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Compression and Analysis of Golden Gate Bridge Sensor Data

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Title: Compression and Analysis of Golden Gate Bridge Sensor Data


1
Compression and Analysis ofGolden Gate
BridgeSensor Data
Guilherme Rocha and Bin Yu Statistics
Department University of California,
Berkeley Joint Work with Shamim Pakzad and
Greg Fenves (CE) Sukun Kim, Jim Demmel and David
Culler (CS)
2
Outline
  • Motivation Structural Health Monitoring
  • About the Golden Gate Bridge
  • About the installed sensor networks
  • Data compression
  • Temperature data compression (lossless)
  • Acceleration (vibration) data need lossy
    compression
  • Physical model for vibration data
  • modal estimation for monitoring, and
  • meaningful (lossy) compression

3
An example
  • Plate girder bridge (e.g. Minneapolis collapsed
    bridge)
  • USA Today (Jan. 15, 2008) plates too thin
  • for the pavements and barriers added later

4
Structural Health Monitoring
  • National Bridge Inventory (DOT Report to
    Congress, 2004)
  • Approx. 591,000 bridges in the U.S.
  • Approx. 81,000 (14) structurally deficient
  • Routine inspections by Federal Highway Adm.
    (FHWA)
  • Annually 71,000 bridges
  • Bi-annually 490,000 bridges
  • Every 4 years 28,000 bridges
  • SHM levels (from Bakir et. al., 2007)
  • Detection (level 1) whether there is damage
  • Localization (level 2) where in the structure
  • Quantification (level 3) how severe
  • Prediction (level 4) remaining life time of
    damaged structure

5
Structural Health Monitoring
  • Structural Health Monitoring Strategies
  • Direct damage detection
  • Visual inspection
  • X-Rays
  • etc.
  • Indirect damage detection
  • Detection of changes in dynamic structural
    behavior
  • Natural frequencies
  • Modes of vibration

6
About the Golden Gate Bridge
  • Suspension span 4,200 ft (1,280m) - the longest
    in the world until 1964
  • Currently 7th longest span
  • Presently, longest span is Akashi-Kaikyo Bridge
    in Japan (1998)
  • Total length 8,981 ft (2,737m)
  • Width 90 ft (27m)

7
About the Golden Gate Bridge
  • Costruction 1933-1937
  • Open to traffic May 28, 1937
  • San Francisco Chronicle A thirty-five million
    dollar steel harp!
  • Chief Engineer Joseph Strauss
  • Wind forces
  • traffic closed to high winds in 6 occasions
    1951, 1982, 1983, 1996, 2005, 2007
  • In the 1982 closing, wind force was strong enough
    to cause visible motion
  • 1983 Wind gusts of 75MPH (120Km/h) 2008, 70MPH

8
InstrumentationOur collaborators did the hard
work )
Figures by Shamim Pakzad and from web sites
9
InstrumentationAccelerometer Characteristics
  • Sensor board
  • Two pairs of accelerometers
  • 2 ADXL 202E accelerometers
  • Vertical and horizontal
  • Coarse measurements
  • 2 Silicon Designs 1221L
  • Vertical and horizontal
  • Finer measurements
  • One thermometer
  • temperature for calibration

Thermometer
Silicon Designs 1221L
ADXL 202E
Figure adapted from Kim et. al. (2006)
10
InstrumentationAccelerometer Characteristics
Tables from Kim et. al. (2006)
11
Instrumentation
  • Hostile Environment
  • Gusty wind
  • Strong Fog
  • Rain
  • Strong condensation (sea fog wind)
  • Corrosive environment

Figure from Kim et. Al. (2006)
12
Instrumentation
  • Sensing equipment
  • Boards are enclosed in waterproof plastic box
  • Plastic box has holes for antenna and battery
    cables
  • Sealed with silicon adhesives
  • Relatively ample supply of energy
  • Communication
  • Linear topology exploited bi-direction antennas

Figure from Kim et. Al. (2006)
13
InstrumentationPosition of the sensors
  • There are 81 cables along west span of bridge
  • Sensors installed at position of every other
    cable (41)
  • Additional sensors installed to reduce packet
    loss (10)
  • There are 8 sensors installed on south tower
  • 4 nodes on west and 4 nodes on east tower

Figure from Kim et. Al. (2006)
14
Time JitteringSynchronization protocol
  • Deviations from ideal sampling rate
  • Capped at 250 ?s (5 of sampling interval _at_
    200Hz)
  • Temporal jitter
  • Delay in data reading within a node
  • Data reading waits until memory write ends
  • Controlled by use of high performance TinyOS
    components
  • Spatial jitter
  • Difference in the time of reading across
    different nodes
  • Variation in the crystal of processors in
    different nodes
  • Imperfect time synchronization
  • Controlled by using FTSP (Flooding Time Sync.
    Protocol)

