Functional sample path properties of subsequence's C-R increments for a Wiener process in Hlder norm

In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen＇s law of iterated logarithm for a Wiener process.

A GENERAL FORM OF THE INCREMENTS OF A TWO-PARAMETER WIENER PROCESS

In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.

A GENERAL FORM OF THE INCREMENTS OF TWO-PARAMETER FRACTIONAL WIENER PROCESS

A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.

Rolling Bearing Remaining Useful Life Prediction Based on Wiener Process

Rolling bearing is the key part of mechanical system.Accurate prediction of bearing life can reduce maintenance costs,improve availability,and prevent catastrophic consequences,aiming at solving the problem of the nonlinear,random and small sample problems faced by rolling bearings in actual operating conditions.In this work,the nonlinearWiener process with random effect and unbiased estimation of unknown parameters is used to predict the remaining useful life of rolling bearings.Firstly,random effects and nonlinear parameters are added to the traditional Wiener process,and a parameter unbiased estimation method is used to estimate the positional parameters of the constructed Wiener model.Finally,the model is validated using a common set of bearing datasets.Experimental results show that compared with the traditional maximum likelihood function estimation method,the parameter unbiased estimation method can effectively improve the accuracy and stability of the parameter estimation results.The model has a good fitting effect,which can accurately predict the remaining useful life of rolling bearing.

OSS Effort Expense Optimization Based on Wiener Process Model and GA

Various open source software are managed by using several bug tracking systems. In particular, the open source software extends to the cloud service and edge computing. Recently, OSF Edge Computing Group is launched by OpenStack. There are big data behind the internet services such as cloud and edge computing. Then, it is important to consider the impact of big data in order to assess the reliability of open source software. Various optimal software release problems have been proposed by specific researchers. In the typical optimal software release problems, the cost parameters are defined as the known parameter. However, it is difficult to decide the cost parameter because of the uncertainty. The purpose of our research is to estimate the effort parameters included in our models. In this paper, we propose an estimation method of effort parameter by using the genetic algorithm. Then, we show the estimation method in section 3. Moreover, we analyze actual data to show numerical examples for the estimation method of effort parameter. As the research results, we found that the OSS managers would be able to comprehend the human resources required before the OSS project in advance by using our method.

Extended Wiener Process in Nonstandard Analysis

Standing on a different view point from Anderson, we prove that the extended Wiener process defined by Anderson satisfies the definition of the Wiener process in standard analysis, for example the Wiener process at time t obeys the normal distribution N(0,t) by showing the central limit theorem. The essential theory used in the proof is the extended convolution property in nonstandard analysis which is shown by Kanagawa, Nishiyama and Tchizawa (2018). When processing the extension by non-standardization, we have already pointed out that it is needed to proceed the second extension for the convolution, not only to do the first extension for the delta function. In Section 2, we shall introduce again the extended convolution as preliminaries described in our previous paper. In Section 3, we shall provide the extended stochastic process using a hyper number N, and it satisfies the conditions being Wiener process. In Section 4, we shall give a new proof for the non-differentiability in the Wiener process.

基于Wiener退化过程的动车组部件状态-机会维修模型分析与研究

针对动车组多部件存在运行维修成本高、欠维修或过维修的现象以及故障影响范围大等问题,提出一种基于Wiener退化过程的部件状态-机会维修优化模型。该模型利用Wiener过程描述部件在运行过程中的劣化程度,通过基于指数分布的随机几何过程反映不完全维修后部件的劣化损伤,同时利用定期检测获取部件的实际劣化值。从随机过程和拓扑的角度,分析不同类型维修策略之间的区别与联系。结合单部件状态维修优化策略,求得各部件的最优状态阈值和维修检测周期。引入机会阈值与状态阈值的比值,结合部件退化过程与状态阈值、机会阈值之间的关系,推导部件状态、机会维修次数期望值的数学表达式,建立状态-机会维修策略模型,采用蒙特卡洛算法进行模拟,确定各部件的最佳机会阈值,达到优化维修费用率的目标。以某型号动车组牵引供电系统为例,通过仿真验证,表明采取状态-机会维修模型,可以有效减少停机次数,降低维修费用率。

基于Wiener过程的多阶段非线性复杂退化产品可靠性分析模型

为提高非线性退化轨迹拟合的精度,针对多阶段退化中的非线性规律建立Wiener过程模型,考虑变点的连续性与部件个体的差异性,给出基于非线性复杂退化的可靠性评估方法。结合幂律函数推导出非线性多阶段Wiener过程模型,得到模型参数的极大似然估计量;通过最小均方误差原则给出变点以及幂参数的初值确定方法;根据SIC(schwarz information criterion)方法得到模型变点的精确值,并检验其准确性;结合不同部件之间的差异性,得到变点的连续分布;推导出非线性Wiener过程连续时段内的可靠度函数估计;利用本模型对高压脉冲电容器电容相对变化量的退化数据建模,与线性建模结果对比,验证多阶段Wiener过程模型在可靠性评估方面的有效性与可行性,估计结果更接近真实值。

