Measurement of wide frequency range structural microvibrations with a pocket digital camera and sub-pixel techniques

David Mas; Julian Espinosa; Ana B. Roig; Belen Ferrer; Jorge Perez; Carlos Illueca

doi:10.1364/AO.51.002664

Abstract

Analysis of vibrations and displacements is a hot topic in structural engineering. Although there is a wide variety of methods for vibration analysis, direct measurement of displacements in the mid and high frequency range is not well solved and accurate devices tend to be very expensive. Low-cost systems can be achieved by applying adequate image processing algorithms. In this paper, we propose the use of a commercial pocket digital camera, which is able to register more than 420 frames per second (fps) at low resolution, for accurate measuring of small vibrations and displacements. The method is based on tracking elliptical targets with sub-pixel accuracy. Our proposal is demonstrated at a 10 m distance with a spatial resolution of 0.15 mm. A practical application over a simple structure is given, and the main parameters of an attenuated movement of a steel column after an impulsive impact are determined with a spatial accuracy of 4 µm.

Full Article | PDF Article

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References

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Author
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Publication

C. Gentile and A. Saisi, “Ambient vibration testing of historic masonry towers for structural identification and damage assessment,” Constr. Build. Mater. 21, 1311–1321 (2007).
[Crossref]
A. K. Chopra, “Equations of Motion, Problem Statement and Solution Methods,” eds.,B. Stenquist and K. Scherwatzky, in Dynamic of Structures: Theory and Applications to Earthquake Engineering, 2nd Ed. (Prentice-Hall, 2001), pp. 23–25.
S. C. Stiros, “Errors in velocities and displacements deduced from accelerographs: An approach based on the theory of error propagation,” Soil Dyn. Earthq. Eng. 28, 415–420 (2008).
[Crossref]
A. Cunha, E. Caetano, and R. Delgado, “Dynamic tests on a large cable-stayed bridge,” J. Bridge Eng. ASCE 6, 54–62 (2001).
H. N. Nassif, M. Gindy, and J. Davis, “Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration,” NDT & E Int. 38, 213–128 (2005).
[Crossref]
M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]
C. Gentile and G. Bernardini, “Output-only modal identification of a reinforced concrete bridge from radar-based measurements,” Nondestr. Test. Eval. 41, 544–553.(2008).
[Crossref]
J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT & E International 39, 425–431 (2006).
[Crossref]
B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]
Edmund Optics Catalog, http://www.edmundoptics.com .
M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the sub-pixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]
M. R. Shortis, T. A. Clarke, and S. Robson, “Practical testing of the precision and accuracy of target image centring algorithms,” Proc. SPIE 2598, 65–76 (1995).
[Crossref]
A. M. Brucksteinand and A. O’Gorman, “Design of shapes for precise Image registration,” IEEE Trans. Inf. Theory 44, 3156–3162 (1998).
[Crossref]
J. C. Trinder, J. Jansa, and Y. Huang, “An assessment of the precision and accuracy of methods of digital target localization,” ISPRS Journal of Photogrammetry and Remote Sensing 50, 12–20 (1995).
[Crossref]
I. Maalen-Johansen, “On the precision of sub-pixel measurements in videometry,” Proc. SPIE 2252, 169–178 (1993).
[Crossref]
J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]
R. Kuritaand and E. R. Weeks, “Experimental study of random close-packed colloidal particles,” Phys. Rev. E 82, 011403 (2010).
[Crossref]
W. Tong, “Sub-pixel image registration with reduced bias,” Opt. Lett. 36, 763–765 (2011).
[Crossref]
O. Gal, http://www.mathworks.com/matlabcentral/fileexchange/3215-fitellipse .
Mathworks Inc, http://www.mathworks.es/help/toolbox/images/ .
LS-DYNA Keyword User’s Manual (v.970), Livermore Software Technology Corporation, April2003.

