Corrosion detection in a 2D domain with a polygonal boundary

Bacchelli, Valeria; Veneziani, Alessandro; Vessella, Sergio

doi:10.1515/jiip.2010.011

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…A surface defect is naturally modeled by means of a function of two variables when it is originated by mechanical collisions or some kind of corrosion (for example, uniform corrosion or erosioncorrosion). On the other hand, pitting corrosion or cracking (see for example [21] (section 1.5)) must be modeled by means of a curve that is not the graph of a function ( [12]).…”

Section: The Inverse Problemmentioning

confidence: 99%

A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

Inglese¹,

Olmi

2017

J Nondestruct Eval

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Let Ω be a metallic plate whose top inaccessible surface has been damaged by some chemical or mechanical agent. We heat the opposite side and collect a sequence of temperature maps u . Here, we construct a formal explicit approximation of the damage θ by solving a nonlinear inverse problem for the heat equation in three steps: (i) smoothing of temperature maps, (ii) domain derivative of the temperature, (iii) thin plate approximation of the model and perturbation theory.Our inversion formula is tested with realistic synthetic data and used in a real laboratory experiment.

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Section: The Inverse Problemmentioning

confidence: 99%

A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

Inglese¹,

Olmi

2017

J Nondestruct Eval

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“…Zhang [19] quantitatively analyzed the relationship between crosssection loss of cable and magnetic signal by establishing a finite element model. Bacchelli [20] studied the reconstruction of the damaged profile of a thin metallic plate, which is possible by measuring an electrostatic current properly induced by a potential in an accessible part of the boundary. Han [21] estimated the location, shape and size of the corrosion area by analyzing the surface temperature distribution of the sample.…”

Section: Introductionmentioning

confidence: 99%

Research on the Method of Predicting Corrosion width of Cables Based on the Spontaneous Magnetic Flux Leakage

Zhang

Zhao

et al. 2019

Materials

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The detection of cable corrosion is of great significance to the evaluation of cable safety performance. Based on the principle of spontaneous magnetic flux leakage (SMFL), a new method for predicting the corrosion width of cables is proposed. In this paper, in order to quantify the width of corrosion, the parameter about intersecting point distance between curves of magnetic flux component of x direction at different lift off heights (Dx) is proposed by establishing the theoretical model of the magnetic dipole of the rectangular corrosion defect. The MATLAB software was used to analyze the influencing factors of Dx. The results indicate that there exists an obvious linear relationship between the Dx and the y (lift off height), and the Dx–y curves converge to near the true corrosion width when y = 0. The 1/4 and 3/4 quantiles of the Dx–y image were used for linear fitting, which the intercept of the fitting equation was used to represent the predicted corrosion width. After the experimental study on the corrosion width detection for the parallel steel wire and steel strand, it is found that this method can effectively improve the detection accuracy, which plays an important role in cable safety assessment.

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On a fixed point study of an inverse problem governed by Stokes equation

Chakib

Nachaoui

et al. 2018

Inverse Problems

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This work deals with domain decomposition like methods for solving an inverse Cauchy problem governed by Stokes equation. As it is well known, this problem is one of highly ill-posed problems in the Hadamard’s sense (Hadamard 1953 Lectures on Cauchy’s Problem in Linear Partial Differential Equations (New York: Dover)). To solve this problem, we develop a technique based on its reformulation into a fixed point one involving a Steklov like operator. Firstly, we show the existence of its fixed point using the topological degrees of Leray–Schauder tools. Then, we propose a fixed point algorithm allowing us to reproduce the alternating one of Kozlov Mazya (1991 Comput. Math. Math. Phys. 31 45–52). So the proposed approach can be considered as a generalization of Kozlov–Mazya algorithm, since it offers the opportunities to exploit other domain decomposition algorithms for solving this inverse problem. Finally, we investigate the numerical approximation of this problem, using Robin–Robin domain decomposition algorithm and the finite element method. The obtained numerical results show the efficiency of the proposed approach.

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Corrosion detection in a 2D domain with a polygonal boundary

Cited by 4 publications

References 8 publications

A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

Research on the Method of Predicting Corrosion width of Cables Based on the Spontaneous Magnetic Flux Leakage

On a fixed point study of an inverse problem governed by Stokes equation

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