CN102789545B - Based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling - Google Patents

Abstract

Based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling, relate to turbine engine method for predicting residual useful life, it is in order to the prediction the solving existing turbine engine residual life problem required that adopts the prediction effect of general RUL forecast model cannot reach prediction, and it is as follows that it comprises concrete steps: step one, data prediction: extract running status variable from the data that collect; Proper vector is collected from sensor; Merged by running status variable and proper vector and obtain health factor; Step 2, set up degradation model storehouse: utilize health factor to set up degradation model; Multiple degradation model composition degradation model storehouse; Step 3, similarity assessment: by the Model Matching in Degradation path and model bank, each model provides a RUL and estimates; Step 4, RUL merge: according to test turbine engine and model matching, adopt Similarity-Weighted, merge and obtain final predicting residual useful life value.Be applicable to turbine engine predicting residual useful life.

Description

Based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling

Technical field

The present invention relates to turbine engine method for predicting residual useful life.

Background technology

Failure prediction can be divided into detection and the remaining life prediction two large divisions of inefficacy omen, the detection of inefficacy omen is normally applied relevant, need the background knowledge relevant to system, and RUL (Remaining Useful Life) prediction is relatively independent, the technology therefore for carrying out RUL prediction is roughly the same for the application of all failure predictions.As the research field that develops rapidly, the research of RUL prediction introduces the technology and calculating method of other research fields many, as: reliability engineering, regretional analysis, time series modeling, artificial intelligence etc.Existing most of RUL prediction algorithm is all obtain a general predictive model by training historical data, these models for may be comparatively effective the application only comprising single system and stand-alone assembly because the degeneration behavior of system is characterized preferably by simple hypothesis or priori.Complication system is a kind of typical nonlinear system, and successfully RUL predicts that example is less up to now, and reason is: 1, lack the knowledge relevant with fault mode to the inefficacy mechanism of system; 2, the Monitoring Data background information collected is imperfect.These two reasons cause the system history data with multiple degradation modes and imperfect background information to mix, therefore adopt the prediction effect of general RUL forecast model cannot reach prediction requirement in the prediction of turbine engine residual life.

For the problems referred to above, there is now the solution of two kinds of main flows: based on integrated modelling approach and the instance-based learning method of machine learning.The technology such as the former adopts boosting, bagging strengthen model performance, but the forecast model that these methods generate is made up of multiple partial model, comparatively complicated, and its internal mechanism is difficult to understand.The forecast model that instance-based learning method IBL (Instance-Based Learning) generates is based upon on the basis of a large amount of history cases, and along with the development of sensing and the communication technology, obtaining a large amount of Monitoring Data from some machine and equipment (as commercial aircraft engine or heavy digger) becomes possibility.The engineer applied of current IBL method mainly concentrates on fault diagnosis aspect, and limited several failure prediction application do not utilize the information of degraded data as the means of similarity between evaluation contents.

Summary of the invention

The prediction that the object of the invention is to solve existing turbine engine residual life adopts the prediction effect of general RUL forecast model cannot reach the problem of prediction requirement, provides the Forecasting Methodology of the turbine engine residual life based on degradation model coupling.

Based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling, it is as follows that it comprises concrete steps:

Step one, data prediction: extract from the raw data collected and determine turbine engine running status variable: c ₁for height, c ₂for Mach number and c ₃for gasoline throttle angle; The numerical value composition set c=(c of described running status variable ₁, c ₂, c ₃) ^t; c _irepresent that c is at moment t _ithe value of corresponding height, Mach number and gasoline throttle angle, c _i=(c _1i, c _2i, c _3i) ^t, wherein i is positive integer;

The sensor being positioned at turbine engine diverse location from 21 collects the numerical value that can characterize turbine engine degenerative process, and described numerical value forms 21 dimensional feature vectors: x=(x ₁, x ₂..., x ₂₁) ^t, x _irepresent that x is at moment t _ithe temperature of the engine difference that corresponding 21 sensors collect, pressure and velocity amplitude;

At moment t _iby described running status variable c _iwith proper vector x _i, obtain the tlv triple (c of measuring period _i, x _i, t _i); By c _iand x _imerge and obtain health factor z _i;

Step 2, set up degradation model storehouse: utilize and merge that form can the health factor z of characterization system degradation trend _idegradation model is set up for training entity accordingly; Multiple degradation model composition degradation model storehouses of described foundation;

Step 3, similarity assessment: models all in the health factor sequence of certain test turbine engine and model bank is carried out Similarity matching, and each model provides a RUL to this test turbine engine and estimates;

Step 4, RUL merge: according to the height of model matching in test turbine engine and model bank, adopt the method for Similarity-Weighted to merge the RUL predicted value obtaining final remaining life.

