CN103020438A - Aero-engine reliability monitoring method based on mixed weibull distribution - Google Patents

Abstract

The invention relates to an aero-engine reliability monitoring method based on mixed weibull distribution, and the method comprises the following steps of extracting state monitoring information and performance degradation information of an aero-engine which is already replaced and repaired; extracting a relation between each monitoring parameter and the performance degradation of the aero-engine by utilizing a support vector method, and realizing the monitoring of the performance degradation value of a wing engine; utilizing a degradation model to describe the accumulated degradation volume of the aero-engine on the basis of the monitoring result of the real-time degradation value of the wing aero-engine; estimating a random parameter in a linear degradation model of the aero-engine, and determining the variation of the random parameter and the upper limit and the lower limit of the accumulated performance degradation volume of the aero-engine; establishing an aero-engine reliability monitoring model based on the dual-parameter mixed weibull distribution; utilizing a maximal likelihood method to give an expression of each parameter in the aero-engine reliability monitoring module; estimating hyper-parameters of the aero-engine reliability monitoring module based on the dual-parameter mixed weibull distribution; and calculating the reliability monitoring value of the aero-engine, and realizing the real-time and precise reliability monitoring of the aero-engine.

Description

A kind of aeromotor monitoring reliability method based on mixing Weibull distribution

Technical field

The present invention relates to aeromotor monitoring reliability technology, particularly in conjunction with aeromotor faults itself rule and operation characteristic, take full advantage of various states monitoring information and maintenance overhaul information, aeromotor is carried out real-time reliability assessment, realization to aeromotor at wing monitoring reliability, guarantee the aeromotor security of operation and improve operational efficiency.

Background technology

The reliability of aeromotor is the basis that guarantees flight safety.Real-time monitoring reliability is convenient to follow the tracks of the reliability Changing Pattern of aeromotor, in time takes for measure, avoids the generation of aeromotor fault.At present, more external advanced persons' theory and technology, such as prognostics and health management (Prognostics and Health Management, PHM), look feelings maintenance (Condition Based Maintenance, CBM), the feelings of looking of expansion are keeped in repair (Condition based maintenance plus, CBM+), self-support (Autonomic Logistics, AL) etc. just progressively is used, assessment is had higher requirement to engine reliability.Wherein, CBM+ rises to key position with " precision ", " real time implementation " of reliability assessment especially, has highlighted the importance of reliability monitoring.The core of the method is with the integrated application of process, technology and knowledge reasoning, realizes improving the target of reliability management, utilization factor and maintenance efficiency, is a kind of more accurate maintenance and health control.Realize " precision ", " real time implementation " of reliability assessment, the realization means of " accurately " just must be arranged, namely the value of full information how utilizes information excavating to go out knowledge.In this course, monitoring reliability is particularly important, and it is the link that connects most crucial, the most critical of " information " and " decision-making ".

Compare with traditional reliability assessment, monitoring reliability more emphasizes to understand " precision " and " real time implementation " of reliability level, and this is the requirement that traditional reliability estimation method can't satisfy.Current in aeromotor reliability assessment field, the following several method of main employing: one is based on the reliability assessment of fault data, because the collectable fault data of aeromotor is less, generally can utilize expert info, the realizations such as component information and other information, the characteristics of this method are to have ignored a large amount of utilizable status monitoring information, and also can't realize " real time implementation "; The 2nd, rely on the status monitoring parameter of on-line monitoring to carry out aero-engine performance degeneration monitoring and evaluation, this method is simple, directly perceived, and can realize " real time implementation ", shortcoming is the information that can not take full advantage of multiple source, namely can't realize " precision ", so can only provide reference for decision-making, and can not provide foundation for decision-making; The 3rd, information fusion and disposal route take proportional hazard model, artificial intelligence approach as representative, the characteristics of these methods are the information that takes full advantage of multiple source, improve " degree of accuracy " of prediction, but the shortcoming of these methods also is obvious, namely all be according to the statistical average effect, when improving accuracy, ignored the impact of risk.In sum, present reliability estimation method, the method that there is no solves " precision ", " accuracy " and " real time implementation " and the good risk control ability in the reliability assessment.

