jerc jose (pre-print)

428 JOURNAL OF STRUCTURAL ENGINEERING Vol. 38, No.5, DECEMBER 2011-JANUARY 2012

Journal of Structural EngineeringVol. 38, No. 5, December 2011-January 2012 pp. 428-439 No.38-37

Sensor development life cycle of embedded fi ber bragg grating sensor forstructural health monitoring

S.K. Ghorai * and Dipta Ranjan Roy*, Email: [email protected]

* Department of Electronics & Communication, Birla Institute of Technology, Mesra, Ranchi-835 215, India.

Received: 28 May 2010; Accepted: 02 November 2010

SHM can sense signs of damage; reduce downtime for maintenance and also increases the safety of a structure. SHM is used to asses the fatigue life, monitor the performance and validate the design assumptions of a structure. It can be extended to any domain like automobiles, civil infrastructures or aerospace. A typical health monitoring system consists of a network of sensors placed at different part of a structure and fi ber optic sensors provide a reliable way for effective health monitoring. The novelty of this work is that we have tried to develop a Waterfall Model (adopted from Software Development Life Cycle2 model) to describe the life cycle of a FBG sensing system. The aim is to reduce the complexity in design, computation and to

achieve an overall improvement in productivity. We found that it became easier for us to introduce new concepts and methodologies at every stage, using the proposed model. A laboratory prototype of an embedded FBG sensing system is developed in our lab (Fiber Optics Research Lab, BIT Mesra), which is thoroughly investigated and cross-checked with the steps of the proposed model, to justify the validity of it. The Sensor Development Life Cycle mainly consists of 6 steps. From the fi rst step of requirement analysis to the fi nal step of deployment, every step is quite self explanatory. The detailed diagram for the various stages of development is shown in Fig.1 and the analysis of each step is done in the upcoming section.

SHM (structural health monitoring) involves the development of an autonomous system for continuous monitoring, inspection and damage detection of structures with minimum involvement of labor. Recent research works has shown that fi ber optic sensors1 has several inherent advantages over conventional electrical, electro-mechanical or mechanical sensors because of its small size, light-weight, non-conductivity, fast response, resistance to corrosion, higher-tempera-ture capability, immunity towards electromagnetic interference and ease of embedding into composite materials. Fiber Bragg grating (FBG) sensors, a special class of fi ber-optic sensor, have distinct advantages over other available form of fi ber optic sensors as well as non-fi ber optic sensor. It can serve both as the sensing element and the signal transmission medium. Moreover, because of its multiplexing capability and wavelength-encoded measurand (strain, temperature, pressure, humidity etc.) information it serves as a reliable source of remote SHM. In this work, we tried to give a complete methodology for designing and using an embedded FBG sensing system for quasi-static strain monitoring. In the process, we came up with a theoretical model, coined by us as SDLC (sensor development life cycle), which is capable of reducing the computational complexities for developing the sensing system. Simple fl owcharts are used to represent our ideolo-gies, and also to make it more useful and acceptable to any engineering domain (viz. civil, mechanical, aerospace etc.). A theoretical analysis for designing FBG, LPG (long period grating) and SFBG (superstructure fi ber Bragg grating) using 2-mode coupling and higher-order mode coupling is also discussed here. A robust digital signal processing technique, to retrieve information about the measurands, from the sensor output signal is given by us.

KEYWORDS: Fiber bragg grating (FBG); higher-order mode coupling; superstructure fi ber bragg grating (SFBG); transfer-matrix method; structural health monitoring (SHM); FBG signal interrogation; digital signal processing (DSP) technique; strain-sensing.

