Detection of void and metallic inclusion in 2D piezoelectric cantilever beam using impedance measurements

doi:10.1007/s11709-018-0496-0

Front. Struct. Civ. Eng.

2019, Vol. 13

Issue (3) : 542-556 https://doi.org/10.1007/s11709-018-0496-0

RESEARCH ARTICLE

Detection of void and metallic inclusion in 2D piezoelectric cantilever beam using impedance measurements

S. SAMANTA^1,², S. S. NANTHAKUMAR¹, R. K. ANNABATTULA², X. ZHUANG^1,³(

)

¹. Institute of Continuum Mechanics, Leibniz University Hannover, 30167 Hannover, Germany
². Indian Institute of Technology, Madras Chennai 600036, India
³. College of Civil Engineering, Tongji University, Shanghai 200092, China

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Abstract

The aim of current work is to improve the existing inverse methodology of void-detection based on a target impedance curve, leading to quick-prediction of the parameters of single circular void. In this work, mode-shape dependent shifting phenomenon of peaks of impedance curve with change in void location has been analyzed. A number of initial guesses followed by an iterative optimization algorithm based on univariate method has been used to solve the problem. In each iteration starting from each initial guess, the difference between the computationally obtained impedance curve and the target impedance curve has been reduced. This methodology has been extended to detect single circular metallic inclusion in 2D piezoelectric cantilever beam. A good accuracy level was observed for detection of flaw radius and flaw-location along beam-length, but not the precise location along beam-width.

Keywords piezoelectricity impedance curve mode shapes inverse problem flaw detection curve shifting

Corresponding Author(s): X. ZHUANG

Just Accepted Date: 25 June 2018 Online First Date: 23 August 2018 Issue Date: 05 June 2019

Cite this article:

S. SAMANTA,S. S. NANTHAKUMAR,R. K. ANNABATTULA, et al. Detection of void and metallic inclusion in 2D piezoelectric cantilever beam using impedance measurements[J]. Front. Struct. Civ. Eng., 2019, 13(3): 542-556.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-018-0496-0
https://academic.hep.com.cn/fsce/EN/Y2019/V13/I3/542

Fig.1 Boundary conditions on 2D piezoelectric cantilever beam

Fig.2 Comparison between piezoelectric and dielectric impedance curve

Fig.3 A cantilever beam with a hole of radius r

Fig.4 Mode shape and impedance curves for 1st mode. (a) The first mode shape of a beam without hole; (b) impedance curves for a hole at different values of x-distance

Fig.5 Mode shape and impedance curves for 2nd mode. (a) The second mode shape of a beam without hole; (b) impedance curves for a hole at different values of x-distance

Fig.6 Mode shape and impedance curves for the 3rd mode. (a) The third mode shape of a beam without hole; (b) impedance curves for a hole at different values of x-distance

Fig.7 Typical curves indicating shift of the peaks with change in radius, r with x = 20 mm, y = 2.5 mm (beam dimension= 40 mm × 5 mm). (a) The first mode; (b) the second mode; (c) the third mode

Fig.8 Typical curves indicating shift of the peaks with change in x-coordinate with r = 0.75 mm, y = 2.5 mm (beam dimension= 40 mm × 5 mm). (a) The first mode; (b) the second mode; (c) the third mode

Fig.9 Typical curves indicating shift of the peaks with change in y-coordinate with r = 0.75 mm, x = 20 mm (beam dimension= 40 mm × 5 mm). (a) The first mode; (b) the second mode; (c) the third mode

Fig.10 Flow chart of method of solution

Fig.11 Variation of optimization function over ‘x’ and ‘r’ for a fixed ‘y’ with hole location at x = 30, r = 6 (value, on ‘x’ and ‘r’ axes indicates the ith data point, hence does not have unit)

Fig.12 Variation of optimization function over ‘x’ and ‘r’ for a fixed ‘y’ with inclusion location at x = 51 mm, y = 6 mm and r = 1.2 mm

Fig.13 Initial guess of void parameters (black: Target void; solid blue: The 1st initial guess; dashed blue: Other initial guesses (one guess at a time))

Fig.14 Optimization function curve for 13 initial guesses (local minima are indicated with coordinates)

Fig.15 Void location after 13 function-evaluations (black: Target void; blue: Computationally found)

Fig.16 Void location after 36 function-evaluations (black: Target void; blue: Computationally found)

Fig.17 Void location after 72 function-evaluations (black: Target void; blue: Computationally found)

Fig.18 Void location after 87 function-evaluations (black: Target void; blue: Computationally found)

Fig.19 Void location after 117 function-evaluations (black: Target void; blue: Computationally found)

Fig.20 Final void location after 155 function-evaluations (black: Target void; blue: Computationally found)

Fig.21 Initial guess of inclusion parameters (black: Target inclusion; solid blue: The 1st initial guess; dashed blue: Other initial guesses (one guess at a time))

Fig.22 Inclusion location after 13 function-evaluations (black: Target inclusion; blue: Computationally found)

Fig.23 Inclusion location after 35 function-evaluations (black: Target inclusion; blue: Computationally found)

Fig.24 Inclusion location after 54 function-evaluations (black: Target inclusion; blue: Computationally found)

Fig.25 Final inclusion location after 65 function-evaluations (black: Target inclusion; blue: Computationally found)

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[1]	Ali KARIMPOUR, Salam RAHMATALLA. Identification of structural parameters and boundary conditions using a minimum number of measurement points[J]. Front. Struct. Civ. Eng., 2020, 14(6): 1331-1348.
[2]	Mohammad SALAVATI. Approximation of structural damping and input excitation force[J]. Front. Struct. Civ. Eng., 2017, 11(2): 244-254.

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