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
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 fail...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.展开更多
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 degrad...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.展开更多
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.
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) ...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展开更多
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 fai...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.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
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
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 degra...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.展开更多
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
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.
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 predic...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.展开更多
This paper proposes a universal framework for constructing bivariate stochastic processes,going beyond the limitations of copulas and offering a potentially simpler alternative.The achieved generality of the construct...This paper proposes a universal framework for constructing bivariate stochastic processes,going beyond the limitations of copulas and offering a potentially simpler alternative.The achieved generality of the construction methods extends its applicability to diverse stochastic processes also including discrete as well as continuous time cases.The initially given two arbitrary univariate stochastic processes{Y_(t)},{Z_(t)},are only assumed to share the same time t.When considered as describing(time dependent)random quantities that are physically separated(the baseline case),the processes are independent.From this trivial case we move to the case when physical interactions between the quantities make them stochastically dependent random variables at any moment t.For each time epoch t,we impose stochastic dependence on two“initially independent”random variables Y_(t),Z_(t) by multiplying the product of their survival functions by a proper“dependence factor”φ_(t)(y_(t), z_(t)),obtaining in this way a universal(“canonical”)form valid for any(!)bivariate distribution.In some known cases,however,this form may become complicated thou it always exists and is unique.The dependence factor,basically,but not always,has the form φ_(t)(y, z)=exp[-∫^(y)_(0)∫^(z)_(0)Ψ_(t)(s ,u )dsdu]whenever such a continuous function Ψ_(t)(s ,u ) exists,for each t.That representation of stochastic dependence by the functions Ψ_(t)(s ,u ) leads,in turn,to the phenomenon of change of the original(baseline)hazard rates of the marginals,similar to those analyzed by Cox and,especially Aalen for single pairs(or sets)of,time independent,random variables.That is why,until Section 4,we consider only single random vectors(Y,Z)'joint survival functions,mostly as a preparation to the theory of bivariate stochastic processes{(Y_(t),Z_(t))}constructions as initiated in Section 4.The bivariate constructions are illustrated by examples of some applications in biomedical and econometric areas.展开更多
With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance s...With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance strategies often struggle to accurately predict the degradation process of equipment,leading to excessive maintenance costs or potential failure risks.However,existing prediction methods based on statistical models are difficult to adapt to nonlinear degradation processes.To address these challenges,this study proposes a novel condition-based maintenance framework for planetary gearboxes.A comprehensive full-lifecycle degradation experiment was conducted to collect raw vibration signals,which were then processed using a temporal convolutional network autoencoder with multi-scale perception capability to extract deep temporal degradation features,enabling the collaborative extraction of longperiod meshing frequencies and short-term impact features from the vibration signals.Kernel principal component analysis was employed to fuse and normalize these features,enhancing the characterization of degradation progression.A nonlinear Wiener process was used to model the degradation trajectory,with a threshold decay function introduced to dynamically adjust maintenance strategies,and model parameters optimized through maximum likelihood estimation.Meanwhile,the maintenance strategy was optimized to minimize costs per unit time,determining the optimal maintenance timing and preventive maintenance threshold.The comprehensive indicator of degradation trends extracted by this method reaches 0.756,which is 41.2%higher than that of traditional time-domain features;the dynamic threshold strategy reduces the maintenance cost per unit time to 55.56,which is 8.9%better than that of the static threshold optimization.Experimental results demonstrate significant reductions in maintenance costs while enhancing system reliability and safety.This study realizes the organic integration of deep learning and reliability theory in the maintenance of planetary gearboxes,provides an interpretable solution for the predictive maintenance of complex mechanical systems,and promotes the development of condition-based maintenance strategies for planetary gearboxes.展开更多
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 equipmen...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.展开更多
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 aircr...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.展开更多
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Projects(51475462,61174030,61473094,61374126)supported by the National Natural Science Foundation of China
文摘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.
基金Projects(51475462,61374138,61370031)supported by the National Natural Science Foundation of China
文摘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.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10131040)China Postdoctoral Science Foundation.
文摘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.
文摘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
基金The National Natural Science Foundation of China(No.50405021)
文摘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.
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.
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Project(60904002)supported by the National Natural Science Foundation of China
文摘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.
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.
