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Qin Pan Ph.D. Thesis Defense Presentation System Identification of Constructed Civil Engineering Structures and Uncertainty Advisor: Dr. A.E. Aktan Committee Members: Drs. Aktan, Gurian, Montalto, Moon, Tan December 17, 2007

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Qin Pan

Ph.D. Thesis Defense Presentation

System Identification of Constructed Civil

Engineering Structures and Uncertainty

Advisor: Dr. A.E. Aktan

Committee Members: Drs. Aktan, Gurian, Montalto, Moon, Tan

December 17, 2007

Key Research Objective: The impact of

Epistemic Modeling Uncertainty Associated with

System Identification of Constructed Systems; System Identification of Constructed Systems;

How to Recognize & Mitigate it

Outline

� Background & Definition

� Past Research: Sys-Id Applications on Civil Structures

� Research Motivations & Objectives

� Impact of Epistemic Modeling Uncertainty on the Reliability of Sys-IdReliability of Sys-Id

� Recognition & Mitigation of Epistemic Modeling Uncertainty

� Model Adequacy Evaluation

� Conclusions

� Recommendations & Future Work

Historical Outline of Characterization of Existing

SystemsTime

1930 1940 1950 1960 1970 1980 1990 2000 2010

Start of dynamic testing

Development of FFT

ARMAV, LSCE, PTD, SSI, CMIF & etc Advanced sensing &

Exp

eri

men

tal

Modal testing

Static testing

sensing & networking

Development of FEM

Start of matrix structural analysis

Production-level FEM program

Sys-Id in control engineering

Hart & Yao (1977)

Liu & Yao (1978)

Farrar et al (2001)

Sys-Id in civil engineering

An

aly

tical

Inte

gra

tive

System Identification (Sys-Id)

Utilization of Model for Simulation, Scenario Analysis

Observation and Conceptualization

(2)

(1)

(6)

System identification is a general term to describe mathematical tools and

algorithms that build/tune dynamical models from measured data (Wikipedia).

Sys-IdA-Priori Modeling

Measurement, Monitoring, Controlled Experimentation

Evaluating Modeling Uncertainty, Model Calibration & Check Model Adequacy

Integration, Processing and Interpretation of Data

(4)

(3)

(5)

Outline

� Background & Definition

� Past Research: Sys-Id Applications on Civil Structures

� Research Motivations & Objectives

� Impact of Epistemic Modeling Uncertainty on the Reliability of Sys-IdReliability of Sys-Id

� Recognition & Mitigation of Epistemic Modeling Uncertainty

� Model Adequacy Evaluation

� Conclusions

� Recommendations & Future Work

Suspended SpanCantilever Arm

Cantilever Arm

Anchor Span Anchor Span

822 ft 411 ft 822 ft 411 ft 822 ft

P.P. 27 P.P. 45

Before Retrofit

Commodore Barry Bridge (Grimmelsman 2005)

Pin

Hanger

Cantilever

Arm

Suspended

Span

Ha

ng

er

Pin

Pin

30

m

1

3D FEM of Hanger Region

After Retrofit

Commodore Barry Bridge (Grimmelsman 2005)

Section B-B

Hanger100

0

-100

-200

-300

-400

-500

- 600

Strain Response of Hanger

Rod/Hanger Force Ratio

calculated from the

strain measurement data

Spreader Beams @ LC

Spreader Beams @ UC

AA

BB Section A-A

- Vibrating Wire

Strain Gage

Rod400

350

300

250

200

100

50

0

150

-50

Strain Response of Rod

using nominal modulus

of elasticity values is

0.726.

Brooklyn Bridge (Grimmelsman 2006)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-7

Accele

ration (

g2/H

z)

B

C

E

G

H

MT

Tower Longitudinal Vibration Output Spectra

18 Peaks in 0-5 Hz Band

V TLL V

TLTLTL

TLTLTL

TLL

TLL

TLL

V V

V V

V V

L L

L L L

L L L

L

L

L

L

L

L

T

T

T

T

T

T

T

TT

T

Measures to rule out spurious results:

• Max MIF

• Shape Plausibility

• Shape agreement

• Coherence

• MAC values

• Phase factor

• Span modes

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency (Hz)

?

Mechanically Transparent System

Conceptualized Analytical model

V VV V

1.387 Hz

0

50

100

150

200

250

-1.0 -0.5 0.0 0.5 1.0

Blong

Clong

Elong

Glong

Hlong

the 1st longitudinal tower mode f = 1.387 Hz

-1.0 -0.5 0.0 0.5 1.0

1.201

1.294

1.387

1.450

1.519

0.313

0.381

0.439

0.566

0.610

0.806

0.972

1.201

1.294

1.387

1.450

1.519

Unit Normalized Modal Amplitude

Demonstrator @ Di3 Lab (Ciloglu 2006)

Reduced-Scaled Deck-on-Beam Bridge Model

Relationship btw Major Sources of Uncertainty & Identified Experimental Modal Parameters

Connections Boundary

Post-processingPreprocessingStructural

Complexity Excitation

Steel Roller

SubstructureNot Distributed

Random Dec.

W/o Exp. Window

Signal L-2

DFT CMIF

PTD

SSI

Correlation Func.