The present invention does not rely on the fault mechanism of turbine engine, failure mode, the priori such as failure criteria and background information, the prediction of RUL only relies on the Degradation path information obtained from the Condition Monitoring Data of turbine engine, simultaneously because it is to the imparametrization expression way of degenerated form, no longer need to suppose the form of degradation trend, therefore DMM (degradation model matching) method is for obtaining the application of continuous Monitoring Data as aeromotor from the Different Individual of same model turbine engine, can obtain and meet the requirements of prediction effect, there is actual application value.

Accompanying drawing explanation

Fig. 1 is structured flowchart schematic diagram of the present invention, Fig. 2 is the block diagram representation of Performance Evaluation of the present invention, Fig. 3 be in embodiment five all training entities at the reading schematic diagram of state 1, Fig. 4 is that in embodiment five, all training entities are at the reading schematic diagram of state 2, and Fig. 5 is the schematic diagram of concrete steps in embodiment five.

Embodiment

Embodiment one: composition graphs 1 illustrates present embodiment, based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling described in present embodiment, it is as follows that it comprises concrete steps:

Step one, data prediction: extract from the raw data collected and determine turbine engine running status variable: c ₁for height, c ₂for Mach number and c ₃for gasoline throttle angle; The numerical value composition set c=(c of described running status variable ₁, c ₂, c ₃) ^t; c _irepresent that c is at moment t _ithe value of corresponding height, Mach number and gasoline throttle angle, c _i=(c _1i, c _2i, c _3i) ^t, wherein i is positive integer;

The sensor being positioned at turbine engine diverse location from 21 collects the numerical value that can characterize turbine engine degenerative process, and described numerical value forms 21 dimensional feature vectors: x=(x ₁, x ₂..., x ₂₁) ^t, x _irepresent that x is at moment t _ithe temperature of the engine difference that corresponding 21 sensors collect, pressure and velocity amplitude;

At moment t _iby described running status variable c _iwith proper vector x _i, obtain the tlv triple (c of measuring period _i, x _i, t _i); By c _iand x _imerge and obtain health factor z _i;

Step 2, set up degradation model storehouse: utilize and merge that form can the health factor z of characterization system degradation trend _idegradation model is set up for training entity accordingly; Multiple degradation model composition degradation model storehouses of described foundation;

Step 3, similarity assessment: models all in the health factor sequence of certain test turbine engine and model bank is carried out Similarity matching, and each model provides a RUL to this test turbine engine and estimates;

Step 4, RUL merge: according to the height of model matching in test turbine engine and model bank, adopt the method for Similarity-Weighted to merge the RUL predicted value obtaining final remaining life.

In DMM method frame, multiple training entity with life-cycle Condition Monitoring Data is used to build degradation model storehouse, certain tests the similarity in turbine engine and model bank between each model to utilize Weighted Grey Incidence Degree and Euclidean distance to assess in same model turbine engine respectively, each degradation model can generate one and estimate the residual life of test turbine engine, and the residual life being fused into final turbine engine according to the similarity between test turbine engine and each degradation model is estimated.

Many engineering systems especially mechanical system, when not carrying out effectively safeguarding, degenerative process is irreversible, but this does not also mean that the feature observed is bound to present dull evolution forms, and nonmonotonic evolution forms often very difficult parametric method carry out modeling.Suppose that an engineering system is not effectively safeguarded in the process of degenerating, so this degenerative process may be made up of a series of irreversible composition, and these processes can represent with the track of the status data monitored or feature.Therefore, if the degradation trend of same model system that the degradation trend in certain system future can lose efficacy with some is expressed, then we can obtain the RUL of this system.

