Amplitude Vibration Measurement by Harmonic Frequency Analysis

of a Distributed Acoustic Sensor

Javier Preciado

1,3

, David Sanahuja

, Carlos Heras

, Jesús Subías

, Lucía Hidalgo

, Iñigo Salinas

Pascual Sevillano

, Juan José Martínez

and Asier Villafranca

Departamento de Ingeniería Electrónica y Comunicaciones, EINA, Universidad de Zaragoza, C/María de Luna 1, 50018

Zaragoza, Spain

Departamento de Física Aplicada, Ciencias, Universidad de Zaragoza, C/María de Luna 1, 50018 Zaragoza, Spain

Aragón Photonics Labs (APL), Prado 5, 50009 Zaragoza, Spain

{p.sevillano, jj.martinez, a.villafranca}@aragonphotonics.com

Keywords: Distributed Acoustic Sensor, Distributed Fiber Sensing, Accelerometer Sensor, Calibration.

Abstract: Distributed acoustic sensors (DAS) based in coherent optical time-domain reflectometry (C-OTDR) provide

a cost-effective solution for intrusion monitoring of large civil infrastructures like pipelines, railways or

motorways. Although detection of events is well demonstrated, an estimation of the amplitude of these events

is difficult to achieve. We propose a new method to recover the amplitude of the vibration from the

conventional C-OTDR backscattered power traces. It is based on the FFT analysis of the DAS signals. Using

a discrete accelerometer as a reference, we have calibrated the response of an optical fiber DAS using known

stimuli. A correlation between the amplitude of the vibration and the ratios of the amplitudes of harmonics to

the fundamental of the DAS signals is demonstrated. This analysis overcomes the main issues of the amplitude

measurement, related to the interaction between the stimulus and the interference pattern.

1 INTRODUCTION

Distributed acoustic sensing (DAS) optical fiber

systems based on coherent optical time-domain

reflectometry (C-OTDR) are currently used for the

detection of events (vibrations) along large

infrastructures for intrusion monitoring and

surveillance purposes (J. Park, 2003), (R. Sifta,

2015), (Y. Lu, 2010).

These systems use the optical fiber as a distributed

sensor, detecting variations in the interference of the

backscattered signal. These variations are generated

by shifts in the phase of the propagating pulse due to

external disturbances.

One of the issues with this technique is the

saturation of the phenomenon due to the nature of the

interference. As the magnitude of the event increases,

so do the phase shift and the amplitude of the

interference. However, when the phase shift reaches

a given point the periodic nature of the interference

phenomenon shows, and the amplitude of the

detected signal does not show a linear variation with

the applied disturbances. The direct C-OTDR

backscattered power analysis results in a non-linear

response of the traces with the input stimulus.

Therefore, true vibrations amplitudes cannot be

directly measured (H. F. Martins, 2014).

To overcome this restriction, C-OTDR

backscattered phase analysis can be used (G. Tu,

2015), (Z. Pan, 2011). By measuring the phase of the

C-OTDR signal and using unwrapping phase

methods to recover phase shifts over 2π, the dynamic

measurement of strains has been demonstrated. Other

authors use chirped pulses to measure strain and

temperature values along an optical fiber (J. Pastor-

Graells, 2016). In those cases however, systems are

more complex and long term-stability is not

sometimes clearly addressed.

This work proposes a new method to recover the

amplitude of the vibrations from the C-OTDR

backscattered power traces. It is based on the FFT

analysis of consecutive traces and on the relation

existing between the ratios of the amplitudes of the

different harmonics and the amplitude of the

vibration. The experimental setup used to validate the

method is presented. It includes a C-OTDR with

random polarization rotation between consecutive

Preciado, J., Sanahuja, D., Heras, C., Subías, J., Hidalgo, L., Salinas, I., Sevillano, P., Martínez, J. and Villafranca, A.

Amplitude Vibration Measurement by Harmonic Frequency Analysis of a Distributed Acoustic Sensor.

DOI: 10.5220/0007373700460051

In Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2019), pages 46-51

ISBN: 978-989-758-364-3

trains of optical pulses to achieve a statistical study of

the interference. The stimulus was a vibration

generator with 50 meters of fiber length strapped

around it. Different frequencies and amplitudes were

tested and discrete accelerometers included for

reference and calibration purpose. The results open

the way to overcome the non-linear response of a

conventional C-OTDR and to provide amplitude

vibration analysis in DAS systems.

