Robust Modeling of a Class of Vibration Signals Through Binary Neural Network-Based Symbolic Regression

In this paper, we propose an automatic method to unveil the nonlinear multi-modulation model that describes vibration signal of certain complex systems. Firstly, we apply a harmonic estimation algorithm to the observed signal to identify all peaks in the spectral domain. Then, using the peaks' location information, a neural network-based symbolic regression is trained to determine a concise expression of the multi-modulation model underlying the considered signal. A regularized objective function is utilized to optimize the neural network weights and enforce their binarization (sparsity), providing a simple mathematical expression for the input signal model. The proposed algorithm improves the robustness of the determined model by eliminating any distortion in the input signal, such as transfer function and phase modulation distortion. This method could potentially be employed in the vibration analysis of rotating machines, such as planetary gearboxes, due to the structural spectral contents of the vibration signal, to reflect the interaction model between system elements.