JOURNAL OF STRUCTURAL ENGINEERING 429 Vol. 38, No.5, DECEMBER 2011-JANUARY 2012

TheoreticalDesign

RequirementAnalysis

PrototypeDevelopment

ParameterSensing

Calibration

Deployment

ErrorFix

ErrorFix

ErrorFix

ErrorFix

ErrorFix

ErrorDetection

ErrorDetection

ErrorDetection

ErrorDetection

ErrorDetection

Fig. 1 A waterfall model for sensor development life cycle

BACKGROUND OF FIBER BRAGG GRATING SENSOR TECHNOLOGYA

FBG is a periodic structure, written into a segment of germanium-doped single-mode fi ber, in which a periodic modulation of the core refractive index (RI) is formed along the grating length by exposure of the core to a spatial pattern of UV light at 197 or 248 nm wavelengths3. In simple words, the gratings can be considered as small walls of silicon written within the fi ber. If light (which is considered as an electromagnetic wave), is induced in the fi ber then some of it gets refl ected due to the presence of grating, while the remaining part is transmitted through the fi ber. The amount of light which is refl ected back or transmitted forward depends upon the grating parameters (grating length, grating period, effective refractive index etc.). Most commonly, the grating period is considered to characterize different kind of grating sensor, i.e. if the grating period is in nano-meters then it is often referred as short-period grating or more commonly FBG, and if the grating period is in micro-meters then it is often referred as long-period grating (LPG) or transmission grating. Thus, when light within a fi ber passes through a FBG, multiple Fresnel refl ections takes place along the entire length of the grating due to the variations in refractive index. Constructive interference, due to the interaction of transmitted wave and refl ected wave, occurs if the wavelength of the propagating light in the fi ber doubles the grating pitch/period. The Bragg (or phase matching) condition is then satisfi ed and it leads to a narrowband back refl ection of light. The refl ected wavelength is known as the Bragg’s wavelength and it

is denoted by λB = 2neff ∧ where, neff is the effective refractive index of the fi ber and ∧ the grating period. The amount and type of interaction, defi ned as coupling, between the transmitted wave and the refl ected wave, depends on the grating parameters of a sensor. Thus, we can infer that if the interaction among the light wave is quantitatively less, a weak coupling has taken place and if the interaction is quantitatively heavy, a strong coupling has taken place. If a forward-going light wave interacts with a backward going refl ected wave, then it is termed as counter-directional coupling as the two interacting waves are opposite to each other, in direction. Similarly, if a forward-going light wave interacts with a forward going transmitted wave, then it is termed as co-directional coupling as the two interacting waves propagates in the same direction. In a FBG normally counter-directional coupling is predominant and in a LPG co-directional coupling is predominant. If we take into consideration only the counter-directional coupling of a forward going wave and a backward going refl ected wave, then it’s referred as 2-mode coupling. On the other hand, when we consider both co-directional and different counter-directional coupling, then it is referred as higher-order mode coupling since the cladding of an optical fi ber can support a large number of modes. A detailed analysis for determining the spectra (nature of output) of different kinds FBG sensors using 2-mode coupling as well as higher-order mode coupling is given by Erdogan4. Understanding the concept of coupling is very important for designing and analyzing the spectra of different kinds of FBG sensor and the methodologies for numerical computation is discussed in a different section of this paper. As both n and Λ depend on temperature and strain, the Bragg wavelength is also sensitive to both strain and temperature. Thus a variation of strain and temperature results in a shift of Bragg’s wavelength. Light that does not satisfy the Bragg condition passes through the FBG with very low loss, as shown in Fig. 1. The changes of index created in FBGs are relatively permanent and FBGs are sensitive to a number of physical parameters. Thus, by monitoring the resultant changes in refl ected wavelength, FBG sensors can be used in a variety of sensing applications to measure physical quantities, for example, strain, temperature, pressure, ultrasound, high magnetic fi eld, force and vibration. A FBG is thus an intrinsic fi ber-optic sensor. Each of the refl ected signals will have a unique wavelength and can be easily


monitored, thus achieving multiplexing of the outputs of multiple sensors using a single fi ber. However, the central wavelength, also referred as the design wavelength or Bragg’s wavelength (the wavelength at which maximum loss occurs) of FBG will vary with the change of these parameters experienced by the fi ber.

Reflectedcomponent

BroadbandOptical Source

wavelengthmonitoring

wavelengthmonitoring

couplergratingsensor

Input signal

Reflected signal

Fibre cladding Period of Bragg grating

Transmission signal

Fibre core

I

λstrain-induced

shift

Transmitted signal

λB

I

λ

λh1=2n∧1

λB

∧

Input spectrumI

λ

Fig. 2 Measurement of strain using fi ber bragg grating sensor (the shift in the refl ected component is directly proportional to the strain induced on the FBG sensor)

