This paper focuses on identifying physical parameters of a mechanical system subjected to random excitation. Stochastic signal is the only input, which eliminates classical harmonic or impulse test signals. A large synthetic dataset is generated by numerically simulating the mechanical quarter Unmanned Ground Vehicle (UGV) model across a set of stiffness and damping values under band-limited white noise excitation. The Power Spectral Density (PSD) of the measured response is computed using Welch's estimator and used as a feature vector. A multilayer perceptron (MLP) regression model is subsequently trained to map the spectral features to the physical parameters (c, k). The results demonstrate that the neural network-based approach achieves R² ≈ 0.97 for c and R² ≈ 0.99 for k in two separate MLP configurations. This indicates that the optimal architectures for the two parameters do not coincide. The performance of the proposed method is evaluated using selected performance metrics. The influence of selected parameters on identification accuracy is systematically investigated, providing practical guidelines for future experimental studies. This work was financed by the Military University of Technology under research project UGB 22-104/2026 (531-000104-W100-22).