15
Transmitted Data
  • Data set
  • 8 minutes _at_ 100Hz 48,000 readings
  • 5 readings/sample _at_ 2 Bytes each 10
    Bytes/reading
  • Total transmitted volume 480 KBytes
  • Volume of data
  • Uncompressed data rate 1KB/sec
  • 2 bytes/sample (for both temperature and
    acceleration)
  • 5 samples/reading (1 temperature, 4 acceleration)
  • 100 readings/sec (sampling frequency 100 Hz)
  • Temperature data currently makes up for 20 of
    byte vol.
  • Acceleration data makes up for 80 of byte volume

16
Temperature Data Description of data
  • Temperature
  • Slow variation (_at_100-200Hz)
  • Small and infrequent jumps
  • Run length code provides good lossless
    compression
  • 94 reduction in number of bytes transmitted
    (conservative)

1,000 readings
17
Histogram of points with temperature change
Worst case Change in 1,278 points (out of 48,000)
18
TemperatureRun Length Code
  • Run Length coding
  • Transmit first reading in full precision (2
    bytes)
  • Transmit packets only when change occurs
  • Each packet contains
  • Number of time steps since last change
  • Temperature variation
  • Packet size
  • Adjustable
  • A conservative choice 4 bytes

19
Temperature Data CompressionRun Length Code
  • Assumptions (conservative) 4 bytes/reading
  • 16 bit representation of temperature variation
  • larger observed temperature variation 3000 units
  • 1 bit for sign of temp. variation
  • 15 bit representation of run length
  • More than enough to present overflow
  • Maximum observed run length 1370 units
  • 11 bits are probably enough

20
Temperature Data CompressionRun Length Code
  • Data volume
  • current 48,000 readings x 2 Bytes / 480 sec
    200 Bps
  • run length coding
  • Each data point corresponds to a change in
    temperature
  • Each data point contains 4 Bytes of data
  • Worst case observed (by our coding)
  • (1,278 x 4 Bytes 2 Bytes) / 480 sec 11 Bps
  • Volume reduction 94.5
  • Average case (49 sensors)
  • (967 x 4 Bytes 2 Bytes) / 480 sec 8.1 Bps
  • Volume reduction 95.9

21
Acceleration Data Compression
  • Possibly useful facts
  • Temporal correlation (LMS tried, more on this
    later)
  • Physical model for the data
  • Redundant measurements

22
Acceleration Data CompressionIn progress
  • Low pass filtering
  • Currently all data is transmitted
  • Expert knowledge
  • For most civil structures, fundamental
    frequencies below 10Hz
  • low-pass filtering is used
  • Correlation of the series in neighboring sensors
  • Particularly convenient to explore in bridge
    setting
  • Good correspondence of network topology and
    correlation structure

23
Acceleration Data CompressionAdaptive filtering
  • Use of LMS to implement predictive coding
  • Xt1 predicted from
  • The weight vector wt is determined adaptively

24
Acceleration Data CompressionAdaptive filtering
with LMS
  • Experiments were conducted
  • On the sensor readings for two different nodes
  • Nodes with the higher R2 for AR models were used
  • Node 30
  • Node 45
  • Different number of lags
  • p set to values between 1 and 250
  • Different settings for ?
  • 100 500 1,000 10,000 and 15,000
  • Standard deviation of the residual series
  • At best 60 of standard deviation of raw series
  • In most cases, above 80 of standard deviation of
    raw series

25
Acceleration data compressionThe series to which
LMS was applied
26
Acceleration data compressionThe series to which
LMS was applied
27
Acceleration data compressionLMS (STD
residuals/STD series)
28
Acceleration data compressionLMS (STD
residuals/STD series)
29
Lossy compression for statistical analysis
In information theory, lossy compression is
about reducing bits of data -- the meaning of
data is NOT taken into account. Lossy
compression for statistical analysis needs a
different metric for measuring loss -- what
matters is the precision lost in estimating a
meaningful model (or parameters). If we know
the data model, we know what to keep
30
Meaningful compression of vibration data
The goal is structural monitoring hence we
need to decide on what information is crucial
for this task. Ideally, wed establish modes of
the bridge and monitor any deviation from normal
modes. Minimally, this mode information has to
be transmitted. Possibly other information as
well in case the chosen estimation method is not
working well.
31
Physical Model for VibrationLumped components
  • Masses
  • Model inertia
  • Force proportional to acceleration
  • Newtons law
  • Dashpots
  • Model dampening
  • Force proportional to speed
  • Viscous friction
  • Springs
  • Model stiffness
  • Force proportional to displacement
  • Youngs law

32
Physical Model for VibrationA simplified
vibrating system
33
Physical Model for VibrationA simplified
vibrating system
From Newtons Law
Hence
34
Physical Model for VibrationA simplified
vibrating system
Collecting equations for all blocks
with
35
Physical Model for VibrationCont. time state
space representation
  • Define, the state variable as
  • The state space representation of the vib.
    system
  • We observe the acceleration

36
Physical Model for VibrationSystem dynamics in
continuous time
  • From the dynamic equation
  • State evolution obeys Stochastic Diff. Eq. (SDE)
  • Assuming the random excitation to be
  • with dWt Gaussian and covariance matrix ?,
  • the solution of the above SDE satisfies
    (Oksendal, 1998)

37
Physical Model for VibrationSystem dynamics in
discrete time
  • Letting
  • a discrete time representation of the system is
  • Our goal is to obtain dynamic properties
  • Focus on estimating A and C matrices.

