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This paper aims to study the influence of different reinforcement methods on crack monitoring characteristics of eddy current array sensors, and the sensors with two different reinforcement methods, SUS304 reinforcement and permalloy reinforcement, are proposed.

First, the finite element model of the sensor is established to analyze the influence of the reinforcement plate’s electromagnetic parameters on the crack identification sensitivity. Then, the crack monitoring accuracy test of sensors with two reinforcement methods is carried out. Finally, the fatigue crack monitoring experiments with bolt tightening torques of 45 and 63 N · m are carried out, respectively.

In this study, it is found that the crack identification sensitivity of the sensor can be improved by increasing the relative permeability of the reinforcement plate. The crack monitoring accuracy of the sensors with two different reinforcement methods is about 1 mm. And the crack identification sensitivity of the sensor reinforced by permalloy reinforcement plate is significantly higher than that of the sensor reinforced by SUS304 reinforcement plate.

The sensor reinforced by reinforcement plate can work normally under the squeezing action of the bolt, and the crack monitoring sensitivity of the sensor can be significantly improved by using the reinforcement plate with high relative permeability.

The flexible eddy current array sensor has the characteristics of lightweight and flexibility, which has a great application prospect in the field of fatigue crack monitoring. But the exciting layout and feature signal extraction have a great influence on the crack monitoring characteristics of the sensor. This paper aims to propose a method using crack disturbed voltage as sensitivity to characterize crack propagation.

Flexible eddy current array sensors with reverse and codirectional exciting layout are proposed, and the advantages and disadvantages of three characterization methods based on the change of trans-impedance amplitude, the change of the trans-impedance’s real and imaginary part and the crack disturbed voltage are compared and analyzed by finite element simulation. Finally, the fatigue crack monitoring experiment is carried out.

The crack disturbed voltage and the change of trans-impedance’s imaginary part can effectively characterize the crack propagation for sensors with different exciting layouts. The codirectional exciting layout sensor has better crack identification sensitivity than the reverse exciting layout sensor, especially the induction coil 2. When the distance between the exciting coil and the induction coil is 0.1, 0.2 and 0.3 mm, it is increased by 372.09%, 295.24% and 231.43%, respectively.

Crack disturbed voltage can effectively characterize the crack propagation for sensors with two different exciting layouts.

Flexible eddy current array (FECA) sensor is flexible and light in weight, which has broad application prospects in structural health monitoring. But, the sensor’s sensing channel number is more, increasing the added mass of sensor networks. This paper aims to reduce the sensing channel number by changing the sensing coil layout.

In this paper, FECA sensors with series sensing coil (SSC) layout and interactive sensing coil (ISC) layout are proposed, which reduce the number of sensor’s channels by half. Then, the variation of the output signal of the sensor when the crack expands along both sides of the hole is analyzed by simulation model. Finally, the fatigue crack monitoring experiment is carried out.

For the SSC layout, the simulation results show that the amplitude of each SSC group of the sensor increases when the crack propagates to the left or right. For the ISC layout, when the crack propagates on the right side of bolt hole, the induced voltage of each ISC group decreases. When the crack propagates on the left side of bolt hole, the induced voltage of each ISC group increases. The experiment results are consistent with simulation results, which verifies the correctness of simulation model. Compared with SSC layout, the ISC layout can judge the crack propagation direction. And the crack monitoring accuracy is 1 mm.

The research results provide a certain reference for reducing the number of sensor’s sensing channels. Results of the simulation and experiment show that the ISC layout can judge the crack propagation direction, and the crack monitoring accuracy is 1 mm.

The purpose of this paper is to introduce an in line non‐destructive inspection tool instrumented pipeline inspection gauge (IPIG) and the need for secondary sensors in it; and to design a proper configuration of eddy current based secondary sensor under given design constraints.

The objective is achieved by designing a simple configuration, testing it experimentally and modifying it as per requirements.

An optimized configuration is arrived at under given set of constraints.

