SE 203 Structural Dynamics Structural Identification...

2/10/2003 1

SE 203Structural Dynamics

Professor Ahmed Elgamal

Structural Identification Project

2/10/2003 2



Crossbow AD2012 Datalogger(http://xbow.com)

Provides power for the sensors & performs the analog to digital conversion.

12-bit A/D Converter8 Analog Inputs

Capable of Storing 540,000 SamplesConfigurable Sampling Rate (1 – 500 Hz)

2/10/2003 3



CXL01L1 Capacitive Accelerometers

Crossbow CXL01L1 and CXL02L1 Accelerometers(http://xbow.com)

1.25 g Measurement Range±

0.000610 g Resolution on Channels 1-40.001221 g Resolution on Channels 5-8

CXL02L1 Capacitive Accelerometers2.50 g Measurement Range

DC – 100 Hz Measurement Range0.001221 g Resolution on Channels 1-40.002441 g Resolution on Channels 5-8

DC – 100 Hz Measurement Range

±

Measurement Direction

2/10/2003 4



Field-Testing

Using the Datalogger and accelerometers, you will need to go and record acceleration time histories at various locations on your structure.

You will need to choose these locations carefully (allowing you to capture the 1st couple of modes).

Once you have recorded your data, you will need to bring the datalogger back to the IT lab (SERF 154) and download the data.

We will then save the acceleration time histories onto a CD allowing you to perform the structural identification on your own.

2/10/2003 5



Checking In and Out the Equipment

As there is only one set of testing equipment, we will set up a series of time slots. Each group will sign up for one of these and will be

expected to do their testing during this time. If more time is needed, you may either trade times with another group or try to find and

unused time slot.

Each group will be responsible for checking in the equipment before it is due back. This will allow us to service the equipment and ensure

that everything is working for the next group.

Any data left on the datalogger will be erased once it is returned.

In order to allow sufficient time for analysis, all testing must be completed by February 28. The equipment cannot be checked out

after this date!!!

2/10/2003 6



Monday Tuesday Wednesday Thursday Friday

9:00 am-12:00 pm

12:00 pm -3:00 pm

3:00 pm -6:00 pm

One possibility:make the equipment available in 3 hour blocks

2/10/2003 7



Crossbow AD2012 Datalogger

Crossbow CXL01L1 Accelerometer

SERF Building Rm. 154

Canon A40 PowerShot Digital Camera

2/10/2003 8



Ch 0 Ch 1 Ch 2

L/4 L/4 L/4L/4

Example

2/10/2003 9



Time Domain Data

2/10/2003 10



Structural Identification Tools

The Fast Fourier Transform (FFT) and the Power Spectrum are powerful tools for analyzing and measuring signals.

FFTs and the Power Spectrum are useful for measuring the frequency content of stationary or transient signals. FFTs produce the average frequency content of a signal over the entire time that the signal was

acquired.

∆tN1∆f⋅

=Note: the frequency resolution

where, N is in the number of samples and ∆t is the time increment.

Additional Resource: http://zone.ni.com/devzone/conceptd.nsf/webmain/C045A890751303A6862568650061EA98/$File/AN041.pdf

2/10/2003 11



Power Spectrum

The units of a power spectrum are often referred to as quantity squared rms, where quantity is the unit of the time-domain signal.

The power spectrum shows power as the mean squared amplitude at each frequency line but includes no phase information.

Because the power spectrum loses phase information, you may want to use the FFT to view both the frequency and the phase

information of a signal.

2/10/2003 12



Fourier Transform

The phase information the FFT yields is the phase relative to the start of the time-domain signal. For this reason, you must trigger from the same point in the signal to obtain consistent phase readings. In many cases, your concern is the relative phases between components, or the

phase difference between two signals acquired simultaneously.

The FFT returns a two-sided spectrum in complex form (real and imaginary parts), which you must scale and convert to polar form to

obtain magnitude and phase. The frequency axis is identical to that of the two-sided power spectrum. The amplitude of the FFT is related to

the number of points in the time-domain signal.

2/10/2003 13



Cross Power Spectrum

Cross Power Spectrum ( )2AB N

AFFTFFT(B)(f)S∗×

=

The cross power spectrum is a useful tool for determining the phase difference between two signals.

