## 4 Conclusions  
In this paper, a novel method is proposed to detect the location of defects using the known excitation power spectra of the torsional waves in guided-wave inspection of pipelines. For doing so, as opposed to traditional inspection using time-domain signal, the spectral domain of the signal is compared with the characteristics of the known excitation sequence. The method works by applying a moving window to the received signal from the inspection, where in each iteration the signal is normalised and its corresponding power spectrum is generated. Since both defect signal and noise are within the same frequency band, by only measuring the correlation between reference and iterations power spectrum, the defect signal will not be distinguishable. Therefore, before measuring the correlation, a total of five conditions were checked to verify that a similar power spectrum to the reference was achieved:  
* Centre frequency shift must be small.
* Considering the 10 dB bandwidth of the iteration's power spectrum, the magnitude of each respective frequency bin must be increased when moving toward the centre frequency.
* The achieved magnitude from the neighbouring bins to the centre frequency must be closely related.
* Frequencies outside the 10 dB bandwidth must have less magnitude than the minimum one achieved from within the 10 dB bandwidth.
* The maximum magnitude achieved must be less than the one from the reference.  
For each condition, a safety margin is set by the user to neglect minor differences due to the digitisation of the signals and the limitation of the available sample in each window. Nonetheless, before applying the algorithm on guided-wave data from pipes, these limits can be fixed as they are set just to provide a tolerance. On the other hand, this method can also be tested in traditional ultrasonic testing, where there might be a need of tweaking these parameters.  
The algorithm was initially developed and validated on synthesised data from FEM. Afterwards, experimental data form real pipes with defect CSA sizes of 2, 3 and 4%, were used to validate its capability and also its limitations. It was illustrated that the choice of excitation frequency is a trade-off between the ability of the system to generate the given excitation sequence and having highly dispersive flexural waves (which are considered as the main source of the noise in these tests). As such, it was observed that frequencies in the range of 34 to 40 kHz are optimal, and can detect defects reliabily with larger CSA sizes than 3% with no or very few outliers. In the case of 2% CSA defect, only frequencies of 34 and 40 kHz provided robust detection, where the ratio of the defect to outlier amplitudes is higher by a factor of 1.5. On the other hand, 38 kHz is the only frequency within this range where no outliers were detected in any of the cases. With regards to the test results, due to the significant changes in the excitation sequences, it is not recommended to use this algorithm with frequencies higher than 42 kHz. Since this method only requires a time-domain signal and the characteristics of the excitation sequence, it can easily be combined with other methods to further enhance the reliability of defect detection in guided-wave testing of pipelines.  
Conceptualisation, H.N.M.; Data Curation, H.N.M.; Formal Analysis, H.N.M.; Funding Acquisition, A.K.N.; Investigation, H.N.M.; Methodology, H.N.M.; Project Administration, A.K.N. and H.N.M.; Resources, H.N.M.; Software, H.N.M.; Supervision, K.Y. and A.K.N.; Validation, H.N.M.; Visualisation, H.N.M., K.Y. and A.K.N.; Writing--Original Draft, H.N.M.; Writing--Review & Editing, H.N.M., K.Y. and A.K.N.  
This research study was made possible by the sponsorship and support of Brunel University London and the National Structural Integrity Research Centre (NSIRC).  
The authors declare no conflicts of interest.