Therefore, the principal requirement for developing a grating-based measurement system, regardless of what specifi c fi elds the gratings are designed to measure, is to track the various grating wavelength refl ection shifts. This method of determining the wavelength shift to measure the required parameters (by applying suitable digital signal processing techniques and hardware) is quite often referred as FBG interrogation techniques. The minimum amount of change in the measurands (strain, temperature, pressure etc.) which results in a shift of the central wavelength is referred as the sensitivity of that particular FBG sensor, for that specifi c parameter. A number of approaches have been proposed, but most of them may be broadly classed into conventional wavelength-division demultiplexers5, scanning Fabry–Perot (SFP) fi lter interrogation6, tunable acousto-optic fi lter (AOTF) interrogation7 and prism/CCD-array techniques8. More recently, a hybrid technique has been demonstrated that retains certain advantages from some of the earlier methods while improves overall performance8, 9. One of the most signifi cant limitations of FBG sensors, ironically is their dual sensitivity to temperature and strain. This creates a problem for sensor systems designed to monitor strain, as temperature variations along the fi ber path can lead to anomalous, thermal-apparent strain readings.

One approach to addressing this issue is to use reference gratings along the array, i.e., gratings that are in thermal contact with the structure, but do not respond to local strain changes. This technique provides some compensation, but a system capable of providing strain and temperature measurements from the same fi ber without requiring that a section of the fi ber be isolated from strain is much more desirable. One approach is to locate two sensor elements which have very different responses to strain (Kε1, Kε2) and temperature (KT1, KT2) at the same point on the structure (collocated sensors). Then a matrix equation

Δ

Δ

λ

λ

εε

ε

1

2

1 1

2 2

⎡

⎣⎢

⎤

⎦⎥=

⎡

⎣⎢

⎤

⎦⎥⎡

⎣⎢

⎤

⎦⎥

K KK K T

T

T (1)

can be written and inverted to yield strain and temperature from measurements of the two wavelength shifts. The success of this technique depends on the ratio of the strain responses of the two sensors being different from the ratio of their temperature responses, so that the determinant of the matrix is nonzero. For FBG’s, the wavelength dependence of the photo-elastic and thermo-optic coeffi cients of the fi ber glass cause a small variation in the ratio of responses of FBG’s written at different wavelengths. Recently, stress has been given on using a single FBG sensor for measuring multiple parameters simultaneously. The main idea of multi-parameter measurement is to discriminate the individual peak shifts caused by the change of the parameters (strain, temperature, pressure etc.). This type of grating, which is capable of measuring different parameters simultaneously is often referred as superstructure/sampled fi ber Bragg grating (SFBG). In practical aspect, to design a SFBG sensor, multiple phase-shifts are introduced along the grating length of a normal FBG sensor. The phase-shifted Bragg grating is obtained when the refractive index is changed in such a way that the phase is not continuous. The refractive index is reduced to zero (null value) where the phase shift occurs and thus we obtain a periodic corrugated structure10. Due to this corrugated structure (i.e. at some point the refractive index is maximum and at other points the refractive index is zero) along the grating length coupling occurs in haphazard fashion and we get different loss peaks. Some of the peaks are responsive to strain and some to temperature. Thus a single grating can respond to two different parameters


and it forms the basis of multi-parameter sensing. The phase-mask method and amplitude-mask11, 12 are some of the most practiced method for designing a SFBG sensor. The schematic representation of a phase-shifted grating structure is shown in Fig.3. The phase-shift Φ is placed in the centre of a uniform grating in this example.

Fig.3 Schematic representation of a phase-shifted grating structure

STEPS FOR DESIGNING THE SENSOR

Requirement Analysis

This is the fi rst and the most basic step in the Sensor Development Life Cycle model. First, the parameters (viz. strain, temperature, vibration, humidity etc.) that are required to be monitored are identifi ed. Second, we need to identify the structure where the sensing system has to be implemented. Based on the above factors, we need to select the sensor (FBG, LPG, SFBG, hybrid system) for measuring different parameters, for effective SHM and proceed with the theoretical design of the sensing system.

Theoretical Design

In this stage mainly the design aspects of grating sensor is taken into consideration. We develop a theoretical model of the sensor (based on the requirement) after a detailed analysis of the structure subjected to health monitoring. The factors that should be taken into consideration (i.e. how much load the structure can withstand, maximum frequency of vibration it can tolerate, maximum pressure it can handle etc.) depends on the complexity of the structure and also on individual preferences. The grating parameters (i.e. grating length, effective index, core-index, clad-index, grating period etc.) are chosen accordingly and the effects of desired measurands (strain, temperature, pressure, humidity etc.) are analyzed on the output (refl ection spectrum or transmission spectrum) of the

sensor. This is normally a calculated hit & trial method and the grating parameters are optimized till the point, where the structure is subjected to failure, remains well within the range of the sensor.

