Fault diagnosis of a planetary gearbox based on a local bi-spectrum and a convolutional neural network

The vibration signals of a planetary gearbox have the characteristics of strong background noise and instability and are non-Gaussian. Bi-spectrums can suppress Gaussian colored noise and are suitable for vibration signal processing of planetary gearboxes. In the traditional fault diagnosis methods based on bi-spectrums, the fault characteristic frequency amplitudes of bi-spectrum or bi-spectrum slices, or the further quantitative calculations of fault characteristic values, are generally used as the basis of fault diagnosis processes. It has been found that bi-spectrum images can directly characterize the faults of the planetary gearboxes. Convolutional neural networks (CNNs) have been used in mechanical fault diagnoses in recent years. One-dimensional original signals are converted into two-dimensional images as CNN input, which is an effective method for mechanical fault diagnoses. At the present time, there has not been any relevant research conducted using bi-spectral images as CNN input. In this study, a fault diagnosis method based on local bi-spectrum and CNN was proposed. A bi-spectral analysis of the vibration signals of the planetary gearbox was first carried out in order to reveal the fault information while retaining the non-Gaussian information. Then, according to the bi-spectrum symmetry, local images containing the entire domain information were taken as the input of the CNN, which reduced the redundancy of the fault information. Then, in order to improve the diagnostic accuracy of the CNN, the key parameters of CNN architecture were optimized. Finally, a CNN diagnosis model was built to realize the classification diagnoses of different fault positions and different fault degrees of planetary gearboxes. This study’s comparison of the diagnosis results of the full bi-spectrum+CNN, local bi-spectrum+SVM, original vibration signal+CNN, and local bi-spectrum+BP neural networks showed that the method proposed in this study had achieved both accuracy and rapidity in the fault diagnoses of planetary gearboxes.

Nano-friction phenomenon of Frenkel-Kontorova model under Gaussian colored noise

The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova model under Gaussian colored noise is investigated by using the molecular dynamic simulation method. The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method. Via the stochastic Runge-Kutta algorithm, the relationship between different parameter values of the Gaussian colored noise (the noise intensity and the correlation time) and the nano-friction phenomena such as hysteresis, the maximum static friction force is separately studied here. Similar results are obtained from the two geometrically opposed ideal cases: incommensurate and commensurate interfaces. It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force, the introduction of noise can accelerate the motion of the system, making the atoms escape from the substrate potential well more easily. Interestingly, suitable correlation time and noise intensity give rise to super-lubricity. It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the Incommensurate interface.

Vector Magnetic Anomaly Detection via an Attention Mechanism Deep-Learning Model

Magnetic anomaly detection (MAD) is used for detecting moving ferromagnetic targets. In this study, we present an end-to-end deep-learning model for magnetic anomaly detection on data recorded by a single static three-axis magnetometer. We incorporate an attention mechanism into our network to improve the detection capability of long time-series signals. Our model has good performance under the Gaussian colored noise with the power spectral density of 1/fα, which is similar to the field magnetic noise. Our method does not require another magnetometer to eliminate the effects of the Earth’s magnetic field or external interferences. We evaluate the network’s performance through computer simulations and real-world experiments. The high detection performance and the single magnetometer implementation show great potential for real-time detection and edge computing.

Stochastic Stability of a Fractional Viscoelastic Plate Driven by Non-Gaussian Colored Noise

In this paper, the moment Lyapunov exponent and stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise is investigated. Firstly, the stochastic dynamic equations with two degrees of freedom are established by piston theory and Galerkin approximate method. The fractional Kelvin–Voigt constitutive relation is used to describe the material properties of the viscoelastic plate, which leads to that the fractional derivation term is introduced into the stochastic dynamic equations. And the noise is simplified into an Ornstein-Uhlenbeck process by utilizing the path-integral method. Then, via the singular perturbation method, the approximate expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulations. Finally, the effects of the noise, viscoelastic parameters and system parameters on the stochastic dynamics of the viscoelastic plate are discussed.

Fokker–Planck approach to neural networks and to decision problems

We review applications of the Fokker–Planck equation for the description of systems with event trains in computational and cognitive neuroscience. The most prominent example is the spike trains generated by integrate-and-fire neurons when driven by correlated (colored) fluctuations, by adaptation currents and/or by other neurons in a recurrent network. We discuss how for a general Gaussian colored noise and an adaptation current can be incorporated into a multidimensional Fokker–Planck equation by Markovian embedding for systems with a fire-and-reset condition and how in particular the spike-train power spectrum can be determined by this equation. We then review how this framework can be used to determine the self-consistent correlation statistics in a recurrent network in which the colored fluctuations arise from the spike trains of statistically similar neurons. We then turn to the popular drift-diffusion models for binary decisions in cognitive neuroscience and demonstrate that very similar Fokker–Planck equations (with two instead of only one threshold) can be used to study the statistics of sequences of decisions. Specifically, we present a novel two-dimensional model that includes an evidence variable and an expectancy variable that can reproduce salient features of key experiments in sequential decision making.

Memory function of memristive Hindmarsh–Rose model driven by colored noise and electromagnetic induction

Based on the three-dimensional memristive Hindmarsh–Rose model, the effects of Gaussian colored noise and electromagnetic induction on memory function of the memristor and neural firing states are investigated in this paper. It is found that the memory function of memristor can be suppressed by a higher signal frequency, while enhanced by a relatively larger coefficient of the memristor. The memory function of memristor is destroyed by larger values of noise intensity and correlation rate between noises. The neural firing state can be transformed from the spiking state to the chaotic state with the increase of noise intensity or correlation rate. The firing states transition induced by the higher electromagnetic induction intensity is opposite to that by the stronger Gaussian colored noise.

Response of Cantilever Model with Inertia Nonlinearity under Transverse Basal Gaussian Colored Noise Excitation

Considering the curvature nonlinearity and longitudinal inertia nonlinearity caused by geometrical deformations, a slender inextensible cantilever beam model under transverse pedestal motion in the form of Gaussian colored noise excitation was studied. Present stochastic averaging methods cannot solve the equations of random excited oscillators that included both inertia nonlinearity and curvature nonlinearity. In order to solve this kind of equations, a modified stochastic averaging method was proposed. This method can simplify the equation to an Itô differential equation about amplitude and energy. Based on the Itô differential equation, the stationary probability density function (PDF) of the amplitude and energy and the joint PDF of the displacement and velocity were studied. The effectiveness of the proposed method was verified by numerical simulation.