The present invention proposes a kind of aeromotor monitoring reliability method based on mixing Weibull distribution, the one, take into full account the characteristics that the aeromotor status information is monitored, solve the problem of utilizing of small sample, non-linear, high dimensional data, carry out the aero-engine performance degradation assessment; The 2nd, the aero-engine performance degenerative process is being described, determine the bound of performance Degradation path; The 3rd, utilize the two-parameter Weibull model of mixing, can process simultaneously the problem of different failure modes and different failure regularities, the engineering that more meets the aeromotor reliability is actual.The method that the present invention proposes has very strong operability, is convenient to promote and implement.

Summary of the invention

The purpose of this invention is to provide a kind of aeromotor monitoring reliability method, the method can consider aeromotor data characteristics, fault rule and fault mode, pass through support vector machine method, extract the relation between aero-engine performance monitoring information and the performance degradation, utilize biparametric mixing Weibull distribution to describe different failure modes and the impact of different failure regularities on the aeromotor reliability, realize the target of " accurately ", " in real time " monitoring aeromotor reliability.

For achieving the above object, the step of the aeromotor monitoring reliability based on mixing Weibull distribution of the present invention is as follows:

1. extract aero-engine condition monitoring information and the performance degradation degree information of having changed and having keeped in repair.In conjunction with aeromotor degradation failure rule trend, selection mode monitoring information from gas circuit performance monitoring, lubricating oil performance monitoring and vibration monitoring respectively.

2. utilize support vector machine method to realize the processing of small sample, higher-dimension " status monitoring " data.Status monitoring parameter and performance degradation information that comprehensive utilization has been extracted, training and checking by support vector machine method, relation between each monitoring parameter that obtains extracting and aero-engine performance are degenerated is implemented in the performance degradation value monitoring of wing engine.

3. based on the monitoring result in the real-time degradation values of wing aeromotor, utilize degradation model to describe the accumulation amount of degradation of aeromotor.Consider aeromotor as the reality of ultrahigh reliability system, calculate for simplifying, adopt the accumulation amount of degradation of linear regression model description aeromotor.

4. estimate the stray parameter in the aeromotor linear regression model.Suppose that it meets normal distribution, estimate average and the variance of stray parameter, determine the bound of random parametric variations and aeromotor accumulative total performance degradation amount, as the basis of describing the performance deterioration law.

5. set up aeromotor monitoring reliability model.Utilize and mix Weibull distribution, different failure regularities and failure mode are described on the impact of aeromotor reliability, give different weights for different failure regularities, wherein the form parameter in the Weibull distribution is used for describing the degradation failure pattern to the reliability effect of aeromotor, and the scale parameter in the Weibull distribution is used for describing burst and lost efficacy to the reliability effect of aeromotor.

Suppose that there are two kinds of failure regularities simultaneously in aeromotor, a kind of probability of failure regularity is P, and the probability of another kind of failure regularity is 1-P, and then the expression formula of monitoring reliability model is:

α wherein _L, α _U, r _L, r _URepresent respectively form parameter and scale parameter under the different failure regularities of aeromotor.

6. based on the parameter estimation of the aeromotor monitoring reliability model that mixes Weibull distribution.Consider the data characteristics of aeromotor itself, in continuing to monitor process, in order to take full advantage of in the past monitoring information, adopt bayes method pair

Each parameter learn, and adopt maximum likelihood method to determine α _L, α _U, r _L, r _UExpression formula with P.

7. based on the super parameter estimation of the aeromotor monitoring reliability model that mixes Weibull distribution.The prior distribution of parameter p adopts Beta to distribute α _LAnd α _UPrior distribution adopt contrary Gamma to distribute γ _LAnd γ _UPrior distribution adopt evenly and distribute, utilize bayes method, estimate the expectation value of each priori parameter.

8. calculate aeromotor monitoring reliability value.With the super parameter expectation value that step 7 is calculated, bring E (p), E (α that step 6 provides into _L), E (α _U), E (γ _L) and E (γ _U) expression formula, and be updated to

Can calculate the expectation value that reaches the aeromotor monitoring reliability, realize the real-time monitoring reliability to aeromotor.

