16.810
Engineering Design and Rapid Prototyping
Lecture 9
Structural Testing
Instructor(s)
Prof. Olivier de Weck
January 18, 2005
Outline
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Structural Testing
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Test Protocol for 16.810 (Discussion)
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16.810
Why testing is important
Types of Sensors, Procedures ….
Mass, Static Displacement, Dynamics
Application of distributed load
Wing trailing edge displacement measurement
First natural frequency testing
2
Data Acquisition and Processing
for Structural Testing
(1) Sensor Overview:
Accelerometers, Laser sensors , Strain Gages ,
Force Transducers and Load Cells, Gyroscopes
(2) Sensor Characteristics & Dynamics:
FRF of sensors, bandwidth, resolution, placement issues
(3) Data Acquistion Process:
Excitation Sources, Non-linearity, Anti-Alias Filtering, Signal
Conditioning
(4) Data Post-Processing:
FFT, DFT, Computing PSD's and amplitude spectra,
statistical values of a signal such as RMS, covariance etc.
(5) Introduction to System Identification
ETFE, DynaMod Measurement Models
16.810
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Why is Structural Testing Important?
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Product Qualification Testing
Performance Assessment
System Identification
Design Verification
Damage Assessment
Aerodynamic Flutter Testing
Operational Monitoring
Material Fatigue Testing
stimulus
u(t)
response
x(t)
Structural
System
DAQ
DAQ = data acquisition
DSP = digital signal processing
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DSP
Example: Ground Vibration Testing
F-22 Raptor #01 during ground
vibration tests at Edwards Air
Force Base, Calif., in April 1999
4
I. Sensor Overview
This Sensor morphology is useful for classification
of typical sensors used in structural dynamics.
Sensor Morphology Table
Type
Linear
Bandwidth Low
Medium
High
Derivative Position
Rate
Acceleration
Reference Absolute
Relative
Quantity
Force/Torque Displacement
Impedance Low
Example: uniaxial strain gage
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Rotational
High
Need units of measurement:
[m], [Nm],[µstrain],[rad] etc…
5
Sensor Examples for Structural Dynamics
Example: fixed-fixed
Goal: Explain what they measure and how they work
beam with center load
laser sensors
excitation
accelerometers
gyroscopes
strain gages
mb
m
load cells
shaker
First flexible mode frequency:
16.810
l
inductive
sensors
ground
EI
ω n = 14 3
l ( m + 0.375mb )
6
Strain Gages
Strain:
∆l
ε=
lo
Strain gages measure strain (differential
displacement) over a finite area via a
change in electrical resistance R=lρ [Ω]
Current Nominal length lo:
lo
With applied strain:
Implementation:
Wheatstone bridge
circuit
bond to test
article
GND
V+
Vin
Io =
lo ρ
Vin
Iε =
(lo + ∆l ) ρ
strain gages feature
polyimide-encapsulated
constantan grids with
copper-coated solder tabs.
Mfg:
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7
Accelerometers
Accelerometers measure linear
acceleration in one, two or three
axes. We distinguish:
!!
x(t ) → s 2 X ( s ) − sx (0) −
dx(0)
dt
(generally neglect initial conditions)
• single vs. multi axis accelerometers
• DC versus non-DC accelerometers
mag
Recorded voltage
Vout (t ) = K a !!
x(t ) + V0
+40dB/dec
rolloff
Accelerometer
response to
base motion
ω
Can measure: linear, centrifugal and gravitational acceleration
Use caution when double-integrating acceleration to get position (drift)
Single-Axis
Accelerometer must be
aligned with sensing axis.
C1
a
C2
Example: Kistler Piezobeam
(not responsive at DC)
Manufacturers: Kistler, Vibrometer, Summit,...
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Example: Summit capacitive
accelerometer (DC capable)
8
Laser Displacement Sensors
sensor
x
target
Records displacement directly
via slant range measurement.
[VDC]
V
out
Typical Settings
+7
I: 2µm-60 ms
II: 15µm-2ms
III: 50µm-0.15ms
x (t ) → X ( s )
0
Resolution tradeoff
spatial vs. temporal
Distance x is recorded via triangulation
between the laser diode (emitter), the
target and the receiver
(position sensitive device - PSD).
-7
Vibrometers include advanced processing
and scanning capabilities.
Manufacturers: Keyence, MTI Instruments,...