Signal L-1

Signal L-3

W/ Exp. Window

SignalModeling

Steel Roller+ Weight

Neoprene Roller

SuperstructureDistributed

SuperstructureNot Distributed

SubstructureDistributed

Demonstrator @ Di3 Lab (Ciloglu 2006)

Support Boundary Sensor

Deck Boundary SensorSensor in the span

1 4 7 10 13 16 19

5 8 11 14 17

3 6 9 12 15 18 21

2 20

Output: Accelerometer on the deck and support plates

Output: Accelerometer under the grid

Input & Output: Instrumented impact hammer, Accelerometer

The modal properties obtained from Impact tests serve as ground truth to evaluate the effects of uncertainty

Effect of Uncertainties due to Preprocessing & Post-processing

0.97

0.98

0.99

1.00

1.01

1.02

1.03

1 2 3 4 5 6 7 8 9 10 11 12

Mode Number

CMIF-RD

PTD-RD

SSI-RD

CMIF-C

PTD-C

SSI-C

The 8th & 12th modes were only

identified by CMIF-RD

PTD-RD PTD-RD PTD-RD PTD-RDPTD-C

PTD-RDSSI –RDCMIF-CCMIF-CSSI-C

PTD-RD PTD-RD PTD-RDPTD-C

PTD-RDSSI –RDCMIF-CCMIF-CSSI-C

Outline

� Background & Definition

� Past Research: Sys-Id Applications on Civil Structures

� Research Motivations & Objectives

� Impact of Epistemic Modeling Uncertainty on the Reliability of Sys-IdReliability of Sys-Id

� Recognition & Mitigation of Epistemic Modeling Uncertainty

� Model Adequacy Evaluation

� Conclusions

� Recommendations & Future Work

Motivation: Lessons from Past Experience

� Significant obstacles for widespread implementations of Sys-Id in engineering practice primarily stem from our inability to reliably simulate, measure and interpret the actual physical behaviors of a constructed system, consequently leading to the skepticism towards the credibility of Sys-Id held by owners/stewards of constructed systems.

� These limitations mainly arise from various sources of uncertainty which smear into Sys-Id process through the choice of model structure, idealization of boundary and continuity conditions as well as the design, idealization of boundary and continuity conditions as well as the design, execution and interpretation of field testing and monitoring program.

� Current applications of Sys-Id usually lump uncertainties inherent in a constructed system as a small number of incorrect model parameters or random variables with assumed probability models.

� Many sources of uncertainty, as demonstrated in previous examples, stem from those unknown or less understood structural behaviors as well as their interactions with surrounding environments. They are difficult to be described with probability models and in some cases they may even not be parameterized.

� This type of uncertainty, as opposed to randomness-based aleatory

uncertainty, arise from a lack of knowledge and is called epistemic

uncertainty. Usually epistemic uncertainty is reducible when more information is available.

� Epistemic uncertainty has more profound impact on the reliability of system identification. However, systematic investigation on the impact of uncertainty, and epistemic uncertainty particularly, on system identification has not been made yet.

Focus Area: Epistemic Uncertainty

identification has not been made yet.

Terms used in literature to describe dual meaning of uncertainty(adapted from Christian 2004)

Uncertainty due to naturally

variable phenomena in time or

space

Uncertainty due to lack of

knowledge or

understanding of nature

Reference citation

Aleatory uncertainty Epistemic uncertainty Hacking 1975; McCann 1999; Ang

and De Leon 2005

Natural variability Knowledge uncertainty NRC 2000

Random or stochastic variability Functional uncertainty Stedinger et al. 1996

Objective uncertainty Subjective uncertainty Chow et al. 1988

External uncertainty Internal uncertainty Chow et al. 1988

Statistical uncertainty Inductive probability Carnap 1936

Irreducible uncertainty Reducible uncertainty

Chance Probability Poisson, Cournot (Hacking 1975)

ACTUAL STATE OF A CONSTRUCTED SYSTEM: M, K, C

CONVERGED SYS-ID

RESULTS

Epistemic Uncertainty

DIVERGED SYS-ID

RESULTS

CONVERGED SYS-ID

RESULTS

Additional Information

Additional Information

Epistemic Uncertainty

1

26

START OF SYS-ID

Gro

un

d t

ruth

Aleatory Uncertainty

Aleatory Uncertainty

Aleatory Uncertainty

Sys-Id

Aleatory Uncertainty

2

3

6

4

5

Gro

un

d t

ruth

(3) Controlled Experimentation

STRUCTURAL COMPLEXITY:

•Non-stationarity of boundary and

continuity conditions

•Changes in intrinsic stresses during

tests (redundancy, deterioration)

•Nonlinearities: Many forms of

material and damping nonlinearity,

friction, intermittent contact and uplift

FORCE AND EXCITATION:•Amplitude

•Spectral distribution

•Spatial distribution and

transmissibility

•Directionality

•Dimensionality (1D, 2D or 3D)

•Duration and Non-stationarity

DATA ACQUISITION:•Spatial aliasing

•Time synchronization

•Hardware filtering options

•Noise & bias in signal

•Measurement bandwidth

•Cabling and installation effects

(2) Preliminary Model(s)

