453 ft
1736.5 ft
453 ft 830.5 ftAnchor Span Anchor SpanMain Span
Brent Spence Bridge
Test StatisticsTest Statistics48 strain gages installed on 12 truss members48 strain gages installed on 12 truss members
Sampling rate of 30 Hz for continuous monitoringSampling rate of 30 Hz for continuous monitoring
Wireless network established for data acquisitionWireless network established for data acquisition
Controlled load testing conducted to support analysis and Controlled load testing conducted to support analysis and interpretation of datainterpretation of data
Monitor all installed strain gages for 311 hoursMonitor all installed strain gages for 311 hours
Stress range histograms developed from critical gages on Stress range histograms developed from critical gages on each member using each member using rainflowrainflow counting methodcounting method
Calculate effective stress range from stress range Calculate effective stress range from stress range histograms for each member to evaluate fatigue lifehistograms for each member to evaluate fatigue life
Installed Strain GagesInstalled Strain Gages
Strain Gages in Chord Strain Gages in Diagonal
w
dStrain Gages: 350 Ohm
Weldable Resistance Strain Gage
Weldable Strain Gage
Typ. Gage Layout
Data Acquisition Cabinet @ Lower Chord
Wireless Local Area Network for Wireless Local Area Network for Fatigue MonitoringFatigue Monitoring
Wireless Bridge
WB02
Server
YagiAntenna
Wireless Bridge
YagiAntenna
~ 1.5 MilesWireless Transmission
Path Burgess & Niple Office Cincinnati, OH
Workstation
Drexel UniversityPhiladelphia, PA
Internet
WB01
Control DA SystemCollect, Process, & Archive Data
0 1 2 3 4 5 60
2000
4000
6000
8000
10000
12000
Cyc
le C
ount
Sress Range (ksi)
Stress Range Histogram - Member UT-L2L4
Stress Range Histogram Stress Range Histogram -- ExperimentExperiment
Data Range: May 04, 2004 to May 19, 2004Total Cycles = 27,504RMC Effective Stress = 0.697 ksi
Member L2L4Upstream Truss
Average Stress Influence Line for Member L4L6Truck 01 = Lane L1, Truck 02 = Lane L2
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 2 4 6 8 10 12 14 16 18 20 22 22p 20p 18p 16p 14p 12p
Trucks @ Panel Point No.
Stre
ss, k
si
UT_L4L6_FLANGE
UT_L4L6_WEB
DT_L4L6_FLANGE
DT_L4L6_WEB
Ohio Tower
Direction of Truck Travel(KY to OH)
Kentucky Tower
Gag
e Lo
catio
n
Processed Data: Two Truck Load CaseProcessed Data: Two Truck Load Case
Conclusions Conclusions -- Uncertainty in Fatigue Uncertainty in Fatigue Evaluation ExperimentEvaluation Experiment
Spurious spikes in data Spurious spikes in data –– mitigate through digital mitigate through digital signal processing during analysissignal processing during analysis
Establishment of threshold stress level for fatigue Establishment of threshold stress level for fatigue damage (mitigated through controlled load testing)damage (mitigated through controlled load testing)
Stress cycle counting method used Stress cycle counting method used –– influences data influences data postpost--processing requirementsprocessing requirements
Duration of monitoring Duration of monitoring –– statistical analyses to statistical analyses to establish stationary resultsestablish stationary results
Even with uncertainties Even with uncertainties –– experiment more reliable experiment more reliable than purely analytical approachthan purely analytical approach
Ambient Vibration Testing of the Ambient Vibration Testing of the Brooklyn BridgeBrooklyn Bridge
Scope and ObjectivesScope and Objectives
Ambient vibration testing a component of Ambient vibration testing a component of seismic evaluation and retrofit studyseismic evaluation and retrofit studyResults used for system identification to Results used for system identification to improve reliability of FE modelsimprove reliability of FE modelsFocus on towers, but span responses also Focus on towers, but span responses also measuredmeasuredIdentify frequencies, mode shapes and Identify frequencies, mode shapes and dampingdamping
Description of ExperimentDescription of Experiment
Fixed array of 43 accelerometers located Fixed array of 43 accelerometers located on towers and spanson towers and spans
Measure longitudinal, transverse and Measure longitudinal, transverse and torsionaltorsional vibrations of towers vibrations of towers
Measure vertical, transverse and Measure vertical, transverse and torsionaltorsionalvibrations of main span and side span vibrations of main span and side span adjacent to Brooklyn Toweradjacent to Brooklyn Tower
