Remaining useful life prediction of aero-engines based on random-coefficient regression model considering random failure threshold

Remaining useful life(RUL)prediction is one of the most crucial components in prognostics and health management(PHM)of aero-engines.This paper proposes an RUL prediction method of aero-engines considering the randomness of failure threshold.Firstly,a random-coefficient regression(RCR)model is used to model the degradation process of aeroengines.Then,the RUL distribution based on fixed failure threshold is derived.The prior parameters of the degradation model are calculated by a two-step maximum likelihood estimation(MLE)method and the random coefficient is updated in real time under the Bayesian framework.The failure threshold in this paper is defined by the actual degradation process of aeroengines.After that,a expectation maximization(EM)algorithm is proposed to estimate the underlying failure threshold of aeroengines.In addition,the conditional probability is used to satisfy the limitation of failure threshold.Then,based on above results,an analytical expression of RUL distribution of aero-engines based on the RCR model considering random failure threshold(RFT)is derived in a closed-form.Finally,a case study of turbofan engine is used to demonstrate the effectiveness and superiority of the RUL prediction method and the parameters estimation method of failure threshold proposed.

Semiparametric estimation of average treatment effect through a random coefficient dummy endogenous variable model

This paper provides an estimation procedure for average treatment effect through a random coefficient dummy endogenous variable model. A leading example of the model is estimating the effect of a training program on earnings. The model is composed of two equations:an outcome equation and a decision equation.Given the linear restriction in outcome and decision equations,Chen(1999) provided a distribution-free estimation procedure under conditional symmetric error distributions. In this paper we extend Chen's estimator by relaxing the linear index into a nonparametric function,which greatly reduces the risk of model misspecification. A two-step approach is proposed:the first step uses a nonparametric regression estimator for the decision variable,and the second step uses an instrumental variables approach to estimate average treatment effect in the outcome equation. The proposed estimator is shown to be consistent and asymptotically normally distributed. Furthermore,we investigate the finite performance of our estimator by a Monte Carlo study and also use our estimator to study the return of college education in different periods of China. The estimates seem more reasonable than those of other commonly used estimators.