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.

In this paper, we propose a novel formulation for the efficient data gathering problem in Wireless Sensor Networks (WSNs) based on Matrix Completion technique. The objective here is to optimize the usage of WSN resources during the data gathering process by taking into account an a priori knowledge about the data to be gathered. More precisely, we model the prior knowledge about the target data via hard convex constraints where the involved regularization parameters are related to some physical properties of the data itself and are then easy to interpret. Hence, the problem of data gathering is reduced to a constrained minimization one. A new class of primal- dual algorithm is extended in order to solve the resulted optimization problem. Experiments carried out on two datasets show that the proposed algorithm outperforms state-of-the-art methods and achieves a good recovery accuracy even if the sampling rate is very low.

International audience

In this paper, we proposed a novel matrix completion algorithm in Wireless Sensor Networks. Our contribution is twofold. First, we propose a general formulation of the problem of data gathering as a tractable convex optimization problem on the Hilbert space of data measurement matrices. The proposed criterion takes full advantage of both the global features, particularly low rank nature of data, and local features namely the sparsity and the spatio-temporal correlation in the sensors data to improve the recovery accuracy. Second, we design a new class of primal-dual optimization approach in order to optimize the resulting regularized criterion. Experiments carried out on two datasets show that the proposed algorithm outperforms state-of-the-art methods for low sampling rate and achieves a good recovery accuracy even if the sampling rate is very low.

In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an additive noise. In this paper, we address the problem of recovering the image components in a wavelet domain by adopting a variational approach. Our contribution is twofold. First, an appropriate multivariate penalty function is derived from a novel joint prior model of the probability distribution of the wavelet coefficients located at the same spatial position in a given subband through all the channels. Secondly, we address the challenging issue of computing the Maximum A Posteriori estimate by using a Majorize-Minimize optimization strategy. Simulation tests carried out on multispectral satellite images show that the proposed method outperforms conventional techniques.