Compared with prior art, the advantage and the effect that have of the present invention is as follows:

(1) realized dynamically grasping in real time aeromotor reliability level.New maintenance theory is had higher requirement to information, dynamically grasps in real time aeromotor reliability level, and is significant for the flexibility that guarantees maintenance decision, collaborative etc., can realize more efficient maintenance.

(2) take full advantage of status monitoring information.Adopt support vector machine to process small sample, high dimensional data, excavated the relation between monitoring information and the performance degradation, the performance degradation track of aeromotor has been described by system, has analyzed the impact of performance degradation on the aeromotor reliability.

(3) utilize biparametric to mix Weibull distribution model, the different performance failure mode of aeromotor, different failure regularities etc. are integrated into the method for analyzing in the framework, more meet the reality of aeromotor monitoring reliability.

Description of drawings

Fig. 1 is based on the aeromotor monitoring reliability process flow diagram that mixes Weibull distribution;

Fig. 2 is based on the real-time reliability assessment process flow diagram of aeromotor that mixes Weibull distribution.

Embodiment

Exist simultaneously with different failure regularities for the aeromotor Multiple Failure Modes, and the characteristics with a large amount of monitoring informations and a small amount of failure message, propose a kind of aeromotor monitoring reliability method, its implementation process can be divided into following 8 steps, as shown in Figure 1.

1. gather aero-engine condition monitoring information and performance degradation information

For checking, change and the aeromotor of keeping in repair, gather its status monitoring information and corresponding performance degradation information thereof.Performance degradation monitoring index of the present invention is chosen from the index of gas circuit performance monitoring, lubricating oil monitoring and vibration monitoring, relates to altogether following 6 monitoring indexes: engine exhaust temperature deviation (DEGT), fuel consumption deviation (GWFM), high pressure rotor rotating speed deviation (GPCN25), lubricating oil pressure deviation (DPOIL), low pressure rotor vibration values deviation (ZVB1F) and high pressure rotor vibration values deviation (ZVB2R).

2. the employing support vector machine method fully utilizes status monitoring information, extracts the relation between each monitoring parameter and the aero-engine performance amount of degradation

The basic thought that extracts status monitoring parameter and aero-engine performance amount of degradation Relations Among is as follows:

If sample set is { (x _i, y _i) | i=1,2 ..., l}, wherein x _i∈ R _nBe input variable, corresponding the status monitoring parameter of aeromotor; y _i∈ R is output variable, generally is the performance degradation result of known corresponding aero-engine condition monitoring parameter.Adopt support vector machine, pass through Nonlinear Mapping

The sample input from former spatial mappings to high-dimensional feature space, is constructed optimal decision function in this feature space: Wherein The inner product that represents vectorial ω and mapping function, b is biasing, then corresponding constrained optimization problem can be expressed as:

$\underset{\mathrm{\ω},b,\mathrm{\ξ},{\mathrm{\ξ}}^{*}}{\min }\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i+{\mathrm{\ξ}}_i^{*})$

Wherein C is penalty factor, it realized empiric risk and fiducial range one compromise, ξ _i,

Be slack variable, it is lower to be illustrated respectively in error ε constraint

The training error upper and lower bound; ε is the defined error of the insensitive cost function of Vapnik-ε.

The determined optimization problem of above-mentioned formula is a typical convex quadratic programming problem, and by the Lagrange theory as can be known, weight vector ω equals the linear combination of each monitoring parameter

Then further, for the engine at the wing, can utilize its performance degradation value of status monitoring information prediction, expression formula is:

Wherein

Be kernel function.

3. set up aeromotor linear regression model

The present invention adopts degradation model to describe the accumulation performance degenerate case of aeromotor.Because aeromotor belongs to the ultrahigh reliability system, when rapid reliability decrease does not occur, in fact just taked the inspection and maintenance countermeasure, so adopt the linear properties degradation model just can describe situation performance degradation situation, its expression formula is:

S(t _i)＝φ+βt _i+ε(t _i)

t _iAccumulation amount of degradation constantly is with S (t _i) expression, φ determines the type variable, value is along with system monitoring and performance degradation process are adjusted.Stray parameter β can regard predetermined normal distribution as, and its average and variance are respectively μ _βWith

ε (t _i) can be regarded as the noise function, be used for measuring the noise data of measurement, satisfy independent same distribution, N (0, σ ²).