2 DAS GENERAL CONCEPTS

Figure 1 shows the basic scheme of a DAS system

based on direct C-OTDR backscattered power

analysis. A pulsed high-coherence laser is amplified

and injected into the sensing fiber. The optical power

backscattered by the fiber produces a pattern of

interferences due to the coherent sum of the M

wavefronts generated by Rayleigh diffusion along the

pulse width at each point k of the fiber. This pattern

is a function of the phase Ω

and amplitude a

of the

different wavefronts, according to expression (1),

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(1)

This backscattered signal is amplified and filtered

to improve the signal-to-noise ratio prior to the

optical detection. The electrical signal coming from

the detector is then sampled and processed.

Figure 1: DAS scheme (direct).

If the phase of the backscattering produced by the

light pulse does not change, the interference of the

backscattered signals remains constant. However,

any mechanical disturbance affects, via the stress-

optic fiber coefficient, the phase of this signal and the

resulting interference. Thus, the optical fiber becomes

a distributed sensor that detects and locates pressure

changes nearby.

As an example of the measured DAS signals,

Figure 2 represents 21 consecutive acquired traces

Figure 2: DAS signal.

with a constant stimulus at 5470 and 6070 meters. It

is clearly seen that those points show much larger

variability compared with the rest of the trace.

3 NON-LINEAR RESPONSE OF

C-OTDR TRACES

The intensity resulting from the interference of

several wavefronts depends on the phase

relationships between them. These variations will

always be within the range allowed by the destructive

(minimum) and constructive (maximum) interference

conditions.

In the case of a C-OTDR, when an external

disturbance changes the relative phases of some of the

components of the backscattered pulse, the intensity

of the detected signal also varies. As the amplitude of

the disturbance is greater, the induced phase variation

is also greater. Since there is a maximum of the

interference amplitude, there is a saturation

phenomenon in the intensity variation of the C-OTDR

trace. Once this saturation point has been reached, the

amplitude increases of the external disturbance are

not reflected as increases in the intensity variation

detected in the DAS.

Figure 3 shows a simplified model of this

phenomenon, with only two wavefronts interfering

and a sinusoidal mechanical stimulus of frequency f

For small induced phase changes, variations of the

traces are linear with the magnitude of the stimulus

(same frequency and proportional amplitude).

However, when there is a large phase shift, the

Figure 3: Interference pattern.

Amplitude Vibration Measurement by Harmonic Frequency Analysis of a Distributed Acoustic Sensor

amplitude of the DAS signal cannot exceed its

maximum value, A', non-linear response is given and

harmonics of the fundamental frequency appear. The

ratio of the amplitudes of these harmonics and the

fundamental is related to the amplitude of the

stimulus (M. Abramovitz, 1972).

Obviously in the case of a C-OTDR pulse, there is

a large number of interfering wavefronts and it is not

possible to obtain a simple analytical relation.

Therefore, it is necessary to perform a large set of

measurements under different intra-pulse interference

conditions to determine experimentally these

relations for DAS systems.

4 EXPERIMENTAL SET-UP

The experimental setup to determine the relationship

between the stimulus amplitude and the amplitudes of

the DAS signals (fundamental and harmonics) is

shown in Figure 4.

Figure 4: Basic scheme of the experimental setup.

The DAS system is based on a C-OTDR as

described in Figure 1. The laser pulses are 600 ns long

and are injected into the optical fiber in trains of 5000

pulses with a repetition rate of 1 kHz. In order to

perform a statistical analysis for every possible

interference condition, the polarization state is

changed randomly from a pulse train to the next.

Thus, each different pulse polarization accounts for a

different intra-pulse interference condition at each

point of the fiber. A controlled vibration system is

placed between two single mode fiber reels of 5 km

(OF1) and 40 km (OF2). It consists of a 50-meter-

long fiber reel fixed to the rod of the vibration

generator. A function generator controls the

amplitude and frequency of the vibration. A

commercial three-axis accelerometer (Analog

Devices 16227) is attached on top of the fiber reel.

This accelerometer provides the reference

measurement of the real amplitude of the mechanical

vibrations that are supported by the fiber. It allows the

amplitude response calibration of the DAS system.

Finally, a computer and a LabJack U3-HV data

acquisition card (DAQ) provide control of the

polarization rotator, the vibrator, the accelerometer

and the DAS system.

5 EXPERIMENTAL RESULTS

The signals from the DAS system and the

accelerometer are captured simultaneously. To

establish the relationship between the amplitude of

the vibration and the DAS signals at a given

frequency, an amplitude sweep of the vibrator is

performed. At each point of the sweep there are 50

iterations using random polarizations, and 5000 DAS

traces are captured for an FFT analysis. As an

example, we present tests carried out for an excitation

frequency of 100 Hz. More frequencies have been

proved in the following range, [50, 110] Hz at several

distances as 5 and 10 km, although the results

presented were at 5 km and 100 Hz.