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CL
range
x [m]
Advantages:
contact-free measurement
Disadvantages:
need reflective, flat target
limited resolution ~ 1µm
9
Force Transducers / Load Cells
Force Transducers/Load Cells are capable of measuring
Up to 6 DOF of force on three orthogonal axes,
and the moment (torque) about each axis, to
completely define the loading at the sensor's location
The high stiffness also results in a high resonant frequency,
allowing accurate sensor response to rapid force changes.
Load cells are electro-mechanical transducers
that translate force or weight into voltage.
They usually contain strain gages internally.
Fz
Mz
My
Fy
Mx
Fx
Manufacturers: JR3, Transducer Techniques Inc. ...
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10
Other Sensors
!
Fiber Optic strain sensors (Bragg Gratings)
input
I
optical fiber
λ
transmitted
reflection Broad spectrum input light s reflected only at a
specific wavelength determined by the grating
spacing which varies with strain.
• Ring Laser Gyroscopes (Sagnac Effect)
• PVDF or PZT sensors
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II. Sensor Characteristics & Dynamics
Goal: Explain performance characteristics (attributes of real sensors)
saturation limit
S
When choosing a sensor for a
non-linear
particular application we must
specify the following requirements:
Sensor Performance Requirements:
linear
Y
• Dynamic Range and Span
• Accuracy and Resolution
• Absolute or Relative measurement
• Sensor Time Constant
• Bandwidth
• Linearity
• Impedance
• Reliability (MTBF)
Constraints:
Power: 28VDC, 400 Hz AC, 60 Hz AC
Cost, Weight, Volume, EMI, Heat
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S(X)
dynamic
range
X
Calibration is the process of
obtaining the S(X) relationship
for an actual sensor. In the physical
world S depends on things other than X.
Consider modifying input Y (e.g. Temp)
E.g. Load cell calibration data:
X= mass (0.1 , 0.5 1.0 kg…)
S= voltage (111.3 , 563.2, 1043.2 mV)
12
Sensor Frequency Response Function
x(t)
m
k
s 2 X ( s)
cs + k
= 2
Ga ( s ) = 2
s X b ( s ) ms + cs + k
c
Ideal Accelerometer FRF from Base Motion
xb(t)
2
Example: Accelerometer
m = 4.5 g
k = 7.1e+05 N/m
c= 400 Ns/m
Magnitude [dBl
0
-2
-6
-8
-10
-12
-14
-16
-18 0
10
Typically specify bandwidth as follows:
Example: Kistler 8630B Accelerometer
Frequency Response +/-5%: 0.5-2000 Hz
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bandwidth
-4
101
102
103
104
105
Frequency [Hz]
Note: Bandwidth of sensor should
be at least 10 times higher than
highest frequency of signal s(t)
13
Sensor Time Constant
How quickly does the sensor respond to input changes ?
Second-Order Instruments
First-Order Instruments
dy
a1 + ao y = bou
dt
Dividing by ao gives:
a1 dy
bo
+y= u
a dt
a
"0
"o
τ
K
In s-domain:
Y ( s)
K
=
U ( s) τ s + 1
τ : time constant
K: static sensitivity
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2
d y
dy
a2 2 + a1 + ao y = bo u
dt
dt
Essential parameters are:
bo
K#
ao
static
sensitivity
In s-domain:
ao
a2
a1
ζn #
2 ao a2
natural
frequency
damping ratio
ωn #
Y ( s)
K
= 2
U ( s ) s + 2ζ nω n s + ω n2
Time constant here is: τ = 1 ζω n
Time for a 1/e output change
14
Sensor Range & Resolution
saturation
Dynamic range= ratio of largest to
smallest dynamic input a sensor measures
dB=20*log(N)
output
Hysteresis due to
internal sensor
friction
High operating limit
range (=span)
threshold
input
resolution
Low operating limit
Resolution = smallest input increment that gives
rise to a measurable output change. Resolution
and accuracy are NOT the same thing !