The two-sided cross power spectrum of two time-domain signals A and B is computed as:

2/10/2003 14



LabVIEW

Excel

Fortran

Matlab

These operations can be done in:

2/10/2003 15



Matlab

Type “help fft”

2/10/2003 16



LabVIEW

2/10/2003 17



ExcelThis operation requires the Analysis ToolPak

2/10/2003 18



Fortran (or similar)

For more information see:

John F. Hall (1982). "AN FFT ALGORITHM FOR STRUCTURAL DYNAMICS", EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, VOL.10, PP.797-811.

.

.

.

.

.

.

2/10/2003 19



Example: Power Spectrum

0.0000080000

0.0000000000

0.0000010000

0.0000020000

0.0000030000

0.0000040000

0.0000050000

0.0000060000

0.0000070000

50.00.0 10.0 20.0 30.0 40.0

Ch 0

Power Spectrum

2/10/2003 20



Averaging

To smooth the spectrum, we need to average the data.

This can be done by:

1. Splitting the time history into a number of equally sized segments.

2. Performing an FFT (or Cross Spectrum) on each of the segments.

3. Averaging each of these segments (Magnitude & Phase). Start by converting to complex form (Real and Imaginary). Then sum the two real components at each increment of frequency and then divide by the number of averages. Do the same for the imaginary. When you are done, convert back to magnitude and phase.

2/10/2003 21



For our beam example:

1. Split the time history into 10 segments each 12 seconds long.1.0000000000

-1.2000000000

-1.0000000000

-0.8000000000

-0.6000000000

-0.4000000000

-0.2000000000

0.0000000000

0.2000000000

0.4000000000

0.6000000000

0.8000000000

12.00.0 2.0 4.0 6.0 8.0 10.0

Acc

Acceleration Segment 1

1.0000000000

-1.2000000000

-1.0000000000

-0.8000000000

-0.6000000000

-0.4000000000

-0.2000000000

0.0000000000

0.2000000000

0.4000000000

0.6000000000

0.8000000000

24.012.0 14.0 16.0 18.0 20.0 22.0

Acc


1.0000000000

-1.0000000000

-0.8000000000

-0.6000000000

-0.4000000000

-0.2000000000

0.0000000000

0.2000000000

0.4000000000

0.6000000000

0.8000000000

36.024.0 26.0 28.0 30.0 32.0 34.0

Acc


0.0035000000

-0.0030000000

-0.0025000000

-0.0020000000

-0.0015000000

-0.0010000000

-0.0005000000

0.0000000000

0.0005000000

0.0010000000

0.0015000000

0.0020000000

0.0025000000

0.0030000000

48.036.0 38.0 40.0 42.0 44.0 46.0

Acc


0.0025000000

-0.0025000000

-0.0020000000

-0.0015000000

-0.0010000000

-0.0005000000

0.0000000000

0.0005000000

0.0010000000

0.0015000000

0.0020000000

60.048.0 50.0 52.0 54.0 56.0 58.0

Acc


0.0025000000

-0.0025000000

-0.0020000000

-0.0015000000

-0.0010000000

-0.0005000000

0.0000000000

0.0005000000

0.0010000000

0.0015000000

0.0020000000

72.060.0 62.0 64.0 66.0 68.0 70.0

Acc


0.0030000000

-0.0025000000

-0.0020000000

-0.0015000000

-0.0010000000

-0.0005000000

0.0000000000

0.0005000000

0.0010000000

0.0015000000

0.0020000000

0.0025000000

84.072.0 74.0 76.0 78.0 80.0 82.0

Acc


0.0025000000

-0.0020000000

-0.0015000000

-0.0010000000

-0.0005000000

0.0000000000

0.0005000000

0.0010000000

0.0015000000

0.0020000000

96.084.0 86.0 88.0 90.0 92.0 94.0

Acc


0.0025000000

-0.0025000000

-0.0020000000

-0.0015000000

-0.0010000000

-0.0005000000

0.0000000000

0.0005000000

0.0010000000

0.0015000000

0.0020000000

108.096.0 98.0 100.0 102.0 104.0 106.0

Acc


0.0025000000

-0.0030000000

-0.0025000000

-0.0020000000

-0.0015000000

-0.0010000000

-0.0005000000

0.0000000000

0.0005000000

0.0010000000

0.0015000000

0.0020000000

120.0108.0 110.0 112.0 114.0 116.0 118.0

Acc


2/10/2003 22



For our beam example:

2. Perform the Power Spectrum on each of the segments.0.0000800000

0.0000000000

0.0000100000

0.0000200000

0.0000300000

0.0000400000

0.0000500000

0.0000600000

0.0000700000

50.0500.0m 10.0 20.0 30.0 40.0

Acc

Power Spectrum Segment 1

0.0005500000

0.0000000000

0.0000500000

0.0001000000

0.0001500000

0.0002000000

0.0002500000

0.0003000000

0.0003500000

0.0004000000

0.0004500000

0.0005000000

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000180000

0.0000000000

0.0000020000

0.0000040000

0.0000060000

0.0000080000

0.0000100000

0.0000120000

0.0000140000

0.0000160000

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000000080

0.0000000000

0.0000000010

0.0000000020

0.0000000030

0.0000000040

0.0000000050

0.0000000060

0.0000000070

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000000060

0.0000000000

0.0000000005

0.0000000010

0.0000000015

0.0000000020

0.0000000025

0.0000000030

0.0000000035

0.0000000040

0.0000000045

0.0000000050

0.0000000055

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000000090

0.0000000000

0.0000000010

0.0000000020

0.0000000030

0.0000000040

0.0000000050

0.0000000060

0.0000000070

0.0000000080

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000000180

0.0000000000

0.0000000020

0.0000000040

0.0000000060

0.0000000080

0.0000000100

0.0000000120

0.0000000140

0.0000000160

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000000120

0.0000000000

0.0000000010

0.0000000020

0.0000000030

0.0000000040

0.0000000050

0.0000000060

0.0000000070

0.0000000080

0.0000000090

0.0000000100

0.0000000110

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000000045

0.0000000000

0.0000000005

0.0000000010

0.0000000015

0.0000000020

0.0000000025

0.0000000030

0.0000000035

0.0000000040

50.0500.0m 10.0 20.0 30.0 40.0

Acc


0.0000000140

0.0000000000

0.0000000020

0.0000000040

0.0000000060

0.0000000080

0.0000000100

0.0000000120

50.0500.0m 10.0 20.0 30.0 40.0

Acc


2/10/2003 23



For our beam example:3. Average each of the segments

0.0000080000

0.0000000000

0.0000010000

0.0000020000

0.0000030000

0.0000040000

0.0000050000

0.0000060000

0.0000070000

50.00.0 10.0 20.0 30.0 40.0

Ch 0

Averaged Power Spectrum (1 Average)

0.0000180000

0.0000000000

0.0000020000

0.0000040000

0.0000060000

0.0000080000

0.0000100000

0.0000120000

0.0000140000

0.0000160000

50.00.0 10.0 20.0 30.0 40.0

Ch 0

Averaged Power Spectrum (2 Averages)

