Reduction of the Velocity Impact on the Magnetic Flux Leakage Signal
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Abstract
The velocity effect on the magnetic flux leakage (MFL) signal was investigated in this paper. Experiments were performed for velocity of the MFL tool within the range of 0–2 m/s. The velocity was not constant during each measurement to imitate real operational conditions of the MFL tool. Two components of the leakage were measured, i.e. the tangential to the motion direction (x) and the normal to the investigated surface (z). In addition to them, the gradient of the normal component in x direction was measured with the use of two adjacent sensors. The normal component was found to be the most sensitive to the velocity effect. It was shown that the baseline value of the normal component is proportional to the velocity. An empirical compensation scheme was formulated, and it was used to minimize distortions of the normal component caused by the velocity effect. The finite element method was used to study the distribution of velocityinduced eddy currents in the investigated plate. It was stated that eddy currents generated below the poles lead to a change of plate magnetization as well as to a change of magnetic field distribution above the top surface of the plate, what is observed as a shift of the MFL signal baselines.
Keywords
Magnetic flux leakage Velocity effect Eddy current Finite element method1 Introduction
Equation (1) indicates that eddy current density reaches the maximum when B is perpendicular to v. In the case of a yoke magnetizer travelling above a surface of a steel object, eddy current is generated mainly under the magnetizer poles. Eddy current generated below the poles reduces the magnetic flux density in the steel object in accordance to Lenz’s law [3, 4]. Furthermore, initially symmetric distribution of B inside the object becomes asymmetric as the velocity rises [3, 6]. The area of the highest magnetization migrates towards the back positioned pole of the magnetizer [4]. Some of components of the MFL signal are also modified due to the velocity. Baselines of this components as well as amplitudes of detected anomalies are in general nonlinearly dependent on the velocity [1, 7, 8]. The anomalies of the MFL signal carry information about shapes of defects e.g. metal losses. However, as reported in [4, 5, 9, 10], a profile of the signal anomaly becomes more distorted (usually more asymmetric) as the velocity increases. All these effects hinder evaluation of defect dimensions and its shape as well. One can define two different approaches to solve this problem. First approach involves optimization of an MFL tool in order to minimize the velocity influence on the MFL signal [11]. Second approach is based on postprocessing and transformation of the signal to its stationary form.
Only few studies among those devoted to the issue of velocityinduced eddy current include a proposition of restoration of the MFL signal to its stationary form [5, 12, 13, 14]. In his thesis [12] Mandayam presented a method of MFL signal processing that lead to a velocity invariant MFL signal. He listed two classes of compensation schemes. A scheme of first class requires the velocity value as input data to perform the compensation of the signal. A scheme of second class does not require such data and this kind of the scheme was used by Mandayam to obtain the velocity invariant MFL signal. In this case, an unsupervised learning algorithm was used to determine coefficients of the restoration filter. Lei et al. [13] used a learning algorithm, which was based on radial basis function neural network, to compensate velocity effect on the MFL signal. Accuracy of those and similar compensation schemes depends on quantity and quality of input training data. Computer simulations can provide large amount of training data. Experiments are more timeconsuming and expensive in this case but a compensation scheme based on experimental data is usually more robust than simulationbased one. In comparison to aforementioned compensation schemes one proposed by Park and Park [5] is much simpler. For a particular class of MFL signal anomalies they performed an analysis of various anomaly parameters such as a peaktopeak value of an anomaly as a function of the velocity. So obtained relations were used to restore the stationary form of the MFL signal. Drawback of this approach is limited application of so formulated compensation scheme to the specific class of MFL signal anomalies.
Most studies presented in literature of the subject include a small number of experimental results. Therefore, in this study MFL signal dependence on the velocity was investigated using experimental data. A range of the velocity was selected so as to fill the data gap existing for relatively low velocities, i.e. up to 2 m/s. Presented study was focused on signal baseline dependence on the velocity of the MFL tool.
2 Experimental Setup
The MFL tool was moved with the use of manual drive. Its displacement was parallel to a plate symmetry plane that is coplanar with the section A. Although signals coming from ten channels were recorded, only those from the channel nearest to the plate center are presented in this study.
3 Results and Discussion
3.1 Experimental Results
3.2 Compensation of the MFL Signal
The tangential component, B_{x}, is less dependent on the velocity compared with B_{z}. Moreover, although B_{x} also increases with the velocity, it does not manifest linear dependence. The gradient, ∂B_{z}/∂x, is the least dependent on the velocity. The relation between ∂B_{z}/∂x and the velocity is nonmonotonic and characterized by weak fluctuations. The most probable reason of these fluctuations is variable acceleration of the MFL tool. B_{z} is an implicit function of time, B_{z}(x(t), v(t)). As B_{z} is approximately proportional to the velocity, v(t), it can be deduced that its partial derivative is proportional to acceleration of the MFL tool, dv(t)/dt.
3.3 Numerical Analysis
Due to material nonlinearity, the problem was solved with the use of GMRES (Generalized Minimal Residual method) algorithm. The criteria of convergence was achieved when the residual was less than ε = 0.01.
4 Conclusions

Geometry and materials of an MFL tool,

Position of sensors,

Properties of a ferromagnetic object under investigation.
The component normal to the top surface of the steel plate, B_{z}, was recognized as the most sensitive to velocity changes in time. Proposed compensation scheme takes into account only the impact of eddy currents induced under the poles of the magnetizer. Reduction of the impact of eddy currents induced in the vicinity of a metal loss will be the subject of future research. Nonetheless, the results obtained with the use of the simplified compensation scheme suggest the possibility of reducing MFL signal distortions, when the velocity of the MFL tool is variable. Strong enough distortions of the MFL signal can be wrongly classified as fingerprints of defects. Proposed compensation scheme reduces probability of this kind of false positive indications. In the presented study, measured MFL signal were postprocessed, but one can imagine that the compensation scheme could work online as well. Online compensation requires a sensor with offset terminals to stabilize the operating point of the sensor. Proportional to the velocity, properly scaled, and inversed voltage feeds the offset input. Such a kind of online compensation can protect the sensor against its saturation. Future work will be focused on implementation of abovementioned solutions to the MFL measuring system.
Notes
Acknowledgements
This work was supported by the National Centre for Research and Development, Poland [project INNOTECHK2/IN2/53/182767/NCBR/12].
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