In this work, we propose a simple fl owchart, for obtaining the spectra of different kinds of gratings using Transfer Matrix method which can reduce the computational complexities. A good point of the fl owchart is that we can introduce sampling in the refractive index variation along the grating length and introduce phase-shifts (discussed before, in section 2) to separate the FBG and LPG peaks for designing a SFBG sensor12 and to use it for multi-parameter sensing. In this research work, our analysis simply follows the methodologies given by Erdogan4, 13 for determining the normal FBG spectra using 2-mode coupling. The fl owchart for obtaining spectra using Transfer-Matrix method is shown in Fig. 4 and the numerical computations are discussed thereafter

Fig. 4 Transfer matrix method for calculating the spectra of FBG

The refractive index variation along the length of the fi ber is described by the equation,

∂ = ∂ + +neff z neff z z( ) ( ){ cos[ ( )]}12

νπ

ΛΦ (2)


where, δneff is the “dc” index change spatially averaged over a grating period, υ is the fringe visibility of the index change, ∧ is the nominal period and Φ(z) describes the grating chirp. The complete deduction for obtaining the Transfer-Matrix from the coupled-mode equation is given by Erdogan4, 13. Here we have shown only the matrix, and other corresponding parameters necessary to simulate and study the spectral properties of a normal FBG.

The Transfer-matrix for normal FBG using 2-mode coupling is given as:

F

z

i z i z

i z

B

B

BB B

B

BB

=

−−

cosh( )

sinh( ) sinh( )

sinh( )

γσ

γγ

κ

γγ

κ

γγ

Δ

ΔΔ

Δ

�

ccosh( )

sinh( )

γσ

γγ

B

BB

z

i z

Δ

Δ+

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥

�

Where the “AC” coupling coeffi cient from and σ∧

is a general “dc” self-coupling coeffi cient defi ned as

σ σ∧

≡∂+ −1 2/ ( / )d dzΦ (3)

The detuning δ, which is independent of z for all gratings, is defi ned as

∂≡ − ∧

= −

β π

β β

/D

= −2 1 1π λ λneff D( / / ) (4)

where λD effn= ∧2 , is the “design wavelength” for Bragg scattering by an infi nitesimally weak grating with a period ∧ . The “dc” coupling coeffi cient is σ

and γ κ σB = −∧

2 2 .

Applying the afore-said methodology the spectrum of a normal FBG is computed and shown in Fig. 5. In this work, we used MATLAB for simulation and numerical computation.

The mathematical deduction for calculating the coupling co-eff., spectral bandwidths and resonance wavelengths, are discussed by Erdogan13 in detail and can be referred for through understanding, for higher-order mode coupling in transmission gratings (LPG). However, a complete Transfer-Matrix for calculation

the spectra of a LPG using higher-order mode coupling is seldom described in any paper. In our work, we deduced the Transfer Matrix method for LPG spectra using higher-order mode coupling by following the work of Erdogan4,13, Zhang14 and Abrishamian15. The Transfer-Matrix is given for LPG spectra using higher-order mode coupling is given as:

F

iLN

iLN

K iLN

K

iLN

iLN

K

B

i

i

i=

−

+Δ

+Δ

− −

−

−Δ

+

−

1

0

0

1

3

1

11

11

1

11

()

()

σ β

β

β

βii

i

i

i

i

iLN

K iLN

K

iLN

iLN

K

iLN

0

1

0

0 0

1

11

1

1

1

1

1

1

− −

+

+Δ

−Δ

−

−

Δ

−Δ

()

(

σ β

β

β

β ))

(

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

with

F

R Z ))( )( )( )

( )( )( )( )

R ZS ZS Z

RRSS

i

i

i

i

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

=

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥

0000

⎥⎥

where, F = FM . FM-1 … Fi …F1 (5)

with the boundary conditions:

R R S z S zi i( ) , ( ) , ( ) , ( ) ,0 1 0 0 0 0= = = =

and σ is the “dc” coupling co-eff., k1 is the “ac” coupling co.-eff of LP01-LP01 mode, ki is the “ac” coupling co.-eff of LP01-LP0i th mode, L1 is the length of the grating, N is the number of sections in the grating, Δβ π λ λ1 2 1 1= −nco

coD( ) is the detuning parameter of

fundamental core-mode, Δβ π λ λi icl

Dn= −2 1 1( ) is the detuning parameter of ith cladding mode, ni

cl is the refractive index of ith clad and nco

co is the refractive index of fundamental core mode. The importance of this


matrix is that we can introduce as many modes as we want, to study it’s effect and behavior on the spectrum of the desired sensor. In this work, we have considered only the fundamental core mode (LP01-LP01) for counter-directional coupling and fi rst few odd cladding mode (co-directional coupling) since the effect of higher-order cladding modes has negligible effect on the spectrum13. The spectral response of a LPG using higher order mode coupling is shown in Fig. 6.

Ref

lect

ivity

Normalized wavelength

Fig. 5 Refl ection spectra of a normal FBG using transfer matrix method

Tran

smiti

vity

Normalized wavelength

Fig 6 Transmission Spectrum of a LPG using higher-order mode coupling

A SFBG has both the properties of FBG and LPG. It is obtained by writing a LPG over a FBG. Thus when its spectrum is analyzed both FBG peaks as well as LPG peaks are obtained. Hence, we can use a SFBG sensor for multi-parameter measurement since it is experimentally proved that the temperature response of LPG is better than FBG and the strain response of

FBG is better than LPG. For the spectral analysis of SFBG, we used the FBG matrix as discussed before but sampled the refractive index variation with rectangular sampling pulses as shown in Fig. 7. The spectral response of SFBG showing both FBG as well as LPG peaks is shown in Fig. 8.

Am

plitu

de

Grating wavelength

Fig. 7 R.I. variation after Rectangular sampling

Tran

smiti

vity

Normal Wavelength

Fig. 8 Transmission spectrum of a SFBG using 2-mode coupling

Whenever there is a change of strain it results in a Bragg wavelength shift. The spectral responses are studied to fi nd the amount of shift to deduce the strain induced on FBG. Here we followed the work by Suleiman15 to deduce the effect of strain shift on the designed gratings and extended it for higher order mode coupling (to measure the strain shift using a LPG). The Bragg wavelength under no loading is given

by λB effn= ∧2 (6)

where, neff is the effective refractive index of the core and ∧ is the grating pitch. When a longitudinal strain εz applied at a nominally constant temperature, the central wavelength of an uniform FBG will vary with the applied strain, which is experienced by the fi ber and the strain effect may be expressed as:


Δ ΔλBeff

effnL

nL

L= ∧∂

∂+

∂∧

∂2( ) (7)

with,

Δλ

λν εB

B

effz

np p p= − − +{ [ .( )]}1

2

2

12 11 12 (8)

= −( )1 pe zε

where,

p

np p pe

eff= − +

2

12 11 122[ .( )]ν

is the strain-optic constant, p11 and p12 are the Pockel’s strain-optic tensor coeffi cients of the fi ber, ν and is Poisson’s ratio of the fi ber material. Subjecting the grating to an axial strain εz, we see that the pitch length then becomes

∧=∧ +0 1( )εz (9)while the effective refractive index also undergoes changes and can be transformed into

n n nn

p p peff eff effeff

z+∂ = + − − +{ [ .( )] }2

12 11 122ν ε

Taking into account these two effects, the refl ectivity of a FBG sensor under strain can be shown to be,

R rBragg = 2

=−

− −

sinh [ . ]

cosh [ . ]

2 212

2 212 1

2κ σ

κ σσ

L

LL

(10)

with,

σπ

λ

π

ε10

21

=+∂

−∧ +

( )( )

n neff eff

z (11)

The important aspect is that we can manipulate the grating parameters at this stage also. If the grating parameters changes after the prototype development, due to manufacturing constraints, we can alter the design parameters accordingly (to predict the spectral shifts), so that the design wavelength remains well within the range of the designed sensor, even after application of maximum strain. Based on the previous theoretical discussion the effect of strain shift is studied on various gratings (normal FBG, higher-order mode LPG, SFBG) and represented in Fig. 9, 10 and 11.

