CN102288412B - Aeroengine hardware damage analysis and service life prediction method based on damage base line - Google Patents

Abstract

The invention provides an aeroengine hardware damage analysis and service life prediction method based on a damage base line. A damage database is built according to engine manual regulations and engine structure definition standard damage description rules; a damage base line model based on a linear degradation rail is built, the linear fitting is carried out on the damage data of a fleet engine, and the maximum likelihood estimation is used for solving the damage base line model parameter estimation values; the damage data of the newly obtained single engine is used for updating the damage sign model to obtain the damage increase model of the single engine; the probability density distribution function of the hardware damage increase model, i.e. the probability density distribution function of the engine rest wing time is solved for the solved hardware damage increase model of the single engine, and a median value of the probability density distribution function is taken to be used as the rest wing service life of the engine. Through the aeroengine hardware damage analysis and service life prediction method, the prediction on the engine dismounting time of the engine by airline companies according to the hardware damage of the engine becomes possible, and further, important decision support is provided for the maintenance plan making of the engine.

Description

Aeromotor hardware breakdown diagnosis and life-span prediction method based on the damage baseline

Technical field

The present invention relates to a kind of aeromotor hardware breakdown diagnosis and life-span prediction method based on the damage baseline, belong to aeromotor detection technique field.

Background technology

The damage of aeromotor hardware may cause the decline of engine operation efficient even cause the generation of catastrophic failure, and the security that engine uses is the key factor that determines whether aeromotor can be used safely.The hardware damage of aeromotor mainly is that the engine core machine is the damage that the core components such as pneumatic plant, firing chamber, turbine occur.Because Core Engine is usually operated under the extreme condition of work such as high pressure, high temperature, and the hardware damages such as crackle, ablation often can occur.

Aeromotor hardware lesion development trend is analyzed, and then the residue time-on-wing of engine that the hardware damage occurs effectively predicted, important decision-making foundation can be provided for the formulation of engine maintenance plan, and this also is the important leverage that engine health is used.But the formation mechanism of aeromotor hardware damage is very complicated, is difficult to set up accurate physical model and effectively analyzes, and the model of setting up often has complicated form and complicated method for solving, is difficult to carry out in the practical engineering application of airline.But utilizing historical damage data is that its rule of development of data analysis is visited in the hole, thereby predicts that its variation tendency but is a kind of practicable method.But in actual use, to the separate unit engine implement tight hole visit a prisoner the control will greatly reduce the utilization factor of engine, thereby increased the operation cost of airline, therefore, it is on the low side to obtain engine hole spy data sample amount in the reality, and obtain be non-fail data, this has also just increased the difficulty of setting up based on the hardware breakdown diagnosis model of historical data, particularly in the especially little situation of damage data amount, be difficult to damage trend and the residue time-on-wing of separate unit engine are effectively predicted.Therefore, in aeromotor engineering management reality, airline generally can only estimate generally all have larger deviation to the residual life of parts that the hardware damage has occured according to slip-stick artist's personal experience.

Summary of the invention

The objective of the invention is to obtain the engine hole to visit the data sample amount on the low side for solving in the reality, and obtain be non-fail data, particularly in the especially little situation of damage data amount, be difficult to the problem that damage trend and the residue time-on-wing of separate unit engine are effectively predicted.And then provide a kind of based on the damage baseline aeromotor hardware breakdown diagnosis and life-span prediction method.

Method of the present invention realizes by following steps:

One, collect and put in order the hardware damage data: at first be used for " the location expression language " of location damage according to the organization definition of engine, and the definition type of impairment; According to type of impairment and damage position definition faulted condition descriptive language, i.e. " state description language ", comprise value type descriptive language and logical type descriptive language, according to defined standardization engine hardware damage description rule, the hardware damage data of collecting each engine;

Two, set up the damage baseline model: will by the hole visits check acquisition damage data as degraded data, set up the following damage model based on the linear regression orbital curve:

Y(t _i)＝α+βt _i+ε(t _i) (1)

Y (t wherein _i) be illustrated in t _iThe damage observed reading of engine constantly, α represents to damage initial value, and β represents the growth rate factor, is stray parameter; ε (t _i) be observational error, suppose that usually it is 0 that ε (t) satisfies average, variance is σ ²Normal distribution, be designated as ε (t _i)～N (0, σ ²); The amount of damage that the stress impact that circulates each time causes engine is stochastic distribution, supposes that the damage increment of circulation is the s Normal Distribution each time, i.e. s～N (μ _s, σ _s ²), suppose that further it is μ that β obeys average ₁, variance is

Normal distribution; The value of supposing α is 0, and the model shown in the formula (1) further is reduced to:

Y(t _i)＝βt _i+ε(t _i)

Above-mentioned model is the overall model for Engine Fleet, claims that this overall model is " the damage baseline " of fleet;

Three, find the solution the damage baseline model: this model engine of N platform is done observation, obtain an observation sample collection { E ₁, E ₂..., E _nN=1,2 ... N, wherein

Be the observation sample of i platform engine, M is this engine observation sample number; At first right

Carry out linear fit, obtain shape as shown in the formula matched curve:

y＝ax+b (3)

The observation sample of whole N platform engines is carried out linear fit to be obtained

With

According to hypothesis, β satisfies normal distribution, and

It is the sample of β; According to

β is carried out parameter estimation; To observation data

The residual error of carrying out the match generation is ε (t _i) sample, calculate the variance of these samples, with it as treating estimated parameter σ ²Estimated value

Four, upgrade baseline model, obtain separate unit engine hardware damage model of growth:

Note L _i=Y (t _i)=β t _i+ ε (t _i), L _i(i=1,2 ... n) be the observed reading of engine hardware damage, according to hypothesis, obtain the likelihood function of following form:

$f\left(L_i\right|\mathrm{\β})=\underset{i=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{2{\mathrm{\π\σ}}^2}}\exp (-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{{(L_i-\mathrm{\β}{t}_i)}^2}{2{\mathrm{\σ}}^2})---\left(4\right)$

If note β is distributed as π (β), known by preamble

The posteriority of then trying to achieve β according to the Bayes formula is distributed as:

$f\left(\mathrm{\β}\right|L_i)=\frac{f\left(L_i\right|\mathrm{\β})\mathrm{\π}\left(\mathrm{\β}\right)}{\underset{\mathrm{\β}}{\∫}f\left(L_i\right|\mathrm{\β})\mathrm{\π}\left(\mathrm{\β}\right)\mathrm{d\β}}---\left(5\right)$

The posteriority of trying to achieve β distributes and parameter estimation:

${\widehat{\mathrm{\μ}}}_{\mathrm{\β}}=\frac{\widehat{{\mathrm{\σ}}_1^2}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left(L_i{t}_i\right)+{\widehat{\mathrm{\μ}}}_1\widehat{{\mathrm{\σ}}^2}}{\widehat{{\mathrm{\σ}}_1^2}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{t}_i^2+\widehat{{\mathrm{\σ}}^2}}---\left(6\right)$

$\hat{{{\mathrm{\σ}}_{\mathrm{\β}}}^2}=\frac{\widehat{{\mathrm{\σ}}_1^2}\widehat{{\mathrm{\σ}}^2}}{\widehat{{\mathrm{\σ}}_1^2}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{t}_i^2+\widehat{{\mathrm{\σ}}^2}}---\left(7\right)$

For the separate unit engine, its damage model of growth is updated to:

Y(t _i)＝βt _i+ε(t _i)，

Five, predicting residual useful life: suppose that the engine hardware damage threshold is D _uThe time, claim that engine lost efficacy at this moment; The time of power failure is T, then moment t (t＜T) reliability function of engine is:

R(t)＝P{t＜T}＝P{y(t)＜D _u} (9)

For the damage model of growth of shape such as (9) formula, have:

$R\left(t\right)=P\{y\left(t\right)\≤D_u\}$

$=P\{\mathrm{\βt}+\mathrm{\ϵ}\left(t\right)\≤D_u\}---\left(10\right)$

$=\mathrm{\Φ}\left(\frac{D_u-{\mathrm{\μ}}_{\mathrm{\β}}t}{\sqrt{{\mathrm{\σ}}_{\mathrm{\β}}^2{t}^2+{\mathrm{\σ}}^2}}\right)$

Φ () is standardized normal distribution in the formula;

Remember that current observation is t constantly _k, Y (t+t _k) be t+t _kDamage observed reading constantly, the residue time-on-wing of then trying to achieve as engine that the damage of this type hardware has occured is T _rBe distributed as

$P(T_r<t|Y)=\mathrm{\&Phi;}\left(\frac{D_u-{\mathrm{\&mu;}}_{\mathrm{\&beta;}}(t+t_k)}{\sqrt{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^2{(t+t_k)}^2+{\mathrm{\&sigma;}}^2}}\right)---\left(11\right)$

Order

Then Time-on-wing is T in the formula (11) _rCodomain be (∞, ∞); In fact T _r〉=0, so T _rDistribution get following truncation and distribute:

P(T _r＜t|Y，T _r≥0)＝P(0≤T _r≤t|Y)＝Φ(g(t))-Φ(g(0))(12)

Further can obtain probability density function

f(t)＝φ(g(t))g′(t) (13)

φ () is the probability density function of standardized normal distribution in the formula.The intermediate value of getting the distribution of engine residue time-on-wing is the residue time-on-wing of engine.

