Gearbox condition monitoring and quality surveillance are crucial techniques to ensure safe and cost-efficient machine operations. In condition monitoring, the interpretation of the different vibration spectrum elements is still an open question, many works show that some predefined vibration models are improper to explain the spectrum contents. In this paper, we investigate a method to identify the mixture model that describes a single-stage planetary gearbox vibration to properly interpret the vibration spectrum. Our method is based on neural network-based symbolic regression, a so-called equation learner that describes the vibration model based on prior knowledge about the planetary gearbox rotation frequencies. The method employs an end-to-end differentiable feed-forward network trained with sparsity regularization that promotes an interpretable and concise expression for the vibration measurement. With this, the obtained model contributes to increasing the effectiveness of vibration-based condition monitoring in the planetary gearbox with proper separation of the elementary vibration sources. Our proposed approach yields promising results in modeling and sources estimation based on simulated data, even at low SNRs.

This paper presents a comprehensive Bayesian framework for FANOVA models. We provide guidelines for tuning and practical implementation to improve scalability of learning and prediction. Our model is very flexible and can handle different levels of sparsity across and within decomposition orders, as well as among covariates. This flexibility enables the modeling of complex real-world data while enhancing interpretability. Additionally, it allows our model to unify diverse deterministic and Bayesian non-parametric approaches into a single equation, making comparisons and understanding easier. Notably, our model serves as the Bayesian counterpart of several deterministic methods allowing uncertainty quantification. This general framework unlocks potential for novel model developments that have been previously overlooked, such as the proposed Dirichlet mixing model that addresses limitations of existing models.

This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to previous work in which we developed a differentiable version of STFT by making the window length a continuous parameter. The resulting differentiable adaptive STFT possesses commendable properties, such as the ability to adapt in the same time-frequency representation to both transient and stationary components, while being easily optimized by gradient descent. We validate the performance of our method in vibration analysis.