Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
Main Topics of APSS
Advanced Sensor Technology
Sensor Informatics
Asia--Pacific Summer School
Asia
on
Smart Structures Technology
Wavelet Domain
s1 s2
105
97
sp
Scale
89
81
Output
73
65
hidden
II
57
49
41
33
hidden I
25
17
200
300
400
500
600
700
Time Step (No. of poiint)
B F
B.
F. Spencer,
S
Jr.
J
Nathan M. and Anne M. Newmark Endowed Chair
of Civil Engineering
University of Illinois at Urbana-Champaign
0 .1 0
Acceleration (m/s )
0 .0 5
0 .0 0
-0 .0 5
C o n tr o l le d b y
H M D m ode
-0 .1 0
20
40
60
80
100
120
140
T im e ( s e c )
Structural Control
Application of SHM
Smart Structures
Technology Laboratory
July 2010
Outline
Conservation of energy yields:
• Trends in Structural Control
E = Ek + Es + Eh + Ed
• Trends in Structural Health Monitoring
• Sensors,
S
D
Data
t A
Acquisition,
i iti
and
d Di
Digital
it l
Signal Processing
• E = total energy
gy input
p to the structure from
f
excitation
• Ek = kinetic energy of the structure
• Es = elastic strain energy of the structure
• Eh = energy dissipated due to inelastic
deformation
• Ed = energy dissipated by supplemental damping
devices
Implementations
Supplemental Damping Devices
Passive Systems
Active Control Systems
non-controllable
no power required
controllable
significant power required
“Smart” Dampers
controllable
little power required
1
Conventional Structure
Passive Control Systems
PED
Structure
Excitation
Response
Excitation
Structure
Response
m
M
M
Tuned Mass Damper
Passive Control Systems
M
M
M
Base Isolation
Passive Damper
World Trade Center in New York
•10,000 Visco-elastic dampers
in each tower
•Evenly distributed from 10th
to the 110th floor
•Damping: 2.5%~3%
•
•
•
•
Dampers
Base Isolation
Tuned Mass Damper
Tuned Liquid Damper /
Tuned Liquid Column Damper
• Aerodynamic Shaping
Visco-elastic
Viscodamper
Visco--elastic Damper
Visco
Steel Damper
Visco-elastic
ViscoMaterial
Low-yield strength steel
Tennozu Project
Brace Type
Visco-elastic Material
ViscoSteel
Steel
鋼
粘
Plate
Plate
板
弾
Shear
鋼
性
Force Ｑ(Q) 板
体
C Building
Shear
Force (Q)
Ｑ
ｖ（速度）
deformation
せん断ひずみ γ＝δ／ｄ
(d)
Thickness (d)
Shear Strain g = d/d
ｄ（厚さ）
Wall Type
M Department Store
Copyright 2008 Shimizu Corporation, All Rights Reserved
42-story high-rise RC condominium
Copyright 2008 Shimizu Corporation, All Rights Reserved
2
Steel Dampers in 42-story RC
condominium
Use of Dampers
in High-rise Building
R.J. Smith and M. R. Willford, The damped outrigger concept for tall buildings
Dissipate energy of
relative vertical
motion between
perimeter columns
and outriggers
Vertically acting
dampers between
coupled shear walls
Copyright 2008 Shimizu Corporation, All Rights Reserved
Beam-type Steel Dampers in RC
Core Walls
Typical Layout at outrigger levels
R.J. Smith and M. R. Willford, The damped outrigger concept for tall buildings
2525
超高強度RCコアウォール
（最大強度80N/mm2）
4650
4650
23650
4650
4650
境界梁型制震ダンパー
2525
3450
6000
6000
6000
6000
3450
30900
超高強度
RCコアウォール
境界梁型
制震ダンパー
Copyright 2008 Shimizu Corporation, All Rights Reserved
Passive Control System
•
•
•
•
Dampers
Base Isolation
Tuned Mass Damper
Tuned Liquid Damper /
Tuned Liquid Column Damper
• Aerodynamic Shaping
Seismic Isolation Methods for
High-rise RC Condominiums
Base Isolation
Device (A total of
32)
Mat slab
35 story RC condominium
Copyright 2008 Shimizu Corporation, All Rights Reserved
3
Seismic Isolation Methods for
High-rise RC Condominiums
Oakland City Hall
Dual-Layer Core Seismic Isolation Method
Earthquake Response
Fixed Base
Base Isolated
Copyright 2008 Shimizu Corporation, All Rights Reserved
21
Base-isolation of LNG Tanks
Base-Isolated Display-Table
for Museum
(Y. S. Kim & S. J. Joo : TS Solution)
Display-Tables on Shaking Table
(Hyundai E&C)
Performance of Base Isolation
2D El Centro Record
fBI
fSLIDING
fNON
NON--BI
(PGA=0.6g)
Without
Base-isolator
Laminated Rubber Bearings
Passive Control Systems
With
Base-isolator
Petronas Towers: TMD
• Supplementary damping
•
•
•
•
Dampers
Base Isolation
Tuned Mass Damper
Tuned Liquid Damper /
Tuned Liquid Column Damper
• Aerodynamic Shaping
– Towers: not necessary
– Sky bridge: 3 TMDs per each leg. (73 kg ea)
– Pinnacles: simple chain impact dampers
TMD
4
Taipei 101: TMD
Taipei 101: Building TMD
• Building TMD
Pinnacle TMDs
– 660 ton. (0.24% of building mass)
Worlds largest.
– TMD and its support occupy five upper
floors.
– Visible from a mezzanine level.
– $3.5-million
$3 5 million turnkey contract.
contract
• Includes Dampers and 60m tall
pinnacle.
• Additional $800k for the damper ball.
– Made of 12.5cm thick steel plate.
– Peak acceleration of the top was reduced
from 7mili-g to 5 milli-g.
– The damper will not have any role during
earthquakes
Building TMD
PARK TOWER
HOTEL & RESIDENCES
Taipei 101: Pinnacle TMDs
CSA
• Pinnacle TMDs
– Two 4.5 ton dampers
– Flat steel masses tuned by springs are able to move horizontally in
any direction.
– To reduce cumulative fatigue damage due to wind-induced motion.
PARK TOWER
HOTEL & RESIDENCES
CSA
• Chicago, Illinois, United States
• 70 story multi-use building
– 48 stories of condos over 18 story hotel
• 824 ft. tall tower
• 5 story parking garage
• Building was designed with a tuned mass
damper to control lateral accelerations
PARK TOWER
HOTEL & RESIDENCES
CSA
• Modified structure
– Initial structural properties:
• T = 7.26 sec
• Drift = 13” = h/700
• Acceleration = 35 mg
– Fi
Finall structurall properties
i without
ih
damper:
• T = 5.18 sec
• Drift = 9.7 in. = h/940
• Acceleration = 20.7 mg
– With addition of damper:
• Acceleration = 15 mg
5
Passive Control System
Random House: TLCD
• Tuned Liquid Column Damper
– Two TLCDs at the roof level (290 tons and
430tons)
– Large U-shaped tanks at right angles.
