Abstract

This paper presents the application of inverse analysis to determine the stress distribution in a way that is insensitive to changes in temperature. For this purpose, a sensor with a fiber Bragg grating (FBG) was used. The paper discusses the direct solution of the task and presents the development and validation of a mathematical model of the Bragg grating sensor. Computer simulations were performed to apply numerical algorithms that completed the calculations according to the mathematical structure of the model and considered the values of all other elements of the FBG sensor. An experimental study was also conducted using a constructed measuring post.

© 2012 Optical Society of America

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References

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  1. A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999), pp. 21–45.
  2. Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106 (2011).
    [CrossRef]
  3. Z. G. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2012).
    [CrossRef]
  4. Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
    [CrossRef]
  5. G. A. Miller, J. R. Peele, C. G. Askins, and G. A. Cranch, “Characterization of strong fiber Bragg gratings using an applied thermal chirp and iterative algorithm,” Appl. Opt. 50, 6617–6626 (2011).
    [CrossRef]
  6. G. A. Cranch and G. A. Miller, “Improved implementation of optical space domain reflectometry for characterizing the complex coupling coefficient of strong fiber Bragg gratings,” Appl. Opt. 48, 4506–4513 (2009).
    [CrossRef]
  7. G. M. H. Flockhart, G. A. Cranch, and C. K. Kirkendall, “Rapid characterization of the ultraviolet induced fiber Bragg grating complex coupling coefficient as a function of irradiance and exposure time,” Appl. Opt. 46, 8237–8243 (2007).
    [CrossRef]
  8. A. M. Abdi, S. Suzuki, A. Schülzgen, and A. R. Kost, “Modeling, design, fabrication, and testing of a fiber Bragg grating strain sensor array,” Appl. Opt. 46, 2563–2574 (2007).
    [CrossRef]
  9. O. Frazão, S. F. O. Silva, A. Guerreiro, J. L. Santos, and L. A. Ferreira, “Strain sensitivity control of fiber Bragg grating structures with fused tapers,” Appl. Opt. 46, 8578–8582 (2007).
    [CrossRef]
  10. M. Froggatt and J. Moore, “Distributed measurement of static strain in an optical fiber with multiple Bragg gratings at nominally equal wavelengths,” Appl. Opt. 37, 1741–1746 (1998).
    [CrossRef]
  11. J. Mroczka and D. Szczuczyński, “Summary results of simulation research on improved regularized solution of inverse problem in spectral extinction measurements,” Appl. Opt. 51, 1715–1723 (2012).
    [CrossRef]
  12. J. Mroczka and D. Szczuczyński, “Improved regularized solution of the inverse problem in turbidimetric measurements,” Appl. Opt. 49, 4591–4603 (2010).
    [CrossRef]
  13. J. Mroczka and D. Szczuczyński, “Inverse problems formulated in terms of first-kind Fredholm integral equations in indirect measurements,” Metrol. Meas. Syst. 16, 333–357 (2009).
  14. R. Aneesh, M. Maharana, P. Munendhar, H. Y. Tam, and S. K. Khijwania, “Simple temperature insensitive fiber Bragg grating based tilt sensor with enhanced tenability,” Appl. Opt. 50, E172–E176 (2011).
    [CrossRef]
  15. J. Botsis, L. Humbert, F. Colpo, and P. Giaccari, “Embedded fiber Bragg grating sensor for internal strain measurements in polymeric materials,” Opt. Lasers Eng. 43, 491–510(2005).
    [CrossRef]
  16. K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
    [CrossRef]
  17. W. Y. Li, C. C. Chenga, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
    [CrossRef]
  18. C. A. Ramos, R. de Oliveira, and A. T. Marques, “Design of an optical fibre sensor patch for longitudinal strain measurement in structures,” Mater. Design 30, 2323–2331 (2009).
    [CrossRef]
  19. R. H. J. M. Otten and L. P. P. P. van Ginneken, “Floorplan design using simulated annealing,” in Proceedings of the IEEE International Conference on Computer-Aided Design (IEEE, 1984), pp. 96–98.

2012

Z. G. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2012).
[CrossRef]

Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

J. Mroczka and D. Szczuczyński, “Summary results of simulation research on improved regularized solution of inverse problem in spectral extinction measurements,” Appl. Opt. 51, 1715–1723 (2012).
[CrossRef]

2011

2010

2009

G. A. Cranch and G. A. Miller, “Improved implementation of optical space domain reflectometry for characterizing the complex coupling coefficient of strong fiber Bragg gratings,” Appl. Opt. 48, 4506–4513 (2009).
[CrossRef]

J. Mroczka and D. Szczuczyński, “Inverse problems formulated in terms of first-kind Fredholm integral equations in indirect measurements,” Metrol. Meas. Syst. 16, 333–357 (2009).

