带有可加白噪音的Cahn-Hilliard方程的吸引子

证明了带有可加白噪音的Cahn-Hilliard方程在（L^^^2（G），‖·‖）空间（见文中第1部分定义）中随机吸引子的存在性．

System reliability assessment based on Wiener process and competing failure analysis

Considering the dependence and competitive relation-ship between traumatic failure and degradation,the reliability assessment of products based on competing failure analysis is studied.The hazard rate of traumatic failure is regarded as a Weibull distribution of the degradation performance,and the Wiener process is used to describe the degradation process.The parameters are estimated with the maximum likelihood estimation（MLE）method.A reliability model based on competing failure analysis is proposed.A case study of the GaAs lasers is given to validate the effectiveness of the model and its solving method.The results indicate that if only the degradation failure is considered,the estimated result will be comparably optimistic.Meanwhile,the correlation between the degradation and traumatic failure has a great influence on the accuracy of reliability assessment.

Remaining useful life estimation based on Wiener degradation processes with random failure threshold

Remaining useful life(RUL) estimation based on condition monitoring data is central to condition based maintenance(CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the failure threshold has not been studied thoroughly. In this work, by using the truncated normal distribution to model random failure threshold(RFT), an analytical and closed-form RUL distribution based on the current observed data was derived considering the posterior distribution of the drift parameter. Then, the Bayesian method was used to update the prior estimation of failure threshold. To solve the uncertainty of the censored in situ data of failure threshold, the expectation maximization(EM) algorithm is used to calculate the posteriori estimation of failure threshold. Numerical examples show that considering the randomness of the failure threshold and updating the prior information of RFT could improve the accuracy of real time RUL estimation.

Life prediction of Ni-Cd battery based on linearWiener process

Predicting the life of Ni-Cd battery for electric multiple units(EMU)can not only improve the safety and reliability of battery,but also reduce the operating costs of EMU.For this reason,a life prediction method based on linear Wiener process is proposed,which is suitable for both monotonic and non-monotonic degraded systems with accurate results.Firstly,a unary linear Wiener degradation model is established,and the parameters of the model are estimated by using the expectation-maximization algorithm(EM).With the established model,the remaining useful life(RUL)of Ni Cd battery and its distribution are obtained.Then based on the unary Wiener process degradation model,the correlation between capacity and energy is analyzed through Copula function to build a binary linear Wiener degradation model,where its parameters are estimated using Markov Chain Monte Carlo(MCMC)method.Finally,according to the binary Wiener process model,the battery RUL and its distribution are acquired.The experimental results show that the binary linear Wiener degradation model based on capacity and energy possesses higher accuracy than the unary linear wiener process degradation model.

随机Cahn-Hilliard方程的有限差分法

对随机Cahn-Hilliard方程建立六点Crank-Nicolson差分格式来求其数值解,以数值解来逼近方程的真解.最后,讨论了该格式的稳定性与收敛性.

Exact Convergence Rates of Functional Modulus of Continuity of a Wiener Process

Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-1)-1/2 - f(x)| and inf0<t<1-h sup0<x<1|(W(t + hx) -W(t))(2hlogh-1)-1/2 - f(x)| for any f ∈ S. As a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.

Objective Bayesian Analysis of Degradation Model with Respect to a Wiener Process

This paper proposes an objective Bayesian method to study the degradation model with respect to a Wiener process.The Jeffreys prior and reference prior for the parameters are derived,and the propriety of the posteriors under these priors is validated.Two sampling algorithms are introduced to compute the posteriors.A simulation study is conducted to investigate the performance of the objective Bayesian procedure.Finally,the authors apply the approach to a degradation data.

A RANDOM FUNCTIONAL CENTRAL LIMIT THEOREM FOR PROCESSES OF PRODUCT SUMS OF LINEAR PROCESSES GENERATED BY MARTINGALE DIFFERENCES

A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

It is proved that φ(s) = s2 log |logs| is the correct function to give the Hausdorff measureof a sample path of the Westwater process.