– Moving water mass is 550 tons (0.33% of
building weight) in each tank.
– Cost effective. Cheaper than a pendulum
TMD.
•
•
•
•
Dampers
Base Isolation
Tuned Mass Damper
Tuned Liquid Damper /
Tuned Liquid Column Damper
• Aerodynamic Shaping
Application of Super Sloshing
Damper in High-rise hotels
Super Sloshing Damper
Tokyo Dome
Hotel
Shin-Yokohama
Prince Hotel
Copyright 2008 Shimizu Corporation, All Rights Reserved
Copyright 2008 Shimizu Corporation, All Rights Reserved
Tuned Mass Dampers for
Tall Buildings
Supplementary Damping System
(Y. S. Kim & S. J. Joo
Joo,, TS Solution)
•
•
•
•
6
5.18
4.95
4.87
Centum Park Apartments
(Busan
Busan,, Korea)
acceleration[gal]
5
3.41
4
2.98
3.12
3.41
3.41
Dampers
Base Isolation
Tuned Mass Damper
Tuned Liquid Damper / Tuned Liquid
Column Damper
• Aerodynamic Shaping
2.94
3
2
1
0
No.101
without TMD
No.103
with TMD
No.105
ISO6897
6
Burj Dubai:
Aerodynamic Shaping
Wind Tunnel Testing at RWDI
•
•
•
•
Rowan Williams Davies & Irwin – Ontario, Canada
1:500 Scale Aero-elastic Model
Structural damping ratio of 1.5% for sway modes 1 and 2
Mounted on turntable
• 36 wind directions at
10 d
degree iinterval
t
l
• Wind speeds between
0.5 and 1.3 times of the
50 year design wind
speed
• Burj Dubai
–
–
–
–
Height: 818m (world’s tallest structure)
Floor: 160
Completion date: Jun 2010
334,000 m2 space
• Damping system
– Conceptual designs for sloshing water and water
column damper systems were developed by
Motioneering
– Shape refinements and structural measures can keep
building sway motions to acceptable levels
– Space for sloshing dampers
Comparison of
Wind Tunnel Results
Wind Tunnel Testing at RWDI
Wind Tunnel #1 Results
Wind Tunnel #3 Results
F = Ma
Disorganized Vortex Shedding
over the height of the tower
Active Control Systems
Active Control Systems
u
x
m
Excitation
Structure
Response
Consider the SDOF system
&&(t ) + cx& (t ) + kx (t ) = bu (t ) + γ w (t )
mx
c,k
with linear state feedback / feedforward
Feedforward
Li k
Link
Control Actuators
Feedback
Li k
Link
w
u = − g1 x − g 2 x& − g 3w
Thus, the closed-loop dynamics are
Sensors
Computer
Sensors
&&(t ) + [c + bg2 ]x& (t ) + [ k + bg1 ]x (t ) = [γ − bg3 ]w (t )
mx
The closed-loop stiffness, damping, and load factor
may be arbitrarily assigned
7
Active Mass Damper (AMD) Experiment:
Acceleration Feedback Control Strategies
Active Control Systems
Actuator
Sensors
Actuator
M
M
Sensor
Sensor
m
M
zact (t )
z&&a3 (t )
Actuator
z&&a2 (t )
Active Mass Damper
Active Base Isolation
Active Bracing
z&&a1(t )
Control
Computer/
DSP Board
z&&g (t )
Control Computer
Kyobashi Seiwa Building (1989)
Rainbow Bridge Tower (1991)
AMD-1
Sensor
AMD-2
Control
Computer
Sensor
Sensor
Yokohama Landmark Tower
(1993): AMD
Sendagaya INTES Building (1992)
8
Shinjuku Park Tower (1994)
Hybrid Mass Damper
ORC200 at Osaka
Roller
2 ×100 ton
Hybrid Mass Dampers for Tower
Floor count: 50, Basement
floor: 2
Shimizuand
Corporation,
MadeCopyright
with2008
SRC
S All Rights Reserved
Shanghai World Financial Center: HMD
(Incheon Int’l Airport)
• Active tuned mass damper
Air Traffic Control Tower: 100. 4 m
Natural Frequency: 0.71 Hz
y
– Two dampers on the 90th floor.
– Sensors are used to measure the building
sway with a computer to control
x
HMD2
HMD1
Hybrid Mass Damper (HMD)
0 .1 0
0 .0 5
0 .0 5
Acceleration (m/s )
0 .1 0
2
Acceleration (m/s )
Location of HMDs: 19th Floor
(80 m above ground)
0 .0 0
-0 .0 5
TM D
m ode
• Shape
0 .0 0
- 0 .0 5
C o n t r o l le d b y
H M D m ode
U n c o n tr o ll e d
-0 .1 0
- 0 .1 0
20
40
60
80
100
120
140
20
40
60
80
100
T im e ( s e c )
T i m e (s e c )
Signal w/o HMD
Signal w/ HMD
120
140
– The Hole in the building reduces vortexshedding induced force.
Harumi Island Triton Square
Next Steps …
• Smart damping strategies can effectively
address a number of these challenges –
devices are low power, fail-safe.
• Studies show that smart dampers can
potentially achieve the majority of the
performance of fully active systems.
9
Smart (Semiactive) Control Systems
Structure
Excitation
Smart Damping?
Response
PED
Control Actuators
Sensors
Computer
Sensors
Smart Damping?
Kajima Shizuoka Building:
Observations from the
May 7, 1999 M4.9
Earthquake
K-Building
R-Building
238.05m, 54 story
172 m, 38 story
Hybrid mass
damper 2
Semi-active
hydraulic
damper 88
356
semi-active
semihydraulic
dampers
10
Magnetorheological Fluid Damper
Smart Base Isolated Building
Using Variable-Orifice Dampers
at Keio University
Magnetic Choke
MR Fluid
x
F
Magnetorheological Fluids
Magnetorheological Fluids
What are they?
• Micron-sized, polarizable, iron particles in oil
What do they do?
