CN107153759B - A kind of aviation turbofan engine method for predicting residual useful life of multisource data fusion - Google Patents

A kind of aviation turbofan engine method for predicting residual useful life of multisource data fusion Download PDF

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CN107153759B
CN107153759B CN201710287759.6A CN201710287759A CN107153759B CN 107153759 B CN107153759 B CN 107153759B CN 201710287759 A CN201710287759 A CN 201710287759A CN 107153759 B CN107153759 B CN 107153759B
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aero
time
health indicator
monitoring data
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吴思思
赵广社
荣海军
鲍容憬
李长军
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Xian Jiaotong University
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Abstract

The invention discloses a kind of aviation turbofan engine method for predicting residual useful life of multi-source statistical data driving, the monitoring data for making full use of engine sensor to acquire predict engine residual life；Firstly, multi-source monitoring data fusion and failure threshold estimation；The modeling of engine degenerative process and parameter Estimation；Engine residual life description；The big step of predicting residual useful life four；Compared with the existing technology, it is based on Common principal component analysis and Euclidean distance, merges multi-source monitoring data, to extract the health indicator and failure threshold of characterization engine operating state, solves the problems, such as that monitoring data use of information is insufficient in traditional prediction method；The indefinite aero-engine degenerative process of the Wiener-Hopf equation characterization degradation ratio with nonlinear drift is established, real-time online life prediction is carried out based on the distribution of aero-engine remaining life；Data are provided for condition maintenarnce technology to support, increases engine time-on-wing, avoids major accident, and there is engineering application value.

Description

A kind of aviation turbofan engine method for predicting residual useful life of multisource data fusion
Technical field
The present invention relates to aviation turbofan engine predicting residual useful life field, the aviations of specifically a kind of multisource data fusion Fanjet method for predicting residual useful life.
Background technique
Aero-engine prognostics and health management technology (Prognostics and Health Management, PHM) is Engine condition maintenarnce (Condition-Based Maintenance, CM) provides technological guidance and priori knowledge, pushes energetically Aircraft engine maintenance technology is gradually from hard time maintenance to condition maintenarnce shifts in technology, it is ensured that flight safety reduces maintenance Expense, therefore cause extensive concern and research.With the progress of sensor technology and electronic equipment, engine raw monitored Data accurately can be monitored and be recorded, and provided enough data for PHM technology and supported.How according to existing engine Primary monitoring data accurately predicts engine residual life, is the research core of aero-engine PHM technology.
The potential information that method based on statistical data driving includes by excavating monitoring data, with the change of display system inside The performance change of system caused by change and external environment influence, avoids the aero-engine System Computer high to complex precise degree Reason is modeled, and is combined forecasting accuracy, is directly realized by the life prediction of fanjet, so that prediction result has mould Paste property provides feasibility in research from now on, to incorporate the more accurate prediction of expertise progress.Statistical data driving method needs To meet system degradation process model building, Wiener-Hopf equation mission nonlinear non-stationary degenerative process, while there is good mathematics Characteristic, the degradation model based on Wiener-Hopf equation is in the side such as aero-engine system degradation modeling analysis and predicting residual useful life Face achieves good effect, sufficiently demonstrates the applicability of the model.
In practical applications, the delivery temperature nargin of aero-engine changes foundation and important as a characterization engine Performance indicator, be commonly used for establishing engine degradation model.Wiener-Hopf equation probability-distribution function based on linear drift is clear, Model is simple.However, but having ignored the portion carried in other monitoring data in existing aero-engine Study on residual life The spy that otherness and engine system operation later period degeneration between part status information, engine operating environment and individual accelerate Point does not consider the monitoring data of multi-source and the combination with nonlinear drift degenerative process simultaneously.
Summary of the invention
For the deficiency of traditional aero-engine method for predicting residual useful life, the present invention is by providing a kind of multi-source statistics The aviation turbofan engine method for predicting residual useful life of data-driven, to solve to ignore in conventional statistics data-driven prediction technique The problem of engine multidimensional monitoring data and equipment operating environment and individual difference.
To achieve the above object, design of the invention is accomplished by with technical solution
Basic conception of the invention is the effective monitoring data for making full use of engine sensor to acquire, and is being unfavorable for the longevity On the basis of life prediction redundancy feature, information fusion is carried out to extract the health indicator of characterization engine operating state and failure threshold Value, solves the problems, such as that monitoring data use of information is insufficient in traditional prediction method.It establishes based on the non-linear of random parameter Wiener-Hopf equation aero-engine failure model, the otherness between uncertainty and equipment individual to characterize running environment, The non-linear degradation process of simulated engine.On this basis, real-time online life prediction is carried out to aero-engine.
Based on above-mentioned basic conception, technical solution provided by the invention is a kind of aviation turbofan of multisource data fusion Engine residual life prediction technique, comprising the following steps:
Step 1: the fanjet performance degradation assessment based on Multi-source Information Fusion:
Step 1.1: multi-source monitoring data dimensionality reduction, based on Common principal component analysis method extraction system monitoring data it is main at Point；Monitoring data are multidimensional time-series, and retention time dimension is constant, carry out common Principle component extraction to variable dimension；
Figure BDA0001281121870000031
Wherein U=[U1,U2,...,Ur]TFor transformation matrix, r indicates the number of selected principal component, UrFor r-th of master point Measure corresponding unit character vector, XnFor n-th aero-engine primary monitoring data,
Figure BDA0001281121870000032
For based on Common principal component analysis N-th aero-engine monitoring data after dimensionality reduction, mnFor the maximum sampling number of n-th engine,
Figure BDA0001281121870000033
It is sent out for n-th aviation The monitoring data of jth time sampling after motivation dimensionality reduction,
Figure BDA0001281121870000034
For m after n-th aero-engine dimensionality reductionnThe monitoring data of secondary sampling, (·)TIndicate transposition.
