## 3 Results
### FEM Test Case
#### 3.1.6 Results Total  
The correlation results of the reference and the iteration's power spectrum is added to the location of maximum voltage in each window. Furthermore, as the correlation result is typically a large number, the final result is normalised by the maximum value, which is typically the pipe end. This is illustrated in Figure 11 where it can be seen that the value of 0.1 is associated exactly to the centre of the defect signal. As illustrated, knowing only the excitation waveform, the approximate location of the defect is clearly detectable using this method.  
Figure 11: The final result (red line) overlaid on the time-domain signal (black line) from the FEM Case. The defect size is 3% cross-sectional area (CSA) and the excitation frequency is 30 kHz.  
Figure 10: Example of an outlier case detected using Condition Four (C4), where (**a**) shows the time domain of the iteration window and (**b**) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.  
The binary detection results of each condition for each iteration, as well as the total results, is demonstrated in Figure 12. In this figure, it is clearly demonstrated outliers exist in the results of each individual condition, but by combining all of them, only the iterations associated with the defect and pipe end are being detected. Furthermore, high correlation results are achieved from all iterations, irrespective of it being noise or defect; which is the main reason why doing a cross-correlation is not enough for detecting the defect location in the case of guided-wave testing. However, even with the existence of the coloured-noise, by checking the mentioned condition, the detection becomes possible.  
Figure 12: The generated results from the FEM test case.  
In the same format, Figures 13 and 14 show the results achieved from the 3% CSA defect from the experimental results. The same aforementioned conclusions can be drawn with regard to Figure 13. However, it can be seen that in the experimental results since the transfer functions are more linear, the outcome of condition 4 (C4) is true in most iterations. The results are shown in Figure 14, where the defect location is clearly marked using this algorithm. In overall, conditions one and three are the most effective ones which filter out most of the outliers from the tests.  
These five conditions have not been optimised. Nevertheless, they were all designed based on the physical phenomena of guided-waves propagation within pipes. As can be seen in both the results of FEA and experimental tests, only in C3 and C4 could the defects be detected. However, having more relevant conditions, especially for practical inspection of pipes, may increase the certainty of the generated results. Nonetheless, the conditions are not necessarily required to be in the same Fourier Domain as stated in this algorithm, and the technique can be combined with other approaches, such as Wiener filtering, in order to improve its performance.  
Figure 13: The generated results from the experimental pipe with a defect of 3% CSA and testing frequency of 38 kHz.