•
•
•
•
Magnetorheological Fluid Damper
Newtonian in the absence of applied field
Develop yield strength when field applied
Bingham Model: τ = τ (u) + ηγ&
Provide reliable means for a low-power,
rapid response interface between
electronic controls and mechanical
devices
Force - Velocity Envelope for
MR Fluid Damper
Large force at small or zero
velocity is possible
F
Magnetic Choke
MR Fluid
x
Constant current
operating curve
Zero current
x&
F
F = μ (u ) sgn( x& ) + c p x&
μ (u )
F = μ (u ) sgn( x& ) + c p x&x, F
Maximum current
Extension
Any arbitrary curve within
operational envelope is
possible
Compression
cp
11
Prototype 20-Ton MR Fluid Damper
Thermal Expansion
Accumulator
3-Stage Piston
Wire
Coils
Prototype 20-Ton MR Fluid Damper
MR Fluid
LORD
RheoneticTM Seismic Damper
MR-9000
LORD
RheoneticTM Seismic Damper
MR-9000
Diameter: 20 cm
Stroke: 16 cm
Power: < 50 watts, 22 volts
Diameter: 20 cm
Stroke: 16 cm
Power: < 50 watts, 22 volts
Performance Testing at the
University of Notre Dame
Performance Testing
2A
Maximum Current
1A
Fo
orce (kN)
0.5 A
Zero Current
0A
Displacement
Velocity (cm/s)
(cm)
Experimental Setup
MR Dampers in a Building
Measured Response
Triangular Displacement
Base Isolation Implementation
Nihon-Kagaku-Miraikan, Tokyo
National Museum of Emerging Science
and Innovation
Two 30-ton, MR Fluid dampers
built by Sanwa Tekki using
Lord MR fluid are installed
between 3rd and 5th floors
12
Tider MRD-160-100 in
JZ20-2NW Offshore Platform (China)
Smart Structures
Technology Laboratory
July 2010
Outline
• Trends in Structural Control
• Trends in Structural Health Monitoring
• Sensors,
S
D
Data
t A
Acquisition,
i iti
and
d Di
Digital
it l
Signal Processing
Why Monitor Infrastructure?
Structural Health Monitoring of
Infrastructure
Smart Structures
Technology Laboratory
July 2010
• To monitor and control the construction process
• To validate the structural designs and characterize
performance (e.g., develop database)
• To characterize loads in situ
g
g maintenance
• To assist with building/bridge
• To detect and localize damage before it reaches a
critical level, thus increasing the safety to the public
• To reduce the costs and down-time associated with
repair of damage
• To assist with emergency response efforts, including
building evacuation and traffic control
Ordinary
situation
Emergency
situation
Strong Wind
Building
Brain
Brain
プチッ
Bridge
・
ボキッ
Pipeline
バキッ
sensor
Earthquake
Structural
Damage & Deterioration
Structural
Performance
Owner, Designer,
Engineer
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
Data
Management
Server
Lantau Fixed Crossing
Database
Owner,
Administrator,
User
Smart Structures
Technology Laboratory
July 2010
Bridges
77
The Hong Kong Polytechnic University
13
Smart Structures
Technology Laboratory
July 2010
Tsing Ma Bridge
Measurements in Four Phases
Phase 1 : Free - standing tower
Smart Structures
Technology Laboratory
July 2010
Phase 2 : Tower - cable system
Structural Health Monitoring
System
•
•
300 Sensors
•
Data acquisition system
Data processing and analysis system
•
Cabling network system
•
$7.8 M
Phase 3 : Tower - cable - deck system
The Hong Kong Polytechnic University
Phase 4 : Completed bridge
The Hong Kong Polytechnic University
Decade of free vibration studies:
Republic Plaza (280M), Singapore
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
Buildings Applications
•
•
•
•
•
81
Smart Structures
Static+dynamic monitoring through Technology
Laboratory
July 2010
construction tracked modal frequencies
70
7
60
storeys,
mass/106kg
6
50
5
40
4
30
3
20
2
10
1
Frequency measurements 1994-1995
AVT conducted 1995
Monitoring since 1996
Originally for wind data
Building used as wind and earthquake
super-sensor’
• Dual rover GPS operational until 3/2005
• Now reverts to seismometer array
Permanent Monitoring
Smart Structures
Technology Laboratory
July 2010
Building
mode
period/sec
Roof level FBA
Basement FBA
‘sonic’ anemometer
GPS antenna
Logger
0
0
200
days
400
0
600
core w all
core Slab
office Slab
CFT Column
curtain Wall
mass
mode A1
mode B1
14
Smart Structures
Technology Laboratory
July 2010
Typical Earthquake Recording
Smart Structures
Technology Laboratory
July 2010
Design Spectrum
L65A acc/mm.s-2
Bengaft5 Lat -4.0 Long 101.7 (619km) Ms 6.7 tremor 13:25:00 16/01/01 GMT
10
0
-10
2
4
6
8
10
12
14
16
18
Hence there is enough information for a local
design spectrum based on tremor
recordings
B1A acc/mm.s-2
10
1
0
-1
2
4
6
8
10
12
14
16
18
800
900
1000
3
2
1
0
B1A F/Hz
Normalised A-dir 1% spectra
2
2
time /minutes since 21:22:30 16 Jan 2001
65A F/Hz
(Aftershock of
Bengkulu
subduction
zone event in
2000), triggered
b strong
by
t
mode
d
2 response
100
200
300
400
500
600
Time
700
Normalised
to peak
ground
acceleration
10
10
3
1
0
0
0.5
1
1.5
2
2
frequency /Hz
2.5
3
1 Sunda
2 SSumat 4
3 NSumat 2
4 Aceh
5 SSumat 3
7 SSumat 1
9 SSumat 5
10 CSumat
11 SSumat 7
12 Sulawesi
13 Bengkulu
14 Bengaftr
15 SSumat 8
16 Bengaft3
17 Bengaft4
18 Sunda 2
20 Bengaft6
21 SSumat 8
22 SSumat 9
23 SSumat10
25 Aceh 2
composite
3.5
4
1
0
100
200
300
400
500
600
time /s
Chicago Full-Scale
Monitoring Program
700
800
900
1000
Smart Structures
Technology Laboratory
July 2010
• Established in 2001 (windycity.ce.nd.edu)
• Partnership between Notre Dame, SOM and the
Boundary Layer Wind Tunnel Laboratory
• Currently monitors 4 signature tall buildings in
Chicago and Korea, with Phase II expansion of
p to three additional buildings
g worldwide
up
• Major Objectives:
– Document level of response, impacts on
habitability and reliability of wind-tunnel response
predictions
– Document in-situ dynamic properties and
correlations with FEM/design assumptions
Smart Structures
Technology Laboratory
July 2010
Monitoring Technologies
• Response:
– Sub-Centimeter Accuracy GPS
– Force Balance Accelerometers
– Digital Accelerometers
• Wind Environment
– Ultrasonic anemometers/met. stations
• Hub & Spoke Data Acquisition:
– Wired datalogger systems
– DAQ over LAN, real-time systems
Sponsors: NSF CMS 00-85109,
CMMI 06-01143, CCHRB,
SEAOI
The R-SHAPE System
Caltech Millikan Library Building (2002)
