SE 207 Lecture May 23, 2006 Topics 1. Structural Dynamics ...jacobsschool.ucsd.edu/EEI/academic/courses/06/... · Topics 1. Structural Dynamics Measurements. ... response is essential

Engineering Education Initiative

SE 207 Lecture May 23, 2006

Topics1. Structural Dynamics Measurements


All SD Sensor Networks are Deployed for Three Possible Uses

1. Detection Problems (existence and location)

– Threshold detection (air bag deployment)– Structural Health Monitoring

2. Model Development, Validation, Uncertainty Quantification

– Finite Element Model Validation– Damage Prognosis (predicting remaining system

life)3. Control Systems

– Avionics– Manufacturing Processes


Sensing Systems for Damage Prognosis

Initial System Information: Design, Test, Maintenance,

Operator “Feel”

Estimate: Remaining Service Life

Time to FailureTime to Maintenance

Data Based

Initial Physics Model

Future Loading Model

Structural Health Model

Prognosis Model

Operational and Environmental Measurement

system

Structural Health Monitoring

Measurement System

Updated Physics Model

Physics Based

Take action, update system information, continue process


The Structural Health Monitoring Process

(or any other detection problem)

1. Operational evaluationDefines the damage to be detected and begins to answer questions regarding implementation issues for a structural health monitoring system.

2. Data acquisitionDefines the sensing hardware and the data to be used in the feature extraction process.

3. Feature extractionThe process of identifying damage-related information from measured data.

4. Statistical model development for feature discriminationClassifies feature distributions into damaged or undamaged category.

• Data Cleansing• Data Normalization• Data Fusion• Data Compression(implemented by

software and/or hardware)


Definition of “Damage”

• Damage is defined as changes to the material and/or geometric properties of a structural that adversely affect its performance.

• All materials used in engineering systems have some inherent initial flaws.

• Under environmental and operational loading flaws will grow and coalesce to produce component level failure.

• Further loading causes system-level failure.

• Must consider the length and time scales associated with damage evolution.


Humans are Enamored by Things of Extreme Size

Radio Telescope MEMS Sensors


Example: UC-Irvine Bridge Pier


Cyclic Loading


Data Acquisition and Cleansing

15.0” (38.1 cm)

34

35

40

32

33

39

30

31

38

28

29

2

26

27

1

24

25

23

22

36, 37(load)

22.67” (57.6 cm)

22.67” (57.6 cm)

22.67” (57.6 cm)

22.67” (57.6 cm)

22.67” (57.6 cm)

22.67” (57.6 cm)

X

Z

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

36” (91.4 cm) dia

30” (76.2 cm)

40 accelerometers mounted on the structure.

Most accelerometers were 1v/g sensitivity.

Data from low sensitivity (10mv/g) accelerometers were discarded.

Data consisted of 8-s duration time histories discretized with 8192 points (Files labeled with T)

No windowing function applied to time histories

Anti-aliasing (512 Hz cutoff frequency) and AC-coupling filters (attenuate below 2 Hz) were applied to the data


Data Acquisition• Obtaining accurate measures of the system’s dynamic

response is essential to model validation.• The data acquisition process can be divided into six parts:

• Signal processing is often integrated with data acquisition systems.

• Data cleansing, normalization compression and fusion is integrated in this process as well.

• The development of “system-on-a-chip” capability is allowing the data acquisition hardware to be directly integrated with thedata interrogation “software”

Data Acquisition

Excitation Sensing DataTransmission

Analogto

DigitalConversion

DataStorage

DataCleansing,

Normalization, Compressionand Fusion


Piezoelectric Accelerometer

Courtesy of PCB, Inc.


The Process of Getting a Measurement

platevibration

QuickTime™ and aAnimation decompressor

are needed to see this picture.

epoxy

viscoelasticeffects

temperature

housingself-dynamics(e.g., resonances)

boundaryconditions

seismicmass

seating

bindingpost

manufacturingtolerances

self-dynamics(e.g., cross-axissensitivity)

boundaryconditions

piezoelectricelement

coupling

stray capacitance

contact wire

contact leads

cabling

EMI

environment

signalconditioning

environmenthuman error(e.g., filter settings)

DAQboard

quantizationerror

DSP

human errorsoftware glitches(e.g., round-off)

observer

datapresentationhuman errorMicrosoft

input


Obtaining Useful SD Measurements I

Level 1:System-Level Considerations

What features will be extractedfrom data for SD application?

Active or passive sensing?

What other factors may need to be considered for accurate assessment?