Step 1.2: on the basis of step 1.1, the statistics of engine health is carried out, research shows that before engine 5% life cycle is considered there is no degenerating, therefore extracts the health that the monitoring data of not degenerating in training set are regarded as engine Parameter；
Engine general health parameter is H=(h1,h2,...hn,...,hN)T, hnJoin for n-th aero-engine health Number, N are engine number of units in training set；Then the aero-engine monitoring data mean value m that do not degenerate is expressed as follows:
Figure BDA0001281121870000041
Wherein m is that aero-engine is not degenerated monitoring data mean value, SnIndicate n-th aero-engine health in training set The maximum sampling number of parameter,
Figure BDA0001281121870000042
For the monitoring data of jth after n-th aero-engine dimensionality reduction time sampling, N is to send out in training set Motivation number of units, ∑ indicate summation；
Step 1.3: on the basis of step 1.2, calculating engine and run health indicator, to assess engine performance degeneration Degree；
The health indicator calculation formula of every engine is as follows:
Figure BDA0001281121870000043
Wherein tjFor the time of n-th engine jth time sampling, yn(tj) it is n-th engine health when jth time samples Index, m are that aero-engine is not degenerated monitoring data mean value,
Figure BDA0001281121870000044
For the prison of jth after n-th aero-engine dimensionality reduction time sampling Measured data；
Step 1.4: being based on engine health indicator, determine power failure threshold value；Studies have shown that aero-engine fails Process is divided into four-stage, last stage is regarded as the power failure stage；Last a kind of cluster centre is calculated as hair Motivation failure threshold ω；
Step 2: aero-engine degeneration modeling and parameter Estimation；
Step 2.1: choosing the Wiener-Hopf equation with nonlinear drift is characterization engine degenerative process model, enables initial degenerate State is zero；
Y (t)=y (0)+atb+σB(t) (7)
Wherein, y (0)=0, t is the sampling time, and nonlinear drift part is atb, diffusion coefficient σ, B (t) are Blang's fortune It is dynamic；Lead to the otherness between engine individual for characterization manufacture deviation and running environment, a is the random of nonlinear drift part Variable meets
Figure BDA0001281121870000045
Wherein N () indicates normal distribution, μaFor the mean value of stochastic variable a, σaFor stochastic variable a's Standard deviation；B is defined as to the identical characteristic of the constant characterization engine of nonlinear drift part simultaneously；
Step 2.2: the aero-engine degradation model parameter Estimation based on maximum likelihood method: establishing fanjet After degradation model, need to carry out parameter Estimation to model based on engine health indicator；Every engine is in multiple sampled points Health indicator obedience multiple normal distribution, therefore Yn~N (μn,Σn), wherein YnFor the health indicator of n-th engine, μnIt is n-th The health indicator mean vector of platform engine；ΣnFor the health indicator covariance matrix of n-th engine；
For different engine samples, degenerative process independent same distribution, therefore about global engine health indicator Y Likelihood function natural logrithm form such as formula (12) shown in:
Wherein a is the stochastic variable of nonlinear drift part, μaFor the mean value of stochastic variable a, σaFor the mark of stochastic variable a Quasi- poor, σ is diffusion coefficient, and b is the constant of nonlinear drift part, and Y is global engine health indicator, and N is to send out in training set Motivation number of units, mnFor the maximum sampling number of n-th engine, ΣnFor the health indicator covariance matrix of n-th engine, | | indicate modulo operation,
Figure BDA0001281121870000052
For ΣnInverse matrix, YnFor the health indicator of n-th engine, μnFor n-th engine Health indicator mean vector；
Parameter Estimation is carried out by maximizing likelihood function；
Figure BDA0001281121870000053
Figure BDA0001281121870000061
Wherein a is the stochastic variable of nonlinear drift part, μaFor the mean value of stochastic variable a, σaFor the mark of stochastic variable a Quasi- poor, σ is diffusion coefficient, and b is the constant of nonlinear drift part,
Figure BDA0001281121870000062
For μaEstimated value, N be training set in engine bed Number,
Figure BDA0001281121870000063
tjFor the time of n-th engine jth time sampling, ΣnFor the health of n-th engine Index covariance matrix, ΣnFor the health indicator covariance matrix of n-th engine, | | indicate modulo operation,For Σn Inverse matrix, YnFor the health indicator of n-th engine, Y is global engine health indicator；
Step 3: establishing aero-engine predicting residual useful life model；
Step 3.1: the aero-engine remaining life description based on Wiener-Hopf equation
There is time-shifting invariance based on engine performance degradation model, then degradation model indicates are as follows:
Figure BDA0001281121870000065
Wherein tcFor aero-engine current run time, liFor aero-engine remaining life, B () indicates Blang's fortune It is dynamic, y (tc) it is aero-engine current health index, y (li+tc) be aero-engine failure when health indicator, a be it is non-thread Property drift components stochastic variable, b be nonlinear drift part constant, σ is diffusion coefficient, Y (li) indicate engine with boat Empty engine residual life liThe Wiener-Hopf equation of degeneration, ∫ indicate integral；Know that engine residual life description still may be characterized as band The Wiener-Hopf equation of nonlinear drift；
Step 3.2: the description of aero-engine remaining life is converted to standard Wiener-Hopf equation, for Nonlinear Diffusion process, If meeting:
Figure BDA0001281121870000071
Wherein μ (y, li) indicate nonlinear drift part, σ ' (li, u) and it is diffusion part, y is health indicator, and li is aviation Engine residual life, c1(li) and c2(li) it is arbitrarily about liFunction, z be Wiener-Hopf equation initial value, ∫ indicate integral,
Figure BDA0001281121870000072
Indicate partial derivative；
Step 4: the aero-engine predicting residual useful life based on performance degradation；
Aero-engine remaining life probability density estimation is established, on the basis of steps 1 and 2,3, progress exists in real time Line life prediction；
The probability density function that Brownian movement passes through failure threshold for the first time is expressed as follows:
Figure BDA0001281121870000073
Wherein pB(t)(ω, t) indicates that Brownian movement passes through the probability density function of failure threshold for the first time, and ω is failure threshold Value, t is the sampling time；
Therefore the remaining life probability density function of aero-engine are as follows:
Figure BDA0001281121870000081
Wherein
Figure BDA0001281121870000082
Indicate that degenerative process passes through the probability density function of threshold value for the first time, ω is failure threshold, liFor boat Empty engine residual life, tcFor aero-engine current run time, y (tc) it is aero-engine current health index, a is The stochastic variable of nonlinear drift part, μaFor the mean value of stochastic variable a, σaFor the standard deviation of stochastic variable a, f (a) is random The probability density function of variable a, b are the constant of nonlinear drift part, and σ is diffusion coefficient, and exp () is indicated using e the bottom of as Exponential function；Result above meets the actual use needs of aero-engine service life prediction.
