# Welding Image Data Augmentation Method Based on LRGAN Model
## 1 Introduction
Additionally, although the least squares loss function improves training stability to some extent, the discriminator's stability is still significantly affected by the gradient vanishing problem caused by large changes in the discriminator's parameters. To address this issue, [PERSON] et al. proposed applying spectral normalization to the parameter matrix during the discriminator's training process, thereby constraining the gradients of the model parameters within a reasonable range, which in turn ensures stable training of the discriminator [22]. Furthermore, [PERSON] et al. suggested that in order to guarantee the stability of the GAN's discriminator training, it is essential to ensure that the discriminator's function satisfies the Lipschitz condition [23]. To further improve this issue, this paper introduces spectral normalization during the discriminator's training process. By limiting the range of parameter gradients, it effectively avoids excessive changes in the discriminator's parameters, thereby enhancing the stability of the training process. Compared to traditional weight clipping methods, spectral normalization effectively controls the Lipschitz constant by normalizing the maximum singular value of the weight matrix in each layer, thereby improving the stability of the model without disrupting the structure of the convolutional kernels. Unlike gradient penalty, spectral normalization does not require the introduction of additional penalty terms, reducing computational overhead. It also avoids the training oscillations that may arise from batch normalization in adversarial training. Therefore, in this study, we adopt the spectral normalization method to impose stability constraints on the discriminator, thereby enhancing the training stability of the discriminator more effectively. In addition, for adversarial generative models, in order for the generator to produce image features that are closer to the original images, a deeper network structure is often required. However, as the network depth increases, the generator typically faces the issue of gradient explosion during training, leading to training failure. This is primarily due to the accumulation of errors during the backpropagation process [24; 25]. Residual structures, by adding shortcut connections between layers of the neural network, weaken the strong dependencies between layers, thus ensuring that the performance of deeper networks is at least as good as that of shallower networks. This has been demonstrated in [26; 27]. In summary, to address the common data bottleneck problem in industrial welding scenarios, this paper proposes a loss-reconstruction-based generative adversarial network (LRGAN), First, a five-layer spectral normalization neural network was designed as the discriminator for the model, using a least squares loss function. Next, a nine-layer residual structure was introduced in the generator. The goal is to overcome the performance bottlenecks of existing GAN models in welding image generation, accelerate the convergence process, limit drastic changes in model parameters, and alleviate issues such as gradient vanishing and mode collapse.