Health Prediction And Maintenance Optimization For Aircraft Gearboxes Based On Monitoring Data

Condition-based maintenance(CBM)and prognostics and health management(PHM)have been hot research topics for several decades with the aim to reduce system downtime,minimize maintenance cost and increase the overall system availability.As one of the key components of the mechanical transmission system,gear is extensively used in aerospace,civil industry and heavy machinery with efficient transmission ratio and the strong load capacity.Examples include helicopters,high-speed trains and wind turbines.Gear failure causes unexpected downtime in the whole mechanical system,resulting in great economic losses and even human casualties.Condition monitoring and fault detection technique can significantly improve the reliability of the gear transmission system and reduce the occurrence of failure.Using gearbox as the key component of the civil aircraft,we study three aspects of the research,respectively are early fault detection,health prediction and maintenance optimization modeling.The main contributions of this thesis are as follows:(1)A novel optimal Bayesian control approach is presented for a partially observable system subject to deterioration and random failure.The system deterioration evolves as a three-state(state 0,1 and 2)continuous time hidden semi-Markov process.States 0 and 1 are unobservable and represent the good and warning system states,respectively.Only state 2 is assumed to be observable and represents the failure state.Considering the optimal maintenance policy,the multivariate Bayesian control scheme based on hidden semi-Markov model(HSMM)is developed,the objective is to maximize the long-run expected average availability per unit time.An effective computational algorithm is designed in the semi-Markov decision process(SMDP)framework.The proposed approach can optimize the sampling interval and control limit jointly.A case study using Markov chain Monte Carlo(MCMC)simulation is provided and a comparison with the Bayesian control scheme based on HMM,the age-based replacement policy,Hotelling's T~2,MEWMA and MCUSUM control charts is given,which illustrates the effectiveness of the proposed method.(2)A new optimal Bayesian control approach is presented to predict early fault of a partially observable gear shaft system subject to deterioration and random failure under fixed sampling interval.Time synchronous averaging(TSA)and vector autoregressive(VAR)models have been combined for preprocessing of multidimensional monitoring data to obtain the residuals.The K-S test distance of the residuals are used as the observation process.The gear shaft system deterioration process is modeled as a three-state continuous time hidden semi-Markov process.The general Erlang distribution is considered for modeling the sojourn time in each of the hidden states,which is closer to the actual deterioration process modeling of the gear shaft system than the exponential sojourn time distribution assumed in a hidden Markov model(HMM).The unknown state and observation parameters of HSMM were estimated using EM algorithm.The optimal maintenance policy represented by a multivariate Bayesian control scheme based on a hidden semi-Markov model(HSMM)is developed.The objective is to maximize the long-run expected average availability per unit time.An effective computational algorithm is designed in the semi-Markov decision process(SMDP)framework to obtain the optimal control limit and the optimal average availability.The Bayesian control approach monitors the posterior probability for maintenance decision-making.If the posterior probability exceeds a certain control limit,the system should be stopped for full inspection and perform preventive maintenance(PM)actions.Using multidimensional data obtained from condition monitoring,the proposed approach can not only predict early fault occurrence of the gear shaft,but also update the remaining useful life(RUL)at each sampling epoch.A comparison with other maintenance policies is given,which illustrates the effectiveness of the proposed approach.(3)Most maintenance optimization models of gear systems have considered single failure mode.There have been very few papers dealing with multiple failure modes,considering mostly independent failure modes.In this paper,we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks.The system failures include degradation failure and catastrophic failure.The Marshall-Oklin binary exponential distribution(BED)is employed to describe the dependence of two failure modes.The deterioration process of the gear system is described by a three-state continuous time homogeneous hidden Markov model(HMM),namely the model with unobservable healthy and unhealthy states,and an observable failure state.The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy.The objective is to maximize the long-run expected average system availability per unit time.The maintenance optimization model is formulated and solved in a semi-Markov decision process(SMDP)framework.The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development.The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results.A comparison with the Bayesian control chart based on the previously published HMM and the age-based replacement policy is given to illustrate the superiority of the proposed approach.The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.(4)The life index of a prodcut plays an important role in reliability verification test.Assumptions accompanying exponential failure models are often not met in the standard sequential probability ratio test(SPRT)of many products.However,for most of the mechanical products,Weibull distribution conforms to their life distributions better compared to other techniques.The SPRT method for Weibull life distribution is derived in this paper,which enables the implementation of reliability compliance tests for gearboxes.Thus,the deficiency of the existing reliability verification test standard(GJB 899A-2009,MIL-STD-781D)is supplemented.Considering that the sequential compliance test plan is extremely sensitive to the estimated value of shape parameter and the true value of shape parameter,the mathematical expression is established to illustrate the relationship between the value of shape parameter and the acceptance probability according to the theory of sequential test plan.The simulation test results show that the greater deviation degree between the estimated and the true value of shape parameter,the greater gap of the corresponding risk,and this is consistent with the theoretical analysis.Using historical failure data and condition monitoring data,a life prediction model based on hidden Markov model(HMM)is established to describe the deterioration process of gearboxes,then the predicted remaining useful life(RUL)is transformed into failure data that is used in SPRT for further analysis,which can significantly save on testing time and reduce costs.(5)A joint optimization model of replacement and spare parts ordering is proposed based on the real-time prediction information,which significantly avoids the disadvantage of the sequential decision model.The concept of condition-based service level(CBSL)is introduced based on the stress-strength interference theory.The maintenance engineer can adjust the the maintenance decision flexibly according to the threshold of the CBSL.When the probability of CBSL is lower than the predetermined reliability threshold,the joint optimization of replacement and spare parts ordering is carried out.Considering the uncertainty of spare parts delivery time,we assume that the delivery time is a random variable,which makes it more realistic for real applications.A case studay is given for the accelerated life test of a gearbox operating under varying load.A comparison with the sequential optimization model and the joint optimization model is given,which illustrates effectiveness of the proposed approach.