The last a kind of cluster centre of calculating described in step 1.4 is as power failure threshold value ω, the specific steps are as follows:
The first step, for n-th engine health indicator
Figure BDA0001281121870000083
What is sampled every time is strong Kang Zhibiao is regarded as a sample；
Second step randomly chooses 4 initial cluster center z1(k),z2(k)…z4(k), k indicates the number of iterations, initial value It is 1, every iteration once adds 1；
Third step, one by one by yn(tp), p=1,2 ..., mnBeing assigned to 4 centers by minimum distance criterion is zi(k) In class；
Third step, point all kinds of new center of calculating:
Figure BDA0001281121870000091
NjSample i.e. in jth class Number, OjIndicate the sample set for belonging to jth class；
4th step, if zj(k+1)≠zj(k) step 2 is then gone to, mode is reclassified, iteration calculates, until Cluster centre convergence, records the maximum value ω of 4 cluster centresmax(n)；
5th step repeats the 1st, 2,3,4 steps for each engine, chooses ωmax(n) minimum value in is regarded as sending out Motivation failure threshold, i.e. ω=min (ωmax(n)), n=1,2 ..., 100, wherein min () expression is minimized.
Beneficial effects of the present invention exist:
The aviation turbofan engine method for predicting residual useful life of multisource data fusion of the present invention is based on multi-source monitoring data, The principal component of monitoring data is extracted using Common principal component analysis, reduces the influence of redundant data and noise data.Multi-parameter Fusion can be to greatest extent using the effective information of sensor monitoring, thus the degenerative process of accurate characterization aero-engine.Hair Motivation degeneration later period degenerative process accelerates, and establishes the Wiener-Hopf equation with nonlinear drift thus.Establish the aero-engine remaining longevity Prediction model is ordered, realizes and the real-time online of engine is predicted, provide priori knowledge for condition maintenarnce, have good engineering and answer With value.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart.
Fig. 2 is training set #1~#10 platform aero-engine high pressure compressor inlet total moisture content measurement data.
Fig. 3 is the first six principal component value after Common principal component analysis dimensionality reduction.
Fig. 4 a is No. #1 engine health indicator curve of the trained engine based on ED.
Fig. 4 b is No. #3 engine health indicator curve of the trained engine based on ED.
Fig. 5 is 4 stages of aero-engine degenerative process.
Fig. 6 is #1, #5, #10, five test engine remaining life probability density functions of #26, #60 and prediction remaining longevity Life, and the comparison of true remaining life.
Fig. 7 is the signal of remaining life burst error.
Fig. 8 is 100 engine residual life frequency disributions in test machine
Fig. 9 is that 100 engine residual lifes predict penalty score in test machine
Specific embodiment
Method proposed by the present invention is verified in publication C-MAPSS data set in 2008 by NASA below by one group.It should Data set utilizes fanjet simulation model, and under the conditions of different operation, simulation generates different degrees of specific disabled status When fanjet primary monitoring data.Data set owner will divide training dataset, test data set, remaining life data set three Point.Wherein, training data concentration acquires 100 fanjets and runs from health status to whole monitoring numbers of failure state According to.Test data set includes the monitoring data of 100 engines, is brought into operation from health status, before thrashing Certain moment stops acquisition.The remaining life data set record true remaining life of test engine.With #1~#10 platform aviation hair For the high pressure compressor inlet total moisture content measurement data of motivation, training set monitoring data are as shown in Figure 2.
Embodiment:
As shown in Figure 1, the present invention is based on the aviation turbofan engine method for predicting residual useful life of multi-source statistical data driving, The following steps are included:
1, the fanjet performance degradation assessment based on Multi-source Information Fusion using Common principal component analysis and is based on Europe Family name's distance (Euclidean Distance, ED) fusion method, under conditions of removing noise jamming and uncorrelated monitoring data, Engine validity feature information is merged, global engine health indicator Y is obtained.
1.1, multi-source monitoring data dimensionality reduction, the principal component based on Common principal component analysis method extraction system monitoring data.Prison Measured data is multidimensional time-series, and retention time dimension is constant, carries out common Principle component extraction to variable dimension.
N-th aero-engine primary monitoring data
Figure BDA0001281121870000111
N=(1,2,3 .., N), xni For the initial data of n-th aero-engine i-th sampling, N is engine number of units in training set, N=100 in the present embodiment, mnFor the maximum sampling number of n-th engine.xni=[xn1,xn2,...,xnj,...xnk], k indicates the dimension of primary monitoring data It counts, the dimension of primary monitoring data is 21 in data set used in the present embodiment, therefore k=21, xnjFor n-th engine J-th of sensor measurement data in i sampled data.
