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
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
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, 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
Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<...Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-1)-1/2 - f(x)| and inf0<t<1-h sup0<x<1|(W(t + hx) -W(t))(2hlogh-1)-1/2 - f(x)| for any f ∈ S. As a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.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
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, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are o...In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest.展开更多
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 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.
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.
基金Supported by NNSFC (10071072) and Science Foundation of Hangzhou Teacher's College.
文摘Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-1)-1/2 - f(x)| and inf0<t<1-h sup0<x<1|(W(t + hx) -W(t))(2hlogh-1)-1/2 - f(x)| for any f ∈ S. As a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.
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the National Natural Science Foundation of China (Grant No. 10071072) by NSC 88-2118-M029-001 of Taiwan of China.
文摘In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest.