Smart Structures
Technology Laboratory
July 2010
Example of Mode Shape
Determined From R-SHAPE Data
Smart Structures
Technology Laboratory
July 2010
st
Millikan Library 1 E-W Mode
10
9
8
Story Levell
7
6
5
Data
4
Rigid Body Rotation
3
Bending (Core)
2
Shear (Core and Frame)
1
Total Calculated
0
0
0.2
0.4
0.6
0.8
1
Normalized Displacement
W. D. Iwan - Some Milestones in Strong Motion Monitoring - EERI, February 9, 2008
W. D. Iwan - Some Milestones in Strong Motion Monitoring - EERI, February 9, 2008
15
Smart Structures
Technology Laboratory
July 2010
University of Tokyo
Guangzhou New TV Tower (610 m in height)
Smart Structures
Technology Laboratory
July 2010
measurement
of ambient
motion
0.4
Seismic retorfit
RMS値（0.1gal）
0.35
RMS
In ambient
motion
0.3
0.25
耐震補強済
耐震補強前
0.2
0.15
Not retrofitted
0.1
0.05
Effectiveness of retrofit
0
x西
x東 x（西
-東）
y西
y東 y（西
-東）
First step of vulnerability
測定位置
assessment
The Hong Kong Polytechnic University
Guangzhou New TV Tower (610 m in height)
Smart Structures
Technology Laboratory
July 2010
Guangzhou New TV Tower (610 m in height)
Smart Structures
Technology Laboratory
July 2010
Photos taken on 30 December 2007
上
下
The Hong Kong Polytechnic University
Guangzhou New TV Tower (610 m in height)
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Total
Type
Monitored Data
Temperature, humidity,
rain, air pressure
Wind speed and direction
Wind pressure
Inclination, leveling,
Total Station
elevation
Z ith l Telescope
Zenithal
Tl
I li ti off tower
Inclination
t
Tiltmeter
Inclination of tower
Level Sensor
Leveling of floors
Theodolite
Elevation
GPS
Displacement
Vibrating Wire Gauge Strain, shrinkage and creep
Thermometer
Temperature of structure
Digital Video Camera Displacement
Seismograph
Earthquake
Corrosion Sensor
Corrosion of reinforcement
Accelerometer
Acceleration
Fiber Optic Sensor
Strain and temperature
Smart Structures
Technology Laboratory
July 2010
The Hong Kong Polytechnic University
http://www.cse.polyu.edu.hk/benchmark
Smart Structures
Technology Laboratory
July 2010
Number of Sensors
In-Construction In-Service
Stage
Stage
Weather Station
1
1
Anemometer
Wind Pressure Sensor
2
2
4
1
2
2
2
2
2
416
96
3
527
2
60
60
3
1
3
22
120
280
The Hong Kong Polytechnic University
The Hong Kong Polytechnic University
16
Smart Structures
Technology Laboratory
July 2010
Structural Health Monitoring (SHM)
Smart Structures
Technology Laboratory
July 2010
• SHM requires more than just data
–
–
–
–
Future Directions
Pertinent information
Timely reporting
Has the structure sustained damage?
The number of sensors required to If so, where?
adequately
adequately monitor civil infrastructure monitor
infrastructure
• F
Fact:
t D
Damage
iis an iintrinsically
t i i llcivilllocally
ll phenomena
h
cannot be sufficiently realized with • Fact: Civil infrastructure
is large and complex
traditional approaches
traditional approaches
• Result: Dense arrays of sensors are required to
effectively monitor civil infrastructure
• Current monitoring systems are expensive with much of
the cost derived from cabling and installation
97
Intelligent Sensory System
Stonecutters Bridge in Hong
Kong (2007)
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
WI
M
Anemometer
Accelerometer & Seismometer
Temperature Sensor
4E
3E
Strain Gauge
The key to development of the
next generation of SHM systems is
embedded computing and sensing.
sensing
2E
GPS Rover Station
1E
Displacement Transducer
Diagnostics
Prognostics
Corrosion Sensor
Digital Video Camera
WI
M
Sensory
System
Safety
Performance
Life-Cycle Cost
East
Tower
Barometer, Rain Gauge, Hygrometer
Sensory
System
Weigh-In-Motion System
Total Number of
Sensors : >1200
@
$11K / sensor
WIM
1W
West
Tower
2W
3W
4W
Seoul
Daejeon (KAIST)
US-Korea-Japan Test Bed on
Smart Wireless Monitoring of the
Second Jindo Bridge
Environmentally Hardened Enclosure
(September 2008 – present)
Antenna Extension Cable
2nd Jindo Bridge
Haenam
(Inland)
Jindo
Bridges
External Antenna
- Range up to 200m
- Cover longer than midspan
Jindo
Jeju Island
Wireless sensor kit
- Battery board
- Imote2
- SHMa sensorboard
Modified battery board
- 3 D-cell batteries
2nd Jindo Bridge
Type
Cable-stayed bridge
Spans
70+344+70 = 484m
Girder
Steel box (12.55m width)
Design velocity
70 km/hr
Designed by
Yooshin cooperation (2000, Korea)
Constructed by
Hyundai construction (2006, Korea)
Owner
Iksan Regional Construction and
Management Administration
Special feature
Twin bridge
10
101
1
AirLock
- Water proof
102
17
Measured Time‐history Data
• Sensors on Pylon
• Sensors on Cable
Cable : 8
Deck : 26
Pylon : 3
Total : 37
P-HE2 : Time-history Acceleration
C-JE7 : Time-history Acceleration
In total, 420 channels of sensors
Z-axis
Y-axis
X-axis
0
0
Y
20
40
60
time(sec)
80
0
20
40
60
time(sec)
80
0
-10
0
20
100
40
60
time(sec)
80
0
5
10
time(sec)
15
Z
X
• Sensors on Deck
D-JE5 : Time-history Acceleration
D-JE8 : Time-history Acceleration
0
-10
-20
0
20
40
60
time(sec)
80
100
-20
10
Z-axis
Y-axis
X-axis
5
0
-5
-10
0
D-HE2 : Time-history Acceleration
10
Z-axis
Y-axis
X-axis
10
amplitude (mg)
amplitude (mg)
Sensor
powered by
solar cell
D-HE13 : Time-history Acceleration
20
Z-axis
Y-axis
X-axis
-10
0
20
40
60
time(sec)
80
100
Z-axis
Y-axis
X-axis
5
amplitude (mg)
20
10
Sensor
3 D-cell
powered by
Batteries
D-cell batteries
100
amplitude (mg)
SHM-A Board
w/ Imote2
[Base Stations are installed on pylons of 1st
Jindo Bridge, parallel to 2nd Jindo Bridge]
Manager node
Base Station
w/ Antenna
(Industrial PC, UPS, ADSL
Internet, Enclosure w/
ventilation)
0
-50
X-axis
Y-axis
Z-axis
5
-5
-5
-10
4 reference sensors
to construct global mode
information
10
X-axis
Y-axis
Z-axis
5
amplitude (mg)
0
-50
P-HT1 : Time-history Acceleration
10
50
Z-axis
Y-axis
X-axis
amplitude (mg)
C-JE2 : Time-history Acceleration
50
amplitude (mg)
Cable : 8
Deck : 22
Pylon : 3
Total : 33
amplitude (mg)
Sensor Deployment
0
-5
0
20
40
60
time(sec)
80
-10
0
20
40
60
time(sec)
103
80
104
Smart Structures
Technology Laboratory
July 2010
Modal Information
• Test Specification
• Result of FDD (Jindo
(Jindo--side)
Result for Singluar Value Decomposition
3