For training dataset, the covariance matrix of every engine is obtained based on Common principal component analysis method, formula is such as Under:
Cn=E [(Xn-E(Xn))T(Xn-E(Xn))] (1)
Wherein CnFor the covariance matrix of the n-th aviation platform engine, XnFor n-th aero-engine primary monitoring data, E () indicates expectation, ()TIndicate transposition；
For N platform engine, it is as follows to calculate average covariance matrices:
Figure BDA0001281121870000112
Wherein
Figure BDA0001281121870000113
For aero-engine average covariance matrices, N is engine number of units in training set, CnIt is sent out for n-th aviation The covariance matrix of motivation；λ i, i=1,2 ..., k is
Figure BDA0001281121870000114
Ith feature value, k indicate primary monitoring data dimension,For
Figure BDA0001281121870000116
Unit character vector matrix, wherein UjFor the corresponding unit character of j-th of characteristic value Vector；According to characteristic value from greatly to small sequence, r eigenvalue λ of selection1≥λ2≥...≥λr, r < k is denoted as r principal component, then U =[U1,U2,...,Ur]TFor transformation matrix, wherein r is main component number；Primary monitoring data projects to new feature space, While obtaining more low dimensional characteristic variable, the effective information for including in primary monitoring data can be retained to greatest extent, disappeared Except the influence of noise and uncorrelated variables.N-th aero-engine primary monitoring data
Figure BDA0001281121870000121
Conversion formula is as follows:
Wherein U=[U1,U2,...,Ur]TFor transformation matrix, r indicates the number of selected principal component, UrFor r-th of master point Measure corresponding unit character vector, XnFor n-th aero-engine primary monitoring data, xniFor n-th aero-engine i-th The primary monitoring data of sampling,
Figure BDA0001281121870000123
For based on n-th aero-engine monitoring data after Common principal component analysis dimensionality reduction, mn For the maximum sampling number of n-th engine,
Figure BDA0001281121870000124
For the monitoring data of jth after n-th aero-engine dimensionality reduction time sampling, For m after n-th aero-engine dimensionality reductionnThe monitoring data of secondary sampling, ()TIndicate transposition.
R=6 is enabled in the present embodiment, retains preceding 6 principal components, and energy proportion reaches 94% or more, and each principal component takes Value is as shown in Figure 3, it was demonstrated that selected principal component number retains the information in primary monitoring data enough.To engine training number It is converted according to the primary monitoring data in collection and test data.
1.2, on the basis of 1.1, the statistics of engine health is carried out.Research shows that preceding 5% service life of engine Period can be considered there is no degenerating, therefore extract the general health that the monitoring data of not degenerating in training set are regarded as engine Parameter H=(h1,h2,...,hN)T, wherein
Figure BDA0001281121870000131
For the health parameters of n-th engine,
Figure BDA0001281121870000132
It is n-th The monitoring data of jth time sampling, S after platform aero-engine dimensionality reductionn, n=1,2 ..., N indicates n-th aviation hair in training set The maximum sampling number of motivation health parameters calculates as follows:
Sn=[0.05mn] (4)
Wherein SnIndicate the maximum sampling number of n-th aero-engine health parameters in training set, mnStart for n-th The maximum sampling number of machine, [] indicate to be rounded downwards, and N is engine number of units in training set；
1.3, after the health data for obtaining engine, calculating aero-engine first is not degenerated monitoring data mean value.Aviation The engine monitoring data mean value m that do not degenerate is expressed as follows:
Figure BDA0001281121870000133
Wherein m is that aero-engine is not degenerated monitoring data mean value, SnIndicate n-th aero-engine health in training set The maximum sampling number of parameter,
Figure BDA0001281121870000134
For the monitoring data of jth after n-th aero-engine dimensionality reduction time sampling, N is in training set Engine number of units, ∑ indicate summation；
The physical meaning of m refers to benchmark monitoring data of the engine when not degenerating.The health indicator of engine can The ED of benchmark health data is determined when not degenerated by current time monitoring data and engine.The health indicator of every engine Calculation formula is as follows:
Figure BDA0001281121870000135
Wherein tjFor the time of n-th engine jth time sampling, yn(tj) it is n-th engine health when jth time samples Index, m are that aero-engine is not degenerated monitoring data mean value,
Figure BDA0001281121870000136
For the monitoring of jth after n-th aero-engine dimensionality reduction time sampling Data；Therefore n-th engine health indicator
Figure BDA0001281121870000137
Wherein mnFor the maximum sampling time of n-th engine Number.
By taking #1, No. #3 trained engine as an example, Fig. 4 a and Fig. 4 b are the engine health indicator curves based on ED, and observation can Know that downward trend is presented in engine overall performance, smaller in initial operating stage degradation ratio, later period catagen speed is accelerated.Thus provable Aero-engine Degradation path has nonlinear drift.
1.4, it is based on engine health indicator, determines power failure threshold value.According to studies have shown that aero-engine is degenerated For process as shown in figure 5, being divided into four-stage, last stage may be regarded as the power failure stage.This research is based on K- Means clustering algorithm, clusters number are set as 4, calculate last a kind of cluster centre as power failure threshold value ω.Specifically Implementation steps are as follows:
The first step, for n-th engine health indicator
Figure BDA0001281121870000141
What is sampled every time is strong Kang Zhibiao is regarded as a sample.
Second step randomly chooses 4 initial cluster center z1(k),z2(k)…z4(k), k indicates the number of iterations, initial value It is 1, every iteration once adds 1；
Third step, one by one by yn(tp), p=1,2 ..., it is z that mn, which is assigned to 4 centers by minimum distance criterion,i(k) In class.
Third step, point all kinds of new center of calculating:
Figure BDA0001281121870000142
NjSample i.e. in jth class This number, OjIndicate the sample set for belonging to jth class.
4th step, if zj(k+1)≠zj(k) step 2 is then gone to, mode is reclassified, iteration calculates, until Cluster centre convergence, records the maximum value ω of 4 cluster centresmax(n)。
5th step repeats the 1st, 2,3,4 steps for each engine, chooses ωmax(n) minimum value in is regarded as sending out Motivation failure threshold, i.e. ω=min (ωmax(n)), n=1,2 ..., 100, wherein min () expression is minimized.
