RELIABILITY EVALUATION MODEL BASED ON DATA FUSION FOR AIRCRAFT ENGINES

Wang Huawei,Wu Haiqiao

(College of Civil Aviation,Nanjing University of Aeronautics and Astronautics,Nanjing,210016,P.R.China)

INTRODUCTION

Engines are the heart of an aircraft,whose failures can affect aircraft safety and lead to heavy economic losses. As such, estimating the reliability is crucial for health management and maintenance decision.Unfortunately,reliability evaluation for aircraft engines is difficult due to the scarcity of failure data.But aircraft engine data are available from a variety of sources including on-board sensor measurements,maintenance histories and component data.Data fusion is the integration of data or information from multiple sources.In this paper,a reliability evaluation model for aircraft engines based on data fusion is proposed. The ultimate goal of reliability evaluation based on data fusion is to maximize the amount of valuable information extracted from disparate data sources to obtain comprehensive reliability knowledge.

Application of fusion techniques in engineering practices has been receiving increasing attentions in recent years.Especially with the rapid progress of advanced sensor and signal processing techniques,fusing largeamount of mutual information had become possible.These developments are expected to bring about the more accurate reliability evaluation. A number of fusion techniques had been identified for reliability domain.For example,Volponi[1]used data fusion technique for aircraft engine health management.Niu,et al[2]used data fusion strategy for improving condition monitoring,heath assessment and prognostics.Basir,et al[3]used Dempster-Shafer fusing data for engine fault diagenosis.Gebraeel,et al[4]developed Bayesian updating methods that used real-time condition monitoring information to update the stochastic parameters of degradation models.Drury,et al[5]provided a framework for information design by combining the concepts from the human factor knowledge base with the specific needs of aircraft inspection. Roemer, et al[6]proposed an intelligent condition monitoring and prognostic system in condition-based maintenance architecture using data-fusion strategy.Feng,et al[7]presented a fusion method based on fuzzy aggregation operator(FAO)to fully embody the degree of redundancy and the complementarities of information from multiple sources.Zhao,et al[8]explored the information fusion technology in the field of reliability applicability and basic application solutions,and discussed the content and essence of the new method more comprehensively. Feng[9]applied various qualitative and quantitative fusion methods to different types of reliability information from different sources. Coble[10]combined several measures of degradation into a single parameter and introduced a dynamic Bayesian updating methodology to incorporate prior information for estimating residual useful life.

However,the applications of data fusion technology on reliability evaluation of complex systems have not yet received sufficient attentions, and relevant cases are rare. The complexity of data fusion on reliability evaluation for complex systems is that degradation failures and catastrophic failures exist simultaneously.For example,failures of aircraft engines are generally classified into two kinds of failure modes: One is catastrophic failures in which aircraft engines break down by some sudden external shocks;and the other is degradation failures in which aircraft engines fail to function due to the physical deterioration. Catastrophic failures and degradation failures are competing failures, which both affect the reliability.Therefore, a reliability evaluation model is developed based on data fusion considering competing risks,which is more suitable for failure mode characteristics of complex systems.

1 RELIABILITY DATA FUSION FOR AIRCRAFT ENGINES

1.1 Condition measurement data

The condition measurement of aircraft engines can be described as follows.

(1)Gas path measurements.The key of aircraft engines is the gas path system,which consists of air-compressor, combustor and turbine,etc.Gas path measurement consists of some subsets of inter-stage pressures and temperatures,spool speeds and fuel flow.The key parameters of gas path measurements include exhaust gas temperature(EGT)and fuel flow(FF).

(2)Oil measurements.Oil measurements consist of various oil system temperatures,pressures, fuel temperature, and delivery pressure. Oil measurements are the auxiliary instruments for aircraft engines,which can be used for monitoring components of lubrication system and its sealing.The key parameters of oil measurements include oil pressure(OP),oil temperature and oil consumption rate(OCP).

(3)Vibration measurements.High and low spools of aircraft engines are composed of blades,plates,axis,and bearings. There are some vibration signals while wear and damage occur during rotation.The key parameters of vibration measurements include low pressure vibration(LPV)and high pressurevibration(HPV).