ƒ System: Jindo-side Sensor Network
10
[Singular Values]
ƒ Date : July 21, 2009
2
ƒ No. of collected data: 5000 data points
ƒ Sampling frequency: 50Hz
Singular Values
10
1
10
0
10
ƒ LPF : 20Hz (by Programmable Filter)
-1
10
0
0.5
1
1.5
2
2.5
Frequency (Hz)
3
3.5
4
4.5
5
l
lessons
from
f
a smartt fish
fi h
0.647Hz
1st vertical mode
: 0.439Hz
0.442Hz
2nd vertical mode
: 0.641Hz
4th vertical mode
: 1.404Hz
1.247Hz
5th vertical mode
: 1.569Hz
1.001Hz
3rd vertical mode
: 1.025Hz
1.735Hz
1.349Hz
6th vertical mode
: 1.837Hz
Smart Structures
Technology Laboratory
July 2010
105
Principle of Active
Electrolocation
Smart Structures
Technology Laboratory
July 2010
Smart Sensing Strategies in Electric Fish
Prof. Mark E. Nelson
Beckman Institute, UIUC
18
Smart Structures
Technology Laboratory
July 2010
Electroreceptors
Something to Ponder …
Smart Structures
Technology Laboratory
July 2010
• Electrosensory images are low resolution, so
why is the sensor density so high?
~15,000 individual sensors
1 nerve fiber per sensor
up to 1000 temporal pulses per sec per nerve fiber
RAW DATA RATE: ~15 Mbps
MacIver, from
Carr et al., 1982
Why so many sensors?
Smart Structures
Technology Laboratory
July 2010
Virtual Sensor Arrays
Smart Structures
Technology Laboratory
July 2010
Virtual Sensor Arrays:
Multi-scale Filtering
Smart Structures
Technology Laboratory
July 2010
• Facts: Individual electro-sensory sensors are
– relatively low resolution devices
– do not provide reliable event detection
– are easy to replicate (developmental biology)
• Solution: Nervous system creates arrays of
VIRTUAL SENSORS with desired resolution
and sensitivity
Smart Structures
Technology Laboratory
July 2010
Virtual Sensor Arrays
Array Name
# virtual
sensor nodes
Skin Sensors
15,000
--
CMS Map
M
2 800
2,800
40
BRAIN PROCESSING
skin sensors
per node
Centromedial map
- High spatial acuity
- Low temporal acuity
SKIN
SENSORS
INPUT
CLS Map
LS Map
1,400
200
900
1000
(from skin receptors)
both
Centrolateral map
- Inter spatial acuity
- Inter temporal acuity
Lateral map
- Low spatial acuity
- High temporal acuity
19
Smart Structures
Technology Laboratory
July 2010
Prey capture behavior
Smart Structures
Technology Laboratory
July 2010
Outline
• Trends in Structural Control
• Trends in Structural Health Monitoring
• Sensors,
S
D
Data
t A
Acquisition,
i iti
and
d Di
Digital
it l
Signal Processing
Prey capture behavior
Outline
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
• What is a sensor?
• Typical sensors for measuring dynamic
structural response
• Collecting
C ll ti Di
Digital
it l D
Data
t
– Quantization and Aliasing
• Digital Signal Processing
Smart Structures
Technology Laboratory
July 2010
Pendulum Response
Vibration Sensor
Smart Structures
Technology Laboratory
July 2010
Can be read
and recorded
M
M
Accelerometers
20
Smart Structures
Technology Laboratory
July 2010
Vibration Sensor
Smart Structures
Technology Laboratory
July 2010
Displacement Meter
For undamped oscillator:
δ&& + ω 2δ = −u&&
If u = A sin pt
We have δ = B sin pt
(1)
(2)
(3)
Carrying out differentiations, and dividing out common terms,
we find a necessary condition for the form (3)
Accelerometer
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
Pendulum Response
M
M
Accelerometers
Piezoelectric Accelerometer
Smart Structures
Technology Laboratory
July 2010
Piezoelectric Accelerometer
Smart Structures
Technology Laboratory
July 2010
Typical Specification: 5~1000Hz, ±10g
21
Smart Structures
Technology Laboratory
July 2010
Vibration Sensor
Influence of natural frequency of the sensor
Specification of sensors
Sensitivity:
S=
Smart Structures
Technology Laboratory
July 2010
Output ( voltage)
Input (vibration)
Resolution: the minimum quantity which can cause
the variation of output.
Frequency range: the range over which the sensitivity
of the transducer does not vary more than
a stated percentage from the rated sensitivity.
Specification of sensors
Smart Structures
Technology Laboratory
July 2010
Ground Loops
Smart Structures
Technology Laboratory
July 2010
Linearity:
Output
y
f (x)
x
Input
⎛ y − f ( xi ) ⎞
⎟⎟ %
max ⎜⎜ i
⎝ f ( xi ) ⎠
Ground Loops
Smart Structures
Technology Laboratory
July 2010
Before and after coupling
Smart Structures
Technology Laboratory
July 2010
22
Smart Structures
Technology Laboratory
July 2010
Ground-loop coupling
Smart Structures
Technology Laboratory
July 2010
Typical Sensors for
Measuring Dynamic
Response
Smart Structures
Technology Laboratory
July 2010
Resistive Accelerometers
• Operating Principle
• Operating Principle
– Voltage output of resistor bridge changes proportionally with applied
acceleration
+ Signal
+ Power - Power
– Utilizes frequency modulation technique through varying capacitor
bridge
Power
- Signal
Fixed Capacitors
Fixed
Resistors
Sensing Resistor
#1
Flexure
Sensing Resistor
#2
Resistive/Capacitive
Accelerometers
•
•
•
•
•
Ground
Signal
Built-In Electronics
~
Insulator
Sensing Capacitor
#1
Mass
Flexure
Mass
Sensing Capacitor
#2
Insulator
Smart Structures
Technology Laboratory
July 2010
Typical Characteristics
•
•
•
•
Smart Structures
Technology Laboratory
July 2010
Capacitive Accelerometers
Measure down to 0 Hz (DC response)
Limited dynamic range (<80 dB = 10,000:1)
Limited high frequency range (<10 kHz)
p frequency
q
y response
p
((0.7% of
Often a damped
critical)
Sensitivity may vary with input (mV/g/V)
Traditionally fragile (limited shock protection)
Operates multi-conductor cable (at least 3 wires)
Micro-machined versions are small and lightweight
Performance matches cost ($10 to $1000 USD)
Piezoelectric
Accelerometers
Smart Structures
Technology Laboratory
July 2010
• Piezoelectric
– Force on self-generating crystal provides charge output proportional to
acceleration
Signal/Power
Ground
Voltage or Charge Amplifier
Preload Ring
Mass
Piezoelectric
Crystal
Base
23
Smart Structures
Technology Laboratory
July 2010
Piezoelectric Materials
• Piezoelectric Effect
Smart Structures
Technology Laboratory
July 2010
Piezoelectric Materials
• Piezoelectric Materials
– Word origin comes from the greek work
“piezen” which translates “to squeeze”.