2011 (2)

B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]

W. Tong, “Sub-pixel image registration with reduced bias,” Opt. Lett. 36, 763–765 (2011).
[Crossref]

2010 (1)

R. Kuritaand and E. R. Weeks, “Experimental study of random close-packed colloidal particles,” Phys. Rev. E 82, 011403 (2010).
[Crossref]

2008 (3)

M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]

C. Gentile and G. Bernardini, “Output-only modal identification of a reinforced concrete bridge from radar-based measurements,” Nondestr. Test. Eval. 41, 544–553.(2008).
[Crossref]

S. C. Stiros, “Errors in velocities and displacements deduced from accelerographs: An approach based on the theory of error propagation,” Soil Dyn. Earthq. Eng. 28, 415–420 (2008).
[Crossref]

2007 (1)

C. Gentile and A. Saisi, “Ambient vibration testing of historic masonry towers for structural identification and damage assessment,” Constr. Build. Mater. 21, 1311–1321 (2007).
[Crossref]

2006 (1)

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT & E International 39, 425–431 (2006).
[Crossref]

2005 (1)

H. N. Nassif, M. Gindy, and J. Davis, “Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration,” NDT & E Int. 38, 213–128 (2005).
[Crossref]

2001 (1)

A. Cunha, E. Caetano, and R. Delgado, “Dynamic tests on a large cable-stayed bridge,” J. Bridge Eng. ASCE 6, 54–62 (2001).

1998 (1)

A. M. Brucksteinand and A. O’Gorman, “Design of shapes for precise Image registration,” IEEE Trans. Inf. Theory 44, 3156–3162 (1998).
[Crossref]

1996 (1)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

1995 (2)

M. R. Shortis, T. A. Clarke, and S. Robson, “Practical testing of the precision and accuracy of target image centring algorithms,” Proc. SPIE 2598, 65–76 (1995).
[Crossref]

J. C. Trinder, J. Jansa, and Y. Huang, “An assessment of the precision and accuracy of methods of digital target localization,” ISPRS Journal of Photogrammetry and Remote Sensing 50, 12–20 (1995).
[Crossref]

1994 (1)

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the sub-pixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

1993 (1)

I. Maalen-Johansen, “On the precision of sub-pixel measurements in videometry,” Proc. SPIE 2252, 169–178 (1993).
[Crossref]

Atzeni, C.

M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]

Bartoli, G.

M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]

Bernardini, G.

C. Gentile and G. Bernardini, “Output-only modal identification of a reinforced concrete bridge from radar-based measurements,” Nondestr. Test. Eval. 41, 544–553.(2008).
[Crossref]

Brucksteinand, A. M.

A. M. Brucksteinand and A. O’Gorman, “Design of shapes for precise Image registration,” IEEE Trans. Inf. Theory 44, 3156–3162 (1998).
[Crossref]

Caetano, E.

A. Cunha, E. Caetano, and R. Delgado, “Dynamic tests on a large cable-stayed bridge,” J. Bridge Eng. ASCE 6, 54–62 (2001).

Chopra, A. K.

A. K. Chopra, “Equations of Motion, Problem Statement and Solution Methods,” eds.,B. Stenquist and K. Scherwatzky, in Dynamic of Structures: Theory and Applications to Earthquake Engineering, 2nd Ed. (Prentice-Hall, 2001), pp. 23–25.

Clarke, T. A.

M. R. Shortis, T. A. Clarke, and S. Robson, “Practical testing of the precision and accuracy of target image centring algorithms,” Proc. SPIE 2598, 65–76 (1995).
[Crossref]

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the sub-pixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

Cunha, A.

A. Cunha, E. Caetano, and R. Delgado, “Dynamic tests on a large cable-stayed bridge,” J. Bridge Eng. ASCE 6, 54–62 (2001).

Davis, J.

H. N. Nassif, M. Gindy, and J. Davis, “Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration,” NDT & E Int. 38, 213–128 (2005).
[Crossref]

Delgado, R.

A. Cunha, E. Caetano, and R. Delgado, “Dynamic tests on a large cable-stayed bridge,” J. Bridge Eng. ASCE 6, 54–62 (2001).

Espinosa, J.

B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]

Ferrer, B.

B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]

Fratini, M.

M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]

Gentile, C.

C. Gentile and G. Bernardini, “Output-only modal identification of a reinforced concrete bridge from radar-based measurements,” Nondestr. Test. Eval. 41, 544–553.(2008).
[Crossref]

C. Gentile and A. Saisi, “Ambient vibration testing of historic masonry towers for structural identification and damage assessment,” Constr. Build. Mater. 21, 1311–1321 (2007).
[Crossref]

Gindy, M.