0.0000350000

0.0000000000

0.0000050000

0.0000100000

0.0000150000

0.0000200000

0.0000250000

0.0000300000

50.00.0 10.0 20.0 30.0 40.0

Ch 0


0.0000500000

0.0000000000

0.0000050000

0.0000100000

0.0000150000

0.0000200000

0.0000250000

0.0000300000

0.0000350000

0.0000400000

0.0000450000

50.00.0 10.0 20.0 30.0 40.0

Ch 0


0.0000700000

0.0000000000

0.0000100000

0.0000200000

0.0000300000

0.0000400000

0.0000500000

0.0000600000

50.00.0 10.0 20.0 30.0 40.0

Ch 0

Averaged Power Spectrum (5 Averages)0.0000900000

0.0000000000

0.0000100000

0.0000200000

0.0000300000

0.0000400000

0.0000500000

0.0000600000

0.0000700000

0.0000800000

50.00.0 10.0 20.0 30.0 40.0

Ch 0


0.0000650000

0.0000000000

0.0000050000

0.0000100000

0.0000150000

0.0000200000

0.0000250000

0.0000300000

0.0000350000

0.0000400000

0.0000450000

0.0000500000

0.0000550000

0.0000600000

50.00.0 10.0 20.0 30.0 40.0

Ch 0


0.0000800000

0.0000000000

0.0000100000

0.0000200000

0.0000300000

0.0000400000

0.0000500000

0.0000600000

0.0000700000

50.00.0 10.0 20.0 30.0 40.0

Ch 0


0.0000350000

0.0000000000

0.0000050000

0.0000100000

0.0000150000

0.0000200000

0.0000250000

0.0000300000

50.00.0 10.0 20.0 30.0 40.0

Ch 0


0.0000350000

0.0000000000

0.0000050000

0.0000100000

0.0000150000

0.0000200000

0.0000250000

0.0000300000

50.00.0 10.0 20.0 30.0 40.0

Ch 0


Do the Same for the Phase Angle

2/10/2003 24



Cross Spectrum Channels 0 & 20.0000300000

0.0000000000

0.0000025000

0.0000050000

0.0000075000

0.0000100000

0.0000125000

0.0000150000

0.0000175000

0.0000200000

0.0000225000

0.0000250000

0.0000275000

50.0500.0m 10.0 20.0 30.0 40.0

Magnitude

Magnitude

4.0000000000

-4.0000000000

-3.0000000000

-2.0000000000

-1.0000000000

0.0000000000

1.0000000000

2.0000000000

3.0000000000

50.0500.0m 10.0 20.0 30.0 40.0

Phase Angle

Phase Angle

2/10/2003 25



Cross Spectrum Channels 0 & 10.0000300000

0.0000000000

0.0000025000

0.0000050000

0.0000075000

0.0000100000

0.0000125000

0.0000150000

0.0000175000

0.0000200000

0.0000225000

0.0000250000

0.0000275000

50.0500.0m 10.0 20.0 30.0 40.0

Magnitude

Magnitude

4.0000000000

-4.0000000000

-3.0000000000

-2.0000000000

-1.0000000000

0.0000000000

1.0000000000

2.0000000000

3.0000000000

50.0500.0m 10.0 20.0 30.0 40.0

Phase Angle

Phase Angle

2/10/2003 26



Construct the Mode Shapes

1. From the Magnitude, determine the relative amplitude.

2. From the Phase Angle, determine the sign.

For our example, let’s start with the 1st mode

2/10/2003 27


Professor Ahmed ElgamalCh 0 Ch 1 Ch 2

0.0026000000

0.0000000000

0.0002000000

0.0004000000

0.0006000000

0.0008000000

0.0010000000

0.0012000000

0.0014000000

0.0016000000

0.0018000000

0.0020000000

0.0022000000

0.0024000000

50.00.0 10.0 20.0 30.0 40.0

Magnitude

Magnitude

At 11 Hz, the amplitude at Ch 0 is 0.00245. We will let this location be our reference location.

2/10/2003 28



At 11 Hz, the amplitude at Ch 1 is 0.00382.

2/10/2003 29



At 11 Hz, the Phase Angle is 0; therefore, locations 0 & 1 are in phase (we will define this as positive).

2/10/2003 30




2/10/2003 31



At 11 Hz, the Phase Angle is 0; therefore, locations 0 & 2 are in phase (positive sign).

2/10/2003 32



0.002450.00382

0.00195

First Mode Shape

2/10/2003 33



Repeat for the 2nd Mode

0.0026000000

0.0000000000

0.0002000000

0.0004000000

0.0006000000

0.0008000000

0.0010000000

0.0012000000

0.0014000000

0.0016000000

0.0018000000

0.0020000000

0.0022000000

0.0024000000

50.00.0 10.0 20.0 30.0 40.0

Magnitude

Magnitude

At 28 Hz, the amplitude at Ch 0 is 0.0022. We will let this location be our reference location.

2/10/2003 34




2/10/2003 35



At 28 Hz, the Phase Angle is π; therefore, locations 0 & 1 are out of phase (we will define this as negative).

2/10/2003 36




2/10/2003 37



At 28 Hz, the Phase Angle is π; therefore, locations 0 & 2 are out of phase (negative sign).