• May determine the type(s) ofprimary data to be acquired

• May determine how oftenthe primary data is collected

• Operational (e.g., loading conditionsduring primary data collection)

• Environmental (e.g., ambient conditionsduring primary data collection)

• Identification of sources of error or variability

• Determines need for activeactuation (i.e., not ambient)

• Strongly influences power,networking, and bandwidth demands

Overall imposed limitations/constraints?

• Economic (e.g.,fixed budgets)• Political (gov’t or social influences)• Environmental (e.g., regulations orrequired procedures)


Unit-to-Unit Variability

Variability in FRFs measured on units manufactured in an identical manner with strict quality control

May need baseline measurement form each unit in this case


Obtaining Useful SD Measurements II

– Type of data to be acquired• Motion (e.g. acceleration)• Environmental (e.g. temperature)• Operational (e.g. traffic volume)

– Define sensor type, number and locations• Bandwidth (how fast do we sample data)• Sensitivity (dynamic range or amplitude)

– Define data acquisition/transmittal/storage system– Define how often data should be acquired

• Periodically• After extreme events

Level II: Define Data Acquisition Components.


Obtaining Useful SD Measurements III

– Define excitation source • Waveform (e.g. ambient, random, swept-sine)• Bandwidth (frequency range)• Amplitude

– Establish data normalization procedures• Temporal (time synchronization for multiple channels)• Level of input

– Cleanse data• Eliminate data from malfunctioning sensors• Window, decimate, filter data

– Compress data– Fuse data from multiple sources– Power for the data acquisition system

Level II: Define Data Acquisition Components (cont.).


Putting it All Together

Data Acquisition Component Considerations

System-level Considerations

Actuator system Sensor modalities

Networking strategy

Signal conditioning module(s),synchronization, scheduling, and control


Excitation

• Excitation is the process of applying a time-varying input to a system.

• Selection of the proper excitation methods will be influenced by many factors including:

– The size of the structure.– Required frequency range and

amplitude of inputs.– Operational constraints associated

with the system.

– Cost.

Frequency (Hz)

Electro-hydraulic

Electro-dynamic

Piezoelectric

1 10 100 1k 10k 100k

Forc

e

• Excitation methods will be classified as those where the input can be measured and those where it can not.


Excitation Signals

• Ambient– Often the only method that can be used

for large structures, or if the structure is not to be taken out of service, or if regulations prohibit introducing energy into the structure.

• Steady-State Deterministic– (stationary periodic; chaotic)

• Nonstationary Deterministic– (impulse; step-relaxation; swept sine/chirp;

quasi-periodic)

• Random– (full random, band limited to actuation

bandwidth window; pseudo-random, constant amplitude, random phase; burst random, short in time but fully random)

Mirage F1-AZ under controlled groundvibration testing.

Ship on the high seas.


Measured Input Excitation Examples

Tensioning cable immediately after release

Tensioning device Load cell

Electro-dynamic shaker applying random excitationto satellite (mid-frequency,fully random)

Tensioning device puttingan impulse force loadon the rotor (wide-band,transient deterministic)

Piezoelectric patches being used to impart high-frequency Lamb waves on a frame structure (periodic deterministic)

PZT patch


Unmeasured Input Excitation Examples

0 100 200 300 400 500 600 700−1000

−500

0

500

1000

Str

ain

Signal 1

Data Point # = 26980Time Period = 601.17 secΔ t = 0.02228 sec

0 100 200 300 400 500 600 700−1000

−500

0

500

1000

Str

ain

Signal 2

0 100 200 300 400 500 600 700−1000

−500

0

500

1000

Time (Sec)

Str

ain

Signal 3

Norwegian Navy composite fast-patrol boat hull vibration strain response to wave impacts.

Di-Wan Towers (Shenzen, China) sway and vibration acceleration response to wind.


Sensing Issues

• Number (optimal vs redundant)• Type• Location• Frequency range (bandwidth) vs frequency resolution• Amplitude sensitivity vs dynamics range• Stability (calibration requirements)• Cost (per data point, not per sensor!)• Reliability• Environmental ruggedness (durability)• Noise• Invasive (size, spark source)


• Most modern sensors used for SD convert measured quantity (force, acceleration, displacement, etc.) to an analog electrical signal.

• Sensors can be classified as contacting and non-contacting.

