Engineering Note
EN-FY1324
Revision 1 –April 8, 2013
Measuring Small Strains with the ODiSI B
Introduction
A simple experiment was performed to demonstrate the capability of measuring very small strains using
Luna’s ODiSI B fiber sensing system. A simple aluminum cantilever beam (21x5x3/16”) was
instrumented with an optical fiber sensor along the length of one side of the beam. A small deflection was
caused by placing a screw near the tip of the beam. Because of the beam’s flexibility, this also caused
small oscillations. The screw was then removed and the oscillations allowed to dampen. Raw data from
the fiber was recorded with the ODiSI B set to acquire at 250 Hz. The data was post processed with 5 mm
sensor spacing and gage lengths of 0.5, 5, and 10 cm to demonstrate the effect of increasing gage length
on strain sensitivity. A running average over time was also performed, resulting in an effective bandwidth
of 25 Hz. Results show that strain changes of 100 nanostrain can be easily detected. With a 10 cm gage
length and 25 Hz bandwidth, the standard deviation of the strain data was 30 nanostrain.
Methods
Luna’s distributed fiber sensing systems measure strain by detecting the change in length of a fiber
sensor as a function of distance. Optical fiber reflects small amounts of light in a random pattern that is
fixed into a fiber when it is manufactured due to the non-crystalline nature of fused silica. This reflected
light is known as Rayleigh scatter. Luna’s sensing systems measure and record the amplitude and phase
of this scattered light as a function of distance down the fiber with microns of spatial resolution. When the
fiber is stretched or compressed, this pattern is also stretched or compressed. These changes are
measured by comparing to the scatter pattern measured in a baseline state. The gage length of a given
measurement is determined by the segment length over which the data is compared. In this example, the
segment length over which the change in length was calculated along the fiber was varied from 0.5 cm
(the default setting) to 10 cm. For small strains, sensitivity is naturally increased by increasing the length
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over which change in length is measured. With Luna’s fiber sensing, this gage length can be adjusted in
post-processing, when the raw recorded data is compared to a baseline and strain is calculated. Strain
can be calculated along a straight length of fiber with large gage lengths even if the strain across the
gage length is non-uniform. This, along with the ability to adjust the gage length in post-processing, is a
unique capability of distributed fiber optic sensing with Rayleigh scatter. Note that the current released
software only allows data to be processed with the default gage length. Please contact your local Luna
representative to discuss processing data with the gage lengths illustrated in this note.
Results and Discussion
Figure 1 shows a plot of strain as a function of location down the beam. This data was from a point in
time near when the screw was placed on the beam. Noise in the data is clearly reduced as the effective
gage length is increased. It should be noted, however, that for the 5 and 10 cm gage length cases, the
data is oversampled, plotted every 5 mm. Due to the relatively short length of the beam, there are only 6
distinct sensor locations along the fiber length shown for a 10 cm gage length.
Figure 1. Strain vs. location along the beam from root to tip for three effective gage lengths, 0.5 (green), 5
(red), and 10 (blue) cm.
A plot of data as a function of time at a point located at 0.37 m, near the root of the beam, is shown in
Figure 2. The beam was oscillating slightly before the screw was placed near the tip just after 6
seconds into the record, which caused a slight load and an increased oscillation. The screw was
removed around 16.5 seconds into the record, causing additional oscillation. Three traces are shown
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for data processed with gage lengths of 0.5 (green), 5 (red), and 10 (blue) cm. The decrease in noise
with increasing gage length is clearly visible.
Figure 2. Strain vs. time at location 0.37, near the root of the beam, for gage lengths of 0.5 (green), 5
(red) and 10 (blue) cm. The reduction in noise with increasing gage length is clearly visible. A screw was
placed near the tip of the beam around 12 seconds into the record and removed around 16.5 seconds.
