The presentation aimed to talk about issues that an engineer can face during the process and analysis of continuous bridge monitored data, focusing on how these can be analysed efficiently to provide signals that can be used for novelty/abnormality detection. Natural frequency and cable tension long-term data from Z24 overbridge and Tamar Suspension Bridge used as example to demonstrate the ideas discussed.

1. NONSTATIONARITY FROM
ENVIRONMENTAL AND
OPERATIONAL VARIATIONS (EOVS)
Iason Iakovidis
Dr. Civil Engineer
Design Bridge Engineer – Ramboll Birmingham (Bridges North)
BRIDGE STRUCTURAL HEALTH
MONITORING (SHM):

2. CONTENTS
• What is SHM (typical system, importance for bridges, sub-categories of SHM)
• Classification of SHM Measures and acquisition (Example: modal properties extraction for Z24
bridge)
• SHM Approaches for Data Analysis (Data-based and Physics-based Approaches)
• Data-based Approach: Key Points
• Impact of Environmental and Operational Variations (EOVs) on SHM Data
• What is stationarity and how it can be tested
• How the EOVs affect the data (surface models)
• How EOVs impact is distributed in different levels of the signal (Multiresolution Method)
• Compensating the Impact EOVs on SHM data (example: Cointegration Method)
• Cable-Tension System of Tamar Bridge
• Natural Frequencies of Z24 bridge
• Physics-Based Approach: FE Model Updating of Z24 Bridge using temperature data

3. SHM ON BRIDGES
• Set of activities to Collect data and generate data-
based information about existent structural condition
• Evaluate current response and identify signs of
abnormality
• Prognosticate future response
A typical SHM system (6 components):
• Data acquisition system (including sensing system)
• Communication System available for information
transmission
• Data Storage System
• Diagnostic Tools/ Methodologies (i.e. SHM pattern
recognition techniques, finite element analysis etc.)
• Systems for Information Retrieval
A simple presentation of a SHM system
(laboratory); Iakovidis (2018)

4. WHY SHM CAN BE IMPORTANT FOR BRIDGES?
• Understand and evaluate the real-time response of a bridge and track it over
time (larger scale structures – not only laboratory testing)
• Validate existing FE models and design assumptions (i.e. dynamic response,
boundary conditions, static response)
• Develop tools to identify issues than can be associated with structural
degradation (signals’ abnormal variability)
• Manage efficiently and provisionally inspection and maintenance activities
(more efficient bridge stock management)
• Apply, test, monitor and evaluate the use of innovative solutions (i.e.
smart/green materials, sensor technologies etc.)
• Make educated decisions and predict structural life-expectancy

5. SHM CAN BE CLASSIFIED INTO 4 MAIN SUB-CATEGORIES
ACCORDING TO THE DATA COLLECTED AND THEIR TIME-SCALES:
• The one we are interested here is continuous monitoring
Static Field
Testing
Dynamic
Field Testing
Periodic
Monitoring
Continuous
Monitoring
Response
Testing
Stress History Field Testing
Active
Monitoring
Diagnostic
Testing
Dynamic Load
Allowance
Structural
Capacity
Determination
Passive
monitoring
Proof Testing
Ambient
Vibration
Pull-out Tests
Panetsos et al. (2009)

6. SHM MEASURES
• Vibrational-based (accelerations, natural frequencies, modeshapes, damping ratios etc.)
• Component-based (strains, tensions, deflections, tilts etc.)
• Environmental and Operational Variations (EOVs), such as temperature, wind
speeds/direction, traffic volumes, relative humidity, rainfall.
How we can acquire these magnitudes?
• Directly from sensors (strains, tensions, deflections, temperature, wind speeds etc.) or
• Processing the acquired data from sensors i.e. (natural frequencies, modeshapes,
damping ratios); Operational Modal Analysis (time to frequency domain decomposition)

7. Z24 OVERBRIDGE MONITORING CAMPAIGN
• Koppingen-Utzendorf, Switzerland
• 3 spans (14, 30, 14m)
• Prestressed Reinforced Concrete
• Skew 13 degrees
• Double Cell Box Girder (8.6m wide; 1.1m depth)

8. Z24 OVERBRIDGE MONITORING CAMPAIGN
17 accelerometers (15 on bridge deck and 2 on piers)
3 reference channels
9 different setups performed (measurements)
Sensors arrangement on Z24 bridge
The campaign performed by
University of Leuven, Belgium

