Random vibration of hysteretic systems under Poisson white noise excitations

Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

Dynamics of a prey-predator system under Poisson white noise excitation

The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.

The Stochastic stability of a Logistic model with Poisson white noise

The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itp differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species.

Poisson Image Restoration via Transformed Network

There is a Poisson inverse problem in biomedical imaging,fluorescence microscopy and so on.Since the observed measurements are damaged by a linear operator and further destroyed by Poisson noise,recovering the approximate original image is difficult.Motivated by the decouple scheme and the variance-stabilizing transformation(VST)strategy,we propose a method of transformed convolutional neural network(CNN)to restore the observed image.In the network,the Conv-layers play the role of a linear inverse filter and the distribution transformation simultaneously.Furthermore,there is no batch normalization(BN)layer in the residual block of the network,which is devoted to tackling with the non-Gaussian recovery procedure.The proposed method is compared with state-of-the-art Poisson deblurring algorithms,and the experimental results show the effectiveness of the method.

Dynamical analysis of an SDOF quasi‐linear system with jump noises and multitime‐delayed feedback forces

In this paper,stochastic dynamics of a single degree‐of‐freedom quasi‐linear system with multitime delays and Poisson white noises are investigated using an approximate procedure based on the stochastic averaging method.The simplified equations,including the averaged stochastic differential equation and the averaged generalized Fokker–Planck–Kolmogorov equation,are obtained to calculate the probability density functions(PDFs)to explore stationary responses.The expression of the Lyapunov exponent is presented to examine the asymptotic stochastic Lyapunov stability.An illustrative example of a quasi‐linear oscillator with two Poisson white noises controlled by two time‐delayed feedback forces is worked out to demonstrate the validity of the proposed method.The approximate stationary PDFs of stochastic responses and asymptotic stochastic stability are demonstrated numerically and theoretically.The results show that the Gaussian white noise has a stronger influence on the dynamics than the Poisson white noise with a small mean arrival rate.Moreover,the influence of the time delay and noise parameters on stochastic dynamics is investigated.It is found that the PDFs under the Poisson white noise approach those under Gaussian white noise as the mean arrival rate increases.The time delay can induce stochastic P‐bifurcation of the system.It is also found that the increase of time delay and the mean arrival rates of the Poisson white noises will broaden the unstable parameter region.The comparison between numerical and theoretical results shows the effectiveness of the proposed method.

Edge detection algorithm based on ICA-domain shrinkage in noisy images

We propose a robust edge detection method based on ICA-domain shrinkage （in- dependent component analysis）. It is known that most basis functions extracted from natural images by ICA are sparse and similar to localized and oriented receptive fields, and in the proposed edge detection method, a target image is first transformed by ICA basis functions and then the edges are detected or recon- structed with sparse components. Furthermore, by applying a shrinkage algorithm to filter out the components of noise in ICA-domain, we can readily obtain the sparse components of the original image, resulting in a kind of robust edge detec- tion even for a noisy image with a very low SN ratio. The efficiency of the proposed method is demonstrated by experiments with some natural images.

Covariances of Linear Stochastic Differential Equations for Analyzing Computer Networks

Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.