4. estimate the stray parameter in the linear regression model, realize the monitoring of " in real time " aero-engine performance accumulation amount of degradation

The aero-engine performance that integrating step 3 is described by the replacement problem to different sequential point π (β) parameter, just can be realized the prediction to aeromotor, and the expression formula of its average and variance is:

$E\left({\mathrm{\μ}}_{{\mathrm{\β}}^{\′}}{x}^{\′}\right)=\frac{n_0{\mathrm{\μ}}_{\mathrm{\β}}+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i}{n_0+n}$

${\mathrm{\σ}}_{{\mathrm{\β}}^{\′}}^2=[\frac{{2E}^2\left[{\mathrm{\σ}}_{\mathrm{\β}}\right]}{V\left[{\mathrm{\σ}}_{\mathrm{\β}}\right]}+4]E\left[{\mathrm{\σ}}_{\mathrm{\β}}\right]+S_n+\frac{n_{0}n}{n_0+n}{({\mathrm{\μ}}_0-\stackrel{\‾}{x})}^2$

The interval that further provides aero-engine performance accumulation amount of degradation is:

$[E\left({\mathrm{\μ}}_{{\mathrm{\β}}^{\′}}{x}^{\′}\right){-t}_{1-\frac{\mathrm{\α}}{2}}\sqrt{{\mathrm{\σ}}_{{\mathrm{\β}}^{\′}}^2/(\frac{{2E}^2\left[{\mathrm{\σ}}_{\mathrm{\β}}\right]}{V\left[{\mathrm{\σ}}_{\mathrm{\β}}\right]}+4+n)}/\sqrt{n_0+n},E\left({\mathrm{\μ}}_{{\mathrm{\β}}^{\′}}\right|x^{\′}){+t}_{1-\frac{\mathrm{\α}}{2}}\sqrt{{\mathrm{\σ}}_{{\mathrm{\β}}^{\′}}^2/(\frac{{2E}^2\left[{\mathrm{\σ}}_{\mathrm{\β}}\right]}{V\left[{\mathrm{\σ}}_{\mathrm{\β}}\right]}+4+n)}/\sqrt{n_0+n}$

5. set up the aeromotor monitoring reliability model that mixes Weibull distribution

Because the mechanism of action of aeromotor degradation failure is different, is difficult to represent with single Weibull distribution form that the present invention adopts the Weibull distribution form of mixing.Suppose that there are two kinds of failure modes simultaneously in aeromotor, a kind of probability of failure mode is P, and the probability of another kind of failure mode is 1-P, and then the expression formula of reliability is in real time:

$R\left(t\right)={p\×e}^{-{\left(\frac{t}{{\mathrm{\α}}_L}\right)}^{{\mathrm{\γ}}_L}}+(1-p)\×e^{-{\left(\frac{t}{{\mathrm{\α}}_U}\right)}^{\mathrm{\γU}}}$

Wherein, 0＜p＜1, α _L, α _U, γ _L, γ _U＞0

α _LAnd α _UTwo Weibull model dimension parameters that represent respectively mixing, γ _LAnd γ _URepresent respectively two Weibull mould shapes parameters.The failure mode major embodiment of comprehensive aeromotor is degradation failure, the probability that burst inefficacy itself occurs is low, it mostly is the function of degradation failure, therefore this project as two kinds of failure modes, is monitored aeromotor reliability level with the bound of the aeromotor accumulation amount of degradation of step 4 estimation.

6. based on the parameter estimation of the aeromotor monitoring reliability model that mixes Weibull distribution

For 5 parameters in the monitoring reliability model, the prior distribution of parameter p adopts Beta to distribute α _LAnd α _UPrior distribution adopt contrary Gamma to distribute γ _LAnd γ _UPrior distribution adopt evenly and distribute.Suppose ω, η is the priori parameter that the Beta of parameter p distributes, and a, b are the parameters that the contrary Gamma of parameter alpha distributes, δ ₁, δ ₂It is the priori Uniform Distribution Families of parameter γ.