Description of ExperimentDescription of Experiment
Wind speed and direction measuredWind speed and direction measured
Ambient temperature measurementsAmbient temperature measurements
Dynamic range adjusted after observing actual Dynamic range adjusted after observing actual responses responses –– minimum range utilizedminimum range utilized
Vibration data sampled at multiple rates (100 Vibration data sampled at multiple rates (100 Hz, 200 Hz, but primarily 20 Hz and 40 Hz)Hz, 200 Hz, but primarily 20 Hz and 40 Hz)
Long data records Long data records –– hours to dayshours to days
Measurements recorded over a monthMeasurements recorded over a month
Tower Instrumentation SchemeTower Instrumentation Scheme
Brooklyn Tower Brooklyn Tower ElevationElevation
Level HLevel H
Level GLevel G
Level FLevel F
Level ELevel E
Level CLevel C
Level BLevel B
Level ALevel AManhattan Tower Manhattan Tower
ElevationElevation
Level DLevel D
272’
272’
-- 6”6”
153’
153’
-- 0”0”
119’
119’
-- 6”6”
Accelerometer LayoutAccelerometer LayoutIntermediate Tower Levels between Top and Deck LevelIntermediate Tower Levels between Top and Deck Level
Transverse AccelerometerTransverse Accelerometer
Longitudinal AccelerometerLongitudinal Accelerometer
T
L
TL TL TL
Accelerometer LayoutAccelerometer LayoutTower Levels Below DeckTower Levels Below Deck
Transverse AccelerometerTransverse Accelerometer
Longitudinal AccelerometerLongitudinal Accelerometer
T
L
TL L
Span Instrumentation SchemeSpan Instrumentation Scheme
V T V T V T
V T
V
V V V
Main SpanMain Span
240’240’
Bro
okly
n To
wer
Brooklyn Brooklyn Bound Bound
Traffic LanesTraffic Lanes
Manhattan Manhattan Bound Traffic Bound Traffic
LanesLanes
Partial PlanPartial Plan
Side SpanSide Span
185’185’393’393’454’454’
Accelerometer Layout for SpansAccelerometer Layout for Spans
RoadwayRoadway RoadwayRoadway
Pedestrian Pedestrian WalkwayWalkway
T
STIFFENING TRUSSESSTIFFENING TRUSSESCross SectionCross Section
VV
Out
er T
russ
Out
er T
russ
Inne
r Tru
ssIn
ner T
russ
Inne
r Tru
ssIn
ner T
russ
Out
er T
russ
Out
er T
russ
33’33’--0”0” 33’33’--0”0”16’16’--6”6”
Transverse AccelerometerTransverse Accelerometer
Longitudinal AccelerometerLongitudinal Accelerometer
T
L
Accelerometer InstallationAccelerometer Installation
Accelerometer InstallationAccelerometer Installation
Uncertainty in ExperimentUncertainty in Experiment
Spurious spikes in data Spurious spikes in data –– remove during remove during preprocessingpreprocessingQuality of ambient excitation:Quality of ambient excitation:
Low level excitationLow level excitationNonNon--stationary excitationstationary excitationAmbient excitation primarily from traffic on Ambient excitation primarily from traffic on spans spans –– transfer to tower only occurs through transfer to tower only occurs through connections with deck, main cables, and staysconnections with deck, main cables, and stays
Identification of critical tower modesIdentification of critical tower modesDamping estimatesDamping estimates
Comparison of Tower and Span Comparison of Tower and Span Ambient ResponsesAmbient Responses
0 2 4 6 8 10 12 14 16 18 20-0.01
-0.005
0
0.005
0.01Filtered Time Domain Data for Several Span & Brooklyn Tow er Top Sensors
Time (s)
Acce
lera
tion
(g)
2.5 3 3.5 4 4.5 5-0.01
-0.005
0
0.005
0.01Zoomed View of Filtered Time Domain Data for Several Span & Brooklyn Tow er Top Sensors
Time (s)
Acce
lera
tion
(g)
HNLN51VN59VS51THST
HNLN51VN59VS51THST
Span Accelerations
Tower Accelerations (Top)
Effect of Spurious SpikesEffect of Spurious Spikes
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
-5
0
5
x 10-4 Filtered Time Domain Data with Noise for Channel #13
Time (sec)
Acc
eler
atio
n (g
)
0 1 2 3 4 5 610-12
10-10
10-8
10-6
PSD for Channel #13
Frequency (Hz)
PS
D (g
2 /Hz)
With NoiseAvg of SegementsComposite of Valid SegmentsComposite of All Segments
TypTyp. Spikes. Spikes
Segments
NonNon--Stationary ExcitationStationary ExcitationFrequency Domain Frequency Domain –– Tower Transverse AccelerationTower Transverse Acceleration
(22(22--NOVNOV--04 16:01 04 16:01 –– 20:00)20:00)
Duration = 4 HoursDuration = 4 Hours
0 1 2 3 4 5 610-14
10-12
10-10
10-8
10-6Brooklyn Tower Transverse - 16:01 to 20:00 - Bandpass 0.3 to 10.0 Hz
Frequency (Hz)
g2 /Hz
0 1 2 3 4 5 610-8
10-6
10-4
10-2
100
Frequency (Hz)
