In this paper, we discuss the problem of extreme value for Brownian motion with positive drift. We obtain the joint distribution of the maximum excursion and the minimum excursion.
As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of im...As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of imperfect maintenance activities usually assumed that maintenance activities have a single influence on the degradation level or degradation rate, but not on both.Aimed at this problem, this paper proposes a new degradation modeling and RUL estimation method taking the influence of imperfect maintenance activities on both the degradation level and the degradation rate into account. Toward this end, a stochastic degradation model considering imperfect maintenance activities is firstly constructed based on the diffusion process. Then, the Probability Density Function（PDF） of the RUL is derived by the convolution operator under the concept of First Hitting Time（FHT）. To implement the proposed RUL estimation method,the Maximum Likelihood Estimation（MLE） is utilized to estimate the degradation related parameters based on the Condition Monitoring（CM） data, while the Bayesian method is utilized to estimate the maintenance related parameters based on the maintenance data. Finally, a numerical example and a practical case study are provided to demonstrate the superiority of the proposed method. The experimental results show that the proposed method could greatly improve the RUL estimation accuracy for the degrading equipment subjected to imperfect maintenance activities.展开更多
基金Supported by the National Natural Foundation of China(10271062,10411076)Supported by the Research Fund for the Doctorial Program of Qufu Normal University(20050701)
文摘In this paper, we discuss the problem of extreme value for Brownian motion with positive drift. We obtain the joint distribution of the maximum excursion and the minimum excursion.
基金co-supported by the National Science Foundation of China(NSFC)(Nos.61573365,61603398,61374126,61473094,and 61773386)the Young Talent Fund of University Association for Science and Technology in Shaanxi,Chinathe Young Elite Scientists Sponsorship Program(YESS)by China Association for Science and Technology(CAST)
文摘As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of imperfect maintenance activities usually assumed that maintenance activities have a single influence on the degradation level or degradation rate, but not on both.Aimed at this problem, this paper proposes a new degradation modeling and RUL estimation method taking the influence of imperfect maintenance activities on both the degradation level and the degradation rate into account. Toward this end, a stochastic degradation model considering imperfect maintenance activities is firstly constructed based on the diffusion process. Then, the Probability Density Function（PDF） of the RUL is derived by the convolution operator under the concept of First Hitting Time（FHT）. To implement the proposed RUL estimation method,the Maximum Likelihood Estimation（MLE） is utilized to estimate the degradation related parameters based on the Condition Monitoring（CM） data, while the Bayesian method is utilized to estimate the maintenance related parameters based on the maintenance data. Finally, a numerical example and a practical case study are provided to demonstrate the superiority of the proposed method. The experimental results show that the proposed method could greatly improve the RUL estimation accuracy for the degrading equipment subjected to imperfect maintenance activities.