A zoomed in view of the data in Figure 2 is plotted in Figure 3 with the color coding of gage lengths
maintained. Here the reduction in noise with gage length is even more obvious. The oscillation
frequency shown is about 6 Hz with an initial peak-to-valley amplitude of about 5 microstrain. Figure 4
shows this same data but with a running average over 10 samples in time applied. This time averaging
reduces the effective bandwidth to 25 Hz and also reduces noise in the data.
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Figure 3. Zoomed in view of the data in Figure 2, plotting from 6 to 8 seconds. Three traces are shown
processed with gage lengths of 0.5 (green), 5 (red), and 10 (blue) cm. The oscillation frequency is about 6
Hz with initial peak-to-valley amplitude of about 5 microstrain.
Figure 4. Data shown in Figure 3, with 10 time averages applied to reduce noise.
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To better illustrate the sensitivity of the measurement with increasing gage length, Figure 5 plots the
strain as a function of time at location near the tip of the beam, where the beam experiences less strain.
In this data, only small drifts in strain are observed likely due to temperature changes. Figure 6 shows
this same data, but with 10 time averages applied.
In Figure 7, the low frequency changes were removed from this data in order to calculate the standard
deviation vs. time. Figure 8 shows the same data with 10 time averages applied. The calculated standard
deviations from the data in Figures 7 and 8 are shown in Table 1.
Table 1: Standard deviation of data near tip of beam with low frequency variation removed.
Standard Deviation (microstrain)
Gage Length (cm)
No Time Average (BW 250 Hz)
10 Time Average (BW 25 Hz)
0.5
0.8
0.32
5
0.1
0.05
10
0.06
0.03
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Figure 5. Strain vs. time for location 0.89 mm, near the tip of the beam. Small drifts in measured strain are
likely due to temperature changes. The average value of strain measured with 0.5 (green), 5 (red), and
10 (blue) cm gage lengths varies slightly because the strain vs. length along the beam is not constant.
Figure 6. Data from Figure 5 with 10 time averages applied, reducing the effective bandwidth to 25 Hz.
Note the high sensitivity to small strain changes. A change of about 120 nanostrain is easily visible near
16.5 s when the screw was removed from the beam.
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Figure 7. Strain vs. time at location 0.89 near the tip of the beam with low frequency variations subtracted
out. The three traces show data processed with gage lengths of 0.5 (green), 5 (red), and 10 (blue) cm.
Noise is clearly reduced with increasing gage length.
Figure 8.The data from Figure 7 with 10 time averages applied, reducing the effective bandwidth to 25
Hz. The standard deviation of the 10 cm gage length data vs. time is 30 nanostrain.
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Histograms of the data in Figure 8 are shown in Figure 9. Figure 10 shows a zoomed look at the
histogram of the data processed with a 10 cm gage length and 10 time averages.
Figure 9. Histogram of data from Figure 8 with 10 time averages and gage lengths of 0.5 (green), 5 (red)
and 10 (blue) cm.
Figure 10. Zoomed in view of histogram of data with 10 time averages and a 10 cm gage length
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Conclusion
In this simple experiment, we demonstrated the ability to measure very small changes in strain using
distributed fiber sensing with the Luna ODiSI B system. By increasing the sensor gage length in postprocessing, the sensitivity of the system is greatly increased. With 10 time averages and a 10 cm gage
length, the standard deviation of the data was only 30 nanostrain. These levels of noise enable
discrimination of strains on the order of 100 nanostrain or less. This ability to measure with large gage
lengths even in the presence of a non-uniform strain field is unique to distributed Rayleigh scatter sensing
with Luna’s fiber sensing systems such as the ODiSI B.
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Product Support Contact Information
Headquarters:
3157 State Street
Blacksburg, VA 24060
Main Phone:
1.540.961.5190
Toll-Free Support: 1.866.586.2682
Fax:
1.540.961.5191
Email:
[email protected]
Website:
www.lunainc.com
Specifications of products discussed in this document are subject to change
without notice. For the latest product specifications, visit Luna’s website at
www.lunainc.com.
© 2012 Luna Innovations Incorporated. All rights reserved.
Engineering Note EN-FY1324
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