# Data-Driven Damage Classification Using Guided Waves in Pipe Structures
## 1 Introduction  
Pipelines play an increasingly important role in modern industries for the supply and distribution of required materials, such as natural gas, crude oil, steam, and hot water. They usually have a long operating life of more than 50 years, meanwhile, they are easy to suffer from aging defects and a wide variety of damages, which might result in terrible accidents. Therefore, damage detection for pipelines has become increasingly necessary. The damages in pipes usually include corrosion, seam weld cracks, stress rupture, material flaws, large deformation, and externally induced damage by a third party, etc. Usually, different damages lead to different influences and results, therefore, they are treated very differently. Current pipe inspection methods include traditional ground-penetrating radar for buried pipelines [1, 2], new but not proven pipeline robotics [3], etc. In comparison, strain measurement [4, 5] and guided wave-based methods are more commonly used [6, 7, 8, 9, 10]. However, the former requires installing sensors for the entire length of the pipe in advance, which is not feasible in many practical situations. The latter has been proven to be effective and promising for damage detection in pipes over a long distance, even if the pipeline is buried. It can cover a large range of pipes from only a single inspection point. Moreover, guided wave-based methods recognize damages through the reflection or the transmission wave signals, which contain more information about the type, location, and degree of damage. They are extracted by a variety of signal processing methods, such as fast Fourier transform, continuous wavelet transform [11], singular value decomposition [12], principal component analysis [13], and machine learning [14, 15]. For these traditional damage detection methods, structural damage is usually assumed to be the ideal shape, but no further differentiation is made. Therefore, damage classification is necessary for structural assessment. In general, the damage type is related to its shape, which can be reconstructed through the interaction of guided wave with damages. [PERSON] and [PERSON] [16] presented a quantitative study of the interaction of the T(0,1) torsional mode with axial and oblique defects in a pipe employing reflection signals from the defects and the mode decomposition technique. [PERSON] et al. [17] used a circular network of piezoelectric disc transducers collect guided wave signals and reconstructed damage images with the total focusing method. The results indicate that crack- and hole-type of damages can be differentiated using geometric circularity and eccentricity shape factors. [PERSON] et al. [18] presented an analytical approach to reconstruct axisymmetric defects in pipelines using the torsional guided wave T(0, 1). This approach employed the reflection coefficients of the guided wave T(0, 1) scattered by different sizes of axisymmetric defects, and performed the reconstruction of defects by the inverse Fourier transform. [PERSON] et al. [19] used the guided wave tomography technique to map the corrosion thickness by transmitting guided waves. [PERSON] [20] realized the size and shape estimation by only three sensors through the reconstruction of the shape of the reflected wavefront. [PERSON] et al. [21] developed a damage shape recognition algorithm, which can capture the damage shape by describing the coordinates of the reflection point from the transducers to the damage edge. The above studies indicate that damage differentiation mainly depends on a complicated transducer array or reconstruction algorithm, which are difficult to carry out in the practical inspections. A data-driven approach, by contrast, can overcome the difficulties of the complicated mathematical-physical model involved in wave propagations [22]. [PERSON] et al. [23] proposed a data-driven approach to conduct damage detection using guided wave responses.