## 1 Introduction  
Current technological developments typically require materials with improved properties. Therefore, methods of detecting and locating defects both on the surface and inside these materials without causing damage are becoming increasingly important. The widely applied industrial methods for addressing those demands are called non-destructive testing (NDT) methods, including the methods of eddy current testing (ECT), radiography testing, ultrasonic testing, magnetic particle testing, penetrant testing and so on. The ECT (Figure 1) is a specialized NDT method for testing conductor material and has been widely used in inspections of aerospace structures and engines, equipment in the nuclear industry, fossil fuel power facilities and pipelines, wires, and plates in the manufacturing process [1; 2; 3; 4]. The ECT method can also be applied in tasks applicable to many industries such as thickness measurements, quality inspections, coating applications and surface treatments. Compared with other NDT methods, the ECT method has many advantages such as high detection sensitivity, no requirement for a coupling agent, and suitability for the on-line detection of work pieces. Moreover, this method is appropriate for magnetic and non-magnetic conductors at common or high temperatures. However, as the frequency increases, the eddy current tends to be distributed on the surface due to the skin effect, therefore comprehensive considerations are required to determine the input parameters for the ECT method. The principle of the ECT is shown in Figure 1. An exciting coil with an alternative current is placed on one side of the material, and a pick-up coil is placed on the other side. In some cases, it is impossible to place the exciting coil and pick-up coil on two sides of sample, they can be set on the same side. The magnetic field generated by the exciting coil will induce eddy current \(\mathbf{j}\) inside the material, which also induces an alternative magnetic field. The magnetic field generated by the exciting coil and inducing eddy current are detected by measuring the impedance of the pick-up coil. When a defect is present, the induced eddy current will change correspondingly and yield to a signal change in the pick-up coil. Note that a phase difference occurs between the exciting coil and pick-up coil as shown in Figure 1a,b. By identifying this signal, the defect in the test sample can be identified as well [5,6]. Magnetic sensors (AMR (anisotropic magnetoresistance), Hall and GMR (giant magnetoresistance)) have been introduced in the ECT system in recent years to provide improved sensitivity and allow for lower frequencies during testing. [PERSON] designed and implemented neural network classification schemes to establish a reduced number of features for two types of defects induced in an aluminium plate [7]. [PERSON] estimated the crack's dimension in aluminium based on two extracted parameters from the GMR output voltage [8]. [PERSON] also proposed a velocity induced eddy current testing (VIECT) excited by a permanent magnet (PM) or a DC coil, in which relative motion occurs between the sample and the excitation [9]. [PERSON] proposed the Lorentz force eddy current testing (LET) method that utilizes a PM to test the defects, which induces eddy current by the relative motion. They use a force sensor to measure the reaction of the Lorentz force acting on the PM [10, 11, 12]. [PERSON] used a laser cantilever magnet (LCM) system to measure the Lorentz force [13, 14, 15] and [PERSON] detected cracks by array probes consisting of PMs based on speckle pattern interferometry [16]. However, the traditional ECT method has a few disadvantages. For example, the output signal of the traditional ECT method is very sensitive to the distance between the probe and the test sample; thus, the signal can be disturbed easily in practice by factors such as varied coating thicknesses, irregular samples surface or operator movement (lift-off).