The performance degradation is usually reflected on the change of condition measurement parameters. For example, if EGT exceeds standard,FF and OCPincrease,or high pressure rotor speed deviation(HPRSD)occurs,thus a conclusion can be drawn that theaircraft engineis deteriorating.

1.2 Event data

Event data include failure data and maintenance data,etc.If there are enough failure data in event data,reliability can be evaluated directly.If not,event data can be used as prior information to support reliability evaluation.Similarly,information of past maintenance and failure is also used to aid in reliability evaluation.

1.3 Data fusion framework based on competing risks

1.3.1 Date fusion for degradation failures

A degradation failure is described through a stochastic process based on condition measurement data. The reliability decrease caused by degradation failures can be evaluated by Bayesian linear model(BLM)for fusing condition measurement data.The advantages of BLM can be concluded as follows.

First,BLM can show the randomness of condition measurement parameters and degradation degreevariable.

Second, with BLM, the relevance is considered to reduce the repetitive data.

Third,BLM can fuse data of different time points by its learning function.

Last,with BLM,noise parameters can be designed to describe the uncertainty of measurement parameters.

1.3.2 Data fusion for catastrophic failure

Reliability evaluation for catastrophic failure is based on even data fusion.When the sample of quantity and failure data is small,the Bayesian method is effective. Bayesian data fusion is widely applied to reliability analysis.Themerit of Bayesian event data fusion for aircraft engines can be summarized as follows.

First,Bayesian method can realize reliability evaluation by fusing longitudinal data from prior density to posterior density.

Second, Bayesian method can realize reliability evaluation by fusing data from different sources.For example,maintenance data can be extended as failure data by some transformation rules.

1.3.3 Data fusion for reliability of system

A competing failure model is proposed to describe the system reliability of aircraft engines.The model allows the data of degradation failures and catastrophic failures into one framework,which means the model fusion.The competing failure model can also be regarded as higher data fusion in comparison with data fusions for degradation failures and catastrophic failures.Fig.1 illustrates the data fusion framework of reliability evaluation for aircraft engines.

Fig.1 Data fusion framework of reliability evaluation for aircraft engine

2 RELIABILITY EVALUATION FOR AIRCRAFT ENGINES

2.1 Reliability evaluation model for degradation failures

Aircraft engines can be deteriorated because of the use, the age, and the continuous accumulation of degradation. The degradation evolution of system is usually modeled by a stochastic process.Let y(t)be the accumulated deterioration at time t,then stochastic process{y(t),t≥0}is continuous in time and monotonically increasing,and y(0)=0.Gamma processes are satisfactorily fit for data of different degradation phenomena.

Assume that{y(t),t≥0}is a gamma process,and it means that the probability density function of degradation level y(t)at time t is a gamma density function with the shape parameter T(t)and the scale parameterλ. The density function of degradation failures can be expressed as

whereΓis the gamma function given byΓ(T)=can be assumed as invariant with the performance degradation during the same monitoring process,and T as variant with the performance degradation, which changes in acceleration with the degradation degree and rate.Therefore,we assume that shape parameter is proportional to expected degradation degree and time power,that is

Further,Eq.(1)can be transformed as follows

Based on the theory of system reliability,the reliability for degradation failures can be depicted as follows

where X is the failure threshold for performance degradation of an aircraft engine.

Further,from Eq.(3),Eq.(4)can be depicted as follows

2.2 Reliability evaluation model for catastrophic failures

It is assumed that the lifetime of aircraft engines obeys the Weibull distribution. The probability density function of catastrophic failures can be expressed as

where U＞ 0 and V＞ 0 are the scale and shape parameters.V is the degradation degree,which is equal to y(t).

When the shape parameter is known,the reliability evaluation for catastrophic failure can be transformed to estimate the scale parameter U.Itis assumed that U has a conjugate gamma prior,that is

where c and d are the hyper-parameters.

The prior mean and variance of U can be shown as follows respectively

In an observed sample{(t1,n1),(t2,n2),…,(tm,nm)},ti is the happening time of catastrophic failure ni the number of catastrophic failure.Posterior estimations of U can be found as follows

If the mean and variance of reliable lifetime tR0can be estimated by using prior inspection and maintenance information under predetermined reliability R0 at the initial phase,U can be estimated by following Eq.(12).