g2 /Hz
HSTGMTFSTESTCSTBSTFNTFMTGST
ANPSD-T
HH
GG
FF
EE
CC
BB
N
MS
Average Normalized PSD
1.587 Hz2.695 Hz 4.468 Hz, 4.531 Hz
4.639 Hz, 4.668 Hz5.000 Hz
NonNon--Stationary ExcitationStationary Excitation
HH
GG
FF
EE
CC
BB
Time Domain Amplitude Time Domain Amplitude –– Tower Transverse AccelerationTower Transverse Acceleration(22(22--NOVNOV--04 17:01 04 17:01 –– 17:16)17:16)
3600 3800 4000 4200 4400-5
0
5x 10-4
Time (s)
Acc
eler
atio
n (g
) HST
3600 3800 4000 4200 4400-5
0
5x 10-4
Time (s)
Acc
eler
atio
n (g
) GMT
3600 3800 4000 4200 4400-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) FST
3600 3800 4000 4200 4400-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) EST
3600 3800 4000 4200 4400-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) CST
3600 3800 4000 4200 4400-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) BST
Duration = 15 minutesDuration = 15 minutes
NonNon--Stationary ExcitationStationary ExcitationFrequency Domain Frequency Domain –– Tower Transverse AccelerationTower Transverse Acceleration
(22(22--NOVNOV--04 17:01 04 17:01 –– 17:16)17:16)HH
GG
FF
EE
CC
BB
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
HST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
GMT
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
FST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
EST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
CST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
BST
NonNon--Stationary ExcitationStationary ExcitationTime Domain Amplitude Time Domain Amplitude –– Tower Transverse AccelerationTower Transverse Acceleration
(22(22--NOVNOV--04 18:31 04 18:31 –– 18:46)18:46)
9000 9200 9400 9600 9800-5
0
5x 10-4
Time (s)
Acc
eler
atio
n (g
) HST
9000 9200 9400 9600 9800-5
0
5x 10-4
Time (s)
Acc
eler
atio
n (g
) GMT
9000 9200 9400 9600 9800-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) FST
9000 9200 9400 9600 9800-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) EST
9000 9200 9400 9600 9800-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) CST
9000 9200 9400 9600 9800-5
0
5x 10
-4
Time (s)
Acc
eler
atio
n (g
) BST
HH
GG
FF
EE
CC
BB
Duration = 15 minutesDuration = 15 minutes
NonNon--Stationary ExcitationStationary ExcitationFrequency Domain Frequency Domain –– Tower Transverse AccelerationTower Transverse Acceleration
(22(22--NOVNOV--04 18:31 04 18:31 –– 18:46)18:46)
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
HST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
GMT
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
FST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
EST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
CST
0 1 2 3 4 510-12
10-10
10-8
10-6
Frequency (Hz)
PS
D (g
2 /Hz)
BST
HH
GG
FF
EE
CC
BB
BROOKLYN TOWER LONGITUDINAL MODE SHAPES
0
50
100
150
200
250
300
-1.5 -1 -0.5 0 0.5 1 1.5
Normalized Amplitude
Hei
ght A
bove
Bas
e (ft
)
0.8060.9721.1961.2941.3871.4501.5191.8071.8361.8701.8801.8992.0313.4963.5113.5213.5303.5353.6083.7063.7653.7943.8043.8133.8433.8624.6684.766
Preliminary Tower Longitudinal Mode Shapes from Preliminary Tower Longitudinal Mode Shapes from Peaks in Amplitude SpectraPeaks in Amplitude Spectra
Bold shapes have best coherence & largest peak in frequency spectra
Tower TopTower Top
Tower BaseTower Base
Brooklyn Tower Resonant Frequencies & Mode ShapesBrooklyn Tower Resonant Frequencies & Mode ShapesTower Mode 1Tower Mode 1
11stst Longitudinal ModeLongitudinal ModeTower Mode 4Tower Mode 4
22ndnd Longitudinal ModeLongitudinal Mode
Hei
ght
(ft)
0
50
100
150
200
250
300
0.0 0.2 0.4 0.6 0.8 1.0 1.2
PP (1.387Hz)
PTD&RD(1.386Hz)
PTD&CORR(1.381Hz)
Amplitude
Top
Base0
50
100
150
200
250
300
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
PP(3.765Hz)
PTD&RD(3.768Hz)
PTD&CORR(3.771Hz)
Amplitude
Top
Base
Brooklyn Tower Mode ShapesBrooklyn Tower Mode Shapes
0
50
100
150
200
250
300
0.0 0.4 0.8 1.20
50
100
150
200
250
300
0.0 0.4 0.8 1.2
PP(1.597Hz)
PTD&RD(1.588Hz)
PTD&CORR(1.588Hz)
0
50
100
150
200
250
300
0.0 0.4 0.8 1.2
Hei
ght
(ft)
Amplitude Amplitude Amplitude
North LegNorth Leg Middle LegMiddle Leg South LegSouth LegTop
Base
Tower Mode 2 Tower Mode 2 -- 11stst Lateral ModeLateral Mode
0
50
100
150
200
250
300
-0.8 -0.4 0.0 0.4 0.8 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
PP (4.668 Hz)
PTD&RD(4.669Hz)
PTD&CORR(4.667Hz)
North LegNorth Leg Middle LegMiddle Leg South LegSouth Leg
Hei