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Threshold= smallest
measurable input
15
Accuracy
Measurement theory = essentially error theory
Accuracy=lack of errors
Total error = random errors & systematic errors
(IMPRECISION)
•Temperature fluctuations
•external vibrations
•electronic noise (amplifier)
±3σ uncertainty limits
(BIAS)
• Invasiveness of sensor
• Spatial and temporal averaging
• human bias
• parallax errors
• friction, magnetic forces (hysteresis)
bias
3σ accuracy quoted as:
“4.79 ± 0.54 µε”
µε
4.25 4.32 4.79 4.91 5.33
Reading Best True
Value (unknown)
Estimate
Probable error accuracy:
ep=0.674σ
σ
“4.79 ± 0.12 µε”
Note: Instrument standard used for calibration should be ~ 10 times more
accurate than the sensor itself (National Standards Practice)
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Linearity
“Independent Linearity”:
Usually have largest errors at
full scale deflection of sensor
+/- A percent of reading or
+/- B percent of full scale, whichever
is greater
B% of full scale
A% of reading
Output
Static Sensitivity =
dS
dX
 mV 
 kg 


(slope of calibration curve)
least squares fit
Input
Point at which A% of reading =
B% of full scale input
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Increasing values
decreasing values
Full scale
17
Placement
Issues
Need to consider the dynamics
of the structure to be tested
before choosing where to place
sensors:
I 
 0 
 0
q= 2
q +  T u

Φ βu 
−2 Z Ω 
 −Ω%&%%
$
$%
'
%&%
'
A
B
y =  β y Φ 0  q + [ 0] u
"
$%&%'
D
C
Observability determined
by product of mode shape matrix
Φ and output influence coefficients βy
Example: TPF SCI Architecture
Mode at 100 Hz unobservable
if sensor placed at this “node”
Observability gramian:
Wo → AT Wo + Wo A + C T C = 0
Other considerations:
• Pole-zero pattern if sensor used for control (collocated sensor-actuator pair)
• Placement constraints (volume, wiring, surface properties etc…)
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Invasiability / Impedance
How does the measurement/sensor influence the physics of the system ?
Remember Heisenberg’s uncertainty principle:
x
∆x ∆p ≥ (
sensor
qi1 ⋅ qi 2 = P [W]
Power
2
P
=
q
i1
drain:
F
Impedance characterizes “loading” effect of sensor on the system.
Sensor extracts power/energy -> Consider “impedance” and “admittance”
k
ks
Want to
Generalized
measure F input impedance:
Error due to measurement:
“measured”
qi1
Z gi #
qi 2
qi1m =
Z go
Effort variable
=
Flow variable
1
qi1u
Z gi + 1
Z gi
Force
Velocity
Z gi ∝ k s
“undisturbed”
Load Cell: High Impedance = ks large vs. Strain Gage: Low Impedance= ks small
Conclusion: Impedance of sensors lead to errors that must be modeled in
a high accuracy measurement chain (I.e. include sensor impedance/dynamics)
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III. Data Acquisition Process
Typical setup
X physical variable
Excitation
X
Transducer
Goal: Explain the measurement chain
Excitation source provides power to
the structural system such that a dynamic
response is observable in the first place
Transducer “transforms” the physical
variable X to a measured signal
Amplifier
Amplifier is used to increase the
measurement signal strength
Filter
Filter is used to reject unwanted
noise from the measurement signal
A/D Converter
Analog to Digital converter samples
the continuous measurement signal
in time and in amplitude
S
DSP
Display
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S signal variable
Digital Signal Processing turns raw digital
sensor data into useful dynamics information
20
System Excitation Types
Type B: Broadband Noise
(Electromechanical Shakers)
Type A
0
-2
0
2
Type B
Type A : Impulsive Excitation
(Impulse Hammers)
Overview of Excitation Types
2
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Type C
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
Time [sec]
4
5
0
-2
0
2
Type D
Type D: Environmental
(Slewing, Wind Gusts, Road,
Test track, Waves)
2
0
-2
0
2
Type C: Periodic Signals
(Narrowband Excitation)
1
0
-2
0
21
Excitation Sources
u (t ) = F (t ) = Foδ (t )
Wide band excitation at various energy levels
can be applied to a structure using impulse force
hammers. They generate a nearly perfect impulse.
t
u(t)
y(t)
G(ω)
Impulse Response h(t)
Broadband
y (t ) =
∫ u (τ )h(t − τ )dτ
(convolution integral)
−∞
Y (ω ) = U
(ω ) H (ω )
"
Fo ⋅1
G (ω ) = H (ω )
(no noise)
The noise-free response to an ideal impulse contains
all the information about the LTI system dynamics
Shaker can be driven by periodic or
broadband random current from a signal generator.