•Analytical representation of

physical members and connections

•Completeness of 3D geometry

•Real-time data quality

assessment, management and

warehousing

(4) Data Processing

Sys-Id

•Health/Performance

Monitoring

•Damage detection, Prognosis

•Scenario Analysis and

Vulnerability Assessment

•Performance-based

Engineering

•Guidelines and Codes

(6) Utilization(1) Conceptualization

•Identify/Leverage Heuristics

•Archival of structural drawings

/design calculations, inspection

reports

•Site visits, geometry

measurements, photogrammetry

•Material Sampling, testing, NDE

•Virtual Reconstruction in 3D CAD

•Completeness of 3D geometry

•Soil-foundation, structural

members, joints: stiffness and

kinematics

•Mechanisms/Forms of Nonlinearity

•Test-analysis correlation

•Parameter grouping

•Sensitivity Analysis

•Modality

•Objective function and

constraints

•Optimization

•Physical interpretation of results

(5) Model Calibration

warehousing

•Error identification/ Cleaning

•Different filtering, averaging and

windowing options

•Data post-processing algorithmsUncertainty

Research Objectives

� Influence of modeling uncertainty due to epistemic mechanisms on analytical modeling of

constructed systems

� Feasible techniques to recognize and mitigate modeling uncertainty

� Adequacy of a field-calibrated model to simulate � Adequacy of a field-calibrated model to simulate

all of the critical physical mechanisms impacting a

constructed system

� Review of model updating procedures including test-

analysis correlation, error localization, sensitivity

analysis, and data informativeness quantification as

well as updating algorithms.

Laboratory Test Bed: Cantilever

Beam with Two Test Configurations

Impact on Identification

Test-Analysis Correlation

Real-Life Constructed System: the

Henry Hudson Bridge

Recognition of Epistemic

Research Design1

2

3

4

5

6Epistemic Modeling Uncertainty in Sys-

Id of Constructed Civil StructuresSys-Id

Research Approach

Identification Results

Recognizing Epistemic

Uncertainty

Mitigating Epistemic

Uncertainty

Model Adequacy Evaluation

Correlation Epistemic Uncertainty

Recognizing Epistemic

Uncertainty

Mitigating Epistemic

Uncertainty

Sensitivity Analysis

Error Localization

Index

Iterative Model

Updating

Heuristics

Outline

� Background & Definition

� Past Research: Sys-Id Applications on Civil

Structures

� Research Motivations & Objectives

� Impact of Epistemic Modeling Uncertainty on the

Reliability of Sys-IdReliability of Sys-Id

� Recognition & Mitigation of Epistemic Modeling

Uncertainty

� Model Adequacy Evaluation

� Conclusions

� Recommendations & Future Work

Cantilever Study

Cantilever Beam Study

Test Configuration 1 Test Configuration 2

Model A Model B

1 2 3 4 5

Time (s)

Fo

rce

117.5 in

Property Value

Density ρ 0.284 lb-f/in3

Young’s Modulus E 29x106 lb-f/in

2

Cross Section Area A 0.954 in2

Moment of Inertia I about weak axis 0.355 in4

Modal Contributions to Simulated Impulse Response functions

Mechanical & Material Properties of the Beam

Analytical Simulation of MRIT

f = 4.910 Hz

f = 30.770 Hz

f = 86.157 Hz

f = 168.846 Hz

f = 279.091 Hz

Simulated Frequency Response functionsModal Parameters Estimated Based on Continuum Theory

( ) ( ) 02

2

2

2

2

2

=

∂+

x

uxEI

xt

uxm

Cantilever Beam Test Configuration 1

1 2 3 4 5 6

Steel Tube X-section

3X1.5X0.125 in

PCB Capacitive

Accelerometer Model

3701G3FA3G

C-shape

Clamp

Steel Pedestal

Cantilever Beam Test Configuration 2

C

B

A

D

12 3 4 5 6

Steel Pedestal

24x3x3/4 in steel plate; center to center

distance btw two rods connected on the

same plate is 18 inch

4-inch long aluminum angle L6x6x3/8 in

A

B

High-strength steel rod with d = 3/8 inch

16-inch long steel angle L3x3x1/2 in

C

D

Steel Tube X-section

3X1.5X0.125 in

PCB Capacitive

Accelerometer Model

3701G3FA3G

C-shape

Clamp

Impact Test

VXI DAC Express Software

Agilent IO Lib Control

DAQ PC

DAQ PC

HPVXI

Data Acquisition Diagram

Impact Excitation

HP VXI

ImpulseHammer 086C02

Microdot cable

Co-ax cable

Breakout box PCB 3701G3FA3G Capacitive Accelerometers

Ch1

Ch2

Ch3

Ch4Ch5

Ch6

Ch 7

Impact Force

FRF

Test Measurements

1

2 3 4 5 6

STATIC LOAD @ PT 5

Celesco PT101 cable-extension transducer

PCB 3701G3FA3G capacitive accelerometer

Static Test

Time-History Displacement Response of the beam

Static Test Sensor Layout

CELESCO PT101

MODE 3

1.2

MODE 2

-0.8

-0.4

0.0

0.4

0.8

1.2

0.0000 20.0000 40.0000 60.0000 80.0000 100.0000 120.0000

Distance (in)

MODE 1

0.0

0.2

0.4

0.6

0.8

1.0

0.0000 20.0000 40.0000 60.0000 80.0000 100.0000 120.0000

Distance (in)

Experimental Results from Configuration 1

Frequencies Mode #

1 2 3 4 5

Initial FE 4.9099 30.7698 86.1576 168.8423 279.1383

Test 1 4.709 29.321 82.913 160.576 260.970

Test 2 4.714 29.355 82.965 160.442 261.429

Test 3 4.712 29.055 82.789 160.701 260.437

Mean 4.712 29.244 82.889 160.573 260.945

STD 0.003 0.164 0.090 0.130 0.496

Diff (%) 4.037 4.960 3.794 4.898 6.518

95% C. I. 4.712±0.013 29.244±0.705 82.889±0.387 160.573±0.559 260.945±2.133

Damping Ratios Mode # 1 2 3 4 5

Test 1 2.106 1.558 0.622 0.288 0.285

Test 2 2.087 1.516 0.628 0.271 0.270

Test 3 2.086 1.596 0.572 0.211 0.285

Mode 1

Mode 2

Mode 3

uniform loading surface (ULS) of the cantilever beam

MODE 5

-1.0

-0.5

0.0

0.5

1.0

0 20 40 60 80 100 120

Distance (in)