• Discrete sensors (surface point, contacting measurements) – Piezoelectric and piezoresistive force transducers– Accelerometers

• Piezoelectric• Piezoresistive• Capacitive• Servo• Fiber optic

– Strain gages• Foil• Fiber optic

– Impedance (piezo)

Primary SD Sensing Modalities


Non-contacting Sensors• Scanning laser Doppler velocimetry (LDV)• Laser holography• Laser/microwave displacement measurement systems• GPS (lower resolution)• Eddy Current Probe

LDV Microwave displacement


Data Transmission

• Most modern data acquisition systems transmit the analog signal from the sensor to the A to D convert through hard-wire connections.

•Alternative is to record analog signal on magnetic tape or to record with a digital tape recorder.

• Current research is focusing on wireless data transmission of digital signals.


Traditional SD Sensing System

sensor

Sensor network

Sensor network

Sensor network

Sensor networkCentralized Data Acquisition

Sensor network

Sensor network

Sensor network

Drawbacks1. Hard to

deploy in retrofit mode

2. Need AC power

3. One-point failure sensitive

4. Wires can be expensive to maintain

AdvantageOff-the-shelf systems readily available


New SD Sensing Systems Paradigms

Sensor Node•Sensor•A/D•Local computing•Telemetry•Power (battery)

Base Station

De-centralized Wireless sensors




Employs reconfigurablehopping protocol to telemeter data to base station

Drawbacks:1.From powerconsumption standpoint, node nearest the base station tend to do more work2. Lot of redundant hardware3.Limited processing


Wireless Sensing Unit Prototype

Completed Wireless Unit

Performance SpecificationCost $100 per unit

Form Factor 10 cm x 6 cm x 2 cm

Energy Source 5 AA Batteries

Power 80 mA @ 5V

Data Rate 38.4 Kbps

Range 100 - 300 m

Sample Rate 100 kHz

Printed Circuit Board with Components Surface Mounted

8-bit Microcontroller128 kB SRAM

4-channel A/D Converter

Sensor Channels

Jerome P. LynchDepartment of Civil and Environmental EngineeringUniversity of Michigan, Ann Arbor MI


Relay-based multiplexing hardware

Drawbacks

Active, Hierarchal Wireless Sensor Paradigm

:1. Nodes nearest the base station still do more work.2. More power needed at a particular node.

Let’s eliminate some of the redundant hardware

sensoractuator

energy harvesting

Proposed scheme by LANL (G. Park) & Motorola

Base StationControlled Sensor/actuator network

Controlled Sensor/actuator network


Control Node

Control Node


•D/A, A/D

•Local computing

•Telemetry

•Rechargeable battery


AccelerometerFBGPZT

strain gage

Interface unitADC, DAC, DSP

6 sensor input4 actuator output

MicrocontrollerSingle Board

ComputerRunning LINUX

MC13192Zigbee

Host Node&

Server(laptop)

Sensor Module Computation Module User InterfaceCommunications

Module

DIAMOND II Software

Healthy?Damaged?

Motorola/LANL SHM System


The Future: Integrating Global and Local Sensing Systems

Examples:– Lamb wave propagation– Impedance method– Time reversal analysis

Examples– Modal testing & analysis– System identification– Operational and Environmental

monitoring

Active Local System – High frequency response– Local damage identification– Active sensing

Passive Global System Response– Low frequency response– Global vibration based monitoring– Passive sensing

1st Torsion

Airplane SpeedR

eson

ance

Fre

quen

cy

1st Bending

Detect local delamination using NDE techniques

Skin delamination can lead to drop in torsion frequency

Flutter speed

The merge of torsion and bending modes leads to FLUTTER!!

(G. Park and H. Sohn)


LANL/Honeywell High Explosives Radio Telemetry System

HERT Mark II with 10 watt power amplifier64 optical inputs10 ns resolutionApproximately 2.2 Kg Field Programmable Gate Array for onboard data processing

Flight hardened!!100 Mbit/s data transmission


Powering Active Sensor Node with RF Energy

Piezoelectric sensor

ADG 408 Multiplexer

(up to 8 sensors)

AD5934 Impedance

Chip

Xbee Radio

ATmega128L

Voltage Multiplication and

Energy Storage

Xbee Base2.4 GHz RF data link

X-band Source

Power delivered to sensor node by X-band radar source

Impedance measurement

chip

Microcontroller/ Telemetry/Energy

Base Station


Networking: RFID with AV Delivery

• Integrate RFid tags and UVs into SHM process for large infrastructure

Force

Conductivemetal block

RFID Reader

Variable Capacitor

Peak Strain SensorRFID Tag

On the structureOn UV

InductiveCoupling

Proposed by Todd and Park (LANL), 2005


Data Storage

• Record analog signals on magnetic tape• Record digital signals on magnetic tape with digital tape

recorder• Store data locally (e.g. flash ROM) with sensor and

download via communication device (hardwired or wireless)

• Store on hard disc of a computer– Store digitized data prior to signal processing– Store processed (and averaged) data after signal

processing


Analog-to-Digital Conversion

• Analog to digital conversion is the process of converting the analog signal from a sensor to a digital signal that accurately represents the measured time-varying physical parameter of interest.