S yy (ω ) = G ( jω ) Suu (ω )G ( jω )
H
Input PSD
Record
Syy,Suu
and solve
for G
Output PSD
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22
Excitation Amplitude / Non-Linearity
Plots Courtesy
Mitch Ingham
damping
frequency
Example from MODE Experiment in µ-dynamics (torsion mode):
non-linear
PZT Excitation
Conclusion: Linearity is only
preserved for relatively small amplitude
excitation (geometrical or material
non-linearity, friction, stiction etc…)
Excitation amplitude selection is a tradeoff between introducing non-linearity
(upper bound) and achieving good signal-to-noise ratio (SNR) (lower bound).
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23
Signal Conditioning and Noise
n(t)
u(t)
Test
Article
y(t)
K
Consider Signal to Noise Ratio
(SNR) =
+∞
Power Content in Signal
Power Content in Noise
Y ( s ) = KG ( s )U ( s ) + N ( s )
Look at PSD’s:
Solve for system dynamics
via Cross-correlation uy
G ( jω ) ≅
Suy (ω )
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S yy (ω )
=
S yy (ω )
∫S
−∞
nn
(ω )
dω
Snn
= KG ( jω ) +
S yy (ω )
Suu
2
Decrease noise effect by:
Noise
•Increasing Suu (limit non-linearity) contribution
•Increasing K (also increases Snn)
•Decreasing Snn (best option)
Suu (ω )
Quality estimate via
coherence function
When we amplify the signal,
we introduce measurement
noise n(t), which corrupts the
measurement y(t) by some
amount.
Cyu(ω)
24
A/D Quantization
Time quantization: f
s
x(t)
analog signal
digital signal
Sampling Frequency:
tk = k ⋅ ∆T
x(t)
t
Amplitude quantization: #bits & range
1
∆T
ˆ
x(k)
A/D
Figure courtesy Alissa Clawson
Signal Amplitude [bits]
Example: 8 bits
1 bit for 1 sign
27 = 128 levels
∆T
fs =
original and quantized actuator signals: X
600
400
200
0
-200
-400
0
0.5
1
1.5
2
2.5
2
2.5
noise signal
200
100
0
-100
-200
0
0.5
1
1.5
time [sec]
Nyquist Theorem: In order to recover a signal x(t) exactly it is necessary to
sample the signal at a rate greater than twice the highest frequency present.
Rule of thumb: Sample 10 times faster than highest frequency of interest !
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Anti-AliasingLPFFiltering
VERY IMPORTANT !
x(t)
Filtering should be done on the
ωf ≤
analog signal, e.g. 4-th order Butterworth
ˆ
x(k)
A/D
2π f s
2
No Anti-Aliasing
1.5
Sample signal x(t)
Want f < 50 Hz
1
5
Signal
analog
sampled
0.5
0
-5
0
0
5
10 15 20 25 30 35 40 45 50
Anti-Aliasing filter 2nd-order with 40 Hz corner frequency
1.5
Fs=100Hz
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1
Amplitudes =[1 1.5 1.5 0.75 ];
frequencies =[2 10 30 85 ];
0.5
0
85 Hz signal is “folded” down
0
from the Nyquist frequency (50 Hz) to 15 Hz
5
10
15
20 25 30 35
Frequency [Hz]
Solution: Use a low pass filter (LPF) which avoids signal
corruption by frequency components above the Nyquist frequency
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40
45
50
Small
attenuation
26
IV. Data Post-Processing
Goal: Explain what we do after data is obtained
Stationary processes
(E[x], E[x2],…) are time invariant
Analyze in frequency-domain
Transient processes
Analyze in time-domain
(Ts, Percent overshoot etc.)
Impulse response
Fourier transform of h(t)->H(ω)
The FFT (Fast Fourier Transform) is the workhorse of DSP
(Digital Signal Processing).
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Metrics for steady state processes
Mean Value:
Steady State Process Example
x 10-6
T /2
1
µ x = E[ x] =
x(t )dt
∫
T −T / 2
2.5
2
Signal x [m]
1.5
(central tendency metric)
1
0.5
Discrete:
0
-0.5
∑x
k =1
k
σ x2 = E[( x − µ x ) 2 ] =
-1.5
E[ x 2 ] − µ x2
-2
1
Rarely interested
in higher moments.
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N
Variance:
-1
0
1
µx =
N
2
3
Time [sec]
4
5
6
(dispersion metric)
Root-mean-square (RMS) =
Equal to σx only for zero mean
E[ x 2 ]
28
Metrics for transient processes
-3
Step Response signal example
4.5 x 10
P.O.