Ref

lect

ivity

Normalized Wavelength

Fig. 9 Spectral shifts in normal FBG due to introduction of strain

Tran

smiti

vity


Fig. 10 Spectral shifts in higher-order mode coupled LPG due to introduction of strain

Tran

smiti

vity


Fig. 11 Simultaneous shift of both temperature and strain in SFBG using 2-mode coupling


Prototype Development

This stage mainly concentrates on the prototype development of the embedded sensor. Based on the requirement, we can embed the sensor in Composite Materials (CFRP, GFRP, Steel-tube etc.) or surface-mount them on the structure, subjected to health monitoring. An embedded FBG sensor has several advantages. Among them, sensor protection and ease of embedding into different structures are the most prominent one. The stages and process for preparing an embedded fi ber Bragg grating sensor is thoroughly discussed in various research works17, 18. The process and specifi cations for amplitude mask and phase mask to prepare a SFBG sensor for multi-parameter sensing is also discussed by many researchers10, 11, 12. It is important to decide how many sensors are required to embed in a composite, so that they can be mounted on a structure. Typically we can embed till 64 sensors in series for error free signal interrogation. In this research work we developed an embedded FBG sensor using acrylic rod to justify the sensor development life cycle. For the ease of signal interrogation and unavailability of Fabry-Perot scanning fi lter we decided to limit ourselves with one FBG sensor to develop the sensing system. The laboratory prototype of the sensor and the experimental setup to measure strain is shown in Fig. 12.

BroadandSource

DSPprocessor

Photodetector

Laptop/PC

2-count supportedBeam structure

2×1 Coupler

boylicmaterial

FBG sensor

StaticLoad

IndexMatching gel

Fig. 12 Experimental Setup for quasi-static strain monitoing using embedded FBG sensor

The laboratory model of the embedded sensor was developed by mounting the fi ber Bragg grating (Bragg’s wavelength: 1528.9 nm, neff =1.45, supplied by CGCRI, Kolkata) between two acrylic rods (dimension: 51cm

× 3cm × 0.6cm). A tunable laser source (ANDO AQ4321D) was used to couple light into the SM-optical fi ber. The output of a fi ber sensor is optical in nature. Therefore, we need to convert the obtained optical signal into corresponding electrical signal, to extract information about the measurands and more importantly, to identify the peak-shifts that occurs due to the change in magnitude for different parameters (viz. strain, temperature, pressure, vibration etc.). It is for this reason we use a photo-detector to sense and convert the optical signal into corresponding electrical signal. The photo-detector output is interfered with system noise and we designed a matched-fi lter (discussed in the next section) to remove the noise. We interfaced the photo-detector output, by a DAQ (data-acquisition) card, to a PC for signal interrogation. A TMS Processor (DSP Kit F2812) was used in conjunction with MATLAB (R14 V7) to design the interrogation system. Suitable DSP technique, discussed in detail in the next section, was applied to measure the peak shift upon application of load. However, due to pre-stressed condition the Bragg wavelength of the embedded sensor shifted to 1528.0nm. Therefore, we went back to theoretical design (possible due to the fl exibility of the proposed model), and made suitable adjustments to obtain the spectral shift, under different loaded conditions. The open end of the fi ber is dipped in an index-matched gel, i.e. a fl uid having the same refractive- index as that of the effective refractive-index of the fi ber (neff). This is done to avoid back-scattering loss at the open-end of the fi ber. In this work, we used a centrally concentrated load and thus the strain induced in the two point supported acrylic rod was found by applying the formula,

StrainW Y

E ILC= (

.. .

).4

where Wc = mg and m=static-load (in gms.), L=length of the rod(51cm), E= Young’s modulus of elasticity (2.8 × 103 N/mm2),

b = width of the rod (30mm), a=thickness of the rod (6mm), Y=distance from neutral axis (3mm),

I b a= ( ). .1

123 moment of inertia ( 540 mm4).

At this stage the fi nite-element analysis of the structure can be done, and optimal positions for mounting the sensors can be located within the structure to obtain best possible result.


Parameter Sensing

This stage almost overlaps with the previous stage in sensing system development. It’s necessary to use a robust DSP technique for interrogating the FBG signals and determine the peak shifts. A number of works are reported for interrogation of FBG sensor signals using DSP techniques19. Another important factor which should be kept in mind is the real-time processing of sensor output with cost effective design. Since, the sensor signal is often interfered with noise a suitable fi lter technique is needed for noise removal. In this work, we closely followed the work by Lu20 to remove noise from photo-detector output. In the process we made the interrogation system real-time and came up with a simple fl owchart to reduce the calculation errors.