After collecting new information, its corresponding time is { t ₁, t ₂..., t _n, ∑ t _l ^kM k rank matrix sum can be calculated the posteriority expectation value of above parameter, adopts maximum-likelihood method to realize that to the parameter estimation in the monitoring reliability model its expression formula is:

$E\left(p\right)=\frac{1}{C(n,u)}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{\left(\begin{array}{c}n\\ k\end{array}\right)}{\mathrm{\Σ}}}\underset{v=0}{\overset{u}{\mathrm{\Σ}}}\{\left(\begin{array}{c}u\\ v\end{array}\right)\frac{\mathrm{\Γ}({\mathrm{\ω}}^{*}+1)\mathrm{\Γ}\left({\mathrm{\η}}^{*}\right)}{\mathrm{\Γ}({\mathrm{\ω}}^{*}+1+{\mathrm{\η}}^{*})}\×\mathrm{\Γ}\left(a_L^{*}\right)\×\mathrm{\Γ}\left(a_U^{*}\right){\∫}_{{\mathrm{\δ}}_{L1}}^{{\mathrm{\δ}}_{L2}}{\∫}_{{\mathrm{\δ}}_{U1}}^{{\mathrm{\δ}}_{U2}}{\left(b_U^{*}\right)}^{a_U^{*}}{\mathrm{\γ}}_S^{n-k}\mathrm{\Π}{\left(t_m^{(n-k)}\right)}^{{\mathrm{\γ}}_U-1}{b}_L^{*}{\mathrm{\γ}}_L^k\mathrm{\Π}{\left(t_m^k\right)}^{{\mathrm{\γ}}_L-1}{\mathrm{d\γ}}_L{\mathrm{d\γ}}_U\}$

$E\left({\mathrm{\α}}_L\right)=\frac{1}{C(n,u)}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{\left(\begin{array}{c}n\\ k\end{array}\right)}{\mathrm{\Σ}}}\underset{v=0}{\overset{u}{\mathrm{\Σ}}}\{\left(\begin{array}{c}u\\ v\end{array}\right)\frac{\mathrm{\Γ}\left({\mathrm{\ω}}^{*}\right)\mathrm{\Γ}\left({\mathrm{\η}}^{*}\right)}{\mathrm{\Γ}({\mathrm{\ω}}^{*}+{\mathrm{\η}}^{*})}\×\mathrm{\Γ}(a_L^{*}-1)\×\mathrm{\Γ}\left(a_U^{*}\right){\∫}_{{\mathrm{\δ}}_{L1}}^{{\mathrm{\δ}}_{L2}}{\∫}_{{\mathrm{\δ}}_{U1}}^{{\mathrm{\δ}}_{U2}}{\left(b_U^{*}\right)}^{a_U^{*}}{\mathrm{\β}}_S^{n-k}\mathrm{\Π}{\left(t_m^{(n-k)}\right)}^{{\mathrm{\β}}_U-1}{\left(b_L^{*}\right)}^{a_L^{*}-1}{\mathrm{\β}}_L^k\mathrm{\Π}{\left(t_m^k\right)}^{{\mathrm{\β}}_L-1}{\mathrm{d\γ}}_L{\mathrm{d\γ}}_U\}$

$E\left({\mathrm{\α}}_U\right)=\frac{1}{C(n,u)}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{\left(\begin{array}{c}n\\ k\end{array}\right)}{\mathrm{\Σ}}}\underset{v=0}{\overset{u}{\mathrm{\Σ}}}\{\left(\begin{array}{c}u\\ v\end{array}\right)\frac{\mathrm{\Γ}\left({\mathrm{\ω}}^{*}\right)\mathrm{\Γ}\left({\mathrm{\η}}^{*}\right)}{\mathrm{\Γ}({\mathrm{\ω}}^{*}+{\mathrm{\η}}^{*})}\×\mathrm{\Γ}\left(a_L^{*}\right)\×\mathrm{\Γ}(a_U^{*}-1){\∫}_{{\mathrm{\δ}}_{L1}}^{{\mathrm{\δ}}_{L2}}{\∫}_{{\mathrm{\δ}}_{U1}}^{{\mathrm{\δ}}_{U2}}{\left(b_U^{*}\right)}^{a_U^{*}-1}{\mathrm{\γ}}_S^{n-k}\mathrm{\Π}{\left(t_m^{(n-k)}\right)}^{{\mathrm{\γ}}_U-1}{\left(b_L^{*}\right)}^{a_L^{*}}{\mathrm{\γ}}_L^k\mathrm{\Π}{\left(t_m^k\right)}^{{\mathrm{\β}}_L-1}{\mathrm{d\γ}}_L{\mathrm{d\γ}}_U\}$

