# Detection of Defects Using Spatial Variances of Guided-Wave Modes in Testing of Pipes
## 1 Introduction
This method has never been tried in the pipes before, and requires many different excitations to be calculated on the same test subject. As it is currently known, due to backward cancellation algorithms and an overall system transfer function [4], it is not perfect, and not all of the frequencies can be used for optimum excitation (it can be varying depending on the pipe and tool set used). This will affect the accuracy of the algorithm if it is converted for pipeline inspection. In 2015, [PERSON] [17] investigated signal processing approaches for the enhancement of results produced by guided-waves signals, in which he reported that Hilbert transform, Gabor wavelet transform, and discrete wavelet decomposition are able to improve the detectability of the results. UGWs have also been used for monitoring purposes. In 2015, [PERSON] et al. implemented independent component analysis (ICA) combined with previously developed temperature compensation methods [18; 19] to enable the successful guided-wave monitoring of pipelines. In 2017, [PERSON] et al. [20] introduced the idea of an adaptive sparse deconvolution method, with the aim of distinguishing the overlapping echoes of an ultrasonic guided-waves signal. All of the algorithms have been developed with one purpose in mind: the improvement of the SNR to increase the possibility of the detection of a defect signal. However, the full potential of the system has not yet been established. The signal information in these systems are received from three rings of (at least) 24 transducers, but in the mentioned work, there is only one signal, which is achieved after the propagation routine of the device by summing the phase-delayed version of all of the transducers together. This routine was created to reduce the received flexural signals and have a unidirectional inspection [4; 5]. Nonetheless, the received informatics can be processed in a better method, i.e., to use all of the available sensors for detecting the defect location rather than changing the information into a single time-domain signal. On the other hand, array processing techniques that use individual signals are generally used for imaging and focusing applications [21; 22; 23; 24; 25; 26; 27]. However, these algorithms are computationally expensive, and might require the individual excitation of transducers [26], or a phased-array focusing of the transducers [23], rather than synthetic focusing, where all of the transducers in the array are excited at the same time [21]. This adds to the complexity of the interpreting the results. Furthermore, the goal of these algorithms is imaging a segment of the pipe rather than the detection of the defect location. In this paper, we propose a new algorithm to solve the problem of detections, which can possibly be combined with all of the above-mentioned methods for SNR enhancement. The aim of this algorithm is to illustrate the possibility of using all of the individual transducers for defect detection instead of using a single signal achieved after the general routine. This way, both the spatial and temporal characteristics of the signal can be examined in more depth, which can lead to more accurate results. Furthermore, unlike imaging techniques, it uses normal excitation sequences, and thus can be applied to all of the data sequences, even if they are achieved in the past. Section 2 explains the nature of noise on the guided-waves signal and the wave formation with regards to unique features. In Section 3, a novel method is proposed that uses the characteristic of axisymmetric waves to allow the detection of the defect signal. Validation was done by laboratory trials using two separate defect locations. The first defect is in a region where less coherent noise exists in the baseline with a varying size of 2% and 3% of the pipe's cross-sectional area (CSA), and the second defect is located in higher spatial noise with a varying size of 4% and 5% CSA. The setup of these tests and the results are reported in sections 4 and 5, respectively.