Failure threshold ω=1.27 of aero-engine are computed in the present embodiment.
2, aero-engine degeneration modeling and parameter Estimation
2.1, in the degenerative process of aero-engine, initial stage degeneration is not significant, and the later period causes to degenerate due to loss failure Speed is accelerated, and increase tendency is presented in health indicator and whole process is irreversible.Therefore, the wiener mistake with nonlinear drift is selected Journey describes the degenerative process of fanjet.For assuming that, in sampling time t, health indicator is y (t), failure threshold ω, base It can be described as following formula in the aero-engine degenerative process of Wiener-Hopf equation:
Y (t)=y (0)+atb+σB(t) (7)
Wherein, t is the sampling time, and nonlinear drift part is atb, diffusion coefficient σ, B (t) are Brownian movement；For table Sign manufacture deviation and running environment lead to the otherness between engine individual, and a is the stochastic variable of nonlinear drift part, full FootWherein N () indicates normal distribution, μaFor the mean value of stochastic variable a, σaFor the standard deviation of stochastic variable a； B is defined as to the identical characteristic of the constant characterization engine of nonlinear drift part simultaneously；Ignore the original abrasion of engine, for For the engine of not running, it is assumed that its initial degenerate state is 0, then has y (0)=0.
When at a time health indicator is equal to or over device failure threshold value, system must stop transporting engine Row.Therefore the service life of aero-engine can be regarded as the time for passing through failure threshold for the first time of Wiener-Hopf equation, be defined as follows:
T=inf t:y (t)>=ω | y (0)<ω } (8)
Wherein: T is the engine life period, and t is the sampling time, and y (t) is t moment health indicator, and ω is failure threshold, Inf { } indicates infimum；
2.2, the aero-engine degradation model parameter Estimation based on maximum likelihood method.In the degeneration for establishing fanjet After model, need to carry out parameter Estimation to model based on engine health indicator.Health of the every engine in multiple sampled points Index obedience multiple normal distribution, therefore the health indicator of n-th engine are as follows:
Figure BDA0001281121870000161
Figure BDA0001281121870000162
Wherein μnFor the health indicator mean vector of n-th engine, a is the stochastic variable of nonlinear drift part, and b is The constant of nonlinear drift part, tjFor in the time of jth time sampling, E () indicates expectation, ()TIndicate transposition；This implementation T in examplej=j.
Figure BDA0001281121870000163
Wherein ΣnFor the health indicator covariance matrix of n-th engine, cov () indicates covariance, and σ is diffusion system Number, σaFor the standard deviation of stochastic variable a, b is the constant of nonlinear drift part,tjIt is n-th The time of engine jth time sampling, ()TIndicate transposition；
For different engines, degenerative process independent same distribution, therefore the likelihood function of degradation model are as follows:
Figure BDA0001281121870000165
Wherein L (μa,σa, σ, b | Y) likelihood function of the expression about global engine health indicator Y, μaFor stochastic variable a Mean value, σaFor the standard deviation of stochastic variable a, σ is diffusion coefficient, and b is the constant of nonlinear drift part, and N is in training set Engine number of units, mnFor the maximum sampling number of n-th engine, YnFor the health indicator of n-th engine, ΣnIt is n-th The health indicator covariance matrix of engine, μnFor the health indicator mean vector of n-th engine, | | indicate modulus behaviour Make,For ΣnInverse matrix, exp () indicate using e as the exponential function at bottom, ∏ indicate quadrature；
Wherein μaFor the mean value of stochastic variable a, σaFor the standard deviation of stochastic variable a, σ is diffusion coefficient, and b is non-linear drift The constant of part is moved, Y is global engine health indicator, and N is engine number of units in training set, mnMost for n-th engine Big sampling number, ΣnFor the health indicator covariance matrix of n-th engine, | | indicate modulo operation,For ΣnIt is inverse Matrix, YnFor the health indicator of n-th engine, μnFor the health indicator mean vector of n-th engine；
Parameter Estimation is carried out by maximizing likelihood function.
Figure BDA0001281121870000174
Wherein
Figure BDA0001281121870000175
tjFor the time of n-th engine jth time sampling,
Figure BDA0001281121870000176
Indicate partial derivative；
Figure BDA0001281121870000177
Wherein a is the stochastic variable of nonlinear drift part, μaFor the mean value of stochastic variable a, σaFor the mark of stochastic variable a Quasi- poor, σ is diffusion coefficient, and b is the constant of nonlinear drift part,For μaEstimated value, N be training set in engine bed Number,
Figure BDA0001281121870000183
tjFor the time of n-th engine jth time sampling, ΣnFor the health of n-th engine Index covariance matrix, ΣnFor the health indicator covariance matrix of n-th engine, | | indicate modulo operation,
Figure BDA0001281121870000184
For Σn Inverse matrix, YnFor the health indicator of n-th engine, Y is global engine health indicator；
Based on the minimum value of simplex method seeking (15), μ is then obtainedaEstimated value.
The present embodiment final argument estimated result is as shown in table 1:
1 aero-engine degradation model parameter of table
Figure BDA0001281121870000185
3, aero-engine predicting residual useful life model is established:
3.1, the aero-engine remaining life description based on Wiener-Hopf equation.When being had based on engine performance degradation model Between translation invariance, then degradation model can be represented as:
Figure BDA0001281121870000187
Wherein tcFor aero-engine current run time, liFor aero-engine remaining life, B () indicates Blang's fortune It is dynamic, y (tc) it is aero-engine current health index, y (li+tc) be aero-engine failure when health indicator, a be it is non-thread Property drift components stochastic variable, b be nonlinear drift part constant, σ is diffusion coefficient, Y (li) indicate engine with boat Empty engine residual life liThe Wiener-Hopf equation of degeneration, ∫ indicate integral；Know that engine residual life description still may be characterized as band The Wiener-Hopf equation of nonlinear drift；Wiener-Hopf equation passes through ω-y (t for the first time at this timec) time be engine remaining life.