• Issues1. Sampling rate (maximum frequency to be resolved)2. Analog filter (prevent aliasing)3. Sampling duration (frequency resolution, Rayleighcriterion: Δf=1/T)4. Averaging (reduction of zero-mean, non-coherent noise)


Analog to Digital Conversion

5. Quantization (converting analog signal to closest discrete value available in A to D converter hardware)– Word size (10-16 bit commonly available)– Voltage Range (amplitude range that A to D converter

can read)

Errors introduced by 3-bit A to D converter not utilizing the full voltage range

Analog signal

Discrete representation of analog signal


Aliasing

• Aliasing is the inability to accurately resolve higher frequency components of a signal when sampling at a specific rate.

• Aliasing is a result of sampling data at a finite rate.

• Requirement: Fsamp > 2.0 x Fmax (Shannon’s Theorem)

• Aliasing is controlled with both analog and digital filters.

• Most modern data acquisitions systems use a single analog anti-aliasing filter that is based on the maximum sampling rate of the system.

• Digital filters are then used for the smaller frequency bandwidths of interest.

• Must account for roll-off in filters.


Aliasing: Time Domain

Sampling too slowly gives a false indication of the signal waveform.

Actual Sinusoidal Waveform

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

10-3

-1

-0.5

0

0.5

1

Time (sec)

Mag

nitu

de

DigitizedWaveform

h ≥ 1/(2*fmax)

h=20*fmax


Folding and the Nyquist Criterion

f

Mag

nitu

de

fN

frequencyNyquist /2

frequency sample

==

=

sN

s

ff

f

• All frequencies not in the range 0 ≤ f ≤ 1/(2*h) will be undersampledand therefore manifest themselves as lower frequency components (alisaing).

• Frequencies fh > fN will be indistinguishable from their alias:

fh=Δf + fN looks like fl= fN - Δf

• The Nyquist frequency is also called the folding frequency since aliased frequencies have principal aliases as if the f’ > fN were folded back into the range < fN


Leakage

• Leakage refers to errors caused by deviations from the assumption that the signal is periodic within the sample period.

• Leakage errors manifest themselves in the form of “smearing” the frequency components of the “true” Fourier transform to other neighboring frequencies. These errors tends to widen and distort the Fourier transform.

• Leakage is one of the most common sources of bias error in signal processing.

• Leakage can be controlled by experimental and sampling procedures such as averaging, increasing the frequency resolution, and using periodic excitation.


Leakage

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

TIME0 5 10 15 20 25 300

100

200

300

400

500

600

FFT

t=[0:999]/1000;x=sin(2*pi*2*t)xf=fft(x);plot(abs(xf(1:30))

t=[0:999]/1000;x=sin(2*pi*2.2*t)xf=fft(x);plot(abs(xf(1:30))

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

0 5 10 15 20 25 300

100

200

300

400

500

If the period fits the time, the spectrum is correct

If the period does not fit the time, spurious spectral lines result

TIME


More Leakage

0 1000 2000 3000-1

-0.5

0

0.5

1

0 200 400 600 800 1000-1

-0.5

0

0.5

1

Plot(x)

0 200 400 600 800 1000-1

-0.5

0

0.5

1

0 1000 2000 3000-1

-0.5

0

0.5

1

Plot([x,x,x])

FT is assuming

FT is assuming


Windowing

• One of the most common methods used to reduce leakage effects (it can not be eliminated) after the data has been acquired is to window the data.

• Windowing is applied to a signal by multiplying it by an appropriate function. This multiplication forces the data to begin and end at the same time, thus preventing a discontinuity in the data when repeated.

10 20 30 40 50 600

0.5

1Hanning Window

w = hanning(N);⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−−=+

12cos15.0]1[

nkkw π

k=0,1,…n-1


0 2 4 6 8 100

500

1000

1500

0 2 4 6 8 100

500

1000

1500

0 2 4 6 8 100

200

400

600

0 0.5 1 1.5 20

500

1000

Time (sec)

Freq

uenc

y (h

z)Fr

eque

ncy

(hz)

Freq

uenc

y (h

z)

t1 = [1:2000]*h; f1 = [0:1999]/2000/h;sig1 = sin(2*pi*t1); sigf1 = abs(fft(sig1));plot(f1,sigf1);

f2 = [0:3999]/4000/h; sig2 = [sig1 zeros(1,2000)];sigf2 = abs(fft(sig2)); plot(f2,sigf2)

sig3 = sig2.*hanning(4000)';sigf3 = abs(fft(sig3));plot(f2,sigf3);

FFT of a sine signal whose periodicity aligns well with the length of the signal.