H. N. Nassif, M. Gindy, and J. Davis, “Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration,” NDT & E Int. 38, 213–128 (2005).
[Crossref]

Grier, D. G.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

Huang, Y.

J. C. Trinder, J. Jansa, and Y. Huang, “An assessment of the precision and accuracy of methods of digital target localization,” ISPRS Journal of Photogrammetry and Remote Sensing 50, 12–20 (1995).
[Crossref]

Iborra, S.

B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]

Jansa, J.

J. C. Trinder, J. Jansa, and Y. Huang, “An assessment of the precision and accuracy of methods of digital target localization,” ISPRS Journal of Photogrammetry and Remote Sensing 50, 12–20 (1995).
[Crossref]

Kuritaand, R.

R. Kuritaand and E. R. Weeks, “Experimental study of random close-packed colloidal particles,” Phys. Rev. E 82, 011403 (2010).
[Crossref]

Lee, J. J.

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT & E International 39, 425–431 (2006).
[Crossref]

Maalen-Johansen, I.

I. Maalen-Johansen, “On the precision of sub-pixel measurements in videometry,” Proc. SPIE 2252, 169–178 (1993).
[Crossref]

Mas, D.

B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]

Nassif, H. N.

H. N. Nassif, M. Gindy, and J. Davis, “Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration,” NDT & E Int. 38, 213–128 (2005).
[Crossref]

O’Gorman, A.

A. M. Brucksteinand and A. O’Gorman, “Design of shapes for precise Image registration,” IEEE Trans. Inf. Theory 44, 3156–3162 (1998).
[Crossref]

Parrini, F.

M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]

Perez, J.

B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]

Pieraccini, M.

M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]

Robson, S.

M. R. Shortis, T. A. Clarke, and S. Robson, “Practical testing of the precision and accuracy of target image centring algorithms,” Proc. SPIE 2598, 65–76 (1995).
[Crossref]

Saisi, A.

C. Gentile and A. Saisi, “Ambient vibration testing of historic masonry towers for structural identification and damage assessment,” Constr. Build. Mater. 21, 1311–1321 (2007).
[Crossref]

Shinozuka, M.

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT & E International 39, 425–431 (2006).
[Crossref]

Short, T.

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the sub-pixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Shortis, M. R.

M. R. Shortis, T. A. Clarke, and S. Robson, “Practical testing of the precision and accuracy of target image centring algorithms,” Proc. SPIE 2598, 65–76 (1995).
[Crossref]

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the sub-pixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Stiros, S. C.

S. C. Stiros, “Errors in velocities and displacements deduced from accelerographs: An approach based on the theory of error propagation,” Soil Dyn. Earthq. Eng. 28, 415–420 (2008).
[Crossref]

Tong, W.

W. Tong, “Sub-pixel image registration with reduced bias,” Opt. Lett. 36, 763–765 (2011).
[Crossref]

Trinder, J. C.

J. C. Trinder, J. Jansa, and Y. Huang, “An assessment of the precision and accuracy of methods of digital target localization,” ISPRS Journal of Photogrammetry and Remote Sensing 50, 12–20 (1995).
[Crossref]

Weeks, E. R.

R. Kuritaand and E. R. Weeks, “Experimental study of random close-packed colloidal particles,” Phys. Rev. E 82, 011403 (2010).
[Crossref]

Constr. Build. Mater. (1)

C. Gentile and A. Saisi, “Ambient vibration testing of historic masonry towers for structural identification and damage assessment,” Constr. Build. Mater. 21, 1311–1321 (2007).
[Crossref]

IEEE Trans. Inf. Theory (1)

A. M. Brucksteinand and A. O’Gorman, “Design of shapes for precise Image registration,” IEEE Trans. Inf. Theory 44, 3156–3162 (1998).
[Crossref]

ISPRS Journal of Photogrammetry and Remote Sensing (1)

J. C. Trinder, J. Jansa, and Y. Huang, “An assessment of the precision and accuracy of methods of digital target localization,” ISPRS Journal of Photogrammetry and Remote Sensing 50, 12–20 (1995).
[Crossref]

J. Bridge Eng. ASCE (1)

A. Cunha, E. Caetano, and R. Delgado, “Dynamic tests on a large cable-stayed bridge,” J. Bridge Eng. ASCE 6, 54–62 (2001).

