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 fo...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.展开更多
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 i...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.展开更多
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-...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.展开更多
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 non...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.展开更多
<div style="text-align:justify;"> <span style="font-family:Verdana;">Various open source software are managed by using several bug tracking systems. In particular, the open source softw...<div style="text-align:justify;"> <span style="font-family:Verdana;">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.</span> </div>展开更多
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 ti...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.展开更多
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...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。展开更多
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 ...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.展开更多
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 th...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.展开更多
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^...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.展开更多
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, ov...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.展开更多
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)...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.展开更多
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 ...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.展开更多
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 a...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.展开更多
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 ...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)<∞.展开更多
基金Supported by the Natural Science Foundation of Hubei Province of China(2011CDB229)
文摘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.
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘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.
文摘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.
基金National Natural Science Foundation of China (51965052,51865045)Scientific Research Project of Higher Education Institutions of Inner Mongolia Autonomous Region (NJZY22114).
文摘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.
文摘<div style="text-align:justify;"> <span style="font-family:Verdana;">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.</span> </div>
文摘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.
文摘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。
基金supported by the National Natural Science Foundation of China(No.51305011)the National Basic Research Program of China(No.2014CB046402)the 111 Project of China
文摘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.
基金supported by the Aeronautical Science Foundation of China(No.201428960221)
文摘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.
文摘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.
基金Acknowledgements This research was partially supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA06030200), the National Natural Science Foundation of China (Grant Nos. M1552006, 61403369, 61272427, and 61363030), Xinjiang Uygur Autonomous Region Science and Technology Project (201230123), Beijing Key Lab of Intelligent Telecommunication Software, Multimedia (ITSM201502), Guangxi Key Laboratory of Trusted Software (kx201418).
文摘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.
基金Project supported by National Science Foundation of ChinaZhejiang Province
文摘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.
基金The work is supported by the Humanities and Social Sciences Foundation of Ministry of Education,China(Grant No.17YJC910003).
文摘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.
基金Rong-Xian Yue’s research was supported by the National Natural Science Foundation of China[grant number 11471216]Daojiang He’s research was supported by the National Natural Science Foundation of China[grant number 11201005].
文摘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.
基金supported by National Natural Science Foundation of China(Grant Nos.11971063 and 11731012)Hunan Natural Science Foundation of China(Grant No.2017JJ2271)+1 种基金the Natural Science Foundation of Guangdong Province of China(Grant No.2015A030313628)the French Government\Investissements d'Avenir"Program(Grant No.ANR-11-LABX-0020-01).
文摘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)<∞.