3.2, it can be carried out with the Wiener-Hopf equation with nonlinear drift according to the remaining life model of 3.1 aero-engines Description.For the remaining life for estimating engine, the Wiener-Hopf equation with nonlinear drift should be converted to Brownian movement first.Aviation Engine residual life description is converted to standard Wiener-Hopf equation, for Nonlinear Diffusion process, if meeting:
Figure BDA0001281121870000191
Wherein μ (y, li) indicate nonlinear drift part, σ ' (li, u) and it is diffusion part, y is health indicator, liFor aviation Engine residual life, c1And c2For arbitrarily about the function of time, z is initial amount of degradation, ∫ indicates integral,
Figure BDA0001281121870000192
Indicate local derviation Number；
Then Nonlinear Diffusion process can be converted into Brownian movement through formula (19).
Figure BDA0001281121870000193
WhereinyFor aero-engine health indicator,
Figure BDA0001281121870000194
For the aero-engine health indicator after conversion, liFor aeroplane engine Machine remaining life,For the remaining life after conversion, ki, (i=1,2,3) is Arbitrary Coefficient and k1> 0, t0For initial time, ti, (i=0,1,2) it is initial time and meets ti>=0, z are initial amount of degradation, c1And c2For arbitrarily about the function of time；
Diffusion part σ (y, l for engine residual life model, in formula (18)i)=σ2, drift components μ (y,li)=ab (li+tc)b-1.As aero-engine remaining life liWhen=0, Y (li)=0 knows initial time t accordingly0=0, Wiener-Hopf equation initial value z=0.Therefore, following formula can be obtained:
Figure BDA0001281121870000201
Wherein a is the stochastic variable of nonlinear drift part, and b is the constant of nonlinear drift part, and σ is diffusion coefficient, tcFor aero-engine current run time, liFor aero-engine remaining life；Enable k1=1, ki=0 (i=2,3), tj=0 (j =1,2), then conversion process is expressed as follows:
WhereinyFor aero-engine health indicator,
Figure BDA0001281121870000203
For the aero-engine health indicator after conversion, liFor aeroplane engine Machine remaining life,
Figure BDA0001281121870000204
For the remaining life after conversion, a is the stochastic variable of nonlinear drift part, and b is nonlinear drift part Constant, σ is diffusion coefficient；
Failure threshold after conversion:
Figure BDA0001281121870000205
Wherein lost for ω engine Imitate threshold value；
4, the aero-engine predicting residual useful life based on performance degradation:
Aero-engine remaining life probability density estimation is established, on the basis of steps 1 and 2,3, progress exists in real time Line life prediction.
The probability density function that Brownian movement passes through failure threshold for the first time is expressed as follows:
pB(t)(ω, t) indicates that Brownian movement passes through the probability density function of threshold value for the first time, and ω is failure threshold, and t is sampling Time；
Therefore aero-engine remaining life probability density function are as follows:
Figure BDA0001281121870000211
Wherein: pX(li)(ω,li) indicate that degenerative process passes through the probability density function of failure threshold, l for the first timeiFor aviation hair Motivation remaining life,
Figure BDA0001281121870000212
For the remaining life after conversion, ω is power failure threshold value,
Figure BDA0001281121870000213
For the failure threshold after conversion, tcFor Aero-engine current run time, y (tc) it is aero-engine current health index, a is the random of nonlinear drift part Variable, b are the constant of nonlinear drift part, and σ is diffusion coefficient,
Figure BDA0001281121870000214
Indicate partial derivative；Result above meets the aero-engine longevity The actual use of life prediction needs.
Due to the stochastic variable of nonlinear drift part
Figure BDA0001281121870000215
The then probability density function of a are as follows:
Figure BDA0001281121870000216
Wherein f (a) indicates the probability density function of the stochastic variable a of nonlinear drift part, μaWith
Figure BDA0001281121870000217
It is respectively random The mean value and variance of variable a；
According to total probability formula, remaining life probability density estimation can be corrected for:
Figure BDA0001281121870000221
Wherein ω is failure threshold, liFor aero-engine remaining life, tcFor aero-engine current run time, y (tc) it is aero-engine current health index, a is the stochastic variable of nonlinear drift part, μaFor the mean value of stochastic variable a, σaFor the standard deviation of stochastic variable a, f (a) is the probability density function of stochastic variable a, and b is the constant of nonlinear drift part, σ For diffusion coefficient, exp () is indicated using e as the exponential function at bottom；
Engine prediction residual Life Calculation is as follows:
Figure BDA0001281121870000222
Wherein, liFor aero-engine remaining life,
Figure BDA0001281121870000223
Indicate that degenerative process passes through the probability density of threshold value for the first time Function；
Fig. 6 randomly chooses #1, #5, #10 according to cycle of operation size, and it is surplus to draw it for five test engines of #26, #60 Remaining service life probability density function and prediction remaining life is calculated, and the comparison of true remaining life.
The evaluation index of engine residual life prediction accuracy includes timely predicted number, determines coefficients R2And punishment Score s.Remaining life burst error is as shown in fig. 7, prediction errorWherein RUL is engine true remaining longevity Life,For Engine prediction remaining life；Determine the calculation method such as following formula of coefficient:
Figure BDA0001281121870000231
Wherein: RULiFor i-th true remaining life of engine,
Figure BDA0001281121870000232
For i-th Engine prediction remaining life,
Figure BDA0001281121870000233
For the average value of the true remaining life of whole engines；
Punish the calculation method such as following formula of score:
Figure BDA0001281121870000234
Wherein E is prediction error,
Figure BDA0001281121870000235
It is the engine number of negative value for prediction error,
Figure BDA0001281121870000236
It is the hair of positive value for prediction error Motivation number；
Determine that coefficients R shows that prediction model performance is better closer to 1, the lower performance for illustrating prediction model of penalty value Better.