Operating condition refer to a series of can the set of variable of decision systems running status, comprise control to arrange, environmental parameter and using forestland etc.In many engineer applied, the monitoring state data of operating condition to system of change have a great impact, and the time series obtained through feature extraction presents larger variance, causes the degradation trend of system comparatively complicated, is difficult to carry out RUL modeling.The Monitoring Data to collecting under the operating condition of change is needed to carry out pre-service to adapt to the needs of DMM modeling.

X=(x ₁, x ₂..., x _n) ^trepresent the N dimensional feature vector of raw data after selecting gathered from system, x _irepresent at x a certain measurement moment t _isampled value, t _erepresent time during end-of-life, t _irepresent time during the last measurement, X _i={ x ₁, x ₂... x _irepresent test entity history feature data till now, ^lx _e={ x ₁, x ₂... x _e, l=1 ..., E represents the life-cycle history feature data of same type system l training entity, now ^lt _e=t _i+ ^lrUL, wherein ^lrUL is that l the RUL of training entity to test entity estimates, illustrating that the RUL of certain training entity to test entity estimates is exactly look for the life-span of training entity and the relation of test entity current time.If system cloud gray model is under the operating condition condition of change, need when image data to measure the operating condition information of test entity and training entity.

Have 21 sensors to be positioned at the different position of turbine engine, the sensor being positioned at turbine engine diverse location from 21 collects the 21 dimensional feature vector x=(x that can characterize turbine engine degenerative process ₁, x ₂..., x ₂₁) ^t, x _irepresent that x is at moment t _i, the sampled value that 21 sensors collect;

C=(c ₁, c ₂..., c _n) ^trepresent the set determining turbine engine running status variable, c _irepresent at c a certain measurement moment t _ioperating condition.

At moment t _iby described running status variable c _iwith proper vector x _i, obtain the tlv triple (c of measuring period _i, x _i, t _i); By c _iand x _imerge and obtain health factor z _i; Then the object of data prediction can be expressed as (c _i, x _i, t _i) → (z _i, t _i), wherein z _iindependent of x _i.

Embodiment two: composition graphs 2 illustrates present embodiment, present embodiment be to described in embodiment one based on the further restriction of Forecasting Methodology of the turbine engine residual life of degradation model coupling, step one data prediction detailed process is:

Set c=(the c of step one by one, to decision turbine engine running status variable ₁, c ₂, c ₃) ^tk-means algorithm cluster is adopted to obtain p class running status Ω={ O ₁, O ₂..., O _p, p is positive integer;

Step one two, the reading of sensor in each training entity extracted to be divided by p class running status Ω, be divided into p group altogether;

Step one three, detect reading time dependent situation under each running status of each sensor in all training entities, select set of sensors Α={ X that reading under all operating conditions all has consistance monotonic trend ₁, X ₂..., X _m, wherein m is positive integer;

Step one four, certain group training entity divide by limited running status Ω the reading of the set of sensors Α selected, and according to carry out linear regression and obtain p group health factor time series;

After step First Five-Year Plan, p group health factor time series press the time-sequencing before state demarcation, be reduced into one group of complete health factor time series X ₀={ X ₀(k) | k=1,2 ..., n}, wherein n is positive integer;

Step one six, determine the health factor time series X reflecting system degradation behavioural characteristic ₀for reference sequences, the sensor time sequence X of influential system behavior _i={ X _i(k) | } be comparative sequences, i=1,2 ..., m;

Step one seven, employing just value carry out nondimensionalization process to reference sequences and comparative sequences, remove in first value of sequence, namely by all data of original data series

Step one eight, calculate the reference sequences x after nondimensionalization process ₀with comparative sequences x _ibetween some correlation coefficient be $r(x_0\left(k\right),x_i\left(k\right))=\frac{\underset{i}{\min }\underset{k}{\min }|x_0\left(k\right)-x_i\left(k\right)|+\mathrm{\ζ}\underset{\text{i}}{\max }\underset{k}{\max }|x_0\left(k\right)-x_i\left(k\right)|}{|x_0\left(k\right)-x_i\left(k\right)|+\mathrm{\ζ}\underset{i}{\max }\underset{k}{\max }|x_0\left(k\right)-x_i\left(k\right)|},$ Wherein ζ ∈ (0, ∞) is called resolution ratio, usually gets ζ=0.5;