Signal x(t) [m]
4
Example: Step Response
(often used to evaluate
performance of a controlled
structural system)
3.5
Peak Time:
3
2.5
πα
ωn
4
Ts =
ζω n
Tp =
Settling Time:
2
Evaluate in
time domain
1.5
1
Ts
0.5
0
Tp
0
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
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P.O. = 100 exp ( −πζα )
Damping α
term:
ζ<1
=
1
1−ζ 2
 1 −ζω nt
−1  1
x(t ) = xo 1 − e
sin(ω nα t + tan 
 αζ
 α
Time t [sec]
If assume one dominant
pair of complex poles:
Percent Overshoot:



29
Metrics for impulse response/decay
from Initial Conditions
Example: Decay process
or impulse response
Oscillatory Exponential Decay
60
x(t=0)=60 (Initial Condition)
Impulse response (time domain)
Signal Strength
50
x(t ) =
40
50e
−t
+∞
∫ u (τ )h(t − τ )dτ
−∞
(convolution operation)
30
Laplace domain:
Y ( s ) = H ( s )U ( s )
20
(multiplication)
10
0
0
0.5
1
1.5
2
2.5
Time [sec]
3
3.5
4
Im
Rate of decay
depended on
poles
Re
x(t ) = 50 exp(−t ) + 10 exp((−1 + 40 j )t )
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30
FFT and DFT
Fourier series:
Discrete Fourier Transform:
N −1
X k = ∑ xr e
Approximates the
continuous Fourier transform:
k
,
T
T
− i 2π f k tr
r =0
fk =
x (t ) = ∑ cn e
iω n t
tr = r
T
N
X (ω ) = ∫ x(t )e −iωt dt
0
k = 0,1,..,N-1
r = 0,1,…,N-1
k and r are integers
Note:
N = # of data points
T= time length of data Xk are complex
The Power Spectral Density (PSD) Function
gives the frequency content of the power in
the signal:
2 ∆T
Wk =
X k ⋅ X kH
N
FFT - faster algorithm if N = power of 2 (512, 1024,2048,4096 …..)
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31
Amplitude Spectra and PSD
Example: processing of Laser displacement sensor data from SSL testbed
-5
x 10 Time Domain Signal
-6
x 10
4
8
6
2
1
6
PSD [m2/Hz]
Amplitude [m]
3
Signal [m]
-10
x 10 Power Spectral Density
Amplitude Spectrum
4
2
4
2
0
5
10
15
Time [sec]
0
20
SUMMARY OF RESULTS
MEAN of time signal: 2.0021e-005
RMS of time signal: 8.6528e-006
RMS of PSD (with fft.m): 8.6526e-006
RMS of AS (with fft.m): 8.6526e-006
RMS of cumulative RMS: 8.6526e-006
Dominant Frequency [Hz]: 40.8234
Dominant Magnitude [m]: 8.5103e-006
-6
x 10
8
8
6
6
4
2
0
2
0
2
10
10
Frequency [Hz]
Cumulative RMS
4
2
0
10
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2
10
10
Frequency [Hz]
-6
x 10 Dominant Frequencies
RMS [m]
0
2
10
10
10
Frequency [Hz]
32
Time domain:
MATLAB coding
Given signal x and time vector t , N samples, dt=const.
dt=t(2)-t(1);
% sampling time interval dt
fmax=(1/(2*dt)); % upper frequency bound [Hz] Nyquist
T=max(t);
% time sample size [sec]
N=length(t);
% length of time vector
(assume zero mean)
x_mean=mean(x);
% mean of signal
x_rms=std(x);
% standard deviation of signal
Amplitude Spectrum:
should match
X_k = abs(fft(x)); % computes periodogram of x
AS_fft = (2/N)*X_k; % compute amplitude spectrum
k=[0:N-1];
% indices for FT frequency points
f_fft=k*(1/(N*dt));
% correct scaling for frequency vector
f_fft=f_fft(1:round(N/2)); % only left half of fft is retained
AS_fft=AS_fft(1:round(N/2)); % only left half of AS is retained
Power Spectral Density:
PSD_fft=(2*dt/N)*X_k.^2; % computes one-sided PSD in Hertz
PSD_fft=PSD_fft(1:length(f_fft)); % set to length of freq vector
rms_psd=sqrt(abs(trapz(f_fft,PSD_fft))); % compute RMS of PSD
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V. System Identification
Goal: Explain example of data usage after processing
Goal:
Create a mathematical model of the system based on input
and output measurements alone.
