# Depth Evaluation of Tiny Defects on or near Surface Based on Convolutional Neural Network
## 1 Introduction  
Critical components often operate in harsh environments and are subjected to cyclic stress and strain in specialized applications, such as aerospace engines, offshore platforms, and other similar scenarios, making them susceptible to the formation of micro-cracks and other defects on or near the surface [1, 2, 3]. If these defects are not detected in a timely manner, they can rapidly propagate and lead to the sudden catastrophic failure of the entire structure [4, 5]. Therefore, the detection of surface microdefects, such as surface or near-surface cracks or incomplete fusion, especially through non-destructive evaluation methods, plays a crucial role in the industrial domain [6, 7].  
The Rayleigh wave is well suited to the evaluation of surface defects due to its high sensitivity to surface defects [8, 9, 10]. The defects can be detected and evaluated based on changes in the signal-noise ratio within echo signals, specifically the amplitude variation inRayleigh waves [11]. However, the accuracy of this method can be significantly decreased when the detected defect size is much smaller than the wavelength of Rayleigh waves [12]. Nonlinear ultrasound methods are more effective in detecting small defects [13], but their correlation with time-domain features and defect locations is weak [14]. Currently, there is a paucity of research and limited methods to precisely evaluate the depth of surface and near-surface tiny defects. The main obstacle is how to extract micro-ultrasonic features associated with these defects, which can be obscured by noise or other interfering signals, making it difficult to establish a quantitative relationship between ultrasonic waves and defects.  
In recent years, the integration of artificial neural networks with ultrasonic detection has undergone significant advancements, which can accurately identify potential features of signals from different sources and have been widely used in the fields of defective signal identification and SNR enhancement, especially in high-attenuation, strong-interference detection scenarios, such as those involving composite materials [15; 16; 17]. Artificial neural networks, represented by BPNN, require the manual feature extraction of ultrasound signals, and their accuracy is affected by the type of extracted features [18; 19; 20]. In contrast, CNN, as one of the deep learning neural networks, has proven its superiority over conventional neural networks in processing SHM signals containing massive numbers of data, enabling automated signal analysis without further extracting features from raw signals [21; 22]. This superiority empowers CNNs to facilitate comprehensive analyses of latent features embedded within ultrasound signals, while simultaneously establishing potential connections. Consequently, CNNs emerge as a suitable choice for the evaluation of micro-defects.  
This paper introduces a novel method for accurately determining the depth of surface and near-surface micro-defects. The proposed approach leverages convolutional neural networks (CNNs) to extract and identify crucial features linked with defects, which might be buried in noise or other disturbance signals, establishing a quantitative relationship between the evolving characteristics of ultrasound signals and the depth of the defects. A substantial volume of ultrasound data, essential for the implementation of deep learning methodologies, is procured through laser ultrasound point-source scanning. The architecture and hyperparameters of the convolutional neural network (CNN) are meticulously crafted and fine-tuned with precision to yield optimal training outcomes.