100 engine residual life frequency disributions and penalty score such as Fig. 8 and Fig. 9 institute in the present embodiment test machine Show, table 2 is predicting residual useful life result.
2 estimated performance index result of table
Figure BDA0001281121870000237
By the result in table 2 it is found that aero-engine predicting residual useful life can be improved in method proposed by the present invention Accuracy considers that the influence of uncorrelated monitoring data improves model prediction performance.
The maximum difference place of the present invention and existing method is to carry out common Principle component extraction to multidimensional monitoring data, disappear Except the feature for life prediction redundancy；Fusion, which is carried out, based on multidimensional monitoring data replaces single argument prediction；Meanwhile it introducing with non- Linear Wiener-Hopf equation describes the nonlinear feature of engine degradation ratio, obtains the probability point of aero-engine predicting residual useful life Cloth carries out engine residual life point estimation.The experiment show practicability of this method.

Claims (2)

1. a kind of aviation turbofan engine method for predicting residual useful life of multisource data fusion, it is characterised in that: make full use of hair Effective monitoring data of motivation sensor acquisition carry out information fusion on the basis of eliminating for life prediction redundancy feature To extract the health indicator and failure threshold of characterization engine operating state, monitoring data information benefit in traditional prediction method is solved With insufficient problem；It establishes based on the non-linear Wiener-Hopf equation aero-engine failure model with random parameter, to characterize Otherness between uncertainty and the equipment individual of running environment, the non-linear degradation process of simulated engine；It is basic herein On, real-time online life prediction is carried out to aero-engine；The following steps are included:
Step 1: the fanjet performance degradation assessment based on Multi-source Information Fusion；
Step 1.1: multi-source monitoring data dimensionality reduction, the principal component based on Common principal component analysis method extraction system monitoring data；Prison Measured data is multidimensional time-series, and retention time dimension is constant, carries out common Principle component extraction to variable dimension；
Figure FDA0002078861540000011
Wherein U=[U1,U2,...,Ur]TFor transformation matrix, r indicates the number of selected principal component, UrFor r-th of principal component pair The unit character vector answered, XnFor n-th aero-engine primary monitoring data,
Figure FDA0002078861540000012
For based on Common principal component analysis dimensionality reduction N-th aero-engine monitoring data afterwards, mnFor the maximum sampling number of n-th engine,
Figure FDA0002078861540000013
For n-th aero-engine The monitoring data of jth time sampling after dimensionality reduction,For m after n-th aero-engine dimensionality reductionnThe monitoring data of secondary sampling, (·)TIndicate transposition；
Step 1.2: on the basis of step 1.1, the statistics of engine health is carried out, research shows that preceding the 5% of engine Life cycle is considered there is no degenerating, therefore extracts the health ginseng that the monitoring data of not degenerating in training set are regarded as engine Number；
Engine general health parameter is H=(h1,h2,...hn,...,hN)T, hnFor n-th aero-engine health parameters, N For engine number of units in training set；Then the aero-engine monitoring data mean value m that do not degenerate is expressed as follows:
Figure FDA0002078861540000021
Wherein m is that aero-engine is not degenerated monitoring data mean value, SnIndicate n-th aero-engine health parameters in training set Maximum sampling number,
Figure FDA0002078861540000022
For the monitoring data of jth after n-th aero-engine dimensionality reduction time sampling, N is to start in training set Board number, ∑ indicate summation；
Step 1.3: on the basis of step 1.2, calculating engine and run health indicator, to assess engine performance degeneration journey Degree；
The health indicator calculation formula of every engine is as follows:
Figure FDA0002078861540000023
Wherein tjFor the time of n-th engine jth time sampling, yn(tj) it is n-th engine health indicator when jth time samples, M is that aero-engine is not degenerated monitoring data mean value,
Figure FDA0002078861540000024
For the monitoring number of jth after n-th aero-engine dimensionality reduction time sampling According to；
Step 1.4: being based on engine health indicator, determine power failure threshold value；Studies have shown that aero-engine failure procedure It is divided into four-stage, last stage is regarded as the power failure stage；Last a kind of cluster centre is calculated as engine Failure threshold ω；
Step 2: aero-engine degeneration modeling and parameter Estimation；
Step 2.1: choosing the Wiener-Hopf equation with nonlinear drift is characterization engine degenerative process model, enables initial degenerate state It is zero；
Y (t)=y (0)+atb+σB(t) (7)
Wherein, y (0)=0, t is the sampling time, and nonlinear drift part is atb, diffusion coefficient σ, B (t) are Brownian movement；For Characterization manufacture deviation and running environment lead to the otherness between engine individual, and a is the stochastic variable of nonlinear drift part, Meet
Figure FDA0002078861540000025
Wherein N () indicates normal distribution, μaFor the mean value of stochastic variable a, σaFor the standard of stochastic variable a Difference；B is defined as to the identical characteristic of the constant characterization engine of nonlinear drift part simultaneously；
Step 2.2: the aero-engine degradation model parameter Estimation based on maximum likelihood method: in the degeneration for establishing fanjet After model, need to carry out parameter Estimation to model based on engine health indicator；Health of the every engine in multiple sampled points Index obedience multiple normal distribution, therefore Yn~N (μn,Σn), wherein YnFor the health indicator of n-th engine, μnIndicate n-th The health indicator mean vector of engine, ΣnIndicate the health indicator covariance matrix of n-th engine；