In the actual operation of airline, be under the jurisdiction of the same aeromotor of being in charge of the base and usually carry out similar aerial mission in same course line, external environment such as atmospheric temperature, Aircraft Load etc. when this shows these engine operation are basic identical, if these engines belong to same model, then the inner structure of engine, material, technique etc. are all identical.Basic thought of the present invention is: suppose that the same engine hardware lesion development of being in charge of the same model in base obeys similar rule, and propose the concept of damage baseline based on this hypothesis.Damage baseline of the present invention refers to and belongs to the same lesion development of being in charge of the engine of the same model in base and can be described with same mathematical model, can be with finding the solution the damage baseline by the damage data of whole fleet, then according to the damage baseline damage trend of separate unit engine is analyzed, this has just realized under poor information condition the analysis to separate unit engine damage development trend, and then can remain the prediction of time-on-wing.

Beneficial effect of the present invention: the present invention is a kind of engine hardware lesion development trend based on hole spy data and the Forecasting Methodology that engine remains in the wing life-span, it is of the present invention that method is simple, become possibility so that airline predicts tearing open of engine according to the engine hardware damage opportunity of sending out, important decision support can be provided for the formulation of engine maintenance plan.Thereby can delay the decline of engine operation efficient, the generation of the incidents that averts a calamity.

Embodiment

The method of present embodiment realizes by following steps:

One, collects and puts in order the hardware damage data.Because numerous, the complex structure of aeromotor parts, and in the zones of different of different parts, its type of impairment and affect damage that aeromotor uses safely to limit each one identical.Therefore, at first be used for " the location expression language " of location damage according to the organization definition of engine, such as zones such as leading edge, trailing edges, and the definition type of impairment.According to type of impairment and damage position definition faulted condition descriptive language, i.e. " state description language " comprises value type descriptive language and logical type descriptive language, and the former mainly describes the size of damage, latter is described other status information of damage, for example " is ablated to the Inner chamber ".According to defined standardization engine hardware damage description rule, the hardware damage data of collecting each engine.

Concrete, can also be according to Engine Manual damage tolerance regulation and engine configuration, the damage description rule of definition standard, the description rule template is: damage description rule: { engine model;

The cell cube title;

Type of impairment;

Location expression;

The damage yardstick is described; }

Adopt above rule that detailed, rational description is carried out in the hardware damage of engine, and set up the hole and visit database, to collect the engine damage data.

Two, set up the damage baseline model.Present embodiment is regarded aeromotor hardware lesion development process as a performance degenerative process, will visit by the hole and check that the damage data that obtains is as degraded data.With reference to engine slip-stick artist's experience, set up the following damage model based on the linear regression orbital curve:

Y(t _i)＝α+βt _i+ε(t _i) (1)

Y (t wherein _i) be illustrated in t _iThe damage observed reading of engine constantly, α represents to damage initial value, generally can be assumed to be constant.β represents the growth rate factor, is stray parameter.ε (t _i) be observational error, suppose that usually it is 0 that ε (t) satisfies average, variance is σ ²Normal distribution, be designated as ε (t _i)～N (0, σ ²).In fact, the amount of damage that the stress impact that circulates each time causes engine is stochastic distribution, might as well suppose that the damage increment that circulates each time is the s Normal Distribution, i.e. s～N (μ _s, σ _s ²), can suppose further that it is μ that β obeys average ₁, variance is

Normal distribution.Because in 0 observation constantly, it is generally acknowledged not damage of engine, the value of present embodiment hypothesis α is 0, so the model shown in the formula (1) can further be reduced to:

Y(t _i)＝βt _i+ε(t _i)

Above-mentioned model is the overall model for Engine Fleet, and what overall model was described is the cluster random graph, the curve in the random graph bunch then be totally in the actual damage curve of certain sample, claim that this overall model is " the damage baseline " of fleet.