– The generation of an electrical signal by a
dielectric material as it is subjected to a
mechanical stress.
F
– Naturally Piezoelectric
• Rochelle Salt
– One of first materials used to make sensors
• Tourmaline
T
li
– Sensitive to hydrostatic pressure
• Exotic, “Man-Made” Materials
+
+
-
+
-
+
-
+
-
+
-
+
-
Piezoelectric
Material
– Langasite
– Lithium Niobate
• Cultured Quartz
-
F
Smart Structures
Technology Laboratory
July 2010
Piezoelectric Materials
Smart Structures
Technology Laboratory
July 2010
Mechanical Design
• Piezoelectric Sensing Element
• Piezoelectric Materials
– Mechanical transduction mechanism as
important as piezoelectric material selection
– The key is to design the sensor so that it only
meas res the parameter of interest and
measures
minimizes the affects of any outside
environmental conditions
– Types
– Artificially Polarized
• Piezofilm
– Made of a special polymer - PVDF
• Piezoceramics
Pi
i
– Lead Zirconate Titanate (PZT)
– Bismuth Titanate
• Compression Mode
• Flexural Mode
• Shear Mode
Smart Structures
Technology Laboratory
July 2010
Mechanical Design
• Compression Mode
• Flexural Mode
– Original sensors utilized this approach;
however, it is not commonly used today
except for special applications
Seismic
Mass
Electrode
Smart Structures
Technology Laboratory
July 2010
Mechanical Design
Preload Stud
- + +
- + +
+- +-
+
- +-
Piezoelectric
Crystal
(d11-Quartz)
(d33-Piezoceramic)
– Utilized only in a few low cost sensor designs
as performance limitations minimize its
widespread use
Piezoelectric
Seismic
Mass
+ + + + +
- - - - -
Crystal
y
(d12-Quartz)
(d31-Piezoceramic)
Fulcrum
Signal (+)
Ground (-)
Signal (+)
Ground (-)
Optional Built-In
Electronics
Optional Built-In
Electronics
24
Smart Structures
Technology Laboratory
July 2010
Mechanical Design
– Most commonly utilized design based on
overall performance
+
+
+
+
-
-+
-+
-+
-+
Preload Ring
Piezoelectric
Crystal
(d26-Quartz)
(d15-Piezoceramic)
Center
Post
Signal (+)
Ground (-)
Optional Built-In
Electronics
Smart Structures
Technology Laboratory
July 2010
Strain Gages
Transverse
strain
Axial
strain
e T = −ν e L
Poisson’s
ratio
Smart Structures
Technology Laboratory
July 2010
Typical Characteristics
• Shear Mode
Seismic
Mass
Piezoelectric
Accelerometers
•
•
•
•
•
Dynamic events only (>0.2 Hz)
Wide dynamic range (>100dB = 100,000:1)
Wide frequency bandwidth (<1 Hz to >10 kHz)
Solid-state ((No moving
gp
parts))
Self-generating piezoelectric elements require no
power
• Operates over two conductors
• Rugged (5,000 g’s)
• High temperature charge versions operate to
1000 F (537 C)
Smart Structures
Technology Laboratory
July 2010
Gage Factor
eT
eL
F
l
Δl
Elastic Modulus:
F
A
E=
σ (stress)
(t
)
e (strain)
Because:
Δl
= eL ;
l
ΔA
ΔD
=2
= 2 e T = 2 (−υ e L )
A
D
Poisson’s
ratio
Material resistivity
Then:
R=
The resistance of a strain gage:
Relative change in resistance:
ρl
Element length
A
Cross section area
Define a Gage factor G:
G=
ΔR
R
eL
When a strain gage is strained, the change in resistance is:
∂R
∂R
⎛ ∂R ⎞
ΔR = ⎛⎜ ⎞⎟Δl + ⎛⎜ ⎞⎟ΔA + ⎜ ⎟Δρ
⎝ ∂l ⎠
⎝ ∂A ⎠
⎝ ∂ρ ⎠
Example of Strain Gage
Specifications
Smart Structures
Technology Laboratory
July 2010
Temperature Range
Normal: -100 to +350 F
Short-Term: -320 to +400 F
Strain Range
+3% for gage lengths under 1/8 in
+5% for 1/8 in and over
Fatigue Life
105 cycles at +1500 microstrain
106 cycles at +1500 microstrain
with low modulus solder.
Gage factor of a strain gage:
Wheastone Bridge
Smart Structures
Technology Laboratory
July 2010
Sensitive instrumentation is
required to measure the small
changes in resistance
produced by strain gauges.
Wheatstone bridge is
typically used to measure
resistances accurately and
dynamically over a very large
range (1 to 1,000,000 Ω).