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

NDT & E Int. (2)

H. N. Nassif, M. Gindy, and J. Davis, “Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration,” NDT & E Int. 38, 213–128 (2005).
[Crossref]

M. Pieraccini, M. Fratini, F. Parrini, C. Atzeni, and G. Bartoli, “Interferometric radar vs. accelerometer for dynamic monitoring of large structures: An experimental comparison,” NDT & E Int. 41, 258–264 (2008).
[Crossref]

NDT & E International (1)

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT & E International 39, 425–431 (2006).
[Crossref]

Nondestr. Test. Eval. (1)

C. Gentile and G. Bernardini, “Output-only modal identification of a reinforced concrete bridge from radar-based measurements,” Nondestr. Test. Eval. 41, 544–553.(2008).
[Crossref]

Opt. Lett. (1)

W. Tong, “Sub-pixel image registration with reduced bias,” Opt. Lett. 36, 763–765 (2011).
[Crossref]

Phys. Rev. E (1)

R. Kuritaand and E. R. Weeks, “Experimental study of random close-packed colloidal particles,” Phys. Rev. E 82, 011403 (2010).
[Crossref]

Proc. SPIE (3)

I. Maalen-Johansen, “On the precision of sub-pixel measurements in videometry,” Proc. SPIE 2252, 169–178 (1993).
[Crossref]

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the sub-pixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

M. R. Shortis, T. A. Clarke, and S. Robson, “Practical testing of the precision and accuracy of target image centring algorithms,” Proc. SPIE 2598, 65–76 (1995).
[Crossref]

Res. Nondestruct. Eval. (1)

B. Ferrer, J. Espinosa, J. Perez, S. Iborra, and D. Mas, “Optical scanning for structural vibration measurement,” Res. Nondestruct. Eval. 22, 61–75 (2011).
[Crossref]

Soil Dyn. Earthq. Eng. (1)

S. C. Stiros, “Errors in velocities and displacements deduced from accelerographs: An approach based on the theory of error propagation,” Soil Dyn. Earthq. Eng. 28, 415–420 (2008).
[Crossref]

Other (5)

Edmund Optics Catalog, http://www.edmundoptics.com .

A. K. Chopra, “Equations of Motion, Problem Statement and Solution Methods,” eds.,B. Stenquist and K. Scherwatzky, in Dynamic of Structures: Theory and Applications to Earthquake Engineering, 2nd Ed. (Prentice-Hall, 2001), pp. 23–25.

O. Gal, http://www.mathworks.com/matlabcentral/fileexchange/3215-fitellipse .

Mathworks Inc, http://www.mathworks.es/help/toolbox/images/ .

LS-DYNA Keyword User’s Manual (v.970), Livermore Software Technology Corporation, April2003.

Supplementary Material (2)

» Media 1: AVI (83977 KB)

» Media 2: AVI (10322 KB)

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Fig. 1.

Detection of a target (black line) is done by a set of pixels, here marked with a grid. A displacement of $1 / 2$ pixel to the left (gray line) is detected by a change in some of the detection pixels, now painted in gray. Although the structure has not moved a whole pixel, the geometrical bindings imposed on the target allow tracing the new contour and obtaining the new position.

Download Full Size | PPT Slide | PDF

Fig. 2.

Accuracy of the sub-pixel method for different dispersion errors. The rough appearance of the graph is due to the discrete nature of the calculations.

Download Full Size | PPT Slide | PDF

Fig. 3.

Video sequence for object tracking. Both sequences have been taken from 10 m distance. Target diameter is 5 cm. (a) Sequence from AOS camera, 250 fps, $100 px \times 100 px$ and no compression 8 bits AVI format (Media 1). (b) Sequence from CASIO camera, 420 fps, $35 px \times 35 px$ and AVI-jpeg RGB format (Media 2). This last sequence has been magnified and equalized in order to improve the visualization.

Download Full Size | PPT Slide | PDF

Fig. 4.

Target position obtained from sequence in Fig. 2(a) AOS and Fig. 2(b) Casio.

Download Full Size | PPT Slide | PDF

Fig. 5.

(a) Measured structure. (b) Position of the camera and pendulum. (c) Scheme of the experiment and model use for the Finite Element simulation.

