Solution to the Kramers barrier crossing problem caused by two noises: Thermal noise and Poisson white noise

2021 ◽  
Vol 155 (1) ◽  
pp. 014902
Author(s):  
Tarun Gera ◽  
K. L. Sebastian
Keyword(s):  
White Noise ◽  
Thermal Noise ◽  
Poisson White Noise ◽  
Barrier Crossing

Influence of Poisson White Noise on the Response Statistics of Nonlinear System and Its Applications to Bearing Fault Diagnosis

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Dawen Huang ◽  
Jianhua Yang ◽  
Dengji Zhou ◽  
Grzegorz Litak ◽  
Houguang Liu
Keyword(s):  
Nonlinear System ◽  
White Noise ◽  
Noise Intensity ◽  
Arrival Rate ◽  
Scale Transformation ◽  
Poisson White Noise ◽  
Noise Background ◽  
Bearing Fault ◽  
Fault Features ◽  
Bearing Structure

In view of complex noise background in engineering practices, this paper presents a rescaled method to detect failure features of bearing structure in the Poisson white noise background. To realize the scale transformation of the fault signal with Poisson white noise, a general scale transformation (GST) method is introduced based on the second-order underdamped nonlinear system. The signal features are successfully extracted through the proposed rescaled method in the simulated and experimental cases. We focus on the influence of Poisson white noise parameters and damping coefficient on the response of nonlinear system. The impulse arrival rate and noise intensity have opposite effects on the realization of stochastic resonance (SR) and the extraction of bearing fault features. Poisson white noise with smaller impulse arrival rate or larger noise intensity is easier to induce SR to extract bearing fault features. The optimal matching between the nonlinear system and the input signal is formed by the optimization algorithm, which greatly improves the extraction efficiency of fault features. Compared with the normalized scale transformation (NST) method, the GST has significant advantages in recognizing the bearing structure failure. The differences and connections between Poisson white noise and Gaussian white noise are discussed in the rescaled system excited by the experiment signal. This paper might provide several practical values for recognizing bearing fault mode in the Poisson white noise.

scholarly journals Dynamics of a Nonlinear Business Cycle Model Under Poisson White Noise Excitation

2015 ◽  
Vol 3 (2) ◽  
pp. 176-183 ◽  
Author(s):  
Jiaorui Li ◽  
Shuang Li
Keyword(s):  
Business Cycle ◽  
White Noise ◽  
Economic System ◽  
Probability Density ◽  
Stationary Probability ◽  
Cycle Model ◽  
Poisson White Noise ◽  
Stationary Probability Density ◽  
White Noise Excitation ◽  
Business Cycle Model

AbstractSeveral observations in real economic systems have shown the evidence of non-Gaussianity behavior, and one of mathematical models to describe these behaviors is Poisson noise. In this paper, stationary probability density of a nonlinear business cycle model under Poisson white noise excitation has been studied analytically. By using the stochastic averaged method, the approximate stationary probability density of the averaged generalized FPK equations are obtained analytically. The results show that the economic system occurs jump and bifurcation when there is a Poisson impulse existing in the periodic economic system. Furthermore, the numerical solutions are presented to show the effectiveness of the obtained analytical solutions.

scholarly journals Noise Removal Based on Tensor Modelling for Hyperspectral Image Classification

2018 ◽  
Vol 10 (9) ◽  
pp. 1330 ◽  
Author(s):  
Salah Bourennane ◽  
Caroline Fossati ◽  
Tao Lin
Keyword(s):  
White Noise ◽  
Spatial Resolution ◽  
Thermal Noise ◽  
Hyperspectral Image ◽  
Additive White Gaussian Noise ◽  
Wiener Filter ◽  
Noise Removal ◽  
Parameters Estimation ◽  
Photon Noise ◽  
Noise Parameters

With the current state-of-the-art computer aided manufacturing tools, the spatial resolution of hyperspectral sensors is becoming increasingly higher thus making it easy to obtain much more detailed information of the scene captured. However, the improvement of the spatial resolution also brings new challenging problems to address with signal dependent photon noise being one of them. Unlike the signal independent thermal noise, the variance of photon noise is dependent on the signal, therefore many denoising methods developed for the stationary noise cannot be applied directly to the photon noise. To make things worse, both photon and thermal noise coexist in the captured hyperspectral image (HSI), thus making it more difficult to whiten noise. In this paper, we propose a new denoising framework to cope with signal dependent nonwhite noise (SDNW), Pre-estimate—Whitening—Post-estimate (PWP) loop, to reduce both photon and thermal noise in HSI. Previously, we proposed a method based on multidimensional wavelet packet transform and multi-way Wiener filter which performs both white noise and spectral dimensionality reduction, referred to as MWPT-MWF, which was restricted to white noise. We get inspired from this MWPT-MWF to develop a new iterative method for reducing photon and thermal noise. Firstly, the hyperspectral noise parameters estimation (HYNPE) algorithm is used to estimate the noise parameters, the SD noise is converted to an additive white Gaussian noise by pre-whitening procedure and then the whitened HSI is denoised by the proposed method SDNW-MWPT-MWF. As comparative experiments, the Multiple Linear Regression (MLR) based denoising method and tensor-based Multiway Wiener Filter (MWF) are also used in the denoising framework. An HSI captured by Reflective Optics System Imaging Spectrometer (ROSIS) is used in the experiments and the denoising performances are assessed from various aspects: the noise whitening performance, the Signal-to-Noise Ratio (SNR), and the classification performance. The results on the real-world airborne hyperspectral image HYDICE (Hyperspectral Digital Imagery Collection Experiment) are also presented and analyzed. These experiments show that it is worth taking into account noise signal-dependency hypothesis for processing HYDICE and ROSIS HSIs.

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