J. Jarmulak, “A Method of Representing and Comparing Eddy Current Lissajous Patterns”, in: Review of Progress in Quantitative Nondestructive Evaluation, Vol. 16, D.O. Thompson and D.E. Chimenti (eds.), Plenum Publishing, New York, 1997, pp. 303-308. (pdf)
In eddy current testing of heat-exchanger pipes the signal of the scanning probe is usually presented in the complex plane as a Lissajous curve. The size (amplitude) of the curve corresponds roughly to the volume of the defect. The phase is related to the depth of the defect and its location (inside or outside defects). Finally, the shape of the curve depends on the form of the defect.
The commercially available systems for EC inspection usually use only the phase and amplitude information. After the detection (with amplitude and phase thresholds), the defects are sized using calibration curves and the phase information. Such a system is not foolproof, usually because of incorrect or spurious defect detection. Therefore, in practice the classification made by the system is usually checked afterwards by a human operator. The operator can quickly determine whether the computer classification is correct just
looking at the shape of the curve.
Use of only amplitude and phase information limits the capabilities of the system. For example, it is possible that defects can have the same phase indication and different depths. This can lead to defect over- or undersizing. Sometimes, however, the defect type could be determined based on the shape of the Lissajous curve and then either correction factors could be applied or different calibration could be curves used. Generally, the Lissajous pattern carries more information about the flaw than can be extracted using amplitude and phase only.
Systems that use the curve-shape information usually comprise various classifiers, which, after having been trained with example patterns, can categorize new signals into predefined classes. However, it seems that such systems are usually limited to applications in nuclear-power and aircraft industries. There the problem areas are relatively well defined, and there are resources available to gather enough data for training of the system.
In common inspection practice the problem is not so well defined, for example various types of heat exchangers with various types of defects can be inspected using the same inspection system. This means that there is always a possibility of coming across a defect type which did not occur before (and therefore was not in the training set) and which could be falsely classified. Classification into several predefined classes is therefore not so appropriate here. In such cases one could try to compare shapes instead of classifying them. Comparison can be used even when the number of example shapes is too small to construct a reliable classifier. Also, not recognized shapes are properly reported as such and not classified into a wrong category, as can be the case when classifiers are used.
An automated system could be constructed which would perform automatic evaluation of the defects it recognizes, and the remaining defects would be presented to the operator for the evaluation. The defects would be recognized by means of comparing their shapes to the example defects.
This paper presents a method for representing Lissajous curves and for comparing them which is based on the curvature of the curve. It also shows why the Fourier descriptors are not directly applicable for curve comparison.