If U is known,c and d can be estimated by Eqs.(8-9).

Then, the reliability evaluation for catastrophic failure can be estimated by Eq.(13).

2.3 System reliability evaluation under competing failuremodel

The degradation failure evaluation and catastrophic failure evaluation can beintegrated in a model,so a competing failure model is proposed to describe the failure process of an aircraft engine under the following hypotheses:

(1)There are two random variables X and Y,where Y denotes the degradation failure and X the sudden failure.X and Y are competing failures.

(2)Performance of an aircraft engine is reduced with the running time gradually,and the degradation process is not reversible.

(3)X is correlated with Y,which is reflected on the shape parameter of reliability function of X.

The system reliability of aircraft engines under competing failures can be expressed as follows

where Rc(t)is the system reliability under the competing risks at time t,andλs(f|y)the failure rate for sudden failure under performance degradation y,which is expressed as

According to the hypothesis(3),the impact of degradation failures on the catastrophic failures is reflected on the shape parameter of reliability function for catastrophic failure by estimating degradation degree of aircraft engines.Then,the simplified calculation can be obtained as follows

Therefore,Rc(t)can be obtained by calculating the reliability Rg(t)for degradation failures and the reliability Rs(t)for catastrophic failures.

3 EXAMPLE

Table 1 shows the key performance measurement parameters and performance degradation degree(PDD)from 35 replacement and repair samples.From the data of Table 1,the relationships between PDD and measurement parameters can be learned by BLM. Table 2 shows measurement parameters and prior information of catastrophic failures for some onwing aircraft engines,where TOW is the time onwing. The reliability estimation and parameter estimation are also listed in Table 2.Moreover,the data in Tables 1-2 are described on the form of deviation and are processed dimensionlessly.

From the data of Table 1,the relationship between PDD and measurement parameters can be learned by BLM,which is the algorithm proposed in Section 2.1.

The vector fusing measurement parameters is

(1) BLM can actually represent more parameters of monitoring information,which reflects the advantages of information fusion.

(2)The predictive value corresponds to the

real value,which shows the accuracy of BLM.

Table 1 Key performancemeasurement parameters for someaircraft engines

Table 2 Key measurement parameters and reliability evaluation f or on-wing aircraft engine

Fig.2 Differenceof perfor mancedegrada tion between real and predictive values

If PDD is known, the reliability for degradation failures can be estimated by Eq.(4).

The prior information of catastrophic failures is gathered by inspection and maintenance information,that is E(R3000)=0.97,e2(R3000)=3.76×10-4.E(U)and e2(U)can be computed by Eq.(12).c^and d^can be computed by Eqs.(8-9).The posterior mean and variance of U^can be computed by Eqs.(10-11),then the posterior mean of Rs can be got.TOW is separated by three different phases: The first is from 0 to 1 707 h,the second is from 1 707 h to 4 740 h,and the third is from 4 740h to 5 595 h.For three measurement points, the probability density function(PDF)is shown in Fig.3,which shows the reliability function is varied and the reliability value multiplicatively decreases for catastrophic failures.

Fig.3 Probability density function of catastrophic failure

Based on the estimations of Rs and Rg,Rc can be estimated by Eq.(16).Fig.4 shows the reliability curve of Rg,Rsand Rc.In most cases,the failure risk of aircraft engines is not complete combination of degradation failures and catastrophic failures. Therefore,the estimation of Rc can be regarded as the lower limits of system reliability for an aircraft engine.

Fig.4 Reliability curve of Rg,Rs and Rc

4 CONCLUSION

In this paper,a data fusion method for reliability evaluation of aircraft engines is presented.BLM is used for fusing measurement data,and then PDD is estimated. Bayesian method is used for fusing event data.Based on data fusion, a higher model fusion under competing failures for reliability evaluation of aircraft engines is presented.And a simplified method is presented for system reliability evaluation of aircraft engines. Example shows that the method is more suitable and has better estimation for reliability evaluation of aircraft engines.

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