## 3 Methodology
### Generative Adversarial Networks  
A Generative Adversarial Network (GAN) is a framework proposed by [PERSON] [41] in 2014, which continuously generates new data through the competition between two neural networks. GAN consists of two modules: the generator and the discriminator. The core idea is that the generator and the discriminator play against each other. The generator generates erroneous samples based on random numbers generated from a Gaussian distribution, attempting to deceive the discriminator. The discriminator, on the other hand, tries to distinguish between correct and erroneous samples. The training process continues until the discriminator cannot differentiate between the generated imitation samples and the original real samples. The structure of GAN is shown in Figure 5. The generator is an unsupervised neural network that establishes a production model based on the mathemati  
Figure 3: Typical schematic diagram of STRC shear walls. cal and statistical information and features of the data, while the discriminator is a binary classification model. Assuming \(z\) is random noise and \(x\) is real data, the generative network and the discriminative network can be represented as \(G\) and \(D\), respectively. \(D\) can be seen as a binary classifier. If the loss function is represented by cross-entropy, the optimization objective function of the model can be expressed as follows:  
\[\mathrm{V}(G,D)=E_{x\sim\mathrm{P_{data}}}[\log D(x)]+E_{x\sim\mathrm{P_{G}}}[ \log D(x)] \tag{1}\]  
Figure 4: An implementation framework for predicting and interpreting the failure modes of STRC shear walls by Blending-CRKL fusion model based on GAN augmented data. Figure 5: GAN model structure. GAN requires consideration of gradient disappearance during training. The above objective function is usually expressed as follows:  
\[\left\{ \begin{aligned} \underset{\theta_{D}}{\text{max}}E_{x \sim P_{\text{data}}(x)}[\text{log}(D(x))]+E_{z\sim P_{z}(z)}[\text{log}(1-D(G (z)))]\\ \underset{\theta_{G}}{\text{min}}E_{z\sim P_{z}(z)}[\text{log}(D(G (z)))]\end{aligned} \right. \tag{2}\]  
The main objective of \(G\) is to minimize the objective function V(\(G\), \(D\)) in the expression. \(G\) aims to make \(G\)(z) closer to real data. In this case, a smaller value of log(1 \(-\)\(D(G\)(z)\)) indicates that the data generated by the generator are closer to real data. On the other hand, the purpose of \(D\) is to maximize the objective function V(\(G\), \(D\)). Ultimately, when the probability of \(D\) recognizing real data is \(D(G(z))\) = 0.5, generator \(G\) can generate data that are extremely similar to real data. \[\text{D}^{*}(\text{x})=\frac{\text{P}_{\text{data}}(\text{x})}{\text{P}_{\text {g}}(\text{x})+\text{P}_{\text{data}}(\text{x})} \tag{3}\]  
The structures of the generator and discriminator are shown in Figure 6a,b, respectively. In the training process of GAN, the parameter values of a GAN model significantly affect the quality of generated data, and choosing values that are too large or too small may lead to suboptimal results. For instance, the learning rate determines the magnitude of parameter updates in each iteration. A high learning rate can result in unstable training and prevent convergence of gradient descent, while a low learning rate can slow down the training process. Therefore, when generating STRC shear wall data, a balance between accuracy and efficiency should be considered to select appropriate parameter values for the GAN. Unfortunately, there are currently no heuristic optimization techniques available to determine the optimal values for each parameter in a GAN [21]. As a result, a trial-and-error strategy is often adopted, manually testing multiple values for each parameter and selecting relatively better ones. In this study, we tested the learning rate between 0.001 and 0.1, batch size between 20 and 132, noise dimension between 20 and 120, hidden layer size between 16 and 72, and the number of iterations between 50 and 2000.