For different engine samples, degenerative process independent same distribution, therefore seemingly about global engine health indicator Y Shown in the natural logrithm form such as formula (12) of right function:
Figure FDA0002078861540000031
Wherein a is the stochastic variable of nonlinear drift part, μaFor the mean value of stochastic variable a, σaFor the standard deviation of stochastic variable a, σ is diffusion coefficient, and b is the constant of nonlinear drift part, and Y is global engine health indicator, and N is engine bed in training set Number, mnFor the maximum sampling number of n-th engine, ΣnFor the health indicator covariance matrix of n-th engine, | | it indicates Modulo operation,
Figure FDA0002078861540000032
For ΣnInverse matrix, YnFor the health indicator of n-th engine, μnFor the health indicator of n-th engine Mean vector；
Parameter Estimation is carried out by maximizing likelihood function；
Figure FDA0002078861540000033
Figure FDA0002078861540000041
Wherein a is the stochastic variable of nonlinear drift part, μaFor the mean value of stochastic variable a, σaFor the standard deviation of stochastic variable a, σ is diffusion coefficient, and b is the constant of nonlinear drift part,
Figure FDA0002078861540000042
For μaEstimated value, N be training set in engine number of units,
Figure FDA0002078861540000043
tjFor the time of n-th engine jth time sampling, ΣnFor the health indicator of n-th engine Covariance matrix, | | indicate modulo operation,
Figure FDA0002078861540000044
For ΣnInverse matrix, YnFor the health indicator of n-th engine, Y is overall Engine health indicator；
Step 3: establishing aero-engine predicting residual useful life model；
Step 3.1: the aero-engine remaining life description based on Wiener-Hopf equation
There is time-shifting invariance based on engine performance degradation model, then degradation model indicates are as follows:
Figure FDA0002078861540000045
Wherein tcFor aero-engine current run time, liFor aero-engine remaining life, B () indicates Brownian movement, y (tc) it is aero-engine current health index, y (li+tc) be aero-engine failure when health indicator, a be non-linear drift The stochastic variable of part is moved, b is the constant of nonlinear drift part, and σ is diffusion coefficient, Y (li) indicate that engine is sent out with aviation Motivation remaining life liThe Wiener-Hopf equation of degeneration, ∫ indicate integral；
Know that engine residual life description still may be characterized as the Wiener-Hopf equation with nonlinear drift；
Step 3.2: the description of aero-engine remaining life is converted to standard Wiener-Hopf equation, for Nonlinear Diffusion process, if full Foot:
Figure FDA0002078861540000051
Wherein μ (y, li) indicate nonlinear drift part, σ ' (li, u) and it is diffusion part, y is health indicator, and li is aeroplane engine Machine remaining life, c1(li) and c2(li) it is arbitrarily about liFunction, z be Wiener-Hopf equation initial value, ∫ indicate integral,
Figure FDA0002078861540000056
It indicates Partial derivative；
Nonlinear Diffusion process is then converted into Brownian movement through formula (19)；
Wherein y is aero-engine health indicator,
Figure FDA0002078861540000053
For the aero-engine health indicator after conversion, liIt is surplus for aero-engine The remaining service life,
Figure FDA0002078861540000054
For the remaining life after conversion, k1For Arbitrary Coefficient and k1> 0, k2For Arbitrary Coefficient, k3For Arbitrary Coefficient, t0It is first Begin the time and to meet t0>=0, t1For t0With liBetween any time and meet t1>=0, t2For t0With liBetween any time and Meet t2>=0, z are initial amount of degradation, c2For arbitrarily about the function of time, τ indicates that the integration variable of time, u indicate the time Integration variable；
Step 4: the aero-engine predicting residual useful life based on performance degradation；
Aero-engine remaining life probability density estimation is established, on the basis of steps 1 and 2,3, carries out the real-time online longevity Life prediction；
The probability density function that Brownian movement passes through failure threshold for the first time is expressed as follows:
Figure FDA0002078861540000055
Wherein: pB(t)(ω, t) indicates that Brownian movement passes through the probability density function of failure threshold for the first time, and ω is failure threshold, and t is Sampling time；
Aero-engine remaining life probability density function indicates are as follows:
Figure FDA0002078861540000061
Wherein
Figure FDA0002078861540000064
Indicate that degenerative process passes through the probability density function of threshold value for the first time, ω is failure threshold, liFor aviation hair Motivation remaining life, tcFor aero-engine current run time, y (tc) it is aero-engine current health index, a is non-thread The stochastic variable of property drift components, μaFor the mean value of stochastic variable a, σaFor the standard deviation of stochastic variable a, f (a) is stochastic variable a Probability density function, b is the constant of nonlinear drift part, and σ is diffusion coefficient, and exp () is indicated using e as the index letter at bottom Number.
2. a kind of aviation turbofan engine method for predicting residual useful life of multisource data fusion according to claim 1, Be characterized in that: the last a kind of cluster centre of calculating described in step 1.4 is as power failure threshold value ω, the specific steps are as follows:
The first step, for n-th engine health indicator
Figure FDA0002078861540000062
The health sampled every time refers to Mark is regarded as a sample；
Second step randomly chooses 4 initial cluster center z1(k),z2(k)…z4(k), k expression the number of iterations, initial value 1, Every iteration once adds 1；
Third step, one by one by yn(tp), p=1,2,...,mnBeing assigned to 4 centers by minimum distance criterion is zi(k) in class； Calculate separately all kinds of new centers:
Figure FDA0002078861540000063
NjNumber of samples i.e. in jth class,OjIt indicates to belong to In the sample set of jth class；
4th step, if zj(k+1)≠zj(k) second step is then gone to, mode is reclassified, iteration calculates, until cluster Centre convergence records the maximum value ω of 4 cluster centresmax(n)；
5th step repeats the first, second, third and fourth step for each engine, chooses ωmax(n) minimum value in is regarded as sending out Motivation failure threshold, i.e. ω=min (ωmax(n)), n=1,2 ..., 100, wherein min () expression is minimized.
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