## 3 Methodology
### A Method of Signal Dimension Conversion  
In the acquisition experiment of Lamb waves, the collected signals are timing signals, which need to be processed and analyzed later. In traditional fault diagnosis methods, the data pre-processing method is vital since most data-driven methods cannot handle the raw signals directly. One of the main functions of the data pre-processing method is to extract the features of the raw signals from a large volume of historic data. However, extracting the proper features is exhaustive work, and these features have great effects on the final results. In addition, current deep learning methods mainly deal with two-dimensional structural data. The depth learning methods used for image processing are relatively mature, and there are many effective methods. Therefore, if we can convert the experimental one-dimensional time series data into two-dimensional (image) data through specific methods, we can better adapt to the current popular and cutting-edge models and improve the training and classification effect. Now, the following methods are adopted to convert the time-domain raw signals to images. Figure 6: Flowchart of overall theory and experimental design. As shown in Figure 7, in this conversion method, the time-domain raw signals fulfill the pixels of the image by sequence. First, we need to obtain an \(M\times M\)-sized image. To fill the square image, we need to randomly intercept a segment signal with the length \(M^{2}\) from the raw signal. First, let \(L(i)\), \(i=1\dots M^{2}\) denote the value of the segment signal. While \(P(j,k)\), \(j=1\dots M,i=1\dots M\) denotes the pixel strength of the image, as shown in equation \(P(j,k)=round\big{\{}\frac{L((j-1)\times\text{M}+k)-Min(L)}{Max(L)-Min(L)} \times 255\big{\}}\)[18]. Later, we will analyze this formula. The value of the segment signal at each position is defined by \(L\), and the value corresponding to a specific position is determined by \(j\) and \(k\). The image intensity at the corresponding position is obtained by performing the operation in the equation. The function _round_ is the rounding function, and the whole pixel value has been normalized from 0 to 255. The number size refers to the pixel intensity of the grayscale image. The 2 \(\times\) 2 filters are commonly used in this study, and the size of image features on each layer would be reduced by half. Therefore, the recommended value of \(M\) in this case is \(2^{n}\). In this study, the selection of 64 \(\times\) 64 and 16 \(\times\) 16 depends on the amount of signal data. In combination with the sparsity of guided wave signal features and the large amount of data collected each time, in order to ensure the features of the data, 64 \(\times\) 64 images are chosen as the research object. The advantage of this data processing method is that it can convert one-dimensional signals into two-dimensional signals through this method, and it provides a way to explore the 2D features of the raw signal [15]. Moreover, this data pre-processing method can be calculated without any predefined parameters and can reduce the experiences as more as possible. These can simplify the training process and optimize the calculation process. In this study, the size of the image varies with the volume of the signal data, and the guided wave signal data targeted in this experiment has a large volume. Moreover, a larger image size can facilitate classification results. Therefore, in this study, the size of the image is 64 \(\times\) 64. In the subsequent processing, we also apply the zero-padding method to the model to prevent dimension loss. The process of quantifying temporal signals into two-dimensional images may introduce noise, which can cause the loss of image clarity and details, thereby affecting image performance to some extent. Therefore, this experiment used filters for the generated images, and in this experiment,  
Figure 7: Schematic diagram of signal dimension conversion principle. we chose the common Gaussian filter to smooth the image and remove noise.