The acceleration measured by the accelerometer

versus the amplitude of the function generator is used

as calibration of the real mechanical vibrations

supported by the fiber. In addition, it assures that no

harmonics of the applied fundamental frequency are

mechanically generated in the vibration setup. Figure

5 shows an example of the signal captured by the

accelerometer for the maximum tension applied by

the function generator in the test, 2 V, and the

corresponding FFT. It shows the 100 Hz fundamental

frequency without evidence of any harmonic. Figure

6 shows the mechanical amplitude displacement

measured in function of the applied tension. The

acceleration has been converted to displacement for a

better understanding of the magnitude of the test

vibrations. The response of the system is clearly

linear, and the curve is used for a direct calibration of

the DAS signal.

Figure 5: Accelerometer signals: time (top) and FFT

(botton).

PHOTOPTICS 2019 - 7th International Conference on Photonics, Optics and Laser Technology

Figure 6: Mechanical amplitude calibration curve of the

vibration setup.

Figure 7 shows a 2D representation of the signal

captured by the DAS system during 5 seconds, with a

constant stimulus of 100 Hz located at 5.6 km. The

trace remains stable within the 5 seconds, except for

the vibration area. When the acquisition is complete,

we search for the stimulus in the frequency domain,

at the excitation frequency and its harmonics (up to

). The location in frequency and distance of each

of the harmonics is shown in Figure 8. The search

area is shaded in frequency and a marker (circle) is

placed in the position of the maximum.

Figure 7: Representation of 5 seconds DAS signal around

the 50 m fiber reel.

Figure 8: Location of the fundamental frequency and its

harmonics in the DAS signal at 5,6 km.

The amplitude of the DAS signal at 100 Hz versus

the displacement amplitude of the vibration at the

same frequency is shown in Figure 9. The central

mark indicates the median, and the bottom and top

edges of the box indicate the 25th and 75th

percentiles, respectively, with 50 data points for each

amplitude. For small displacements, the dependence

is approximately linear but, contrary to the results of

the accelerometer in Figure 6, it soon reaches a

saturation level due to the non-linear response of the

DAS signal, as predicted in section 3.

The signal missing from the 100 Hz tone is

distributed between its harmonics, as shown in

Figures 9-12. These harmonics are not generated by

the vibrating structure but by the saturation effect of

the DAS, as evidenced by the frequency response of

the accelerometer in Figure 5.

Figure 9: DAS signal at the fundamental frequency f

=100

Hz.

Figure 10: DAS signal at the first harmonic of the excitation

frequency (f

=200 Hz).

These graphs represent the non-linear dependence

of the DAS signal with the displacement amplitude of

the vibrations, and can be used to estimate the real

magnitude of unknown excitations despite the

saturation effect. Figure 13 shows the calibration

curves obtained from these measurements. It shows,

in function of the vibration amplitude, the normalized

variation of the fundamental to its maximum and the

ratio of harmonics to the fundamental. From this

Amplitude Vibration Measurement by Harmonic Frequency Analysis of a Distributed Acoustic Sensor

Figure 11: DAS signal at the second harmonic of the

excitation frequency (f

=300 Hz).

Figure 12: DAS signal at the third harmonic of the

excitation frequency (f

=400 Hz).

Figure 13, given a stimulus of unknown amplitude,

after FFT analysis of the C-OTDR traces, the

harmonic to fundamental amplitude ratios will allow

the estimation of the magnitude of the excitation.

The distribution of the measured values for a

given vibration condition accounts for the statistical

behavior of the interference phenomenon. Thus, it is

clear that the accuracy of the method is strongly

related to the use of random polarization states for the

launched pulses, in order to ensure a large enough

sample.

Figure 13: Calibration curves of the non-linear behavior of

DAS signals.

6 CONCLUSIONS

A new method to recover the magnitude of the

stimulus from DAS signals has been described. It is

based on the FFT analysis of C-OTDR traces using

random polarization states in consecutive trains of

pulses and on the relation existing between the

magnitude of the vibration and the ratios of the

amplitudes of the harmonics to the amplitude of the

fundamental tone.

The experimental setup used to validate the

method has also been presented. It uses discrete

accelerometers for reference and calibration. The

results demonstrate the viability of the method, which

overcomes some of the issues in the magnitude

measurement. It opens the way to work through the

non-linear response of conventional C-OTDR to

provide not only detection of events in DAS systems,

but also vibration amplitude analysis.

ACKNOWLEDGEMENTS

This work was supported in part by the Spanish

“Agencia de Investigación Estatal" through

“Doctorados Industriales” grant DI-17-09169 and

“Retos-Colaboración” grant RTC-2016-5212-8.

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PHOTOPTICS 2019 - 7th International Conference on Photonics, Optics and Laser Technology

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Amplitude Vibration Measurement by Harmonic Frequency Analysis of a Distributed Acoustic Sensor