Step one nine, the degree of association between computing reference sequence and comparative sequences, represent at the mean value of the correlation coefficient in each moment with reference sequences and comparative sequences, that is: $r(x_0,x_i)=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}r(x_0\left(k\right),x_i\left(k\right));$

The degree of stability of step one ten, calculation level inteerelated order Number Sequence $S\left(r_{0,i}\right)=\sqrt{\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{(r(x_0\left(k\right),x_i\left(k\right))-r_{0,i})}^2};$

Grey relational grade after step one 11, computed improved

Step one 12, the degree of association calculated to be sorted from big to small; This comparative sequences of the larger explanation of the degree of association is larger relative to reference sequences degree of correlation;

Step one 13, step one four to step 12 is repeated to all training entities, obtain the statistical information of each sensor reading and corresponding health factor relational degree taxis in all test turbine engines, select the subset of sensor B={X that the degree of association is high ₁, X ₂..., X _t.

Embodiment three: composition graphs 2 illustrates present embodiment, present embodiment be to described in embodiment one based on the further restriction of Forecasting Methodology of the turbine engine residual life of degradation model coupling, the detailed process that step 2 sets up degradation model storehouse is:

Step 2 one, the reading of the set of sensors B selected divided by running status Ω and according to carry out linear regression and obtain p group health factor time series;

Step 2 two, p group health factor time series are by being reduced into one group of complete health factor time series X after the time-sequencing before state demarcation ₀={ X ₀(k) | };

Step 2 three, step 2 one and step 2 two are repeated to all training entities, make each training entity have one group of corresponding health factor time series;

Step 2 four, employing Exponential Regression Model matching is carried out to the health factor time series often organizing training entity corresponding, obtains degradation model storehouse.

Embodiment four: composition graphs 2 illustrates present embodiment, present embodiment be to described in embodiment one based on the further restriction of Forecasting Methodology of the turbine engine residual life of degradation model coupling, the concrete steps that step 3 comprises are:

Step 3 one, test turbine engine directly adopt the parameter of aforementioned training entity linear regression model (LRM) to calculate health factor, and 1 relatively each linear regression model (LRM) of test turbine engine has 1 group of corresponding health factor sequence Z=z ₁, z ₂..., z _r;

Step 3 two, will test turbine engine health factor sequence Z=z ₁, z ₂..., z _rthe model corresponding with Exponential Regression Model storehouse carries out Similarity matching, namely calculates minimum euclidean distance d (τ, Z, M between test turbine engine health factor sequence and corresponding Exponential Regression Model respectively _i) and maximum grey relational grade S (τ, Z, M _i), this two indices corresponding, in model bank, each model can provide 1 RUL to this test turbine engine respectively and estimates.

Embodiment five: present embodiment be to described in embodiment one based on the further restriction of Forecasting Methodology of the turbine engine residual life of degradation model coupling, the RUL predicted value of testing the final residual life of turbine engine described in step 4 adopts expression formula: calculating obtains.

Wherein L represents the number of degradation model in model bank, ^lrUL _rrepresent the estimated value of l degradation model for test turbine engine residual life, ^ls represents the maximum similarity between l degradation model and test turbine engine, respectively with maximum grey relational grade S (τ, Z, M _i) and exp (-d (τ, Z, M _i)) represent.

Composition graphs 3, Fig. 4 and Fig. 5, utilize the turbine engine degeneration emulated data collection in NASA Ames failure prediction data storehouse to carry out DMM method performance verification.The process of DTSM process propeller for turboprop machine data is divided into seven steps, belongs to training (model development) and test (RUL estimation) two stages.