2/10/2003 38



0.0022 0.0013

0.00195

Second Mode Shape

2/10/2003 39



Hints

1. In order to determine the mode shape, you will need to establish a reference location on your structure.

Depending on the geometry of the structure, you may not be able to keep the same reference point. In this case, you will need to use a moving reference. For example on the bridge below, you would probably need to take a data sets with a repeated sensor location. One possibility is to record at 1&2, then 2&3, and finally 3&4.

1 2 3 4

2/10/2003 40



Hints (continued)

The Crossbow CXL01L1 and CXL02L1 are capacitive accelerometers. Therefore, they will record a DC signal when used for measuring vertical acceleration. In a vertical configuration, the CXL01L1 has only a 0.25 g measurement range.

Measurement Direction

When measuring vertical acceleration on a horizontal surface, you may need to use one

of the anchor plates.

2/10/2003 41



Hints (continued)

Before you get very far into your testing, you may want to check to ensure that you are measuring a meaningful signal. This can be done by making a simple preliminary test at one or two locationsand checking the Power Spectra of the data.

0.0000000007

0.0000000000

0.0000000001

0.0000000002

0.0000000003

0.0000000004

0.0000000005

0.0000000006

50.0500.0m 10.0 20.0 30.0 40.0

Magnitude

Avg'd Power Spectrum

2/10/2003 42



Hints (continued)

1 2 3 4

When choosing the location for your sensors, make sure you choose locations that will allow you to capture the first few modes.

While the configuration shown below may work well for the 1st

Mode, it may not work for higher modes.

2 3 4

2/10/2003 43



Running theCrossbow DataReady Software

2/10/2003 44



Crossbow DataReady Startup Window

2/10/2003 45



Datalogger Status

2/10/2003 46



Current Datalogger Configuration

2/10/2003 47



Configuring the Datalogger

Select Active ChannelsConfigure each of the channels

Set Sampling Frequency

Set Total Run Time

2/10/2003 48



Step 1 – Activate Channel 1

2/10/2003 49



Step 2 – Enter Channel 1 Details

2/10/2003 50



Step 3 - Select the Appropriate Sensor Type & Serial Number from the Drop Down Window

2/10/2003 51



If you select a serial number from the drop downwindow, you do not need to worry about the “scaling” tab.

2/10/2003 52



Step 4 – Select Additional Channels (Repeat Steps 1-3 For Each Additional Channel)

2/10/2003 53



Step 5 – Set Desired “Sample Frequency” In the Drop Down Window

2/10/2003 54



Step 6 – Enter “Total Run Time”

The “Total Run Time” is limited by the

maximum number of

samples that the data logger

can store.

2/10/2003 55



Configuration Details

# Active Channels

Max # of configured sequences that can be run before the memory on the datalogger is filled.

% of dataloggermemory used by each sequence.

2/10/2003 56


Professor Ahmed ElgamalClick “Send Configuration” to Datalogger and Then Click “OK”.

Note: this will erase any data stored on the logger.

2/10/2003 57



When the upload is complete it will display“The datalogger was configured successfully”

2/10/2003 58



Connecting the Accelerometers to the Datalogger

2/10/2003 59



Plug the accelerometer into the desired port on the junction box.

Ports on the junction box are numbered

2/10/2003 60



Plug the 25 pin cable into the junction box.

2/10/2003 61


Professor Ahmed ElgamalPlug the 25 pin cable into the datalogger.Note: Once the datalogger is connected to the junction box, the datalogger will start supplying

power for the sensors. Please conserve the battery by not connecting to the datalogger until you are ready to start taking measurements.

2/10/2003 62



To start collecting data, press the green “Start/Stop” button.

Indicator Light

Start/Stop Button

Once, the “Start/Stop” button is pushed once, the indicator light will turn green. When the measurement is complete this light will turn off.

2/10/2003 63



Uploading Recorded Data

1. Connect the datalogger to a PC using the RS-232 cable

2. Run the Crossbow DataReady Software

2/10/2003 64



Click on the “Receive Data” Button

2/10/2003 65



Recorded Data

2/10/2003 66



To plot the data, press the “Graph (Quick)” button

2/10/2003 67



To save your data, press the “Save” button.

Location(Choose save as

.txt type)

Export File Option

Date post:	28-Feb-2019
Category:	Documents
Upload:	hanhi
View:	257 times
Download:	0 times

SE 203 Structural Dynamics Structural Identification...

Documents