MODE 4

-1.0

-0.5

0.0

0.5

1.0

0 20 40 60 80 100 120

Distance (in)

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

Distance (in)

X- Modal

Test 3 2.086 1.596 0.572 0.211 0.285

Mean 2.093 1.557 0.607 0.257 0.280

STD 0.011 0.040 0.031 0.040 0.009

95% C. I. 2.093±0.047 1.557±0.172 0.607±0.133 0.257±0.172 0.280±0.039

Mode 4

Mode 5

uniform loading surface (ULS) of the cantilever beam

Frequencies Mode #

1 2 3 4 5 6 7 8

Test 1 3.337 24.606 70.818 127.913 140.516 150.968 188.372 245.359

Test 2 3.338 24.608 70.819 127.921 140.527 150.972 188.389 245.372

Test 3 3.337 24.611 70.823 127.931 140.537 150.983 188.379 245.397

Test 4 3.336 24.616 70.822 127.943 140.548 150.980 188.418 245.362

Test 5 3.337 24.614 70.819 127.940 140.543 150.969 188.399 245.399

Test 6 3.342 24.618 70.820 127.943 140.541 150.963 188.413 245.406

Mean 3.338 24.612 70.820 127.932 140.535 150.973 188.395 245.381

STD 0.002 0.005 0.002 0.013 0.012 0.008 0.018 0.019

95% C. I. 3.338

±0.005

24.612

±0.012

70.820

±0.005

127.932

±0.032

140.535

±0.030

150.973

±0.020

188.395

±0.047

245.381

±0.050

Damping Ratios Mode #

1 2 3 4 5 6 7 8

Test 1 2.861 1.157 0.298 0.181 0.231 0.291 0.312 0.337

Test 2 2.842 1.155 0.293 0.181 0.230 0.287 0.312 0.335

Test 3 2.823 1. 155 0.294 0.181 0.239 0.286 0.317 0.339

Test 4 2.860 1.132 0.298 0.181 0.236 0.288 0.318 0.344

Experimental Results from Configuration 2uniform loading surface (ULS) of the cantilever beam

MODE 1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80 100 120

DISTANCE (in)

PTD1

PTD2

PTD3

PTD4

PTD5

PTD6

MODE 2

-1.0

-0.5

0.0

0.5

1.0

1.5

0 20 40 60 80 100 120

DISTANCE (in)

PTD1

PTD2

PTD3

PTD4

PTD5

PTD6

MODE 3

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

PTD1

PTD2

PTD3

PTD4

PTD5

PTD6

Mode 1

Mode 2

Mode 3

Test 4 2.860 1.132 0.298 0.181 0.236 0.288 0.318 0.344

Test 5 2.846 1.113 0.302 0.182 0.236 0.292 0.321 0.353

Test 6 2.843 1.101 0.306 0.181 0.235 0.299 0.323 0.349

Mean 2.844 1.136 0.299 0.181 0.235 0.291 0.317 0.343

STD 0.015 0.024 0.005 0.000 0.003 0.005 0.005 0.007

95% C. I. 2.844

±0.038

1.136

±0.062

0.299

±0.013

0.81

±0.001

0.235

±0.009

0.291

±0.012

0.317

±0.012

0.343

±0.018

uniform loading surface (ULS) of the cantilever beam

DISTANCE (in)

MODE 4

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

PTD1

PTD2

PTD3

PTD4

PTD5

PTD6

MODE 5

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

PTD1

PTD2

PTD3

PTD4

PTD5

PTD6

MODE 6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

PTD1

PTD2

PTD3

PTD4

PTD5

PTD6

MODE 7

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

PTD1

PTD2

PTD3

CMIF4

PTD5

PTD6

MODE 8

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

PTD1

PTD2

PTD3

PTD4

PTD5

PTD6

Mode 4 Mode 5

Mode 6 Mode 7

Mode 8

Updating Parameter: E

Identification Results Using Model A

1

2

3

4

5

6

7

8

initial

updated

Frequency before and after calibration in Run 1

270

275

280

285

290

E (

x10

5 p

si)

Change of E with iteration in Run 1

Identification Run 1: Cantilever Beam under Configuration 1

-2

-1

0

1

1 2 3 4 5

MODE

-10

0

10

20

30

40

50

1 2 3 4 5

MODE

initial

updated

1 2 3 4260

265

270

Iterations

1 2 3 4 5180

200

220

240

260

280

300

Iterations

E (

x10

5 p

si)

Frequency before and after calibration in Run 2Change of E with iteration in Run 2

Configuration 1

Identification Run 2: Cantilever Beam under Configuration 2

261.724

194.896

Initial value of Eis 290 (x10^5) psi

Observations & Discussions About Identification

Results Using Initial Model A� All of the five observed vibration modes from the cantilever beam under test configuration 1 could be paired up with the analytical predictions from initial model A.

� The test-analysis correlation were improved after calibration by adjusting the Young’s modulus of steel. With a decrease of less than 10 percent of its nominal value, the difference in natural frequency was under 2 percent. The mode shapes remained because they were independent on the updating parameter. independent on the updating parameter.