38
System IdentificationDifferent methods
  • Methods for model identification
  • SRIM System Realization from Information Matrix
  • Juang, 1997 Journal of Guidance, Control and
    Dynamics
  • Based on state space model (second order method)
  • Future
  • State-space model MLE
  • or Bayesian

39
Using the dataModel Identification using SRIM
  • Recall the discrete time state space
    representation
  • Define
  • From discrete time state space representation

40
Using the dataModel Identification using SRIM
  • Let
  • We must have

41
Using the dataModel Identification using SRIM
  • identification
  • Any invertible linear map of state variable is a
    state variable
  • Hence A and x are not unique
  • Let
  • If x has (intra-temporal) conditional covariance
    ?xxu,
  • write the spectral decomposition ?xxu R?R
  • and define
  • to obtain one state representation with diagonal
    covariance.

42
Using the dataModel Identification using SRIM
  • SRIM Estimates
  • Modal parameters
  • Modal frequencies arg(eigenvalues of A)/(2??t)
  • Damping ratios 1-expabs(eigenvalues of
    A)-1/(?t)
  • Modes of vibration C?
  • where ??stems from the Schur decomposition A
    ???

43
Using the dataModel Identification using SRIM
  • Issues
  • Choice of p (number of lags)
  • Choice of d (state space dimension)
  • Behavior in small samples

44
Model Identification using SRIM Simulation
results
  • Simulation set-up
  • System with 5 unit masses (mj1Kg, for all j)
  • Forces are i.i.d. standard Gaussian random
    variables
  • Stiffness
  • k12k23k45160 N/m, k3440 N/m, k01k0515 N/m
  • Dampening (Raleighs simplification)
  • S ? K, with ? 5?10-3 (units N?s/m)

45
Model Identification using SRIM Simulation
results
  • Dynamic characteristics

46
Model Identification using SRIM Simulation
results
  • Geometric characteristics (mode shapes)

47
Model Identification using SRIM Simulation
results
  • Est. frequencies 1st mode of vibration (1.29 Hz)

48
Model Identification using SRIM Simulation
results
  • Est. frequencies 2nd mode of vibration (2.04Hz)

49
Model Identification using SRIM Simulation
results
  • Est. frequencies 3rd mode of vibration (3.14 Hz)

50
Model Identification using SRIM Simulation
results
  • Est. frequencies 4th mode of vibration (4.50 Hz)

51
Model Identification using SRIM Simulation
results
  • Est. frequencies 5th mode of vibration (4.54 Hz)

52
Model Identification using SRIM Simulation
results est. modes of vib.
  • 1st mode of vibration (4.54 Hz)

Lags spanning 0.4s (40 lags _at_ 100Hz)
Lags spanning 1.2s (120 lags _at_ 100Hz)
53
Model Identification using SRIM Simulation
results est. modes of vib.
  • 2nd mode of vibration (2.04 Hz)

Lags spanning 0.4s (40 lags _at_ 100Hz)
Lags spanning 1.2s (120 lags _at_ 100Hz)
54
Model Identification using SRIM Simulation
results est. modes of vib.
  • 3rd mode of vibration (3.14 Hz)

Lags spanning 0.4s (40 lags _at_ 100Hz)
Lags spanning 1.2s (120 lags _at_ 100Hz)
55
Model Identification using SRIM Simulation
results est. modes of vib.
  • 4th mode of vibration (4.50 Hz)

Lags spanning 0.4s (40 lags _at_ 100Hz)
Lags spanning 1.2s (120 lags _at_ 100Hz)
56
Model Identification using SRIM Simulation
results est. modes of vib.
  • 5th mode of vibration (4.54 Hz)

Lags spanning 0.4s (40 lags _at_ 100Hz)
Lags spanning 1.2s (120 lags _at_ 100Hz)
57
Model Identification using SRIM Simulation
results
  • Est. dampening ratio 1st mode of vibration (1.29
    Hz)

58
Model Identification using SRIM Simulation
results
  • Est. dampening ratio 2nd mode of vibration (2.04
    Hz)

59
Model Identification using SRIM Simulation
results
  • Est. dampening ratio 3rd mode of vibration (3.14
    Hz)

60
Model Identification using SRIM Simulation
results
  • Est. dampening ratio 4th mode of vibration (4.50
    Hz)

61
Model Identification using SRIM Simulation
results
  • Est. dampening ratio 5th mode of vibration (4.54
    Hz

62
Future directions
  • How to reduce bias of SRIMs damping ratio
    estimation
  • regularization and choice of p
  • in the eigen-analysis and in LS for A?
  • SRIM on real data
  • how to choose d?
  • Other methods for modal estimation and compare
    with SRIM
  • comparison metrics
  • distance to true parameters
    in simulations, and
  • prediction performance
  • On-line SRIM modal estimation
  • on-line PCA is needed
  • distributed computation
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