Saxena etc. have carried out the degraded performance that a series of life-cycle emulation carrys out exploratory flight device turbine engine in 2008, Building of Simulation Model is on CMAPSS (commercial modular avionics propulsion system simulation).CMAPSS is a simulation system of NASA exploitation, is similar to a virtual aeromotor.By performing Multi simulation running under different state of flights, obtain the Monitoring Data of the multiple entity of same engine.Emulation often runs once, engine experienced by the complete procedure of life-cycle, namely from brand-new engine (there is different running-in wears and engineering variance) to the failure criteria pre-set, the life-span of engine represents with total airborne period number that this process experiences, the packet that each airborne period gathers is containing 3 dimension operating condition variablees (highly, Mach number and gasoline throttle angle) and 21 dimension measurement value sensors (temperature of engine difference, pressure and speed), and the time series that therefore the entire run process of each entity can be tieed up with 24 represent.The multivariate time series of a certain entity is taken passages as shown in table 1.

The life-cycle data sample of certain engine entity of table 1

Attention: turbine engine data set does not provide the information such as fault mechanism, failure mode and failure criteria, and DMM method does not need these information to carry out RUL estimation.NASA provides four groups of independently data sets altogether, and each data set comprises different fault mode numbers, operating condition number, training entity number and test entity number, as shown in table 2.

The Setup Experiments of table 2 four data sets

Training dataset comprises complete life-cycle data, can be used for developing Life Prediction Model.Test data set comprises the historical data in certain moment before thrashing, also provided is the considered repealed time, can be used for RUL and estimates and algorithm performance assessment.#2 data set is selected to carry out DMM method validation herein.Notice that test data set is not for proof of algorithm, because its test entity comprised does not have complete life-cycle data, be therefore not suitable for the performance estimating method carrying out continuous RUL prediction based on the sampling time point in whole entity lifetime interval.260 groups of training entities can be used for training and testing, and front 200 groups of training entities are used for model development.

1.1 performance metric

The performance of RUL prediction algorithm is evaluated by multiple measure, traditional measure existing defects under the application background of failure prediction based on precision or robustness, may the performance of not bery good assessment algorithm.Saxena etc. proposed the novel performance metric index of 4 kinds of being suitable for failure prediction application background in 2010, these indexs carry out continuous RUL prediction based on to each training entity, will simply introduce below.

1) forecast interval (Prediction Horizon-PH)

PH is defined as the RUL prediction that first meets α-bound standard:

$\mathrm{PH}=t_E-t_{i_{\mathrm{\α}}}$

Wherein i _αrepresent first work period meeting the RUL prediction correspondence of α-bound.Work period t _icorresponding RUL point estimate is r _i, α-bound standard can assess r _iwhether drop on true RUL value r _i ^*=t _e-t _iα-bound scope in, as shown in the formula:

$t_{i_{\mathrm{\α}}}=\min \left\{t_i\right|t_i\∈[t_s,t_f],{r_i}^{*}-\mathrm{\α}\·t_E\≤r_i\≤{r_i}^{*}+\mathrm{\α}\·t_E\}$

Wherein t _srepresent the initial time of RUL prediction, t _frepresent the end time of RUL prediction.

2) prediction ratio (Rate of Acceptable Predictions-AP) can be accepted

T is worked as in AP assessment _i>=t _htime fall into the ratio of the RUL point estimation predicted value that can accept within the scope of the taper of predicated error, as follows:

AP＝Mean({δ _i|t _H≤t _i≤t _f})

${\mathrm{\δ}}_i=\left\{\begin{array}{c}1,\mathrm{if}(1-\mathrm{\α}){r_i}^{*}\≤r\≤(1-\mathrm{\α}){r_i}^{*}\\ 0,\mathrm{otherwise}\end{array}\right.$

Wherein $t_H=t_{i_{\mathrm{\α}}}.$

3) relative accuracy (Relative Accuracy-RA)

T is worked as in RA assessment _i>=t _htime average absolute percent difference, homometric(al) standard A P compares, and which provides the quantitative measurment of precision of prediction:

$\mathrm{RA}=1-\mathrm{Mean}\left(\right\{\frac{|r_i-{r_i}^{*}|}{{r_i}^{*}}|t_H\≤t_i\≤t_f|\left\}\right)$

4) convergence (Convergence-CG)

CG assesses the increase along with available historical data, the speed that algorithm predicts performance improves, given t _ithe performance metric E in moment _i, CG may be defined as:

$\mathrm{CG}=1-(\frac{\frac{1}{2}{\mathrm{\Σ}}_{i=s}^f({t_{i+1}}^2-{t_i}^2)E_i}{{\mathrm{\Σ}}_{i=s}^f(t_{i+1}-t_i)E_i}-t_p)\·\frac{1}{t_f-t_s}$

The span of tolerance CG is 0 to 1, makes E _i=r _i-r _i ^*, as CG > 0.5, show that prediction has convergence.