� In Run 1, the information in all five modes was included in model updating, while the fourth mode was excluded in identification Run 3. However, the updated values of the model parameter as well as the natural frequencies were very similar.

� A total of eight modes were identified from the beam under test configuration 2. The first three and the eighth mode were paired up with the analytical first three and the fifth mode from initial model. The rest four experimental modes all demonstrate deflection shapes similar to the analytical fourth bending mode.

� Immense uncertainty was associated with the correlation between the measured and simulated fourth bending mode. Only four pairs of modes were thus included in identification Run 2.

� Although the gap in natural frequency between the analytical model and experiment observation narrowed considerably after updating, relatively large difference remained, especially in the natural frequency of the first mode.

Observations & Discussions About Identification

Results Using Initial Model A (Cont’d)

frequency of the first mode.

� The calibration process forced the pre-selected updating parameter to decrease by about 33 percent of its initial (nominal) value, which already lost its physical meaning.

� Significant discrepancy was observed in the estimated values for the model parameter E from the identification cases of configurations 1 and 2, which were supposed to converge to the same value because they represented the material property of the same beam.

Additional Test on Configuration 2

5

Vertical sensor on top plate

Longitudinal sensor on top plate Lateral sensor on beam

Vertical sensor on beam

6

741 23

SteelPedestal Instrumentation Plan

2

Chan 1

Frequency Response Functions (FRFs)

Sensors Installed on the Boundary Assembly

0 50 100 150 200 250 300

10-8

10-6

10-4

10-2

100

102

Frequency (Hz)

log

X/F

Chan 1

Chan 2

Chan 3

Chan 4

Chan 5

Chan 6

Chan 7

127.9

127.9 142.9 151 188.4

Chan 1 & 2 – Longitudinal sensors on top plates;

Chan 3 & 4 – Vertical sensors on top plates;

Chan 5 & 6 – Vertical sensors on cantilever;

Chan 7 – Transverse sensor on cantilever;

Additional Test on Configuration 2

Beam Mode 4

FRFs Output @ Chan 6

121.3

127.9

132.6142.9

151

164.7 178.3

188.4

282

284

286

288

290

E (

x10

5 p

si)

Identification Results Using Initial Model B

Frequency before and after calibration in Run 4

Change of E

Updating parameters: E, Kr

0

1

2

3

4

5

initial

updated

460

470

480

490

500

Kr

(x10

4 p

si)

Change of Kr

Identification Run 4: Cantilever Beam under Configuration 1

Initial value of E is 290 (x10^5) psi; Initial value of Kr is 500 (x10^4) psi;

0 5 10 15 20200

210

220

230

240

250

260

270

280

290

Iterations

E (

x10

5 p

si)

0 2 4 6 8 10 12 14 16 18278

280

282

Iterations

Frequency before and after calibration in Run 5

Change of E

-2

-1

1 2 3 4 5

MODE

-5

0

5

10

15

20

25

30

35

40

45

1 2 3 4 5

MODE

initial

updated

0 2 4 6 8 10 12 14 16 18440

450

460

Iterations

Kr

(x10

0 5 10 15 200

100

200

300

400

500

Iterations

Kr

(x10

4 p

si)

Change of Kr

Identification Run 5: Cantilever Beam under Configuration 2

279.603

280.983

MODE 1

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120

Distance (in)

test

initial

updated

MODE 2

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

Distance (in)

test

initial

updated

MODE 3

-0.8

-0.4

0.0

0.4

0.8

1.2

0 20 40 60 80 100 120

Distance (in)

test

initial

updated

MODE 4

-1.0

-0.5

0.0

0.5

1.0

0 20 40 60 80 100 120

Distance (in)

test

initial

updated

MODE 5

-1.0

-0.5

0.0

0.5

1.0

0 20 40 60 80 100 120

Distance (in)

test

initial

updated

Initial Updated

1 1.0000 1.0000

2 0.9987 0.9988

3 0.9989 0.9989

4 0.9965 0.9966

5 0.9958 0.9958

mode #MAC

Identification Results with Model BBeam with Configuration 1 (Run 4)

Distance (in) Distance (in) 5 0.9958 0.9958

MODE 2

-0.8

-0.4

0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

test

initial

updated

MODE 4

-0.8

-0.4

0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

test

initial

updated

MODE 3

-0.8

-0.4

0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

test

initial

updated

MODE 5

-0.8

-0.4

0

0.4

0.8

1.2

0 20 40 60 80 100 120

DISTANCE (in)

test

initial

updated

MODE 1

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

DISTANCE (in)

test

initial

updated

initial updated

1 0.9941 1.0000

2 0.9831 0.9996

3 0.9604 0.9972

4 0.9849 0.9949

5 0.9759 0.9959

Mode #MAC

Beam with Configuration 2 (Run 5)

Observations & Discussions

� Additional dynamic test on the beam with configuration 2 revealed the interaction between the beam and boundary assembly. This observation was conceptualized as rotational spring at the beam support in initial model B.

� Among the four modes which demonstrated similar deflection shapes, f = 150.99 Hz was dominated by the vibrations of the beam and was only included in the calibration process.

� With initial model B, the beam under two test configuration 1 and 2 were calibrated in identification Run 4 and 5 respectively. In Run 4, the calibrated model converged to the similar level as that in Run 1 and 3. In Run 5 the discrepancy between the predicted natural frequencies and their experimental counterparts were significantly reduced and only ±3 percent difference remained.