W. Y. Li, C. C. Chenga, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
[CrossRef]

C. A. Ramos, R. de Oliveira, and A. T. Marques, “Design of an optical fibre sensor patch for longitudinal strain measurement in structures,” Mater. Design 30, 2323–2331 (2009).
[CrossRef]

2007

2005

J. Botsis, L. Humbert, F. Colpo, and P. Giaccari, “Embedded fiber Bragg grating sensor for internal strain measurements in polymeric materials,” Opt. Lasers Eng. 43, 491–510(2005).
[CrossRef]

2001

K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
[CrossRef]

1998

Abdi, A. M.

Aneesh, R.

Askins, C. G.

Botsis, J.

J. Botsis, L. Humbert, F. Colpo, and P. Giaccari, “Embedded fiber Bragg grating sensor for internal strain measurements in polymeric materials,” Opt. Lasers Eng. 43, 491–510(2005).
[CrossRef]

Cantwell, W. J.

K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
[CrossRef]

Chalker, P. R.

K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
[CrossRef]

Chenga, C. C.

W. Y. Li, C. C. Chenga, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
[CrossRef]

Colpo, F.

J. Botsis, L. Humbert, F. Colpo, and P. Giaccari, “Embedded fiber Bragg grating sensor for internal strain measurements in polymeric materials,” Opt. Lasers Eng. 43, 491–510(2005).
[CrossRef]

Cranch, G. A.

de Oliveira, R.

C. A. Ramos, R. de Oliveira, and A. T. Marques, “Design of an optical fibre sensor patch for longitudinal strain measurement in structures,” Mater. Design 30, 2323–2331 (2009).
[CrossRef]

Ferreira, L. A.

Flockhart, G. M. H.

Frazão, O.

Froggatt, M.

Giaccari, P.

J. Botsis, L. Humbert, F. Colpo, and P. Giaccari, “Embedded fiber Bragg grating sensor for internal strain measurements in polymeric materials,” Opt. Lasers Eng. 43, 491–510(2005).
[CrossRef]

Guerreiro, A.

Humbert, L.

J. Botsis, L. Humbert, F. Colpo, and P. Giaccari, “Embedded fiber Bragg grating sensor for internal strain measurements in polymeric materials,” Opt. Lasers Eng. 43, 491–510(2005).
[CrossRef]

Kalli, K.

A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999), pp. 21–45.

Kenny, R.

K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
[CrossRef]

Khijwania, S. K.

Kirkendall, C. K.

Kost, A. R.

Kuang, K. S. C.

K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
[CrossRef]

Li, W. Y.

W. Y. Li, C. C. Chenga, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
[CrossRef]

Lo, Y. L.

W. Y. Li, C. C. Chenga, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
[CrossRef]

Maharana, M.

Marques, A. T.

C. A. Ramos, R. de Oliveira, and A. T. Marques, “Design of an optical fibre sensor patch for longitudinal strain measurement in structures,” Mater. Design 30, 2323–2331 (2009).
[CrossRef]

Miller, G. A.

Moore, J.

Mroczka, J.

Munendhar, P.

Othonos, A.

A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999), pp. 21–45.

Otten, R. H. J. M.

R. H. J. M. Otten and L. P. P. P. van Ginneken, “Floorplan design using simulated annealing,” in Proceedings of the IEEE International Conference on Computer-Aided Design (IEEE, 1984), pp. 96–98.

Peele, J. R.

Ramos, C. A.

C. A. Ramos, R. de Oliveira, and A. T. Marques, “Design of an optical fibre sensor patch for longitudinal strain measurement in structures,” Mater. Design 30, 2323–2331 (2009).
[CrossRef]

Santos, J. L.

Schülzgen, A.

Silva, S. F. O.

Suzuki, S.

Szczuczynski, D.

Tam, H. Y.

van Ginneken, L. P. P. P.

R. H. J. M. Otten and L. P. P. P. van Ginneken, “Floorplan design using simulated annealing,” in Proceedings of the IEEE International Conference on Computer-Aided Design (IEEE, 1984), pp. 96–98.

Whelan, M. P.

K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
[CrossRef]

Yang, W. X.

Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106 (2011).
[CrossRef]

Zang, Z. G.

Z. G. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2012).
[CrossRef]

Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106 (2011).
[CrossRef]

Zhang, Y. J.

Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Appl. Opt.

M. Froggatt and J. Moore, “Distributed measurement of static strain in an optical fiber with multiple Bragg gratings at nominally equal wavelengths,” Appl. Opt. 37, 1741–1746 (1998).
[CrossRef]

A. M. Abdi, S. Suzuki, A. Schülzgen, and A. R. Kost, “Modeling, design, fabrication, and testing of a fiber Bragg grating strain sensor array,” Appl. Opt. 46, 2563–2574 (2007).
[CrossRef]

G. M. H. Flockhart, G. A. Cranch, and C. K. Kirkendall, “Rapid characterization of the ultraviolet induced fiber Bragg grating complex coupling coefficient as a function of irradiance and exposure time,” Appl. Opt. 46, 8237–8243 (2007).
[CrossRef]

