## 5 Machine Learning Models
### Data Analysis  
The model takes into account various inputs, such as the tuning ratio (\(T_{s}/T_{1}\)), \(\xi_{s}\), floor level, soft-story level, and excitation direction. These inputs are used to predict the corresponding CDAF values, which serve as the model's output. The statistical characteristics of the input parameters can be summarized as follows: \((T_{s}/T_{1})\) ranged between 0 and 4.587 for five-story models and varied between 0 and 2.125 for ten-story models; \(\xi_{s}\) ranged between 0.1% and 10%; five and ten floors for the five- and ten-story buildings, respectively; four soft-story conditions are considered (where 0, 1, 2, and 3 are assigned to reference, bottom, middle, and top soft-story models, respectively); two excitation directions (where,  
Figure 10: Values of CDAF at different damping ratios for (**a**) 5-story buildings and (**b**) 10-story buildings. 0 and 1 are assigned to two orthogonal directions (X and Y), respectively). Figure 11 shows the statistical distributions of the input parameters generated from dataset of both five- and ten-story buildings. Tables 7 and 8 represent the statistical characteristics of both five-story and ten-story models. The correlation matrix, presented in Tables 9 and 10, reveals noteworthy associations among the variables. Notably, the tuning ratio (\(T_{s}/T_{1}\)) exhibits the most pronounced negative correlations, reaching 0.516 (five-story) and 0.399 (ten-story), with CDAFs. Following this, \(\zeta_{s}\) displays correlations of 0.181 (five-story) and 0.293 (ten-story) with CDAFs. Regarding the floor and excitation direction, positive correlation coefficients are observed for  
Figure 11: Distribution of the input parameters generated for the dataset from (**a**) five- and (**b**) ten-story models. have proven to be more accurate tools for calculations and predictions compared to conventional computational methods [75; 76; 77; 78]. The primary challenge in constructing this model lies in determining the optimal architecture, including the number of hidden layers, epochs, batch size, and more. While machine learning algorithms learn parameter values like node weights and biases through forward and backpropagation, there are additional parameters--known as hyperparameters--that control the learning process itself. Tuning these hyperparameters is crucial to ensure that the model effectively addresses the machine learning problem reliably. In this study, the trial-and-error method was employed to identify the most suitable hyperparameter combinations for various machine learning models. Through an iterative approach, trial and error proves its value by progressively refining hyperparameters. We initiated with a basic hyperparameter set, closely observed the outcomes of the performance measurement function, and fine-tuned them based on our observations. This method becomes especially practical when dealing with limited datasets, as advanced techniques like Bayesian optimization might falter due to data constraints. In such scenarios, trial and error emerges as a straightforward and effective alternative. In analogous prediction problems, several researchers have opted for trial-and-error methodologies to construct ANN-based prediction models in their research [79; 80; 81; 82]. In our study, we comprehensively addressed all essential hyperparameters for optimizing the model, with the exception of the learning rate. Notably, the Levenberg-Marquardt (LM) algorithm introduces a distinct concept of a learning rate compared to conventional gradient descent-based approaches. Unlike the traditional fixed learning rate, the LM algorithm dynamically adapts step size using a damping factor, ensuring the effective navigation of the error surface for convergence. Specifically, three types of neural networks were evaluated: function fitting neural networks, feedforward neural networks, and cascade forward neural networks. These networks utilized a range of training and transfer functions (with consistent transfer functions across hidden layers).