基于Wiener随机过程模型的橡胶老化性能预测及剩余寿命分析

橡胶老化性能预测及寿命分析是橡胶工程应用中关键技术。开展了硅橡胶95℃、105℃、115℃、125℃不同温度加速老化试验,根据硅橡胶性能特点及其应用过程需要,选择硅橡胶永久压缩变形作为老化性能表征量。结合橡胶老化机理,分析了橡胶老化性能随机特性,提出利用Wiener随机过程构建橡胶老化模型,进行了硅橡胶老化性能预测,给出了各试验点预测性能概率密度,分析结果表明预测误差最大10.15%。结合Wiener随机过程理论,开展了硅橡胶剩余寿命分析,对寿命分析方法进行了精度分析,计算分析结果表明寿命分析最大误差为11.76%,寿命分析方法可信,计算结果可靠。利用Arrhenius加速模型,给出了不同加速温度下硅橡胶寿命,计算得到常温25℃温度下,硅橡胶平均寿命为76年。

Remaining useful life prediction based on the Wiener process for an aviation axial piston pump

An aviation hydraulic axial piston pump＇s degradation fiom comprehensive wear is a typical gradual failure model. Accurate wear prediction is difficult as random and uncertain char- acteristics must be factored into the estimation. The internal wear status of the axial piston pump is characterized by the return oil flow based on fault mechanism analysis of the main frictional pairs in the pump. The performance degradation model is described by the Wiener process to predict the remaining useful life （RUL） of the pump. Maximum likelihood estimation （MLE） is performed by utilizing the expectation maximization （EM） algorithm to estimate the initial parameters of the Wiener process while recursive estimation is conducted utilizing the Kalman filter method to estimate the drift coefficient of the Wiener process. The RUL of the pump is then calculated accord- ing to the performance degradation model based on the Wiener process. Experimental results indi- cate that the return oil flow is a suitable characteristic for reflecting the internal wear status of the axial piston pump, and thus the Wiener process-based method may effectively predicate the RUL of the pump.

Remaining useful life prediction based on variation coefficient consistency test of a Wiener process

High-cost equipment is often reused after maintenance, and whether the information before the maintenance can be used for the Remaining Useful Life （RUL） prediction after the maintenance is directly determined by the consistency of the degradation pattern before and after the maintenance. Aiming at this problem, an RUL prediction method based on the consistency test of a Wiener process is proposed. Firstly, the parameters of the Wiener process estimated by Maximum Likelihood Estimation （MLE） are proved to be biased, and a modified unbiased estimation method is proposed and verified by derivation and simulations. Then, the h statistic is constructed according to the reciprocal of the variation coefficient of the Wiener process, and the sampling distribution is derived. Meanwhile, a universal method for the consistency test is proposed based on the sampling distribution theorem, which is verified by simulation data and classical crack degradation data. Finally, based on the consistency test of the degradation model, a weighted fusion RUL prediction method is presented for the fuel pump of an airplane, and the validity of the presented method is verified by accurate computation results of real data, which provides a theoretical and practical guidance for engineers to predict the RUL of equipment after maintenance.

Functional Limit Theorems for C-R Increments of lp-Valued Wiener Processes in the Norm

In this paper, based on accurately large deviation formulae established in strong topology generated by the Holder norm for l^2-valued Wiener processes, we obtain the functional limit theorems for C-R increments of l^p-valued Wiener processes in the Holder norm.

Boosting imbalanced data learning with Wiener process oversampling

Learning from imbalanced data is a challenging task in a wide range of applications, which attracts significant research efforts from machine learning and data mining community. As a natural approach to this issue, oversampling balances the training samples through replicating existing samples or synthesizing new samples. In general, synthesization outperforms replication by supplying additional information on the minority class. However, the additional information needs to follow the same normal distribution of the training set, which further constrains the new samples within the predefined range of training set. In this paper, we present the Wiener process oversampling （WPO） technique that brings the physics phenomena into sample synthesization. WPO constructs a robust decision region by expanding the attribute ranges in training set while keeping the same normal distribution. The satisfactory performance of WPO can be achieved with much lower computing complexity. In addition, by integrating WPO with ensemble learning, the WPOBoost algorithm outperforms many prevalent imbalance learning solutions.

Exact Rates of Convergence of Functional Limit Theorems for Csorgo-Revesz Increments of a Wiener Process

Let {W(t): t≥0} be a standard Wiener process and S be the Strassen set of functions. We investigate the exact rates of convergence to zero (as T→∞) of the variables sup_(0≤≤T-a_T inf_(f∈S sup_(0≤r≤1 |Y_t, T(x)-f(x)] and inf_(0≤t≤T-a_T sup_(0≤x≤1|Y_(t.T)(x)-f(x)| for any given f∈S, where Y_(t.T)(x)=(W(t+xa_T)-W(t))(2a_T(logTa_T^(-1)+log logT))^(-1/2). We establish a relation between how small the increments are and the functional limit results of Csrg-Revesz increments for a Wiener process. Similar results for partial sums of i.i.d, random variables are also given.