O. Frazão, S. F. O. Silva, A. Guerreiro, J. L. Santos, and L. A. Ferreira, “Strain sensitivity control of fiber Bragg grating structures with fused tapers,” Appl. Opt. 46, 8578–8582 (2007).
[CrossRef]

G. A. Cranch and G. A. Miller, “Improved implementation of optical space domain reflectometry for characterizing the complex coupling coefficient of strong fiber Bragg gratings,” Appl. Opt. 48, 4506–4513 (2009).
[CrossRef]

J. Mroczka and D. Szczuczyński, “Improved regularized solution of the inverse problem in turbidimetric measurements,” Appl. Opt. 49, 4591–4603 (2010).
[CrossRef]

R. Aneesh, M. Maharana, P. Munendhar, H. Y. Tam, and S. K. Khijwania, “Simple temperature insensitive fiber Bragg grating based tilt sensor with enhanced tenability,” Appl. Opt. 50, E172–E176 (2011).
[CrossRef]

G. A. Miller, J. R. Peele, C. G. Askins, and G. A. Cranch, “Characterization of strong fiber Bragg gratings using an applied thermal chirp and iterative algorithm,” Appl. Opt. 50, 6617–6626 (2011).
[CrossRef]

J. Mroczka and D. Szczuczyński, “Summary results of simulation research on improved regularized solution of inverse problem in spectral extinction measurements,” Appl. Opt. 51, 1715–1723 (2012).
[CrossRef]

Compos. Sci. Technol.

K. S. C. Kuang, R. Kenny, M. P. Whelan, W. J. Cantwell, and P. R. Chalker, “Embedded fibre Bragg grating sensors in advanced composite materials,” Compos. Sci. Technol. 61, 1379–1387 (2001).
[CrossRef]

J. Appl. Phys.

Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106 (2011).
[CrossRef]

J. Mod. Opt.

Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Mater. Design

C. A. Ramos, R. de Oliveira, and A. T. Marques, “Design of an optical fibre sensor patch for longitudinal strain measurement in structures,” Mater. Design 30, 2323–2331 (2009).
[CrossRef]

Metrol. Meas. Syst.

J. Mroczka and D. Szczuczyński, “Inverse problems formulated in terms of first-kind Fredholm integral equations in indirect measurements,” Metrol. Meas. Syst. 16, 333–357 (2009).

Opt. Commun.

Z. G. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2012).
[CrossRef]

Opt. Lasers Eng.

J. Botsis, L. Humbert, F. Colpo, and P. Giaccari, “Embedded fiber Bragg grating sensor for internal strain measurements in polymeric materials,” Opt. Lasers Eng. 43, 491–510(2005).
[CrossRef]

Sens. Actuators A

W. Y. Li, C. C. Chenga, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
[CrossRef]

Other

R. H. J. M. Otten and L. P. P. P. van Ginneken, “Floorplan design using simulated annealing,” in Proceedings of the IEEE International Conference on Computer-Aided Design (IEEE, 1984), pp. 96–98.

A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999), pp. 21–45.

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Figures (3)

Fig. 1.
Fig. 1.

Laboratory post for strain distribution measurements for a specific temperature: 1, white light source; 2, single mode optical fiber with recorded Bragg grating; 3, optical fiber link; 4, measurement Bragg grating; 5, adhesive-bonded link; 6, element examined (sample strained with force); 7, reference Bragg grating; 8, optical spectrum analyzer; 9, thermal chamber; 10, thermometer; 11, laboratory post to generate mechanic loads; 12, samples tested (sheared); 13, flow direction of input air, with a regulated temperature.

Fig. 2.
Fig. 2.

Block diagram of laboratory post for determining the strain distribution when using FBGs (right) and the layout of Bragg grating, adhesive and sample covered with FEM grid (left). FBG 1, measurement grating; FBG 2, reference grating.

Fig. 3.
Fig. 3.

Distributions of the grating strain: actual (green line), initial (red line) and the distribution determined using the simulated annealing method (blue line) for (a) Sample 1, (b) Sample 2, (c) Sample 3, and (d) Sample 4. The drawings also display the system tested: 1, optical fiber with Bragg grating; 2, adhesive; 3, sample.

Tables (1)

Tables Icon

Table 1. Values of the Relative Mean Square Error for Each Sample

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

[TcRc]=[cosh(γBzi)i2πneff(1/λ1/λB)+(2π/λ)δneff¯γBsinh(γBzi)ikγBsinh(γBzi)ikγBsinh(γBzi)cosh(γBzi)+i2πneff(1/λ1/λB)+(2π/λ)δneff¯γBsinh(γBzi)]·[10],
k(z)=πλδn(z)exp[a(zL/2L)2],
δ=1Ni=1N(εiMESεialg)2,
Tk+1=Tk1Mk·Tk3σ2Tk.
Mk=FCmax+Tk·ln(1+δ)δ2(Tk)·ln(1+δ)·Tk,
FC=1mi=1m(TmTcTc)2,

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