基金financially supported by the National Key Research and Development Program of China(Grant No.2022YFC3004802)the National Natural Science Foundation of China(Grant Nos.52171287,52325107)+3 种基金High Tech Ship Research Project of Ministry of Industry and Information Technology(Grant Nos.2023GXB01-05-004-03,GXBZH2022-293)the Science Foundation for Distinguished Young Scholars of Shandong Province(Grant No.ZR2022JQ25)the Taishan Scholars Project(Grant No.tsqn201909063)the sub project of the major special project of CNOOC Development Technology,“Research on the Integrated Technology of Intrinsic Safety of Offshore Oil Facilities”(Phase I),“Research on Dynamic Quantitative Analysis and Control Technology of Risks in Offshore Production Equipment”(Grant No.HFKJ-2D2X-AQ-2021-03)。
文摘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.
文摘This paper proposes a universal framework for constructing bivariate stochastic processes,going beyond the limitations of copulas and offering a potentially simpler alternative.The achieved generality of the construction methods extends its applicability to diverse stochastic processes also including discrete as well as continuous time cases.The initially given two arbitrary univariate stochastic processes{Y_(t)},{Z_(t)},are only assumed to share the same time t.When considered as describing(time dependent)random quantities that are physically separated(the baseline case),the processes are independent.From this trivial case we move to the case when physical interactions between the quantities make them stochastically dependent random variables at any moment t.For each time epoch t,we impose stochastic dependence on two“initially independent”random variables Y_(t),Z_(t) by multiplying the product of their survival functions by a proper“dependence factor”φ_(t)(y_(t), z_(t)),obtaining in this way a universal(“canonical”)form valid for any(!)bivariate distribution.In some known cases,however,this form may become complicated thou it always exists and is unique.The dependence factor,basically,but not always,has the form φ_(t)(y, z)=exp[-∫^(y)_(0)∫^(z)_(0)Ψ_(t)(s ,u )dsdu]whenever such a continuous function Ψ_(t)(s ,u ) exists,for each t.That representation of stochastic dependence by the functions Ψ_(t)(s ,u ) leads,in turn,to the phenomenon of change of the original(baseline)hazard rates of the marginals,similar to those analyzed by Cox and,especially Aalen for single pairs(or sets)of,time independent,random variables.That is why,until Section 4,we consider only single random vectors(Y,Z)'joint survival functions,mostly as a preparation to the theory of bivariate stochastic processes{(Y_(t),Z_(t))}constructions as initiated in Section 4.The bivariate constructions are illustrated by examples of some applications in biomedical and econometric areas.
基金funded by scientific research projects under Grant JY2024B011.
文摘With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance strategies often struggle to accurately predict the degradation process of equipment,leading to excessive maintenance costs or potential failure risks.However,existing prediction methods based on statistical models are difficult to adapt to nonlinear degradation processes.To address these challenges,this study proposes a novel condition-based maintenance framework for planetary gearboxes.A comprehensive full-lifecycle degradation experiment was conducted to collect raw vibration signals,which were then processed using a temporal convolutional network autoencoder with multi-scale perception capability to extract deep temporal degradation features,enabling the collaborative extraction of longperiod meshing frequencies and short-term impact features from the vibration signals.Kernel principal component analysis was employed to fuse and normalize these features,enhancing the characterization of degradation progression.A nonlinear Wiener process was used to model the degradation trajectory,with a threshold decay function introduced to dynamically adjust maintenance strategies,and model parameters optimized through maximum likelihood estimation.Meanwhile,the maintenance strategy was optimized to minimize costs per unit time,determining the optimal maintenance timing and preventive maintenance threshold.The comprehensive indicator of degradation trends extracted by this method reaches 0.756,which is 41.2%higher than that of traditional time-domain features;the dynamic threshold strategy reduces the maintenance cost per unit time to 55.56,which is 8.9%better than that of the static threshold optimization.Experimental results demonstrate significant reductions in maintenance costs while enhancing system reliability and safety.This study realizes the organic integration of deep learning and reliability theory in the maintenance of planetary gearboxes,provides an interpretable solution for the predictive maintenance of complex mechanical systems,and promotes the development of condition-based maintenance strategies for planetary gearboxes.
基金supported by the National Defense Foundation of China(7160118371901216)the China Postdoctoral Science Foundation(2017M623415)
文摘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.
基金supported by the Fundamental Research Funds for the Central Universities(NS2015072)
文摘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.