Input time histories
ui(t) , i=1,2,…n
Transfer functions
Estimator
Output time histories
xj(t) , j=1,2,…m
?
State space system
n(t)
white
noise
input
u(t)
Gyu
Gyu is the actual plant we are trying to
identify in the presence of noise
q! = Aq + Bu
y = Cq + Du
y(t)
output
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Transfer matrix: G(s)
Want to obtain Gyu from:
Y ( jω ) = G ( jω )U ( jω ) + V ( jω )
34
Empirical Transfer Function
Estimate (ETFE)
Yk ( jω )
ˆ
Gkl ( jω ) =
U l ( jω )
Obtain an estimate of
the transfer function
from the I-th input to
the j-th output
Compute:
N ( jω )
ˆ
Gkl ( jω ) = Gkl ( jω ) +
U l ( jω )
Estimated TF
True TF
Noise
What are the consequences of neglecting
the contributions by the noise term ?
S yu = E[Y ( s )U * ( s )]
SUU = E[UU *] , SYY = E[YY *]
Quality Assessment of transfer function estimate via the coherence function:
function
2
C yu
=
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S yu
2
S yy Suu
C yu → 1
Implies small noise (Snn ~ 0)
C yu → 0
Implies large noise
Poor Estimate
Typically we
want Cyu > 0.8
35
Averaging
data subdivided in Nd parts
Y(t)
Gˆ ( s) =
T1
T2
T3
1
Nd
∑
1
Nd
... TNd
Nd
Y ( s)U i (− s )
i =1 i
∑ i=1 U i (s)
Nd
2
ETFE with 10 averages
ETFE with no averaging
30
30
ETFE
True System
20
ETFE 10 avg
True System
20
10
10
0
Magnitude [dB]
Magnitude [dB]
0
-10
-20
-30
-10
-20
-30
-40
-40
-50
-50
-60
12-state system
-60
Error improves with:
-70
Bias E[G − G ] ∝ 1
-70
-80
-2
10
16.810
-1
10
0
10
Frequency [Hz]
1
10
2
10
-80
-2
10
-1
10
0
10
Frequency [Hz]
Nd
1
10
2
10
36
Model Synthesis Methods
Example: Linear Least Squares
Polynomial form:
bn −1s n −1 + ... + bo
B( jω ,θ )
G ( s) = n
=
n −1
s + an −1s + ... + ao A ( jω ,θ )
We want to obtain an estimate of the polynomial coefficient of G(s)
θ T = [ ao
a1 ... an −1 bo
Define a cost function:
1
J=
N
... bn −1 ]
B( jω k ,θ ) 
1 ˆ
∑ k =1 2 G( jω k ) − A( jω ,θ ) 
k


2
N
J is quadratic in θ: can apply a gradient search technique to minimize cost J
Search for:
∂J
= 0 → θ optim
∂θ
Simple method but two major problems
•Sensitive to order n
•Matches poles well but not zeros
Other Methods: ARX, logarithmic NLLS, FORSE
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State Space Measurement Models
Wheel -> ENC
0
-50
2
10
0
-50
-2
10
-20
0
10
2
10
Wheel -> DPL
Gimbal -> DPL
0
10
-40
-60
-80
-2
10
50
0
-50
-100
-2
10
50
Wheel -> Gyro
-100
-2
10
50
Gimbal -> Gyro
Gimbal -> ENC
Measurement models obtained for MIT
ORIGINS testbed (30 state model)
0
10
2
10
0
10
2
10
0
-50
-2
10
0
0
10
2
10
-50
data
fit
-100
-2
10
0
10
2
10
Software used: DynaMod by Midé Technology Corp.
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Summary
Upfront work before actual testing / data acquisition is considerable:
• What am I trying to measure and why ?
• Sensor selection and placement decisions need to be made
• Which bandwidth am I interested in ?
• How do I excite the system (caution for non-linearity) ?
The topic of signal conditioning is crucial and affects results :
• Do I need to amplify the native sensor signal ?
• What are the estimates for noise levels ?
• What is my sampling rate ∆T and sample length T (Nyquist, Leakage) ?
• Need to consider Leakage, Aliasing and Averaging
Data processing techniques are powerful and diverse:
• FFT and DFT most important (try to have 2^N points for speed)
• Noise considerations (how good is my measurement ? -> coherence)
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