ght
(ft)
Amplitude Amplitude Amplitude
Top
Base
Brooklyn Tower Mode ShapesBrooklyn Tower Mode ShapesTower Mode 5 Tower Mode 5 –– 22ndnd Lateral ModeLateral Mode
0
50
100
150
200
250
300
-1.4 -0.7 0.0 0.7 1.4
PP (2.705Hz)PTD&RD(2.717Hz)PTD&CORR(2.726Hz)
0
50
100
150
200
250
300
-1.2 -0.6 0.0 0.6 1.2 1.8
PP(4.766Hz)PTD&RD(4.766Hz)PTD&CORR(4.768Hz)
Brooklyn Tower Mode ShapesBrooklyn Tower Mode ShapesTower Mode 3Tower Mode 3
11stst TorsionalTorsional ModeModeTower Mode 6Tower Mode 6
22ndnd TorsionalTorsional ModeMode
Hei
ght
(ft)
Amplitude Amplitude
Top
Base
Top
Base
ConclusionsConclusionsUncertainty due to data quality and errors (bias error, Uncertainty due to data quality and errors (bias error, spikes) spikes) –– corrected through digital signal processing and corrected through digital signal processing and manual removal of spikesmanual removal of spikes
Uncertain excitation due to transfer of traffic excitation Uncertain excitation due to transfer of traffic excitation through structural connections to the towersthrough structural connections to the towers
NonNon--stationary excitation stationary excitation –– sample for longer timesample for longer time
Tower oscillations coupled with span oscillations Tower oscillations coupled with span oscillations –– reflection reflection of motions between the two componentsof motions between the two components
Uncertainty related to identifying the tower modes from the Uncertainty related to identifying the tower modes from the coupled motions of the spans and towerscoupled motions of the spans and towers
Seismic evaluation requires identifying those modes that Seismic evaluation requires identifying those modes that determine the tower demands during earthquakedetermine the tower demands during earthquake
ConclusionsConclusions
Dynamic testing and modal analysis of real structures Dynamic testing and modal analysis of real structures are often driven by real engineering objectivesare often driven by real engineering objectivesA process oriented approach to taking data, processing, A process oriented approach to taking data, processing, and identifying the modal properties may fail to satisfy and identifying the modal properties may fail to satisfy the real engineering objectivesthe real engineering objectivesThe physics of the problem must be considered during The physics of the problem must be considered during each stage of experiment and analysis so that we may each stage of experiment and analysis so that we may reach meaningful interpretations of the results reach meaningful interpretations of the results –– we we cannot simply present a large quantity of identified cannot simply present a large quantity of identified frequencies/mode shapes for the purpose of seismic frequencies/mode shapes for the purpose of seismic retrofittingretrofittingidentifying the subset of peaks in frequency spectra identifying the subset of peaks in frequency spectra associated with resonant motion of the tower is essential associated with resonant motion of the tower is essential and this represents a significant challenge in ambient and this represents a significant challenge in ambient vibration testingvibration testing
SummarySummaryThe mechanisms of uncertainty in testing of actual The mechanisms of uncertainty in testing of actual structures are abundantstructures are abundantExplicit consideration and mitigation of uncertainty Explicit consideration and mitigation of uncertainty in test design, execution, processing, and in test design, execution, processing, and interpretation is critical for providing real interpretation is critical for providing real engineering benefits from the experimentengineering benefits from the experimentAlthough some uncertainty can be mitigated through Although some uncertainty can be mitigated through proper design and execution of a field experiment, proper design and execution of a field experiment, we may have to accept that some level of we may have to accept that some level of uncertainty will always remain uncertainty will always remain –– heuristics related to heuristics related to structure and test objectives an important structure and test objectives an important component of interpretation and decision making component of interpretation and decision making based on experimentbased on experiment
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