Transcript Modal parameter estimation of ASAHI KASEI low

Modal parameter estimation
of low-rise building
using sine sweep vibration tests
Le Thai Hoa
Wind Engineering Research Center
Tokyo Polytechnic University
Contents
1. Sine Sweep Force (Measured &
Simulated)
2. Frequency Response Functions (FRF)
3. Smoothing Techniques for FRF
4. Modal Parameter Estimation [DX1 only]
Objectives
o Estimating modal parameters (natural
frequencies and damping ratios) using sine
sweep vibration data
o Identifying Frequency Response Functions
(FRFs) from measured/theoretical input and
measured response
o Sine sweep input force has been measured and
simulated theoretically
Exciter
o Linear sine sweep force
o Constant sweep force
(Constant amplitude)
o Variable frequency range
o Starting frequency
fo= 2Hz
o Ending frequency
fe 6Hz
o Sweep rate
=0.01 Hz/s
Reference (Exciter)
S-ACC
TABLE-ACC: Input
acceleration
 TABLE-DISP: Input
displacement
Exciter
Sensors
2F
PU4-Y
(CH5)
PU4-X
(CH4)
Sampling rate: 100Hz
Y
X
PU5-X
(CH6)
PU1-X
(CH1)
1F
PU6-Y
(CH8)
PU6-X
(CH7)
Y
Exciter
Accelerometer
PU2-X
(CH2)
X
2F
PU3-X
(CH3)
Sine sweep excitation
Measured sweep force
Simulated sweep force
Measurement of sine sweep force
DX1-Small Amplitude
Table - Disp
Table - Disp
0.012
0.3
Table - Disp
Input displacement
0.2
2.573Hz
0.01
0.008
0
PSD
Acce. (m/s2)
0.1
-0.1
3.013Hz
3.428Hz
3.843Hz
4.283Hz
4.697Hz
5.137Hz
T
PSD
5.552Hz
5.943Hz
2.207Hz
0.006
0.004
-0.2
0.002
-0.3
-0.4
0
100
200
300
400
Time (s)
500
600
700
0
0
800
Table - ACC
3.5
2
PSD
Acce. (m/s2)
0
1
-0.15
0.5
300
400
Time (s)
500
600
700
800
16
14
16
PSD
1.5
-0.1
200
14
S - ACC
3
-0.05
8
10
12
Frequency (Hz)
3.697Hz
2.5
100
6
x 10
Table - ACC
Input acceleration
0.05
-0.2
0
4
-3
0.15
0.1
2
0
0
10.02Hz
2
4
6
8
10
12
Frequency (Hz)
Input / Output (PSD)
DX1-Small Amplitude
PU4X - 2F
10
0.08
PU4X
Segment 0-360seconds
0
3.697Hz
2.622Hz 3.452Hz 4.258Hz 5.088Hz
0.06
0.02
10
0
2.207Hz
-2
3.037Hz 3.843Hz 4.673Hz
Input
Output
-0.02
-0.04
-0.06
100
200
300
400
Time (s)
500
600
700
10
800
PSD
-0.08
0
10
0-360s 360-720s
10
10
10
10
10
PSD
Acce. (m/s2)
0.04
10
10
10
Pu4x
Table-dips
-4
-6
-8
-10
0
1
2
3
0
4
5
6
Frequency (Hz)
Segment 360-720seconds
3.672Hz
3.062Hz 3.965Hz 4.844Hz
3.526Hz 4.405Hz
-2
7
8
10
Pu4x
Table-dips
5.772Hz
5.283Hz
9
Input
Response
-4
-6
-8
-10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Spectral
leakage
due to
periodic
excitation
Input / Output (Wavelet)
DX1-Small Amplitude
Input
Table - Disp
0.3
Table - Disp
0.2
Acce. (m/s2)
0.1
0
-0.1
-0.2
-0.3
200
300
500
300÷500s
400
Time (s)
600
700
800
500÷700s
100
100÷300s
-0.4
0
PU4X - 2F
0.08
PU4X
0.06
Acce. (m/s2)
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
0
100
200
300
400
Time (s)
500
Response
600
700
800
Input / Output (Wavelet)
Input
Table - Disp
0.3
Table - Disp
Input displacement
Table - Disp
0.3
0.3
Input displacement
0.2
Input displacement
0.2
0.2
0.1
0.1
0
-0.1
Disp. (m)
Disp. (m)
Disp. (m)
0.1
0
-0.1
-0.2
-0.2
120
140
160
180
Response
200
Time (s)
220
240
260
-0.2
280
320
340
360
380
PU4X - 2F
400
Time (s)
420
440
520
140
160
180
200
Time (s)
220
240
260
280
600
Time (s)
620
640
0
-0.1
660
680
Acceleration
0.05
0