Download Full Size | PPT Slide | PDF

Fig. 6.

Coordinates of the tracked center of the target.

Download Full Size | PPT Slide | PDF

Fig. 7.

(a) Fourier transform of the vibration of the column obtained from the horizontal position of the target (see Fig. 5). (b) Data fitting to Eq. (5).

Download Full Size | PPT Slide | PDF

Tables (1)

Table 1. Results from $F = the Target Position to an Attenuated Movement$

View Table

Equations (7)

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

A x^{2} + B x y + C y^{2} + D x + E y + F = 0 .

(x_{c}, y_{c}) = (\frac{- D}{2 A}, \frac{- E}{2 C}),

a = 2 \times \max [\sqrt{\frac{D^{2}}{4 A^{2}} + \frac{E^{2}}{4 A C} - \frac{F}{A}}, \sqrt{\frac{D^{2}}{4 A C} + \frac{E^{2}}{4 C^{2}} - \frac{F}{C}}] b = 2 \times \min [\sqrt{\frac{D^{2}}{4 A^{2}} + \frac{E^{2}}{4 A C} - \frac{F}{A}}, \sqrt{\frac{D^{2}}{4 A C} + \frac{E^{2}}{4 C^{2}} - \frac{F}{C}}] .

θ = \frac{1}{2} \arctan (\frac{B}{C - A}) .

(x^{'}, y^{'}) = (x + rnd (w), y + rnd (w)),

y (t) = A e^{- μ t} \sin (2 π f t + ϕ),

\begin{array}{l} A_{s} = 0.0933 mm & [0.0936 mm, 0.0943 mm], \\ μ_{s} = 14.61 s^{- 1} & [14.60 s^{- 1}, 14.75 s^{- 1}], \\ f_{s} = 66.7 Hz & [66.5 Hz, 66.8 Hz], \\ ϕ_{s} = - 1.572 rad & [- 1.575 rad, - 1.568 rad] . \end{array}

	$A (mm)$	$μ (s^{- 1})$	$f (Hz)$	$r^{2}$
Test 1	0.103 [0.089, 0.117]	15.6 [12.5, 18.7]	61.0 [60.5, 61.5]	0.9548
Test 2	0.096 [0.087, 0.105]	15.5 [12.5, 18.1]	61.6 [61.1, 62.5]	0.9675
Test 3	0.103 [0.093, 0.114]	15.8 [13.2, 18.3]	61.3 [60.9, 61.6]	0.9693
$Mean \pm std$	$0.101 \pm 0.004$	$15.6 \pm 0.4$	$61.3 \pm 0.3$

Abstract

References

2011 (2)

2010 (1)

2008 (3)

2007 (1)

2006 (1)

2005 (1)

2001 (1)

1998 (1)

1996 (1)

1995 (2)

1994 (1)

1993 (1)

Atzeni, C.

Bartoli, G.

Bernardini, G.

Brucksteinand, A. M.

Caetano, E.

Chopra, A. K.

Clarke, T. A.

Crocker, J. C.

Cunha, A.

Davis, J.

Delgado, R.

Espinosa, J.

Ferrer, B.

Fratini, M.

Gentile, C.

Gindy, M.

Grier, D. G.

Huang, Y.

Iborra, S.

Jansa, J.

Kuritaand, R.

Lee, J. J.

Maalen-Johansen, I.

Mas, D.

Nassif, H. N.

O’Gorman, A.

Parrini, F.

Perez, J.

Pieraccini, M.

Robson, S.

Saisi, A.

Shinozuka, M.

Short, T.

Shortis, M. R.

Stiros, S. C.

Tong, W.

Trinder, J. C.

Weeks, E. R.

Constr. Build. Mater. (1)

IEEE Trans. Inf. Theory (1)

ISPRS Journal of Photogrammetry and Remote Sensing (1)

J. Bridge Eng. ASCE (1)

J. Colloid Interface Sci. (1)

NDT & E Int. (2)

NDT & E International (1)

Nondestr. Test. Eval. (1)

Opt. Lett. (1)

Phys. Rev. E (1)

Proc. SPIE (3)

Res. Nondestruct. Eval. (1)

Soil Dyn. Earthq. Eng. (1)

Other (5)

Supplementary Material (2)

Cited By

Figures (7)

Tables (1)

Equations (7)

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