This paper presents a novel method to design an eddy current sensor, and especially addresses electromagnetic experts involved in coil based sensor designs.

The purpose of this study is to determine the contamination level in natural water resources because the tremendous development in the agriculture sector has increased the amount of contamination in natural water sources. Hence, the water is polluted and unsafe to drink.

Three types of sensor arrays were suggested: parallel, star and delta. The simulation of all types of sensor array was carried out to calculate the sensors’ impedance value, capacitance and inductance during their operation to determine the best sensor array. The contamination state was simulated by altering the electrical properties values of the environmental domain of the model to represent water contamination.

The simulation results show that all types of sensor array are sensitive to conductivity, σ, and permittivity, ɛ (i.e. contaminated water). Furthermore, a set of experiments was conducted to determine the relationship between the sensor’s impedance and the water’s nitrate and sulphate contamination. The performance of the system was observed where the sensors were tested, with the addition of distilled water with different concentrations of potassium nitrate and potassium sulphate. The sensitivity of the developed sensors was evaluated and the best sensor was selected.

Based on the outcomes of the experiments, the star sensor array has the highest sensitivity and can be used to measure nitrate and sulphate contaminations in water.

The star sensor array presented in this paper has the potential to be used as a useful low-cost tool for water source monitoring.

The purpose of this paper is to present a new approach for computing by measuring and testing related 3D Eddy currents. In the process, a magnetic vector is formulated from the theoretical setup and obtained results from relevant applications are checked for the consistency of the theory. Besides, cracks detection as well as its propagation is studied through the two parameters: SIF and J-integral. A simulation by a numerical approach using finite-element discretization of 3D governing equations is employed to detect damaged zones and cracks. This approach has been used in the aircraft industry to control cracks. Besides, it makes it possible to highlight the defects of parts while preserving the integrity of the controlled products. Obtained results are compared and agreed with those of other researchers.

Finite-element discretization of 3D for solving problem in eddy current testing is presented in this paper. The main idea is the introduction of categorization for the shape reconstruction using the non-destructive testing by 3D-EC. The results are presented for a simple eddy current problem using the finite-element method as an experimental support.

In this research work, results of the various cases of simulation have been obtained. From these results of various boxes of simulation, one can conclude that the calculation of the impedance in only one point is not enough to confirm the presence or the absence of a defect for materials. Then, this confirmation leads us to the calculation of the impedance along the plate. The detection of an external defect requires the energy of the sensor by high frequencies .The position of defect (internal, in the middle, external) has a large effect on the impedance. The use of this sensor type in industrial application is frequent because of its precision (minimal error) and its low costs. The major disadvantage of this type of sensor lies in the fact that it is unable to detect a defect.

This paper fulfills an identified need to detect cracks in materials and eventually to study their propagation.

The purpose of this paper is to solve an inverse problem of structure recognition arising in eddy current testing (ECT) – type NDT. For this purpose, the space mapping (SM) technique with an extraction based on the Gauss‐Newton algorithm with Tikhonov regularization is applied.

The aim is to have a computationally fast recognition procedure of defects since the monitoring results in a large amount of data points that need to be analyzed by 3D eddy current model. According to the SM optimization, the finite element method (FEM) is used as a fine model, while the model based on an integral method such as the volume integral method (VIM) serves as a coarse model. This approach, being an example of a two‐level optimization method, allows shifting the optimization load from a time consuming and accurate model to the less precise but faster coarse surrogate.

The application of this method enables shortening of the evaluation time that is required to provide the proper parameter estimation of surface defects.

In this work only the specific kinds of surface defects were considered. Therefore, the reconstruction of arbitrary shapes of defects when using real measurement data from ECT system can be treated in further research.

The paper investigated the eddy current inverse problem. According to aggressive space mapping method, a suitable coarse model is needed. In this case, for the purpose of 3D defect reconstruction, the reduced VIM approach was applied. From a practical view point, the authors demonstrated that the two‐level inversion procedures allow saving of up to 50 percent CPU time in comparison with the optimization by means of regularized Gauss‐Newton algorithm in the same FE model.