-0.05
-0.05
120
580
PU4X - 2F
Acce. (m/s2)
Acce. (m/s2)
0
560
0.1
0.05
-0.05
540
Acceleration
0.05
Acce. (m/s2)
480
0.1
Acceleration
-0.1
460
PU4X - 2F
0.1
0
-0.1
320
340
360
380
400
Time (s)
420
440
460
480
-0.1
520
540
560
580
600
Time (s)
620
640
660
680
Simulation of sine sweep force
o Sine sweep excitation:
: Amplitude (m)
: Argument (rad)
: Instantaneous
frequency
o Linear sweep:
: Starting frequency (Hz)
: Ending frequency (Hz)
: Sweep rate (Hz/s)
o Linear argument:
o Input sweep:
Amplitude
Sweep
Initial frequency& phase
Simulation of sine sweep force
Initial condition (phase)
o Setting initial parameters
Input: Measured
0.4
Measured displacement
0.3
Disp.(m)
0.2
0.18s
To=0.5s
0.1
0
-0.1
-0.2
X: 0
Y: -0.259
-0.3
-0.4
0
0.1
0.2
0.3
0.4
0.5
Time (s)
Simulated sine sweep input
Theoretical Input
0.4
10
0
0.6
0.7
-0.2
10
-5
10
10
-10
-15
-0.3
-0.4
2.62Hz 3.45Hz 4.28Hz 5.11Hz
2.20Hz 3.03Hz 3.86Hz 4.69Hz 5.50Hz
Magnitude
Disp.(m)
0.2
-0.1
1
Theoretical input
0.3
0
0.9
PSD
Theoretical displacement
0.1
0.8
10
-20
Comparison bt. simulation & measure
Simulated input
Theoretical Input
0.4
10
PSD
0
Theoretical displacement
Theoretical input
0.3
10
-5
2.62Hz 3.45Hz 4.28Hz 5.11Hz
2.20Hz 3.03Hz 3.86Hz 4.69Hz 5.50Hz
0.1
Magnitude
Disp.(m)
0.2
0
-0.1
-0.2
10
10
-10
-15
-0.3
-0.4
0
50
100
150
200
Time (s)
250
300
350
10
400
-20
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Simulated and measured input
Input displacement
0.4
10
Measured
Theoretical
0.3
10
0.1
Magnitude
Disp.(m)
0.2
0
-0.1
-0.2
10
10
-0.3
-0.4
0
PSD
0
Phase difference happens
1
2
3
4
5
6
7
8
9
10
10
Measured input
Theoretical input
Measured output
-5
-10
-15
-20
0
1
2
3
4
5
6
7
8
9
10
Frequency Response Function (FRF)
Measured FRF
Theoretical FRF
Smoothing techniques for FRF
FRF
o FRFs: Relationship between input forces x(t) and
output responses y(t) in the frequency
domain
Second order FRFs:
Type1:
Cross spectrum
Exciter
Type2:
Auto spectrum
Inputs
x(t)
Phase:
Coherence:
Measured FRF
Floor 2
FRF
1
DX1-Small Amplitude
FRF
1
10
10
PU4X/Input
PU5X/Input
3.67Hz
3.67Hz
0
10
0
Magnitude
Magnitude
10
-1
10
-1
10
-2
10
-2
10
-3
10
-4
-3
10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Floor 1
FRF
0
FRF
0
10
10
PU1X/Input
PU2X/Input
-1
10
3.67Hz
-1
10
3.67Hz
10
Magnitude
Magnitude
-2
10
-2
-3
10
-3
10
-4
10
-4
10
-5
10
-5
10
0
-6
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Measured FRF
FRF
1
10
PU4X/Input
DX1-Small Amplitude
3.67Hz
0
FRF
Magnitude
10
-1
10
-2
10
-3
10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Phase
25
PU4X/Input
20
Phase
Degree
15
10
5
0
-5
-10
0
1
2
3
4
5
6
Frequency (Hz)
Coherence
7
8
9
10
1
PU4X/Input
0.8
Coherence
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
10
PU4X and
Measured Input
Theoretical FRF
Floor 2
FRF
4
DX1-Small Amplitude
FRF
4
10
10
PU5X/Measured Input
PU5X/Theoretical Input
PU4X/Measured Input
PU4X/Theoretical Input
2
2
10
3.67Hz
0
Magnitude
Magnitude
10
10
-2
10
0
10
-2
10
-4
-4
10
-6
10
10
10
0
3.67Hz
-6
1
2
3
4
5
6
Frequency (Hz)
7
8
9
0
1
2
3
Floor 1
FRF
2
10
9
10
PU2X/Measured Input
PU2X/Theoretical Input
0
0
10
3.67Hz
-2
10
-4
-2
10
-4
10
10
-6
0
3.67Hz
10
Magnitude
Magnitude
8
10