9. OPERATIONAL MODAL ANALYSIS (OMA): EXAMPLE Z24 OB
• Acceleration recordings
• Transform from Time to
Frequency Domain
• Enhanced Frequency Domain
Decomposition (EFDD)
• Stochastic Subspace
Identification (SSI)
(Covariance, Principal
Components, Unweighted
Principal Components)

10. OPERATIONAL MODAL ANALYSIS (OMA) EXAMPLE
Wire model for Operational Modal Analysis (ARTeMis Modal)
Eigenvalues identification using stabilisation diagrams

11. OMA: IDENTIFICATION OF MODESHAPES
3.85Hz:
Vertical
bending.
4.626Hz:
Transversal rocking,
horizontal bending.
9.632Hz: Anti-
symmetric bending.
10.064Hz: Vertical
bending and torsion.
11.623Hz: Vertical
bending and torsion.
13.25Hz: Vertical
bending.

12. OMA: CONFIRMATION OF OMA RESULTS
Modal Assurance Criterion (MAC)
Table showing the correlation between identified natural frequencies mode
shapes.
Table showing the identified natural frequencies and damping ratios. Mathworks (Matlab)

13. SHM APPROACHES FOR DATA ANALYSIS
• Data-based Approach
Includes methods based on pattern recognition, machine learning, such as
Artificial Neural Networks (ANNs), Principal Component Analysis, Cointegration,
Support Vector Machine etc.
Idea: Learn relationships/correlation between data and build mathematical
models
• Physics-based Approach
This approach includes numerical methods aiming to simulate the structural
behavior based on: MASS-DAMPING-STIFFNESS. Finite Element Analysis
Analyses: Sensitivity, what-if, model refinement, Uncertainty, Update/Calibration
Farrar & Worden (2012)

14. DATA-BASED APPROACH: KEY POINTS
• Fields: Pattern Recognition, Machine Learning (Supervised or Unsupervised)
• Learning relationships from data
• Develop mathematical models to obtain information
• Test the signals for non-stationarity and its sources
• Evaluate the impact of environmental and operational variations (EOVs) on
the SHM signals
• Compensate the impact of EOVs
• Provide signals capable for damage detection
• Detect, identify existence of abnormal signal that can associated with damage

15. IMPACT OF ENVIRONMENTAL AND OPERATIONAL VARIATION
(EOVS) ON SHM DATA
**Sensors do not measure
damage
• Variability from EOVs (traffic
volumes, temperature, wind
speeds/direction, humidity etc.),
noise, cyclic component
• EOVs introduce non-stationarity on
SHM signals
• Mask the effect of damage
• Same amount of variation between
damage and EOVs
• I-40 bridge example (Figure)
Damage test in I-40 Bridge over Rio Grande in Albuquerque,
New Mexico (Los Alamos National Laboratory). To simulate
fatigue cracking used torch cuts (web and flange) (Farrar et
al. 1994; Technical Report).

16. STATIONARITY: WHAT IT MEANS?
Weak stationarity (Samples)
• Mean constant over time:
𝑚 𝑡 = 𝐸 𝑋𝑡 = 𝑚 (𝑐𝑜𝑛𝑠𝑎𝑛𝑡)
• The autocorrelation function
(𝜑 𝑥𝑥) depends only on time
difference :
𝐸 𝑋𝑠 𝑋𝑡 = 𝜑𝑥𝑥 𝑠, 𝑡 = 𝜑𝑥𝑥 𝑠 − 𝑡 ∀𝑠, 𝑡
Nonstationarity can be
associated with: EOVs and
Damage/abnormal signal
ADF test to judge if a signal is
stationary or non-stationary

17. NON-STATIONARITY: Z24 FREQUENCY SIGNAL
Non-stationarity introduced due to:
• Low temperatures (under 0 oC)
the natural frequency increases
significantly
• At very low temperatures (apr. -
10 oC), natural frequency from 4
to 4.4Hz (10% increase)
• As the temperature increases, the
natural frequency decreases
• Ice formed on the deck, stiffness
increased and boundary
conditions changed

18. CABLE TENSION SYSTEM OF TAMAR SUSPENSION BRIDGE
Cable System
• 18 stay cables
• S1-S4 Saltash
Tower
• P1-P4:
Plymouth
Tower
• Another 8 at
the south side
of Towers
• Two
longitudinal
under deck
Locations of sensors placed on the deck of Tamar Bridge.
Sheffield - Exeter University (VES)

19. CABLE TENSION SYSTEM OF TAMAR BRIDGE
Tension sensors placed at the anchorage of the South side
and the deck level of the north side of the bridge.
Sheffield - Exeter University (VES) – Cross (2012)

