Modelagem e Identificação de Sistemas Dinâmicos com Redes Recorrentes Profundas aplicados em Pedais de Distorção e Robôs Móveis

Abstract

This work addresses the Identification and Modeling of Dynamic Systems Using Deep Neural Networks, applying Multilayer Perceptron (MLP), Recurrent Neural Networks (LSTM and GRU), and the extended xLSTM (Extended Long Short-Term Memory) architecture in two distinct projects: the modeling of electric guitar signal distortion and the dynamic behavior of the TurtleBot 3 mobile robot. In the first project, MLP and LSTM were used to model the distortion applied to a guitar audio signal, simulating the effect of different resistances. The results were analyzed using the Cumulative Distribution Function (CDF), the Kolmogorov-Smirnov (KS) test, and the Mean Squared Error (MSE). LSTM demonstrated a strong ability to capture temporal dependencies in the audio signal, while MLP effectively modeled the relationship between inputs and outputs. The results showed low MSE values and a good match in the KS test, demonstrating that both architectures are effective in modeling audio distortions. In the second project, the modeling of the dynamic behavior of the TurtleBot 3 was carried out using four models: MLP, GRU, LSTM, and xLSTM. The goal was to predict its trajectories and velocities based on simulated data. The evaluation metrics included the Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Median Absolute Error (MdAE), and the coefficient of determination R2 . Among the evaluated models, xLSTM achieved the best results across almost all metrics, standing out as the most accurate architecture for modeling the robot’s dynamic system. However, MLP also demonstrated excellent performance, surpassing the GRU and LSTM models despite being a simpler approach. This finding reinforces the efficiency of MLP in capturing nonlinear relationships between inputs and outputs, making it a competitive alternative for dynamic system modeling. In conclusion, the results obtained in both projects highlight the capability of deep neural networks, including MLP, LSTM, GRU, and xLSTM, in modeling complex dynamic systems. The metric analysis confirms the robustness of the proposed methodology, making it a promising approach for Digital Twin applications, with potential for real-time monitoring and control.