Three, find the solution the damage baseline model.Suppose this model engine of N platform is done observation, obtain an observation sample collection { E ₁, E ₂..., E _nN=1,2 ... N, wherein

Be the observation sample of i platform engine, M is this engine observation sample number.At first right

Carry out linear fit, obtain shape as shown in the formula matched curve:

y＝ax+b (3)

The observation sample of whole N platform engines is carried out linear fit to be obtained

With

According to hypothesis, β satisfies normal distribution, and

It is the sample of β.Therefore, can basis

β is carried out parameter estimation.To observation data

The residual error of carrying out the match generation is ε (t _i) sample, calculate the variance of these samples, with it as treating estimated parameter σ ²Estimated value

Four, upgrade baseline model, obtain separate unit engine hardware damage model of growth.What the damage baseline was described is fleet lesion development average tendency, and the residue time-on-wing that draws according to this model solution also is the average time-on-wing of Engine Fleet.In fact for concrete engine, its hardware lesion development has the characteristic of itself, and for the specific engine that the hardware damage has occured, the estimation of its residue time-on-wing also should differ from the average time-on-wing of fleet.Can utilize observed reading estimation to model parameter on the basis of formula (12) of specific engines hardware damage to recomputate, so that parameter estimation can embody the lesion development characteristics of separate unit engine.

Note L _i=Y (t _i)=β t _i+ ε (t _i), L _i(i=1,2 ... n) be the observed reading of engine hardware damage, according to hypothesis, then can obtain the likelihood function of following form:

$f\left(L_i\right|\mathrm{\&beta;})=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\frac{1}{\sqrt{2{\mathrm{\&pi;\&sigma;}}^2}}\exp (-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{{(L_i-\mathrm{\&beta;}{t}_i)}^2}{2{\mathrm{\&sigma;}}^2})---\left(4\right)$

If note β is distributed as π (β), known by preamble

Then can be distributed as in the hope of the posteriority of β according to the Bayes formula:

$f\left(\mathrm{\&beta;}\right|L_i)=\frac{f\left(L_i\right|\mathrm{\&beta;})\mathrm{\&pi;}\left(\mathrm{\&beta;}\right)}{\underset{\mathrm{\&beta;}}{\&Integral;}f\left(L_i\right|\mathrm{\&beta;})\mathrm{\&pi;}\left(\mathrm{\&beta;}\right)\mathrm{d\&beta;}}---\left(5\right)$

Can distribute and parameter estimation in the hope of the posteriority of β:

${\widehat{\mathrm{\&mu;}}}_{\mathrm{\&beta;}}=\frac{\widehat{{\mathrm{\&sigma;}}_1^2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(L_i{t}_i\right)+{\widehat{\mathrm{\&mu;}}}_1\widehat{{\mathrm{\&sigma;}}^2}}{\widehat{{\mathrm{\&sigma;}}_1^2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^2+\widehat{{\mathrm{\&sigma;}}^2}}---\left(6\right)$

$\hat{{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}}^2}=\frac{\widehat{{\mathrm{\&sigma;}}_1^2}\widehat{{\mathrm{\&sigma;}}^2}}{\widehat{{\mathrm{\&sigma;}}_1^2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^2+\widehat{{\mathrm{\&sigma;}}^2}}---\left(7\right)$

Therefore for the separate unit engine, its damage model of growth can be updated to:

Y(t _i)＝βt _i+ε(t _i)，

Five, predicting residual useful life.Present embodiment is set up based on the hole from the angle of performance reliability and is visited the aeromotor of data and damage baseline model at wing predicting residual useful life model.Suppose that the engine hardware damage threshold is D _uThe time, engine can not continue to use, and should be removed repairing, claims that engine lost efficacy at this moment.If the time of power failure is T, then moment t (t＜T) reliability function of engine is:

R(t)＝P{t＜T}＝P{y(t)＜D _u} (9)

For the damage model of growth of shape such as (9) formula, have:

$R\left(t\right)=P\{y\left(t\right)\&le;D_u\}$

$=P\{\mathrm{\&beta;t}+\mathrm{\&epsiv;}\left(t\right)\&le;D_u\}---\left(10\right)$

$=\mathrm{\&Phi;}\left(\frac{D_u-{\mathrm{\&mu;}}_{\mathrm{\&beta;}}t}{\sqrt{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^2{t}^2+{\mathrm{\&sigma;}}^2}}\right)$

Φ () is standardized normal distribution in the formula.

Remember that current observation is t constantly _k, Y (t+t _k) be t+t _kDamage observed reading constantly, the residue time-on-wing of then being not difficult to try to achieve for engine that the damage of this type hardware has occured is T _rBe distributed as

$P(T_r<t|Y)=\mathrm{\&Phi;}\left(\frac{D_u-{\mathrm{\&mu;}}_{\mathrm{\&beta;}}(t+t_k)}{\sqrt{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^2{(t+t_k)}^2+{\mathrm{\&sigma;}}^2}}\right)---\left(11\right)$

Order

Then

Be not difficult to find out thus formula

(11) time-on-wing is T in _rCodomain be (∞, ∞).In fact T _r〉=0, so T _rDistribution get following truncation and distribute:

P(T _r＜t|Y，T _r≥0)＝P(0≤T _r≤t|Y)＝Φ(g(t))-Φ(g(0))(12)

Further can obtain probability density function

f(t)＝φ(g(t))g′(t) (13)

φ () is the probability density function of standardized normal distribution in the formula.

