The Uniqueness of Stationary Solution for Nonlinear Random Reaction-diffusion Equation

We study a nonlinear random reaction-diffusion problem in abstract Banach spaces, driven by a real noise, with random diffusion coefficient and random initial condition. We consider a polynomial non linear term. The reaction-diffusion equation belongs to the class of parabolic stochastic partial differential equations. We assume that the initial condition is an element of Hilbert space. The real noise is a Wiener process. We construct a suitable stochastic basis and define the solution of reaction-diffusion problem in the weak sense. We define the stationary process in abstract Banach spaces in the strong sense of Doob-Rozanov. That is, the probability density function of the stochastic process is independent of time shift. We define the invariant measure for random reaction-diffusion equation in the sense of Arnold, DaPrato, and Zabczyk [1,2]. In other words, we define the invariant measure for random dynamical system, associated with random reaction-diffusion problem. Using the Variation Inequalities Theory, we prove the uniqueness of stationary solution for nonlinear random reaction-diffusion problem. The obtained theoretical results have several applications in Quantum Physics, Biology, Medicine, and Economic Sciences. Especially, we can study the existence of stationary solution for the stochastic models of tumor growth.

Noise Modeling to Build Training Sets for Robust Speech Enhancement

The performance of Deep Neural Network (DNN)-based speech enhancement models degrades significantly in real recordings because the synthetic training sets are mismatched with real test sets. To solve this problem, we propose a new Generative Adversarial Network framework for Noise Modeling (NM-GAN) that can build training sets by imitating real noise distribution. The framework combines a novel U-Net with two bidirectional Long Short-Term Memory (LSTM) layers that act as a generator to construct complex noise. The Gaussian distribution is adapted and used as conditional information to direct the noise generation. A discriminator then learns to determine whether a noise sample is from the model distribution or from a real noise distribution. By adversarial and alternate training, NM-GAN can generate enough recall (diversity) and precision (quality of noise) in its samples for it to look like real noise. Afterwards, realistic-looking paired training sets are composed. Extensive experiments were carried out and qualitative and quantitative evaluation of the generated noise samples and training sets demonstrate that potential of the framework. An Speech enhancement model trained on our synthetic training sets and on real training sets was found to be capable of good noise suppression for real speech-related noise.

Application of machine learning to microseismic event detection in distributed acoustic sensing data

This study presents the first demonstration of the transferability of a convolutional neural network (CNN) trained to detect microseismic events in one fiber-optic distributed acoustic sensing (DAS) data set to other data sets. DAS increasingly is being used for microseismic monitoring in industrial settings, and the dense spatial and temporal sampling provided by these systems produces large data volumes (approximately 650 GB/day for a 2 km long cable sampling at 2000 Hz with a spatial sampling of 1 m), requiring new processing techniques for near-real-time microseismic analysis. We have trained the CNN known as YOLOv3, an object detection algorithm, to detect microseismic events using synthetically generated waveforms with real noise superimposed. The performance of the CNN network is compared to the number of events detected using filtering and amplitude threshold (short-term average/long-term average) detection techniques. In the data set from which the real noise is taken, the network is able to detect >80% of the events identified by manual inspection and 14% more than detected by standard frequency-wavenumber filtering techniques. The false detection rate is approximately 2% or one event every 20 s. In other data sets, with monitoring geometries and conditions previously unseen by the network, >50% of events identified by manual inspection are detected by the CNN.

Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise

This manuscript investigated the response of a strongly non-linear vibro-impact (VI) system with Coulomb friction. The impact model is used with classical impact. The excitation is modelled by real noise. First, the VI system is converted into a simplified system without any barrier by non-smooth transformation (symmetric transformation). The stochastic averaging method is adopted to obtain the theoretical stationary probability function of the VI system. Next, the Duffing Van der Pol VI system with Coulomb friction is used to verify the validity of the proposed theoretical method compared with numerical simulations. Moreover, the influence of bandwidth, noise intensity, and friction amplitude are further analyzed in detail on the probability density function (PDF) of distribution of the VI system. The P-bifurcation is studied by a qualitative change of friction amplitude and restitution coefficient on the stationary probability distribution, which indicated that these parameters can arouse the emergence of stochastic P-bifurcation.