A Semi-supervised Gaussian Mixture Variational Autoencoder method for few-shot fine-grained fault diagnosis.

In practical engineering, obtaining labeled high-quality fault samples poses challenges. Conventional fault diagnosis methods based on deep learning struggle to discern the underlying causes of mechanical faults from a fine-grained perspective, due to the scarcity of annotated data. To tackle those issue, we propose a novel semi-supervised Gaussian Mixed Variational Autoencoder method, SeGMVAE, aimed at acquiring unsupervised representations that can be transferred across fine-grained fault diagnostic tasks, enabling the identification of previously unseen faults using only the small number of labeled samples. Initially, Gaussian mixtures are introduced as a multimodal prior distribution for the Variational Autoencoder. This distribution is dynamically optimized for each task through an expectation-maximization (EM) algorithm, constructing a latent representation of the bridging task and unlabeled samples. Subsequently, a set variational posterior approach is presented to encode each task sample into the latent space, facilitating meta-learning. Finally, semi-supervised EM integrates the posterior of labeled data by acquiring task-specific parameters for diagnosing unseen faults. Results from two experiments demonstrate that SeGMVAE excels in identifying new fine-grained faults and exhibits outstanding performance in cross-domain fault diagnosis across different machines. Our code is available at https://github.com/zhiqan/SeGMVAE.

Constructed complex motions and chaos.

Constructed motions and dynamic topology are new trends in solving nonlinear systems or system interactions. In nonlinear engineering, it is significant to achieve specific complex motions to satisfy expected dynamical behaviors (e.g., nonlinear motions, singularities, bifurcations, chaos, etc.), and complex motion application and control. To achieve such expected motions and global dynamical behaviors, mapping dynamics, constructed networks, random/discontinuous dynamic theorems, etc., are applied to quantitatively determine the complex motions. These theories adopt the symbolic dynamic abstracts and topological structures with nonlinear dynamics to investigate constructed complex motions to satisfy expected dynamical behaviors.

Stability and bifurcations of complex vibrations in a nonlinear brush-seal rotor system.

A brush seal has the advantages of adapting to different vibration conditions and increasing the stability of the nonlinear rotor system. In this research, the stability and bifurcations of complex vibrations in a brush-seal rotor system are studied. An analytical seal force model is obtained through the beam theory and mutual coupling dynamics of the bristles and the rotor. The interaction between the bristles and the rotor is clearly depicted by a geometric map. Periodic and chaotic vibrations as well as the corresponding amplitude-frequency characteristics are first predicted by a numerical bifurcation diagram and 3D waterfalls. Discrete dynamic eigenvalue analysis is adopted for a detailed investigation of the stability and bifurcations of nonlinear vibrations. Jumping, quasi-periodic, and half-frequency vibrations are warned during the speeding up and down process. Four separate nonlinear vibration evolving routes are discovered. Two period-doubling bifurcation trees evolving to chaos are illustrated for the observation of global and independent periodic vibrations. Nonlinear vibration illustrations are presented through displacement orbits as well as harmonic amplitudes and phases. Chaotic vibration and unstable semi-analytical vibration solutions are compared. The obtained results and analysis methods provide new perspectives on nonlinear vibrations in the brush-seal rotor system.

Analytical predictions of stable and unstable firings to chaos in a Hindmarsh-Rose neuron system.

In this paper, analytical predictions of the firing cascades formed by stable and unstable firings in a Hindmarsh-Rose (HR) neuron system are completed via an implicit mapping method. The semi-analytical firing cascades present the route from periodic firings to chaos. For such cascades, the continuous firing flow of the nonlinear neuron system is discretized to form a special mapping structure for nonlinear firing activities. Stability and bifurcation analysis of the nonlinear firings are performed based on resultant eigenvalues of the global mapping structures. Stable and unstable firing solutions in the bifurcation tree exhibit clear period-doubling firing cascades toward chaos. Bifurcations are predicted accurately on the connections. Phase bifurcation trees are observed, which provide deep cognitions of neuronal firings. Harmonic dynamics of the period-doubling firing cascades are obtained and discussed for a better understanding of the contribution of the harmonics in frequency domains. The route into chaos is illustrated by the firing chains from period-1 to period-16 firings and verified by numerical solutions. The applied methods and obtained results provide new perspectives to the complex firing dynamics of the HR neuron system and present a potential strategy to regulate the firings of neurons.