# Detection of Defects Using Spatial Variances of Guided-Wave Modes in Testing of Pipes
## 1 Introduction  
Pipelines are the main means of transferring oil and gas. They are usually installed in a hostile environment and suffer from defects such as corrosion or mechanical damage. To prevent the failure of pipelines, there is a need to inspect them in service in order to ensure their structural integrity. One of the many methods for the non-destructive testing of pipes is ultrasonic guided waves (UGW). This technology uses sets of transducer arrays to generate a low-frequency ultrasound signal. This ensures that elastic waves are guided through the boundary of the pipe; hence, the name guided waves [1]. Therefore, from one test point, the long-range inspection of pipelines is possible. However, the interoperation of UGW signals tends to be difficult due to the existence of the coherent noise in the tests. Despite using arrays of transducers, UGW testing systems use a general routine process that outputs a single monodirectional signal in a time domain [2; 3; 4; 5]. The generated signal is then usedby inspectors to report any anomalies above the regional signal noise level [6]. To allow an ease of inspection, many types of research have been defined to use the characteristics of guided waves to increase the signal-to-noise ratio (SNR), increasing the defect detection accuracy. One of the widely used techniques in the signal processing of guided waves is the work of [PERSON] et al., which uses previously calculated dispersion curves in order to compensate for the effect of dispersion for the wave mode of interest in a certain propagation distance [7]. In 2013, [PERSON] et al. [8] used the basis of the dispersion compensation technique and introduced a novel method to design waveforms in order to pre-compensate for a certain propagation distance. Various researchers investigated the pulse compression approach, which consisted of exciting a known coded sequence and match-filtering the results in order to detect the known sequence [9; 10; 11; 12]. [PERSON] et al. [9; 10] introduced an iterative dispersion compensation for removing the dispersion effect of guided-wave propagation. In 2016, [PERSON] et al. [11] reported on the performance of different excitation sequences in terms of their ability to achieve \(\delta\)-like correlation on Lamb waves. Most recently, [PERSON] et al. [12] developed a two-dimensional compressed pulse analysis in order to enhance the achieved SNR of each wave mode. Coded waveform approaches have also been implemented in the enhancement of SNR in the inspection of Long Bones using guided waves [13]. In the pulse compression approaches, the results are always a trade-off between the spatial resolution and SNR; for having a high-energy, \(\delta\)-like correlation result, the wavelength must be increased. Furthermore, the transfer function of the excitation system can affect the accuracy of the coded waveforms. These two factors mean that the initial waveform design and the accuracy of inspection using this method depend on the testing conditions. Furthermore, if non-dispersive regions of wave modes are used, there will be no need to use dispersion compensation algorithms. Another method for filtering the guided waves signal is the work of [PERSON] et al. in Split-Spectrum Processing (SSP) [14; 15], whereby through selecting the optimum filter parameters, the coherent noise of the test cases can be removed. However, automatic selection of the optimum filtering parameter is not possible at present. These parameters can be varying with regard to central excitation frequencies and the pipe geometries. On a similar note, frequency sweep examination, which was developed by [PERSON] et al. [16] in 2014, uses a similar concept in a way that defect features should exist in all of the frequency bands. Based on this fact, a novel method was developed that processes signals with different excitation frequencies, and is able to distinguish between the dispersive and non-dispersive wave modes that exist in the test.