� The values for the common model parameter in Run 4 and 5, the Young’s modulus E, both decreased by about 3 percent of its nominal value, although they did not converge to the exact same value.

Observations & Discussions

� Good correlation between the values of common updated parameter as well as the modal predictions implied that the initial model Befficiently conceptualize the influences of the rotary movement of the boundary assembly on the beam without explicitly incorporating the boundary assembly in the initial model.

� Epistemic modeling uncertainty associated with the initial model Awould seriously impair the reliability of the identification for the beam under configuration 2.

Updating

Parameter Nominal

Run 1: Config 1

with model A

Run 2: Config 2

with model A

Run 4: Config 1

with model B

Run 5: Config 2

with model B

E (×105 psi) 290 261.724 194.896 279.603 280.983

Diff (%) -9.750 -32.795 -3.585 -3.109

under configuration 2.

� The selected updating parameter tended to compensate for the influence of epistemic modeling error by distorting itself. As a result, the updated value for E lost its physical significance. The calibrated model still failed to accurately predict the experimental frequencies.

Outline

� Background & Definition

� Past Research: Sys-Id Applications on Civil

Structures

� Research Motivations & Objectives

� Impact of Epistemic Modeling Uncertainty on the

Reliability of Sys-IdReliability of Sys-Id

� Recognition & Mitigation of Epistemic Modeling

Uncertainty

� Model Adequacy Evaluation

� Conclusions

� Recommendations & Future Work

Henry Hudson Bridge

The Henry Hudson Bridge

South

ApproachSouth

Viaduct Arch SpanNorth

Viaduct

North

Approach

South

Tower

North

Tower

East Elevation

300’409’ 45’ 45’ 270’300’840’

Preliminary 3D FE Model

Upper

Level VV VV L LL L

Test on the north part of the bridge

Instrumentation Plan

Sensor @ Lower Level of Arch Span

Sensor @ Upper Level of Arch Span

Sensor @ Half Height of Tower DAQ

D

To

we

r

To

we

r

CL

South Viaduct

North Viaduct

Level

Lower

Level

181716

5957

1515.2715.2515.22

5553525149464238

131211 14 15.1 15.3 15.6

3027252423212019

T T T

T

T

TT

T

T

TT

TT

T

T

T

T

T

T

T

T

T

T

TT

TV

V

V

V

VV

V

VV

V

L L

L L L L

TT

V

VEast Side Vertical

Accelerometer

West Side Vertical

Accelerometer

East Side Transverse

Accelerometer

West Side Transverse

Accelerometer

L

LEast Side Longitudinal

Accelerometer

West Side Longitudinal

AccelerometerV T V T

Sensors Which Stay for the Tests on

North & South Part of the Bridge

D

D

0 200 400 600 800 1000 1200 1400 1600 1800 2000-8

-6

-4

-2

0

2

4

6

8x 10

-3

0 20 40 60 80 100 120-6

-4

-2

0

2

4

6x 10

-7

0 1 2 3 4 5 6 7 8 9 1010

-7

10-6

10-5

10-4

Time-domain measurements under ambient conditions

Pseudo IRF generated by spectrum estimation methods

Pseudo FRF generated by spectrum estimation methods

Imported in X-Modal and process with PTD

Stability plot to present consistency of poles with different model order

Modal Parameters:

Preprocessing

Data Analysis

• Stationarity

Check;

• Effect of Traffic Load Amplitude;

• Effect of

Sampling

Bandwidth;

Data Processing

Imported in X-Modal and process with CMIF

CMIF plot generated based on singular value decomposition

Modal Parameters: ω, ζ, Φ

Post-processing by CMIFPost-processing by PTD

-200

0

200

400

Model Calibration

Global (Modal)

Calibration: The correlation

between analytical and

experimental frequencies

and mode shapes was

achieved in modal space by

adjusting the stiffness or

mass or a combination of

Mo

del C

ali

bra

tio

n

Sensitivity

Analysis

Correlation:

� Numerical

comparison of

� To make sure that

analytical mode order

is consistent with

experimental;

� To make sure that

analytical frequency

values have minimum

PROCESS TOOL PURPOSE

mass or a combination of

both.

Local (Flexibility)

Calibration: The correlation

between analytical and

experimental strain and/or

displacement was achieved

by adjusting the structural

stiffness.

Mo

del C

ali

bra

tio

n

comparison of

frequencies;

� Graphical

comparison of

mode shapes;

� Numerical

comparison of

mode shapes

Heuristics

values have minimum

discrepancy with those

of experiment;

� To ensure that the

analytical model is

complete so that the

global stiffness and

force distribution

mechanisms are

properly simulated.