3.4.1 Digital Matched Filter (DMF)

If the input signal and the noise signal pass through a fi lter , then the output is

x t x t t h t x t t( ) [ ( ) ( )]* ( ) ( ) ( )∧

= + = +ν ν0 0 (12)

where, the true output signal x0(t) has the form

x t X H e dj t0

12

( ) ( ) ( )= ∫−∞

+∞

πω ω ωω (13)

The variance of the output noise v0(t) is

ν νσπ

σ ω ω0

2 2 212

= ∫−∞

+∞H d( ) (14)

By Schwarz inequality,

x t X H e d

Xd

j t

j t

02

2

2

12

12

12

12

( ) . ( ) ( )

.( )

= ∫

≤

−∞

+∞

−∞

+∞

π πω ω ω

π π

ω

σω

ω

ω

ν∫∫ ∫

−∞

+∞

νσ ω ω2 2H d( ) (15)

The signal-to-noise ratio (SNR) x t0

20

( )

νσ of the output

can be written as,

x t X

dj t

02

2

20

12

( ) ( )

ν

ω

νσ π

ω

σω≤ ∫

−∞

+∞ (16)

Because of the Schwarz inequality,

A B d

A d B

( ) ( ) ( )

( ) ( )

ω ω ω

ω ω ω

2

2 2

≤∫

∫ ∫

−∞

+∞

−∞

+∞

−∞

+∞ (17)

The equation can be true when B(ω) = CA*. Comparing with the equation (15), we can get the maximum SNR when

HCX e j t

( )( )*

ωω

σ

ω

ν=

−

2 (18)

where “*” represents complex conjugate; C/σ2ν is a possible amplitude; the delay factor j e-jωt is a constant when t = t0 and the output SNR reaches the maximum.

Fig. 13 Flowchart for real-time monitoring of strain using digital matched fi lter (DMF)

It is found the transfer function of a matched fi lter is the complex conjugate of the spectrum of signal to which it is matched. The DMF is actually a low pass Gaussian fi lter. A Gaussian fi lter is chosen because it has similar impulse response in both frequency and time domain.


Theoretically, the DMF was designed by sampling the ideal Gaussian FBG spectrum and taking the discrete Fourier transform of it. We then complex conjugated the resultant signal and did an inverse discrete Fourier transform. The fl owchart for the construction of DMF and the point where it needs to be applied is shown in Fig. 13. The photo-detector output, shown in Fig. 14 was interfered with noise. Hence we applied the DMF technique for noise removal and observed the peak shift which is shown in Fig. 15. However, some attenuation is observed in the output signal as the noise is random in nature and interferes with FBG signal randomly at different times.

Am

plitu

de


Gaussian Noised Signal

Fig. 14 Photodetector output (Gaussian noised signal)

Am

plitu

de

Wavelength (nm)

Fig. 15 Determination of peak-shift using DMF technique for different strain

In this research work only a single grating is interrogated. However, this fi ltering technique can be applied to interrogate an array of FBG sensor by using scanning fi lter (Febry-Perot) techniques5.

Calibration

The unknown parameters can be determined easily, by simply measuring the peak shifts as the output of the sensing system is linear in nature. In this work, we determined the unknown loads on extrapolating the load line, obtained using known loads. The unknown loads measured experimentally showed absolute accordance with the theoretical measurement. Fig. 16 depicts the obtained results. However, a delay can be noticed between the theoretical and experimental data. This delay is a system generated delay and can be easily ignored as it doesn’t affect the sensitivity (the amount of peak-shift on application of minimum amount of load/strain) of the system. The strain sensitivity of the sensing system is found to be 1.16pm/μ∈, with an accuracy of +- 20 μ∈.

Applied Strain (ue)

FBG

Wav

elen

gth

Fig. 16 Load line for the calculation of unknown strain

Deployment

The sensing system thus developed can be deployed in any real life scenario. Since, re-engineering can be done, the system is adaptive to communicate changes in future. Since, the signal interrogation is done using software program, new methodologies can be adapted


at any point of time to increase the sensing capability of the system.

CONCLUSION

In this work, only one parameter (strain) is measured using FBG sensor. However, in future other fi ber sensors (SFBG, LPG, hybrid sensing system, Mach-Zender Interferrometric sensor) can be developed using this technique for simultaneous measurement of different parameters. It can also be extended for interrogating fully-distributed load and dynamic load measurement.

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(Discussion on this article must reach the editor before March 31, 2011)

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