Objective Bayesian analysis for the accelerated degradation model usingWiener process with measurement errors

The Wiener process as a degradation model plays an important role in the degradation analysis.In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wienermodel which is subjected to measurement errors. The Jeffreys prior and reference priors underdifferent group orderings are first derived, the propriety of the posteriors is then validated. It isshown that two of the reference priors can yield proper posteriors while the others cannot. A simulation study is carried out to investigate the frequentist performance of the approach comparedto the maximum likelihood method. Finally, the approach is applied to analyse a real data.

Step-stress accelerated degradation test planning based on Wiener processwith correlation

To assess the lifetime distribution of highly reliable or expensive product,one of the most commonly used strategies is to construct step-stress accelerated degradation test(SSADT)which can curtail the test duration and reduce the test cost.In reality,it is not unusual for a unit with a higher degradation rate which exhibits a more volatile degradation path.Recently,Ye,Chen,and Shen[(2015).A new class of Wiener process models for degradation analysis.Reliability Engineering and System Safety,139,58–67]proposed a Wiener process to capture the positive correlation between the drift rate and the volatility.In this paper,an optimal SSADT plan is developed under the assumption that the underlying degradation path follows the Wiener process with correlation.Firstly,the stochastic diffusion process is introduced to model a typical SSADT problem.Then the design variables,including the sample size,the measurement frequency and the numbers of measurements under each stress level,are optimised by minimising the asymptotic variance of the estimated p-percentile of the product’s lifetime distribution subject to the total experimental cost not exceeding a pre-specified budget.Finally,a numerical example is presented to illustrate the proposed method.

Asymptotic expansions in the central limit theorem for a branching Wiener process

We consider a branching Wiener process in R^(d),in which particles reproduce as a super-critical Galton-Watson process and disperse according to a Wiener process.For B⊂R^(d),let Z_(n)(B) be the number of particles of generation n located in B.The study of the central limit theorem and related results about the counting measure Z_(n)(·)is important because such results give good descriptions of the con guration of the branching Wiener process at time n.In earlier works,the exact convergence rate in the central limit theorem and the asymptotic expansion until the third order have been given.Here,we establish the asymptotic expansion of any order in the central limit theorem under a moment condition of the form EX(logX)^(1+λ)<∞.

基于Wiener过程的密封圈可靠性研究

针对传统寿命试验方法评估液压缸可靠性出现的耗时长、费用高且无法满足实际需求等问题,基于性能退化的可靠性评估方法,通过性能退化随时间的变化规律对液压缸进行了寿命预测与可靠性评估。采用数值模拟手段判定了各个密封圈的安全性与稳定性,利用Archard磨损模型得到了密封圈的磨损体积曲线。基于考虑随机效应的Wiener过程建立的密封圈可靠性模型,得到了首达时间失效定义下的寿命分布,确立了退化模型参数与可靠度之间的关系,并建立了液压缸密封圈的可靠度数学表达式。搭建了往复式试验平台,试验结果表明,基于Wiener过程的性能退化模型能够更好地描述密封圈的性能退化过程,与传统寿命试验方法相比,对密封圈性能退化的预测更为准确和有效。

盐雾干湿循环作用下基于Wiener过程的钢筋混凝土劣化行为研究

针对西部盐渍土地区钢筋混凝土结构病害严重问题,通过盐雾与烘干相结合的方法模拟该地区大气环境,对钢筋混凝土进行室内加速腐蚀劣化试验。设置未掺矿物掺合料(P组)、单掺30%粉煤灰(PF组)、单掺30%矿粉(PS组)及15%粉煤灰与15%矿粉复掺(PFS组)4个配合比,采用混凝土相对动弹性模量(Er)和钢筋腐蚀电流密度(icorr)作为性能劣化指标,分别表征钢筋混凝土保护层及内部钢筋在盐雾干湿循环环境下的劣化规律及矿物掺合料掺量、种类对其劣化行为的影响作用。基于钢筋混凝土性能劣化规律研究结果,结合Wiener随机过程对其性能劣化全过程进行描述,并进行可靠性分析。研究结果表明:在盐雾干湿循环作用下,钢筋混凝土内部钢筋及外部混凝土保护层的耐腐蚀性呈现出先强化后劣化的变化趋势,活性矿物掺合料的掺入可以有效抑制其腐蚀劣化速度,其大小关系为:PS>PFS>PF>P;icorr增量与Er增量随时间的变化规律均服从正态分布,即Wiener随机过程可有效描述盐雾干湿循环作用下钢筋混凝土性能劣化全过程;P组可靠度在200 d左右接近于0,而PS组可靠度在400 d左右接近于0,与试验测试结果相吻合。研究结果可为西部盐渍土地区钢筋混凝土结构耐久性设计及低碳长效运维提供理论支撑。