Test-Analysis Correlation

Analytical Experimental Mode

Freq (Hz) Description Freq (Hz) Description Diff (%)

1 0.505 2nd vertical bending 0.739 2nd vertical bending -31.664

2 0.512 1st lateral bending (arch) 0.616 1st lateral bending (arch) -16.883

3 0.890 3rd vertical bending 0.952 3rd vertical bending -6.513

4 0.977 2nd lateral bending (arch) 1.182 2nd lateral bending (arch) -17.343

5 1.257 1st lateral bending (global) 1.587 1st lateral bending (global) -20.794

6 1.535 1st vertical bending 1.506 1st vertical bending 1.926

7 1.651 4th vertical bending 1.732 4th vertical bending -4.677

8 2.393 5th vertical bending 2.556 5th vertical bending -6.377

9 3.137 6th vertical bending 3.300 6th vertical bending -4.939

10 3.955 7th vertical bending 4.110 7th vertical bending -3.771

-800

-600

-400

-200

0

200

400

600

800

-50050

20

40

60

80

100

120

140

160

180

200

220

-800 -600 -400 -200 0 200 400 600 8000

100

200

300

● EXP MODE SHAPE

- SAP MODE SHAPE

- - UNDEFORMED SHAPE -800

-600

-400

-200

0

200

400

600

800

-50050100

20

40

60

80

100

120

140

160

180

200

-800 -600 -400 -200 0 200 400 600 800-100

0

100

● EXP MODE SHAPE

- SAP MODE SHAPE

- - UNDEFORMED SHAPE

2nd Vertical Mode f = 0.739 Hz 1st Lateral Mode f = 0.616 Hz

Sensitivity Analysis

The model parameters/conditions selected for sensitivity analysis include:

� The Young’s modulus of the steel;

� The Young’s modulus of the deck concrete;

� Variations in boundary conditions;

� The continuity conditions between viaduct-deck-arch interface at both the upper and lower decks;

� The stiffness of the lateral translational springs located at each end of the two viaduct spans;

1.8 1.8

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.85 E 0.90 E 0.95 E 1.00 E 1.05 E 1.10 E 1.15 E

Variation of E of Steel

Mo

dal

Fre

qu

en

cy (

Hz)

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

Mode 6

Mode 7

Mode 8

Mode 9

Mode 10

Mode 11

Mode 12

Mode 13

Mode 14

Mode 15

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Equal Constraint in

Uy, Uz

Body Constraint in

Uy, Uz

Body Constraint in

Uy, Uz, Rx, Ry &

Rz

Body Constraint in

all Six DOFs

Variation of Continuity Condition at Deck-Tower Interface

Mo

dal

Fre

qu

en

cy (

Hz)

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

Mode 6

Mode 7

Mode 8

Mode 9

Mode 10

Mode 11

Mode 12

Mode 13

Mode 14

Mode 15

Heuristics for Calibration

� Correct joint constraints btw arch rib &lower deck;

� Remove frame end releases for vertical members btw arch rib & lower deck;

� Adjust joint rigidity factors at

column-floor connections

� Adjust the continuity conditions at the arch-tower-viaduct interface

Calibration Results

0.9

MA

C V

alu

es o

f V

ert

ical M

odes

Mode

#

Experimental

(Hz)

Initial

(Hz) Diff (%)

Updated

(Hz) Diff (%) Description

1 0.616 0.512 -16.883 0.588 -4.545 1st lateral bending (arch)

2 0.739 0.505 -31.664 0.721 -2.436 2nd vertical bending

3 0.952 0.890 -6.513 0.973 2.206 3rd vertical bending

4 1.182 0.977 -17.343 1.054 -10.829 2nd lateral bending (arch)

5 1.506 1.257 -16.534 1.404 -6.773 1st lateral bending (global)