Zero-padding the signal produces a discontinuity which causes side lobes.

Applying a Hanningwindow to the data increases the width of the main lobe, but eliminates most of the side lobes.

Windowing Example


Windowing Reduces Leakage

• Hanning window reduces leakage, but broadens effective bandwidth.

• Also increases distortion and reduces signal to noise ratio.

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1Sine wave, 20 hz, no window

Time (sec)

Mag

nitu

de

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1Sine wave, 20 hz, hanning window

Time (sec)

Mag

nitu

de

0 50 100 150 200 250

-60

-40

-20

0

F (h )

log(

Mag

nitu

de)

No Window

Window

Autospectrum


Coherence

)()()(* fXfHfYxhy =⇒=

)()(

)()(

)()()()()()()()(

)()()()(

2

2

fHfH

fHfX

fHfXfXfHfXfXfHfX

fYfXfYfX

===⋅

=γ

• The magnitude squared of the coherence function is then:

• The magnitude-squared coherence is a real function between 0 and 1.

• It provides a measure of the noise present in the system.

• Let’s assume that Y is produced from X via a linear-time invariant process:

1)()(2 ==

fHfHγ


Coherence

• A common use for the coherence function is in the validation of input/output data collected in a vibration experiment for purposes of system identification.

• For example, X(t) might be a known signal which is input to an unknown system and Y(t) is the recorded response. Ideally, the coherence should be 1 at all frequencies. However, this is not always true.


Coherence

• Coherence can be used to measure the degree to which the response Y is a linear function of the Input X.

( )( ) ( )

( ) ( )∑ ∑∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛

=blocks blocks

ii

blocksii

fXfY

fXfYf 22

2

2γ

( )( )

( ) ( )∑ ∑∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛

=blocks blocks

ii

blocks

fXfX

fXf

i

222

22

2

α

αγ

( )( )

( ) ( )∑ ∑∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛

=blocks blocks

ii

blocks

fXfX

fXf

i

222

222

2

α

αγ

( )( ) ( )

( ) ( )∑ ∑∑∑

=blocks blocks

ii

blocksblocks

fXfX

fXfXf

ii

22

22

2γ

( ) 0.12 =fγ (indicates linear relationship)

Let Y(f) =αX(f)


Why is Coherence Sometimes Low?

1. Fundamentally, response is not a linear function of the input. The system is nonlinear.

2. Noise uncorrelated to input contaminates the system response.

3. Leakage between blocks (explained next).

4. Inadequate frequency resolution.

5. Poor signal to noise ratio


Poor SNR and Frequency Resolution

If you remove the noise from the system, the coherence drops only at the resonances, indicating inadequate frequency resolution.

Drops at ends due to noise outside the passband.


References

• Excitation Methods and Signals,Sensors, Data Acquisition– McConnell,K. G., Vibration Testing Theory and Practice, John Wiley, New York,

1995.– Fraden, J., Handbook of Modern Sensors, 2nd Edition, Springer Verlag, New

York, 1996.– Dally, J. W., W. F. Riley and K. G. McConnell, Instrumentation for Engineering

Measurements, John Wiley, New York, 1992.– Doebelin, E. O., Measurement Systems : Application and Design, 4th Edition,

McGraw Hill, New York, 1990.– The Measurement, Instrumentation, and Sensors Handbook, John G. Webster

(Editor), CRC Press, 1998. – Figliola, Richard and Donald Beasley, Theory and Design for Mechanical

Measurements, 3rd Edition, John Wiley, New York, 2000– http://www.sensors-research.com

• Signal Processing– Bendat, J. and A. Piersol, Engineering Application of Correlation and Spectral

Analysis, John Wiley, New York, 1980.– Bendat, J. and A. Piersol, Random Data, John Wiley, New York, 2000.– Wirsching, P. H., T. L. Paez, K. Ortiz, Random Vibrations : Theory and Practice,

John Wiley, New York, 1995.

http://www.sensors-research.com/

Documents

SE 207 Lecture May 23, 2006 Topics 1. Structural Dynamics ...jacobsschool.ucsd.edu/EEI/academic/courses/06/... · Topics 1. Structural Dynamics Measurements. ... response is essential