PU1X/Measured Input
PU1X/Theoretical Input
10
7
FRF
2
10
4
5
6
Frequency (Hz)
-6
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Theoretical FRF
FRF
4
10
DX1-Small Amplitude
PU4X/Measured Input
PU4X/Theoretical Input
2
FRF
Magnitude
10
3.67Hz
0
10
-2
10
-4
10
-6
10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Phase
50
PU4X/Measured Input
PU4X/Theoretical Input
40
30
Degree
Phase
20
10
0
-10
-20
-30
0
1
2
3
4
5
6
Frequency (Hz)
Coherence
7
8
9
10
1
PU4X/Measured Input
PU4X/Theoretical Input
0.8
Coherence
0.6
0.4
0.2
0
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
PU4X and
Measured Input
Smoothing techniques for FRF
o Single Block Technique (SBT): One block
o Block Overlapping Technique (BOT): Many blocks
o Frequency Averaging Technique (FAT): Many blocks
PU4X - 2F
BOT
1 data blocks
Acce. (m/s2)
0.04
0.02
0
-0.02
-0.04
-0.06
0
2N data blocks
FAT
PU4X
Block 2
SBT
Block 1
0.06
50
100
150
nfft nfft samples
No overlapping
200
Time (s)
250
300
350
400
nfft nfft samples
50% overlapping
Block=4096 samples
Total 10 blocks
Frequency resolution
DX1-Small Amplitude
Smoothing FRF
DX1-Medium Amplitude
FRF: PU4X/Input
1
0
0
Effects of smoothing techniques
10
on frequencies and damping
-1
10
-2
10
Smoothing
techniques
-3
10
-4
0
Single block
No overlapping
50% overlapping
10
Magnitude
Magnitude
10
Single block
No overlapping
50% overlapping
10
10
FRF: PU4X/Input
1
10
1
2
3
0
10
-1
10
-1
-2
10
Natural
frequency
10
[Hz]
Damping
ratio
[%]
-3
-4
10
8
9
10
Single 7block
Block overlapping
FRF: PU4X/Input
(No overlapping)
50% block overlapping
Block overlapping
(50%overlapping)
0
1
3.67
3.67
4
5
6
Frequency (Hz)
2
3
4
5
6
0.27
Frequency (Hz)
0.28
7
8
9
10
FRF: PU4X/Input
0
10
3.67
0.57
50% block overlapping
Magnitude
Magnitude
-1
10
(DX1 - Small amplitude)
-2
10
-2
10
-3
10
-4
10
0
-3
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
10
0
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
Natural frequencies &
Damping ratio estimation
Half-power bandwidth method (HPB)
Least-squares complex frequency
domain method (LSCF)
Half power bandwidth (SDOF system)
DX1-Small Amplitude
FRF: Input/Output
1.6
1.4
1.54Hz
Magnitude
1.2
1 1.09Hz
0.8
0.6
0.4
0.2
3.67Hz
0
2
2.5
3
3.5
4
4.5
Frequency (Hz)
5
5.5
6
DX1-Medium amplitude
FRF: Input/Output
1.4
1.32Hz
1.2
Amplitude
Small
Medium
Large
f [Hz]
3.67
3.67
no data
[%]
0.27
0.26
no data
Magnitude
1
0.93Hz
0.8
0.6
0.4
0.2
0
2
3.67Hz
2.5
3
3.5
4
4.5
Frequency (Hz)
5
5.5
6
Lease squares complex frequency
domain (MDOF system)
o Relationship bt. input force and output response
: Complex value FRF matrix
m: Number of measured
points
n: Number of excited
points
f: Frequency variable
o FRF matrix identified by measured inputs/ outputs
o Least squares solution
Min
Further work
• Natural frequencies can be estimated using
identified FRFs. Smoothing should be applied to
reduce noise
• Both theoretical or measured inputs can be used
to identified FRFs
• Damping estimation of the first mode can be
obtained by the half power method, however,
comprehensive approach via LSCF should be
used
• Next work will be based on the LSCF method for
estimating damping ratios
Thank you for your attention