6 1.587 1.535 -3.277 1.566 -1.323 1st vertical bending

7 1.732 1.651 -4.677 1.714 -1.039 4th vertical bending

8 2.556 2.393 -6.377 2.505 -1.995 5th vertical bending

9 3.300 3.137 -4.939 3.276 -0.727 6th vertical bending

10 4.110 3.955 -3.771 4.061 -1.192 7th vertical bending

1

2

3

4

1

2

3

4

0

0.2

0.4

0.6

0.8

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2

3

4

1

2

3

4

0

0.2

0.4

0.6

0.8

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

MA

C V

alu

es o

f V

ert

ical M

odes

Befo

reA

fter

Befo

reA

fter

MA

C V

alu

es o

f Late

ral M

odes

Model Adequacy Check By Sensitivity Analysis of E

NORM OF ERROR IS DEFINED AS: ∑=

−=

7

1

2

i EXPi

EXPiFEi

FREQ

FREQFREQNORM

VERTICAL FREQUENCIES & NORMS OF ERROR (Hz) FROM INITIAL MODEL

MODE # 0.85 E 0.90 E 0.95 E 1.00 E 1.05 E 1.10 E 1.15E 1.20 E 1.25 E EXP

1 0.4660 0.4795 0.4925 0.5053 0.5177 0.5298 0.5416 0.5532 0.5645 0.739

2 0.8204 0.8441 0.8671 0.8895 0.9114 0.9328 0.9537 0.9741 0.9941 0.952

3 1.4152 1.4561 1.4958 1.5345 1.5723 1.6091 1.6451 1.6804 1.7149 1.506

4 1.5234 1.5671 1.6096 1.6510 1.6913 1.7307 1.7692 1.8068 1.8437 1.732

5 2.2083 2.2716 2.3332 2.3931 2.4515 2.5086 2.5643 2.6182 2.6724 2.5560.3

0.4

0.5

0.6

No

rm o

f E

rro

r

UPDATED

INITIAL

VERTICAL FREQUENCIES & NORMS OF ERROR (Hz) FROM UPDATED MODEL

6 2.8965 2.9789 3.0589 3.1369 3.2128 3.2868 3.3592 3.4298 3.4989 3.300

7 3.6551 3.7579 3.8578 3.9549 4.0495 4.1416 4.2303 4.3151 4.4086 4.110

NORM 0.4684 0.4190 0.3754 0.3389 0.3108 0.2927 0.2855 0.2893 0.3034

DIVERGENCE DIVERGENCE

DIVERGENCE DIVERGENCE

MODE # 0.85 E 0.90 E 0.95 E 1.00 E 1.05 E 1.10 E 1.15E EXP

1 0.6723 0.6889 0.7050 0.7207 0.7360 0.7510 0.7656 0.739

2 0.8981 0.9237 0.9486 0.9729 0.9966 1.0196 1.0422 0.952

3 1.4445 1.4862 1.5268 1.5663 1.6048 1.6424 1.6792 1.506

4 1.5852 1.6294 1.6723 1.7141 1.7556 1.7949 1.8337 1.732

5 2.3128 2.3787 2.4428 2.5052 2.5659 2.6252 2.6832 2.556

6 3.0259 3.1114 3.1945 3.2755 3.3543 3.4312 3.5064 3.300

7 3.7531 3.8587 3.9612 4.0610 4.1582 4.2531 4.3457 4.110

NORM 0.2091 0.1449 0.0883 0.0583 0.0844 0.1355 0.1914

0.0

0.1

0.2

0.3

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

x E

No

rm o

f E

rro

r

Observations & Discussion

� It is feasible to apply integrative paradigm of system identification on large-scale complex structures such as the long-span steel arch bridge.

� Before identifying model uncertainty, it is important to understand uncertainty due to experiment/data processing. The stationarity of recorded data, as well as the effect of the traffic load amplitude and sampling frequency bandwidth on the identified modal parameters sampling frequency bandwidth on the identified modal parameters was carefully examined to exclude possible epistemic measurement uncertainty.

� Global calibration in modal space was conducted based on: (1) Heuristics; (2) test-analysis correlation, and, (3) sensitivity analysis. The calibrated model was shown to accurately predict the modal properties of the bridge in the vertical direction. The test-analysis correlation in lateral direction is not as good most likely due to a lack

of sufficient excitation in the lateral direction.

Observations & Discussion (Cont’d)

� The sensitivity of the modal parameters with respect to the elasticity modulus of the steel was leveraged to assess the adequacy of the field-calibrated model.

� The level of discrepancy was significantly decreased after calibration: The elasticity modulus decreased after calibration: The elasticity modulus converged around its nominal value, which indicated the calibrated model was the most admissible model given the available information.

Conclusions: Impact of Epistemic Modeling Uncertainty

� Epistemic modeling uncertainty is usually closely related to the choice of model form, element type, idealization of geometry, material properties as well as boundary and continuity conditions.

� In real-life applications of system identification, epistemic modeling uncertainty is coupled with other sources of uncertainty. Its impacts propagate and manifest this phenomenon in various ways as identification progresses from Step 2 on.

� Compared with aleatory modeling uncertainty which may affect the � Compared with aleatory modeling uncertainty which may affect the accuracy of model parameters, the modeling uncertainty due to epistemic mechanisms could lead to divergence in identification results (large test-analysis discrepancy may remain the calibrated model, and/or the updated parameters may lose their physical significance).

� Epistemic modeling uncertainty may cause those updating parameters associated with little random variability (e.g Es) to appear as if they are the dominant uncertainty sources. In this study when there was epistemic modeling uncertainty, Es exhibited large variations during the updating process in order to compensate for the test-analysis discrepancy.

Conclusions: Recognition & Mitigation of

Epistemic Modeling Uncertainty

� The abnormality of the updated value for the elasticity modulus of steel in the cantilever investigation served as a good indicator for the presence of unacknowledged epistemic modeling uncertainty in analytical model.

� Therefore a feasible and effective indicator for the presence of epistemic modeling uncertainty associated with the a priori model of a constructed system was to incorporate into updating procedure one or constructed system was to incorporate into updating procedure one or more of the global model parameters of little known variability. If these appear to be sensitive to the change of dynamic properties, we will use this to identify the presence of epistemic model uncertainty.

� Most effective solution to reduce epistemic uncertainty is to obtain additional information about the system and fully leverage heuristics. The additional dynamic test on the configuration 2 of the cantilever revealed the interactions between the beam and boundary assembly.

Conclusions: Evaluating Model Adequacy

� System identification paradigm is a powerful tool to characterize the actual behaviors of a constructed system and it is feasible to be used on large-scale complex civil engineering structures.

� In real-life applications, systematical utilization of engineering heuristics often played a critical role in reducing modeling uncertainty and epistemic modeling uncertain in particular embedded in the a priori model of the structure.

� The sensitivity analysis of the model properties predicted by analytical � The sensitivity analysis of the model properties predicted by analytical models before and after calibration with respect to the elasticity modulus of steel indicated that the field-calibrated model of the bridge was the most admissible one with available information.

� With limited information embedded in available test data, it is often extremely difficult to determine an unique and converged calibrated model. The proposed model adequacy evaluation tool was intended to assist in checking whether critical physical mechanisms of the system under study were properly incorporated in the analytical model.

� A feasible technique to recognize epistemic modeling uncertainty in the analytical model are proposed in the thesis. This idea could be further investigated with designed laboratory tests and candidates for the dummy model parameters should also include global and sensitive parameters such as the mass of the system or a subsystem.

� Additional research is required in order to better pinpoint the sources of epistemic modeling uncertainty. This would lead to more efficient

Recommendations & Future Work

of epistemic modeling uncertainty. This would lead to more efficient mitigation of epistemic modeling uncertainty.

� A stochastic framework should be incorporated into the system identification paradigm.

� The global calibration which mainly takes advantage of modal data from vibration tests should be utilized in conjunction with local calibration based on static data from load tests.

Thank You