# Pipe Crack Recognition Based on Eddy Current NDT and 2D Impedance Characteristics
## 3 Feature Extraction of the ECT Signal Based on the Impedance Diagram
### Synthesis of the Impedance Diagram  
To synthesize the impedance diagram, we first retrieve the real and imaginary parts of the eddy current signal. As the original signal possesses low energy and low signal-to-noise ratio, the LIA is used to extract and decompose the signal. It should be noted that not only the real and imaginary parts of the eddy current signal reflecting the coil impedance are achieved, but also the signal-to-noise ratio of the detection signal is greatly improved [19; 20]. Figure 5 shows the test signal and impedance diagram of the defects in the girth weld. Specifically, Figure 5a plots the real part achieved by the LIA, and Figure 5b plots the imaginary part.  
The real and imaginary parts of the ECT signal represent the abscissa and the vertical coordinate, respectively. A two-dimensional trajectory map reflecting the impedance change of the probe may be achieved, hereinafter referred to as an impedance diagram. Figure 5c plots the impedance diagram of a defect in the girth weld. It may be seen from this figure that the impedance diagram is a pattern composed of two straight lines with different slopes. Experimentation shows that different geometric characteristics occur in the impedance diagrams generated by defects of different types and sizes. The physical properties of the cracks have a certain impact on the measurement and characteristics of the impedance maps. The larger the depth of the crack is, the larger the amplitude of the original eddy current signals. This, in turn, results in a more obvious geometric characteristic of the impedance map. However, when the width of the crack is close to the probe, the characteristics of the impedance map significantly change. Moreover, the positions of the cracks have a certain influence. The result is greatly different between the two sides of the girth weld and the middle of the weld. This paper discusses a particular situation where the crack is located in the middle of the girth weld. Figure 6 demonstrates typical impedance diagrams of girth weld defects. From this figure, great differences may be seen in the geometrical characteristics between the impedance diagrams of defective and non-defective welds. Therefore, the key problem of the identification system is to determine which geometric characteristic parameters in the impedance diagram should be extracted as the input parameters of the neural network.  
Figure 5: Original signal and impedance diagram of a defect in the girth weld. (**a**) Real part of the defect signal. (**b**) Imaginary part of the defect signal. (**c**) Impedance diagram of the defect at the girth weld.  
Figure 6: Impedance diagram of typical defective and non-defective girth welds.  
By selecting five of the characteristic components of the maximum criterion values as the characteristic parameters of the impedance diagram, the classification of the data set yields satisfactory results. The selected feature components are as follows: the expectation of the slope of fitted straight lines, the expectation of closed curve areas, the variance of closed curve areas, the variance of the slope of fitted straight lines and the number of closed curves that exceed the threshold area. We next use the Hough transform and the contour extraction algorithm to extract the characteristic parameters of the impedance diagram.