20. CABLE TENSION SYSTEM OF TAMAR BRIDGE: S3 CABLE TENSION
EXAMPLE

21. S3 CABLE TENSION EXAMPLE OVER EOVS

22. CABLE TENSION SYSTEM OF TAMAR BRIDGE: S3 CABLE
TENSION EXAMPLE SURFACE MODEL
OBSERVATIONS
• Normalised MSE of
Regression 11.51%
• Normal state
considered
• Temperature main
driver
Linear Regression Model Forecast

23. IMPACT OF EOVS ON SHM DATA: Z24 NATURAL FREQUENCIES

24. OBSERVATIONS
• The temperature by
its own is not able to
explain the
variability of the
series
• Probably other SHM
if were available can
improve the
prediction
IMPACT OF EOVS ON SHM DATA: Z24 NATURAL FREQUENCIES
f1 = -0.7426 T f2=-0.4169 T
f3=-0.7269 T f4=-0.7391 T
Main Point: EOVs affect the variability of SHM Measures
however EOVs measures cannot be always available

25. EOVS EFFECT EVALUATION IS NOT A STRAIGHT-FORWARD
PROCEDURE (MULTIRESOLUTION METHOD)
• The lower levels can be associated with non-
stationarity parts of the signal (up to L6)
• Stationary levels associated with the
cyclic/repetitive component of the signal
• The highest levels with the noisy
component.

26. IDENTIFYING THE PARTS OF THE SIGNAL
Autocorrelation function (degree of
dependency between points of the
signal):
The noise part: φxx= δk
(delta-correlated/step function)
At 99.7%
significance level:
t-statistic is -3.
Autocorrelation functions for the Wavelet levels.

27. IDENTIFYING THE PARTS OF THE SIGNAL
Important Point: EOVs effect evaluation is not a
straight-forward procedure, because nonstationarity is
manifested in different levels and time-scales.

28. SUMMARISED EFFECT OF EOVS ON SHM DATA
• Introduce non-stationary on SHM data:
So it is important to understand the sources of this non-stationarity.
• The impact of EOVs is more or less in the same level as damage associated
variability.
So it can mask/hide the impact of damage in continuous signals.
• The effect of EOVs on the SHM signals is manifested in different amount to
different signal levels.
So, evaluating the impact of EOVs on a SHM signal is not a straight-forward
procedure.
• In some cases, EOVs are not measured during SHM. So, it is difficult to have
an information based on previous mathematical analysis.
So the next step is to identify a way/methodology to deal with these issues

29. A SOLUTION: JOHANSEN’S APPROACH TO LINEAR
COINTEGRATION
• Needs multiple SHM series to be performed.
• Can eliminate the similar trends between variables.
• Compares assured normal/undamaged condition data with
respect to potentially abnormal.
• Does not need the existence of environmental and operational
variations
• Provides an output (stationary cointegration residual) capable
for novelty/abnormality detection

30. Tension signals of 12 cables over two years of monitoring.
JOHANSEN’S APPROACH TO LINEAR COINTEGRATION:
EXAMPLE ON TAMAR BRIDGE CABLE TENSION SYSTEM

31. Cointegration residual obtained from the 12 cable tension signals
JOHANSEN’S APPROACH TO LINEAR COINTEGRATION:
EXAMPLE ON TAMAR BRIDGE CABLE TENSION SYSTEM
• First 12000
observations/points
consist the training
state.
• Remaining
observations/points
consist the testing
state.
• Thresholds at ±3std
from the signal mean
(99.7% significance
level)

32. JOHANSEN’S APPROACH TO COINTEGRATION:
EXAMPLE ON TAMAR BRIDGE CABLE TENSION SYSTEM
• Introduced a slightly
abnormal signal inside
the cointegration residual.

33. JOHANSEN’S APPROACH TO LINEAR COINTEGRATION:
EXAMPLE ON Z24 NATURAL FREQUENCY DATA

34. JOHANSEN’S APPROACH TO COINTEGRATION (LINEAR):
EXAMPLE ON Z24 NATURAL FREQUENCY DATA
Cointegration Residual using natural frequencies of Z24 Overbridge
• First 1000
observations/points
consist the
training state.
• Remaining
observations/points
consist the testing
state.
• Thresholds at
±2.58std from the
signal mean
(99.5% significance
level)

35. NONLINEAR COINTEGRATION
EXAMPLE ON Z24 NATURAL FREQUENCY DATA
Non-linear Cointegration Residual (Regime Switching) using natural frequencies of
Z24 Overbridge (Shi et al [6])