25
Common Strain Gage
Arrangements
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
Strain-Type Load Cells
F
R1
R2
+
Strain gages are used
in pillar type load cells
VS
-
+
VS
R2
-
R1
R4
R4
R3
R3
R3 , R1
eT
R2 , R4
R1
R2
eL
+
R2
VS
-
+
VS
-
R1
R4
R4
R3
R3
Single point
Platform scales
1-1000 Kg
S-type
F
Smart Structures
Technology Laboratory
July 2010
Strain-Type Load Cells
σ
F
=−
A⋅E
E
υ⋅F
eT = +
= −υ e L
A⋅E
eL = −
Piezoelectric Load Cells
Poisson’s
ratio
Smart Structures
Technology Laboratory
July 2010
Bending beam
Low profile: load and
pallet scales
5-500
5
500 Kg
Compression
Silos, tanks and weighbridges
5,000-60,000 Kg
Shear beam
(tension-compression)
Low profile: load and pallet scales
500-5000 Kg
Can not measure static loads
Hanging scales 50 – 5000 Kg
Smart Structures
Technology Laboratory
July 2010
LVDT
LVDT
Smart Structures
Technology Laboratory
July 2010
Linear Voltage Differential Transformer
(LVDT)
Coil Assembly
Core
26
Smart Structures
Technology Laboratory
July 2010
LVDT
•
•
•
•
•
•
•
•
•
•
Friction-Free Operation
Infinite Resolution
Unlimited Mechanical Life
Overtravel Damage Resistant
Single Axis Sensitivity
Separable Coil And Core
Environmentally Robust
Null Point Repeatability
Fast Dynamic Response
Absolute Output
Core at Center, Eout is Zero
+
SECONDARY 1
Smart Structures
Technology Laboratory
July 2010
Eout -
PRI
PRIMARY
SECONDARY 2
Smart Structures
Technology Laboratory
July 2010
-
+
Ein
-
Eout
Ein
Core
SEC2
SECONDARY 2
Cable Extended Transducer
PRIMARY
Core right-of-center
Eout Non-Zero and Out-of-Phase with Input
Eout
Eout
Core
SEC1
SECONDARY
1
-
LVDT Operation
+
-
-
Core
Core Left-of-Center
Eout Non-Zero and In-phase with input
+
Eout
+
LVDT Operation
+
Smart Structures
Technology Laboratory
July 2010
LVDT
SECONDARY 1
Smart Structures
Technology Laboratory
July 2010
PRIMARY
SECONDARY 2
Cable Extended Transducer
Smart Structures
Technology Laboratory
July 2010
CETs are ideal in many instances:
• Where Large Displacements are Expected
• Up to 100” for Laboratory Models
• Up to 1750” (145ft) for Industrial Models
Cable is wound around a precision
machined spool attached to either a:
• Potentiometer (variable resistor,
analog)
• Incremental Encoder ((optical,
p
, digital)
g )
• Where Perfect Alignment is Not Possible
A spring provides controlled recoil of
the cable.
• Cannot use LVDT Here!
27
Smart Structures
Technology Laboratory
July 2010
Optical Encoder
Quadrature (or Incremental)
Encoder
Smart Structures
Technology Laboratory
July 2010
Channel A
Channel B
Photo Detector
Channel I
Light
Source
Code Track on Disk
Channel A
Shaft
Code Track
Channel B
90
Rotating Disk
Channel I
Digital Output
Smart Structures
Technology Laboratory
July 2010
Collecting Digital Data
Collecting Digital Data
Smart Structures
Technology Laboratory
July 2010
• Because analysis, results, and conclusions
are only as good as the data on which it is
based, special care must be taken to
ensure that high quality data are obtained.
• The quality of the data often depends on
the purpose for which the data will be
used.
The Measurement Process
Smart Structures
Technology Laboratory
July 2010
• Data Acquisition: The process of representing
an analog signal as a series of digital values is a
basic requirement of modern digital signal
processing analyzers. In practice, the goal of the
analog to digital conversion (ADC) process is to
obtain the conversion while maintaining sufficient
accuracy in terms of frequency, magnitude, and
phase.
• Two basic related concepts dictate accuracy:
Sampling and Quantization
Smart Structures
Technology Laboratory
July 2010
• Primarily, sampling considerations alone affect
the frequency accuracy.
• Both sampling and quantization considerations
affect magnitude
g
and p
phase accuracy.
y
• The dynamic range of the ADC (84 dB for 14
bits, 96 dB for 16 bits, etc.) is only meaningful if
the quantization of an input signal of interest
involves all of the bits of the ADC.
– Sampling and Quantization
28
The Measurement Process
Smart Structures
Technology Laboratory
July 2010
Sampling and Quantization
Sensors (e.g., Accelerometers,
LVDT, strain gage, etc.) all
produce analog voltage signals
that must be calibrated with
physical response.
A/D
Converter
Sensor
Δt
Sensor Volta
age
Physical
Response
Digital
Computer
1. Sample and Hold
2. Quantize
Sampling and Quantization
t
Output Code
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
Quantization
Δt
Sensor Volta
age
Smart Structures
Technology Laboratory
July 2010
Physical
Response
Sensor
Gain
S
Sensor
t
A/D
Converter
Digital
Computer
Output Code
Smart Structures
Technology Laboratory
July 2010
Aliasing
1
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
Measure
ed Frequency
0.6
-1
Nyquist Frequency Nf = fs/2
• Consider a 48 Hz signal
• What if the signal is
sampled at 50 Hz?
• The resulting measured
signal has an apparent
frequency of 2 Hz
0.8
After a signal is
sample the aliasing
sample,
Aliasing
problem cannot be
?
◊ Cannot have significant energy resolved!
above the Nyquist frequency (f /2)
0.05
0.1
0.15
0.2
0.25
0.3
Time (sec)
0.35
0.4
0.45
Smart Structures
Technology Laboratory
July 2010
Aliasing
0.5
Nf
Nf
fs
Excitation Frequency
s
◊ Anti‐aliasing filters must be used in dynamic measurements to preserve signal integrity
Illustration of Aliasing in the frequency Domain
fN
fs
29
Smart Structures
Technology Laboratory
July 2010
Antialiasing Filters
Aliased Square Wave
Smart Structures
Technology Laboratory
July 2010
Calibration of System
Smart Structures
Technology Laboratory
July 2010
Physical
Response
Sensor
Sensor
Gain
Antialiasing
Filters
A/D
Converter
Unaliased Square Wave
Digital
Computer
Smart Structures
Technology Laboratory
July 2010
Physical
Response
S
Sensor
Sensor
Gain
A/D
Converter
Other ADC Issues
Smart Structures
Technology Laboratory
July 2010
• Differential Nonlinearity: If the round-off that occurs to
cause quantization error is not regular (some of the spacing
between counts varies) this type of error results. This causes
the “noise” from quantization error to be biased.
• Bit Dropout: One bit in the ADC may never be set.
Obviously, any sample requiring this bit in the ADC word to be
set will be in error and the error will be biased. A similar
problem exists if one bit of the ADC word is always set.
• Reference Voltage: The reference voltage used by the ADC
may drift within or between sample periods. Since this drift is
not known or measured, this error will cause a bias in any
resulting estimate of the dependent variable.
Other ADC Issues
Digital
Computer
Smart Structures
Technology Laboratory
July 2010
• Overload and Overload Recovery: When the ADC is
overloaded, it may take several sampling increments to
recover. This is normally only a problem under severe
overloads but if it occurs the result will be a bias in the
estimate of the amplitude.