The inverse problem in the eddy current (EC) imaging of metallic parts is an ill‐posed problem. The purpose of the paper is to compare the performances of regularized algorithms to estimate the 3D geometry of a surface breaking defect.

The forward problem is solved using a mesh‐free semi‐analytical model, the distributed point source method, which allows EC data to be simulated according to the shape of the considered defect. The inverse problem is solved using two regularization methods, namely the Tikhonov (l2) and the 3D total variation (tv) methods, implemented with first‐ and second‐order algorithms. The inversion performances were evaluated in terms of both mean square error (MSE) and computation time, while considering additive white and colored noise, respectively, standing for acquisition errors and model errors.

In presence of colored noise, the authors found out that first‐ and second‐order methods provide approximately the same result according to the SEs obtained while estimating the defect voxels. Nevertheless, in comparison with (l2), the (tv) regularization was proved to decrease the MSE by 10 voxels, at the cost of less than twice the computational effort.

In this paper, an easy to implement mesh‐free model, based on virtual defect current sources, was used to generated EC data relative to a defect positioned at the surface of a metallic part. A 3D total variation regularization approach was used in combination with the proposed model, which appears to be well suited to the reconstruction of volumic defects.

Eddy current testing (ECT) is widely used in the non-destructive evaluation of materials in different industries. In this paper, ECT has been used to detect the presence of cracks in boiler tubes. The most important feature in ECT is the way in which the eddy currents are induced and detected in the sample. The authors have tried to design a new sensor that is effective in detecting cracks in boiler tubes. The purpose of this paper is to study the response of this sensor to cracks of different depths and dimensions.

The designed eddy current sensor is equipped with an exciting and a sensing coil. An alternating current is passed through the exciting coil thus producing eddy currents. The sensing coil scans the outer surface of the boiler tube and looks for abrupt changes in output signals resulting from sharp discontinuities in structure.

The sensor designed can detect the position of the crack. The presence of crack is indicated by a reduction in the induced voltage in the sensing coil. The sensor is also used for characterisation of the cracks, and can distinguish between cracks of varying shape, size and depth. The sensitivity of the sensing coil to cracks is dependent on operating conditions, such as frequency and voltage of the excitation signal.

The new sensor designed is used to detect defects in boiler tubes in power plants. However, the operating conditions, such as excitation frequency and amplitude will vary with composition of the boiler tubes.

The new eddy current sensor designed for crack detection is an E-shaped core coil. The shape of the coil provides a high permeability path to the magnetic field lines, thus reducing the loss of the field produced. This helps in improving the sensitivity of the coil, and makes the detection system effective in detecting hairline cracks.

The purpose of this paper is to introduce a perturbation method for the A‐χ geometric formulation to solve eddy‐current problems and apply it to the feasibility design of a non‐destructive evaluation device suitable to detect long‐longitudinal volumetric flaws in hot steel bars.

The effect of the flaw is accurately and efficiently computed by solving an eddy‐current problem over an hexahedral grid which gives directly the perturbation due to the flaw with respect to the unperturbed configuration.

The perturbation method, reducing the cancelation error, produces accurate results also for small variations between the solutions obtained in the perturbed and unperturbed configurations. This is especially required when the tool is used as a forward solver for an inverse problem. The method yields also to a considerable speedup: the mesh used in the perturbed problem can in fact be reduced at a small fraction of the initial mesh, considering only a limited region surrounding the flaw in which the mesh can be refined. Moreover, the full three‐dimensional unperturbed problem does not need to be solved, since the source term for computing the perturbation is evaluated by solving a two‐dimensional flawless configuration having revolution symmetry.

A perturbation method for the A‐χ geometric formulation to solve eddy‐current problems has been introduced. The advantages of the perturbation method for non‐destructive testing applications have been described.