36. PHYSICS BASED APPROACH:
FINITE ELEMENT MODEL UPDATE OF Z24 BRIDGE
Hidden
layer
Ec
Output
layer
Kap
Kf
f1
f2
f3
f4
f5
Input
layer
Eigenfrequencies
1
2
....
....
11
12
Non-linear
sigmoid
functions
Linear
functions
Model
Parameters
Ec
(GPa)
Kap
(MN/m3)
Kf
(MN/m3)
Values
Range
36.5-39 80-180 180-300
Procedure for Sensitivity Analysis
• 140 modal analyses results used for
training the Artificial Neural
Network (ANN). Bowles and Kezdi (1971); modulus of subgrade reaction
(MN/m³)

37. PHYSICS BASED APPROACH:
FINITE ELEMENT MODEL UPDATE OF Z24 BRIDGE (RESULTS)
Measured
Eigenvalues
FE before
Update
Deviation
from Real
FE after
Update
Deviation from
Real
MAC
Values
3.841 3.665 4.582% 3.815 0.677% 0.979
4.688 4.443 5.226% 4.595 1.984% 0.855
9.717 9.543 1.791% 9.884 1.718% 0.938
11.882 11.507 3.156% 12.137 3.095% 0.929
12.858 12.344 3.997% 12.911 0.412% 0.911
Ec= 38.7 Gpa
Kap=175.7 MN/m3
Kf=261.7 MN/m3

38. FINITE ELEMENT MODEL UPDATE OF Z24 BRIDGE
USING TEMPERATURE DATA
Hassan et al. (1995) and Treacy & Bruhwiler
(2014), from in-situ testing on 88 RC concrete
and PRC bridges in Switzerland (E~T):

39. FINITE ELEMENT MODEL UPDATE OF Z24 BRIDGE
USING TEMPERATURE DATA
Forecast of the first three natural frequencies using the Updated FE Model and
comparison with real-time measurements for 11 months of monitoring.
1.38% error
6.67% error
12.24% error

40. CONCLUSIONS
• What is SHM (typical system, importance for bridges, sub-categories of SHM)
• Classification of SHM Measures and acquisition
• SHM Approaches for Data Analysis (Data-based and Physics-based)
• Data-based Approach: Key Points
• Impact of Environmental and Operational Variations (EOVs) on SHM Data
• What is stationarity and how it can be tested
• How the EOVs affect the data
• How EOVs effects distribute different levels (Multiresolution Method)
• Compensating the Impact of EOVs from SHM data (Cointegration Method)
• Cable-Tension System of Tamar Bridge
• Frequencies of Z24 bridge
• Physics-Based Approach: FE Model Updating of Z24 Bridge using temperature data

41. SUPPORTING PUBLICATIONS
1. I.Iakovidis,K.Worden, E.J.Cross.OnStationarityand theInterpretationofADFstatistic.Proceedings oftheInternational
Conference ofModalAnalysis (IMAC)XXXVI,11-15February2018
2. I.Iakovidis,K.Worden, E.J.Cross.APrincipled MultiresolutionApproachforSHMSignals Decomposition.Proceedings ofthe
InternationalConference onModernPracticeofStressand VibrationAnalysis (MPSVA2018).Cambridge,U.K.2-4July2018.
3. I.Iakovidis,K.Worden, E.J.Cross.NewResultsinNonstationarySignalAnalysis withaViewTowardsStructuralHealth
Monitoring.Proceedings oftheRoyalSocietyA.2019
4. I.Iakovidis.On Non-stationarityfromOperational and Environmental Effects inSHMBridgeData. 2018.PhDThesis.
University ofSheffield.
5. I.Iakovidis,K.Morfidis,V.Lekidis. FEMupdatefortheverification oftheseasonal natural frequencies variationofBridges
based onArtificial NeuralNetworks:ApplicationonZ24Swiss Bridge.Proceedings ofthe17thPanhellenicConcreteConference
(EPES).Thessaloniki,Greece.10-12November 2016.
6. I.Iakovidis,V.Lekidis.Z24BridgeFEMUpdateBased onTemperatureDependentConcreteandAsphaltElasticityModuli.
Proceedings ofthe16th EuropeanConference onEarthquakeEngineering.Thessaloniki,2017
7. I.Iakovidis,V.Lekidis.ProcessingofBridgeSHMsignals:DistinguishingDamage fromNormalCondition Levels. 4th
PanhellenicConference ofSeismic Engineering.Athens 2019