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.

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.

Real time remaining useful life prediction based on nonlinear Wiener based degradation processes with measurement errors

Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item's individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.

How big are the Csorgo-Revesz increments of two-parameter Wiener processes?

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.

Necessary Conditions for Renewal Processes Approximating to Wiener Processes

Let {X, X i ; i≥1} be a sequence of i.i.d.r.v’.s, Z (t)= t i=1 X i,t≥0. Consider the renewal process N(t) =inf{x; Z(x) 】t}. In this paper we study the necessary momentconditions for { N(t) ; t≥0} approximating to Wiener processes.Our results have improved those of Csrg, Horváth and Stei, Horváth and Steinebach

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.

Residual life estimation based on bivariate Wiener degradation process with measurement errors

An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.

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.

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.

ON THE FRACTAL NATURE OF INCREMENTS OF THE INFINITE SERIES OF OU PROCESSES RELATED TO THE CHUNG LIL

Abstract The author proves that the set of points where the Chung type LIL fails for the path of the infinite series of independent Ornstein Uhlenbeck processes is a random fractal, and evaluates its Hausdorff dimension.

Remaining Useful Life Prediction Method for Multi-Component System Considering Maintenance:Subsea Christmas Tree System as A Case Study

Maintenance is an important technical measure to maintain and restore the performance status of equipment and ensure the safety of the production process in industrial production,and is an indispensable part of prediction and health management.However,most of the existing remaining useful life(RUL)prediction methods assume that there is no maintenance or only perfect maintenance during the whole life cycle;thus,the predicted RUL value of the system is obviously lower than its actual operating value.The complex environment of the system further increases the difficulty of maintenance,and its maintenance nodes and maintenance degree are limited by the construction period and working conditions,which increases the difficulty of RUL prediction.An RUL prediction method for a multi-omponent system based on the Wiener process considering maintenance is proposed.The performance degradation model of components is established by a dynamic Bayesian network as the initial model,which solves the uncertainty of insufficient data problems.Based on the experience of experts,the degree of degradation is divided according to Poisson process simulation random failure,and different maintenance strategies are used to estimate a variety of condition maintenance factors.An example of a subsea tree system is given to verify the effectiveness of the proposed method.

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.

Remaining useful lifetime prediction for equipment based on nonlinear implicit degradation modeling

Nonlinearity and implicitness are common degradation features of the stochastic degradation equipment for prognostics.These features have an uncertain effect on the remaining useful life(RUL)prediction of the equipment.The current data-driven RUL prediction method has not systematically studied the nonlinear hidden degradation modeling and the RUL distribution function.This paper uses the nonlinear Wiener process to build a dual nonlinear implicit degradation model.Based on the historical measured data of similar equipment,the maximum likelihood estimation algorithm is used to estimate the fixed coefficients and the prior distribution of a random coefficient.Using the on-site measured data of the target equipment,the posterior distribution of a random coefficient and actual degradation state are step-by-step updated based on Bayesian inference and the extended Kalman filtering algorithm.The analytical form of the RUL distribution function is derived based on the first hitting time distribution.Combined with the two case studies,the proposed method is verified to have certain advantages over the existing methods in the accuracy of prediction.

Joint optimization of maintenance inspection and spare provisioning for aircraft deteriorating parts

With the wide application of condition based maintenance(CBM) in aircraft maintenance practice, the joint optimization of maintenance and inventory management, which can take full advantage of CBM and reduce the aircraft operational cost, is receiving increasing attention. In order to optimize the inspection interval, maintenance decision and spare provisioning together for aircraft deteriorating parts, firstly, a joint inventory management strategy is presented, then, a joint optimization of maintenance inspection and spare provisioning for aircraft parts subject to the Wiener degradation process is proposed based on the strategy.Secondly, a combination of the genetic algorithm(GA) and the Monte Carol method is developed to minimize the total cost rate.Finally, a case study is conducted and the proposed joint optimization model is compared with the existing optimization model and the airline real case. The results demonstrate that the proposed model is more beneficial and effective. In addition, the sensitivity analysis of the proposed model shows that the lead time has higher influence on the optimal results than the urgent order cost and the corrective maintenance cost, which is consistent with the actual situation of aircraft maintenance practices and inventory management.

Remaining lifetime prediction for nonlinear degradation device with random effect

For the large number of nonlinear degradation devices existing in a project, the existing methods have not systematically studied the effects of random effect on the remaining lifetime(RL),the accuracy and efficiency of the parameters estimation are not high, and the current degradation state of the target device is not accurately estimated. In this paper, a nonlinear Wiener degradation model with random effect is proposed and the corresponding probability density function(PDF) of the first hitting time(FHT)is deduced. A parameter estimation method based on modified expectation maximum(EM) algorithm is proposed to obtain the estimated value of fixed coefficient and the priori value of random coefficient in the model. The posterior value of the random coefficient and the current degradation state of target device are updated synchronously by the state space model(SSM) and the Kalman filter algorithm. The PDF of RL with random effect is deduced. A simulation example is analyzed to verify that the proposed method has the obvious advantage over the existing methods in parameter estimation error and RL prediction accuracy.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

Fiber optical gyroscope(FOG)is a highly reliable navigation element,and the degradation trajectories of its two accuracy indexes are monotonic and non-monotonic respectively.In this paper,a flexible accelerated degradation testing(ADT)model is used for analyzing the bivariate dependent degradation process of FOG.The time-varying copulas are employed to consider the dynamic dependency structure between two marginal degradation processes as the Wiener process and the inverse Gaussian process.The statistical inference is implemented by utilizing an inference function for the margins(IFM)approach.It is demonstrated that the proposed method is powerful in modeling the joint distribution with various margins.

REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE

We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2（DN, σ） space, where DN is an arbitrary （bounded or unbounded） domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.

Moments and limiting distribution of a portfolio of whole life annuity policies

A dual random model of a portfolio of variable amount whole life annuity is set with the mth moment of the present value of benefits, and the respective expressions of the moments under the assumption that the force of interest accumulation function is Wiener process or Ornstein-Uhlenbeck process. Furthermore, the limiting distribution of average cost of this portfolio is discussed with the expression of the limiting distribution under the assumption that the force of interest accumulation is an independent increment process.