• Aperture Error - Clock Jitter: The value of the amplitude
recorded does not correspond to the assumed instant in time,
t. This type of error will result in a bias in the estimate of time
and frequency parameters.
• Digitizer Noise: The random setting of plus or minus one bit
when the input is zero is referred to as digitizer noise. This
error may become dominant in transient excitation since a
large pert of the observed histories may be very small or
actually zero as in the case of impact testing. This error can
be controlled to some extent by averaging and the use of
special window functions.
30
Smart Structures
Technology Laboratory
July 2010
Smart Structures
Technology Laboratory
July 2010
Spectrum analysis
Digital Signal Processing
Smart Structures
Technology Laboratory
July 2010
Frequency Response Function
• One of the most important
measurements to be made is the
frequency response function.
• But,
But what is the frequency response
function?
• Another important function
impulse response function:
1
1/ m
=
− mω 2 + icω + k −ω 2 + i2ζωnω + ωn2
Smart Structures
Technology Laboratory
July 2010
• Recall that the forward Fourier transform and
the inverse Fourier transform are defined by
X (ω ) = F
∞
{ x (t )} = ∫
is
the
&&(t ) + cx& (t ) + kx (t ) = f (t )
mx
h(t ) =
&&(t ) + cx& (t ) + kx (t ) = f (t )
mx
H (ω ) =
Smart Structures
Technology Laboratory
July 2010
The Impulse Response Function
1 − ωnt
sin(ωdt )
e
mωd
Extraction of Modes
#1
Smart Structures
Technology Laboratory
July 2010
#2
#3
x (t )e -iωt dt
−∞
x (t ) = F
-1
1
{ X (ω )} =
2π
∞
∫ X (ω )e
iω t
dω
−∞
• The Frequency Response Function and the
Impulse Response Function form Fourier
Transform pairs
H (ω ) = F {h(t )} , h(t ) = F
-1
Mode 1
2.38 Hz
0.36%
{H (ω )}
31
Extraction of Modes
#1
Smart Structures
Technology Laboratory
July 2010
#2
Extraction of Modes
#3
#1
Smart Structures
Technology Laboratory
July 2010
#2
#3
Mode 2
6.57 Hz
0.4%
Smart Structures
Technology Laboratory
July 2010
Mode 1
2.38 Hz
0.36%
Mode 2
6.57 Hz
0.4%
Smart Structures
Technology Laboratory
July 2010
Frequency Response Function
u (t )
Single-Input,
Hvu (f )
v (t )
Single-Output
Hvu (f ) =
• There are several methods to
experimentally obtain the Frequency
Response Function:
H1 Frequency Response Function
• Including noise:
V (f ) V (f ) Gvv (f )
=
V * (f ) U (f ) Gvu (f )
+
Hvu (f )
m (t )
x (t )
Gxy (f )
Gxx (f )
+
y (t )
v (t )
+
+
H1(f ) =
Smart Structures
Technology Laboratory
July 2010
n(t )
u (t )
V (f )
Hvu (f ) =
U (f )
U * (f )V (f ) Guv (f )
Hvu (f ) = *
=
U (f ) U (f ) Guu (f )
*
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July 2010
Frequency Response Function
– Swept-Sine
– Random Excitation
– Impulse Excitation
– Step-Relaxation Excitation
Mode 3
11.3 Hz
1.68%
• For the
system:
Mode 3
11.3 Hz
1.68%
=
Cov [ m (t ), n(t )] = 0
Guv (f )
Hvu (f )
=
Guu (f ) + Gmm (f ) 1 + Gmm (f )
Guu (f )
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Smart Structures
Technology Laboratory
July 2010
H2 Frequency Response Function
• Including noise:
n(t )
u (t )
+
y (t )
x (t )
+
H2 (f ) =
Gyy (f )
Gxy (f )
u (t )
v (t )
+
=
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Technology Laboratory
July 2010
n(t )
+
Hvu (f )
m (t )
AA-Filter Effect on the
Transfer Function
Cov [ m (t ), n(t )] = 0
Gvv (f ) + Gnn (f )
G (f )
= Hvu (f ) + nn
Guv (f )
Guu (f )
Smart Structures
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July 2010
Digital Signal Processing
+
Hvu (f )
+
y (t )
H AA2 (f )
If the AA
filters onvthe
(t ) input and
+
m (t )
y AA (t )
output are amplitude
and phase
H AA1(f )
+
x
(
t
)
x (tthen
)
matched,
they will
AA not affect
the signal in the frequency range
Gx y of
(f )interest.
H AA1(f )H AA 2 (f )Gxy (f )
H1(f ) =
=
AA AA
Gx AA x AA (f )
H AA1(f )H AA1(f )Gxx (f )
Digital Signal Processing
Smart Structures
Technology Laboratory
July 2010
• The Discrete Fourier Transform is a
discretized, finite time-interval,
approximation of the Fourier Transform
integral.
N −1
X (fk ) = Δt ∑ x (t n )e
⎛ kn ⎞
− i 2π ⎜
⎟
⎝ N ⎠
n=0
N −1
x (t n ) = Δf ∑ X (fk )e
⎛ kn ⎞
i 2π ⎜
⎟
⎝ N ⎠
k =0
Spectral Leakage
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July 2010
Leakage Experiment
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July 2010
• Leakage is probably the most common and,
therefore, the most serious digital signal processing
error. Unlike aliasing and many other errors, the
effects of leakage can only be reduced, not
completely eliminated.
• Leakage is basically due to a violation of an
assumption of the discrete Fourier transform
algorithm (i.e., the true signal is periodic within the
sample period used to observe the sample function).
• Common ways of reducing leakage include: (i)
windowing or weighting functions, (ii) periodic
excitation, and (iii) increase in frequency resolution.
• Effect on coherence function
• Transient vs. Stationary signals
33
Actual Power Spectrum
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July 2010
Power Spectrum:
Boxcar Window
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July 2010
Power Spectrum:
Hanning Window
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July 2010
Power Spectrum:
Flattop Window
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July 2010
Power Spectrum:
Zoom w/ Flattop Window
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July 2010
Windows Scorecard
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July 2010
For more information, see:
http://www.lds-group.com/docs/site_documents/AN014%20Understanding%20FFT%20Windows.pdf
34
Conclusions
Smart Structures
Technology Laboratory
July 2010
• Use appropriate sensors for the job and know their
limitations.
• Obtaining accurate data requires high quality data
acquisition equipment, and the system must be calibrated.
• Generally
Generally, more bits in the A/D converter is better (e
(e.g.,
g 16
bits). Preamplify the sensor signal so that it uses the
maximum span of the A/D converter.
• Always use high-quality antialiasing filters, typically 8-pole
elliptic filters are generally the best for experimental modal
analysis.
• Spectral leakage is a critical problem that must be
addressed in experimental structural dynamics
35