$E\left({\mathrm{\γ}}_L\right)=\frac{1}{C(n,u)}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{\left(\begin{array}{c}n\\ k\end{array}\right)}{\mathrm{\Σ}}}\underset{v=0}{\overset{u}{\mathrm{\Σ}}}\{\left(\begin{array}{c}u\\ v\end{array}\right)\frac{\mathrm{\Γ}\left({\mathrm{\ω}}^{*}\right)\mathrm{\Γ}\left({\mathrm{\η}}^{*}\right)}{\mathrm{\Γ}({\mathrm{\ω}}^{*}+{\mathrm{\η}}^{*})}\×\mathrm{\Γ}\left(a_L^{*}\right)\×\mathrm{\Γ}\left(a_U^{*}\right){\∫}_{{\mathrm{\δ}}_{L1}}^{{\mathrm{\δ}}_{L2}}{\∫}_{{\mathrm{\δ}}_{U1}}^{{\mathrm{\δ}}_{U2}}{\left(b_U^{*}\right)}^{a_U^{*}}{\mathrm{\γ}}_S^{n-k}\mathrm{\Π}{\left(t_m^{(n-k)}\right)}^{{\mathrm{\γ}}_U-1}{\left(b_L^{*}\right)}^{a_L^{*}}{\mathrm{\γ}}_L^{k+1}\mathrm{\Π}{\left(t_m^k\right)}^{{\mathrm{\γ}}_L-1}{\mathrm{d\γ}}_L{\mathrm{d\γ}}_U\}$

$E\left({\mathrm{\γ}}_U\right)=\frac{1}{C(n,u)}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{\left(\begin{array}{c}n\\ k\end{array}\right)}{\mathrm{\Σ}}}\underset{v=0}{\overset{u}{\mathrm{\Σ}}}\{\left(\begin{array}{c}u\\ v\end{array}\right)\frac{\mathrm{\Γ}\left({\mathrm{\ω}}^{*}\right)\mathrm{\Γ}\left({\mathrm{\η}}^{*}\right)}{\mathrm{\Γ}({\mathrm{\ω}}^{*}+{\mathrm{\η}}^{*})}\×\mathrm{\Γ}\left(a_L^{*}\right)\×\mathrm{\Γ}\left(a_U^{*}\right){\∫}_{{\mathrm{\δ}}_{L1}}^{{\mathrm{\δ}}_{L2}}{\∫}_{{\mathrm{\δ}}_{U1}}^{{\mathrm{\δ}}_{U2}}{\left(b_U^{*}\right)}^{a_U^{*}}{\mathrm{\γ}}_U^{n-k+1}\mathrm{\Π}{\left(t_m^{(n-k)}\right)}^{{\mathrm{\γ}}_U-1}{\left(b_L^{*}\right)}^{a_L^{*}}{\mathrm{\γ}}_L^k\mathrm{\Π}{\left(t_m^k\right)}^{{\mathrm{\γ}}_L-1}{\mathrm{d\γ}}_L{\mathrm{d\γ}}_U\}$

7. based on the super parameter estimation of the aeromotor monitoring reliability model that mixes Weibull distribution

In the expression formula of the real-time reliability assessment of aeromotor, further estimate super parameter, for the different super parameter of several classes, in different ways:

(1) the super parameter priori of the Beta (ω, η) of parameter p and posteriority parameter learning

Prior distribution for distribution parameter p is π (p)=B (p, ω, η), generally supposes p ₀=0.5, then the pass of prior imformation and super parameter is: ω/ω+η=p ₀

The relation that the super parameter of prior distribution and posteriority distribute between the super parameter can be expressed as:

ω′＝(ω-1)/B(ω，η)

η′＝(η-1)/B(ω，η)

(2) form parameter α _LAnd α _UThe super parameter priori of contrary Ga (a, b) and posteriority parameter learning

Known

Burst inefficacy fiduciary level and variance constantly, then scale parameter α can be expressed as:

$\mathrm{\α}={\left[\frac{t_{R_0}}{\ln {(1/R_0)}^{1/\mathrm{\γ}}}\right]}^{1/\mathrm{\γ}}$

The average of known parameters α is closed variance, and then super parameter a and b can be expressed as:

$a=\frac{E^2\left(\mathrm{\α}\right)}{{\mathrm{\σ}}^2\left(\mathrm{\α}\right)}$

$b=\frac{E\left(\mathrm{\α}\right)}{{\mathrm{\σ}}^2\left(\mathrm{\α}\right)}$

For the observation data { (t that collects ₁, n ₁), (t ₂, n ₂) ..., (t _m, n _m), t wherein _iThe time of origin that the expression burst was lost efficacy, n _iExpression inefficacy sample number, posteriority parameter a ' and b ' after study can be expressed as:

$a^{\′}=a+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{t}_i$

$b^{\′}=b+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{n}_i$

8. calculate aeromotor monitoring reliability value

With the super parameter expectation value that step 7 is calculated, bring E (p), E (α that step 6 provides into _L), E (α _U), E (γ _L) and E (γ _U) expression formula, and further be updated to

Just can calculate the expectation value that reaches the aeromotor monitoring reliability, realize the real-time monitoring reliability to aeromotor.

Claims (9)

1. one kind based on the aeromotor monitoring reliability method of mixing Weibull distribution, it is characterized in that its step is as follows:

Step 1: extract aero-engine condition monitoring information and the performance degradation degree information of having changed and having keeped in repair;

Step 2: utilize support vector machine method, extract the relation between each monitoring parameter and the performance degradation value, realize the performance degradation value monitoring at wing engine;

Step 3: the utility monitoring result, set up the linear regression model of describing aeromotor accumulation amount of degradation;

Step 4: estimate the stray parameter in the aeromotor linear regression model;

Step 5: set up the aeromotor monitoring reliability model based on two-parameter mixing Weibull distribution;

Step 6: estimate the parameter based on the aeromotor monitoring reliability model that mixes Weibull distribution;

Step 7: estimate the super parameter based on the aeromotor monitoring reliability Model Parameter that mixes Weibull distribution;

Step 8: calculate aeromotor monitoring reliability value.

2. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1, it is characterized in that, in described step 1, from check, change with the aeromotor of keeping in repair extract aero-engine performance degradation values and status monitoring parameter, the present invention is selection mode monitoring information from gas circuit performance monitoring, lubricating oil performance monitoring and vibration monitoring respectively;

3. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1, it is characterized in that, utilize support vector machine method, by training and checking, extract the relation between aero-engine performance degradation values and each monitoring parameter, realize the monitoring of degenerating in the real-time performance of wing engine;

4. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1, it is characterized in that, in its described step 3, utilize Real-Time Monitoring at wing aero-engine performance degeneration monitor value, set up linear aero-engine performance degradation model, describe aeromotor accumulation amount of degradation;

5. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1, it is characterized in that, in described step 4, estimate the stray parameter in the aeromotor linear regression model, determine the bound of aeromotor accumulation performance amount of degradation;

6. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1, it is characterized in that, in described step 5, set up biparametric and mix Weibull distribution model, realize the description to aeromotor Multiple Failure Modes and multiple failure regularity;

7. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1, it is characterized in that, in described step 6, adopt maximum likelihood method, provide the expression formula based on the two-parameter monitoring reliability Model Parameter that mixes Weibull distribution;

8. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1, it is characterized in that, in described step 7, adopt bayes method, estimate the super parameter based on the aeromotor monitoring reliability model that mixes Weibull distribution;

9. the aeromotor monitoring reliability method based on mixing Weibull distribution according to claim 1 is characterized in that, in described step 8, utilizes the Output rusults of step 6 and step 7, calculates aeromotor monitoring reliability value.

Images