On the basis of foundation based on the damage baseline model of fleet damage data, adopt separate unit engine damage Data Update model to obtain embodying the Degradation model of separate unit engine damage development trend, and then try to achieve the residual life probability density function according to performance reliability, getting the intermediate value that engine residue time-on-wing distributes is the residue time-on-wing of engine.

Claims (2)

1. , a kind of based on the damage baseline aeromotor hardware breakdown diagnosis and life-span prediction method, it is characterized in that, realize by following steps:

   One, collect and put in order the hardware damage data: at first be used for " the location expression language " of location damage according to the organization definition of engine, and the definition type of impairment; According to type of impairment and damage position definition faulted condition descriptive language, i.e. " state description language ", comprise value type descriptive language and logical type descriptive language, according to defined standardization engine hardware damage description rule, the hardware damage data of collecting each engine;

   Two, set up the damage baseline model: will by the hole visits check acquisition damage data as degraded data, set up the following damage model based on the linear regression orbital curve:

   

   (1)

   Wherein

   

   Be illustrated in

   

   The damage observed reading of engine constantly,

   

   Expression damage initial value,

   

   The expression growth rate factor is stray parameter;

   

   Be observational error, usually hypothesis

   

   Satisfying average is 0, and variance is Normal distribution, be designated as

   

   The amount of damage that the stress impact that circulates each time causes engine is stochastic distribution, supposes that the damage increment of circulation is each time

   

   Normal Distribution, namely

   

   , further suppose

   

   The obedience average is

   

   , variance is

   

   Normal distribution; Suppose

   

   Value be 0, the model shown in the formula (1) further is reduced to:

   (2)

   Above-mentioned model is the overall model for Engine Fleet, claims that this overall model is " the damage baseline " of fleet;

   Three, find the solution the damage baseline model: right This model engine of platform is done observation, obtains an observation sample collection

   

   , wherein

   

   Be

   

   The observation sample of platform engine,

   

   Be this engine observation sample number; At first right

   

   Carry out linear fit, obtain shape as shown in the formula matched curve:

   

   (3)

   To all

   

   The observation sample of platform engine carries out linear fit and obtains

   

   With , according to hypothesis, Satisfy normal distribution, and

   

   Be

   

   Sample; According to

   

   Right

   

   Carry out parameter estimation; To observation data

   

   The residual error of carrying out the match generation is

   

   Sample, calculate the variance of these samples, with it as treating estimated parameter

   

   Estimated value

   

   Four, upgrade baseline model, obtain separate unit engine hardware damage model of growth:

   Note

   

   Observed reading for the engine hardware damage according to hypothesis, obtains the likelihood function of following form:

   

   (4)

   If note Be distributed as

   

   , known by preamble

   

   , then try to achieve according to the Bayes formula

   

   Posteriority be distributed as:

   

   (5)

   Try to achieve

   

   Posteriority distribute and parameter estimation:

   

   (6)

   

   (7)

   For the separate unit engine, its damage model of growth is updated to:

   (8)

   Five, predicting residual useful life: suppose that the engine hardware damage threshold is

   

   The time, claim that engine lost efficacy at this moment; The time of power failure is

   

   , then at moment t, the reliability function of engine is when t＜T:

   

   (9)

   For the damage model of growth of shape such as (9) formula, have:

   

   (10)

   φ () is standardized normal distribution in the formula;

   Remember that current observation constantly is

   

   ,

   

   For

   

   Damage observed reading constantly, the residue time-on-wing of then trying to achieve as engine that the damage of this type hardware has occured is

   

   Be distributed as

   

   (11)

   Order

   

   , then

   

   , time-on-wing is in the formula (11)

   

   Codomain be In fact

   

   , therefore

   

   Distribution get following truncation and distribute:

   

   (12)

   Further can obtain probability density function

   

   (13)

   φ () is the probability density function of standardized normal distribution in the formula.
2. According to claim 1 based on the damage baseline aeromotor hardware breakdown diagnosis and life-span prediction method, it is characterized in that, on the basis of foundation based on the damage baseline model of fleet damage data, adopt separate unit engine damage Data Update model to obtain embodying the Degradation model of separate unit engine damage development trend, and then try to achieve the residual life probability density function according to performance reliability, getting the intermediate value that engine residue time-on-wing distributes is the residue time-on-wing of engine.