5) performance evaluation

K test entity correspond to K group Measure Indexes { PH, AP, RA, CG} _k, in order to evaluate the overall estimated performance of RUL prediction algorithm to K test entity, adopt intermediate value corresponding to Measure Indexes to carry out performance evaluation:

PH＝Median({ ^kPH} _K)

AP＝Median({ ^kAP} _K)

RA＝Median({ ^kRA} _K)

CG＝Median({ ^kCG} _K)

The size of what PH represented is time interval, only for referencial use when performance evaluation, the span of AP, RA and CG all between zero and one.

1.2 running statuses divide

Due to the form that the raw data provided has been multidimensional time-series, therefore do not need to carry out feature extraction again.Draw 3 dimension figure to three variablees characterizing operating condition in all 200 groups of training entities, display operating condition one is copolymerized into 6 bunches, the operating condition that expression 6 is discrete respectively.The data of different airborne period collection may have different operating conditions.If do not divided running status, sensor reading almost can not the trend of display system traffic coverage, if extract the data of same running status, sensor reading is obvious ascendant trend.

1.3 sensors are selected

In order to M _ithe form of model is consistent, and makes C ^adj=C-unit life, wherein C is the airborne period number that in each training entity, data are corresponding, and unit life is the complete life-span of this training entity, works as C ^adjwhen being 0, represent that this training entity lost efficacy, | C ^adj| in expression, thrashing also has how many time cycles.The degradation trend of system now can be demonstrated from the operative sensor data of all training entities.

The selection of sensor is from observing the reading of each mode of operation condition lower sensor.The reading of operative sensor has single or multiple discrete value, without monotonic trend, can first reject.Major part sensor has the continuous-reading in monotonic trend between the whole lifetime region of training entity, but the sensor reading of different training entity can present inconsistency in the near failure stage, and the help of these type of data to the degenerative process modeling of system is little.Therefore, only select all have the sensor reading of consistance monotonic trend to carry out the matching of health factor in all operations state herein.Have according to the sensor that said method is tentatively selected: #2, #3, #4, #7, #11, #12, #15, #20 and #21.

On the basis of aforementioned initial option, adopt the degree of association between grey correlation analysis calculating sensor reading and health factor improved, select the subset of sensor of the larger sensor of the degree of association as DMM modeling.Therefore first need to carry out performance estimation, carry out after the selection of concrete subset of sensor is placed on Performance Evaluation.

1.4 Performance Evaluation

For a certain training entity, the step introducing Performance Evaluation is as follows:

1) this training entity is divided into 6 groups of data (#2, #3, #4, #7, #11, #12, #15, #20, #21) by mode of operation;

2) often organize data and obtain one group of health factor (HI) by linear regression;

3) 6 groups of health factors are by being reduced into 1 group of complete health factor time series after the time-sequencing before state demarcation;

Sample set Ω={ (x, y) } for carrying out linear model matching, wherein x be complete by state demarcation after one group of data, y be pre-set to the value should organizing data.It is 0 that work period close to failpoint arranges y value, close to arrange y value with the work period of starting point be 1, its method to set up as shown in the formula:

$\mathrm{\&Omega;}=\left\{(x_i,0)\right|C_i^{\mathrm{adj}}>C_{\max }\}\&cup;\{(x_i,1)|C_i^{\mathrm{adj}}<C_{\min }\}$

According to C _maxand C _minthe difference of threshold value value, the linear regression model (LRM) that can be formed is also different.This empirical method of number percent of usual employing training entity entire life is chosen, the C that this experiment is selected _maxand C _minbe respectively-t _e* 10% and-t _e* 90%, finally obtain 162 groups of health factor time serieses (amounting to 200 test entities), the health factor obtained after the linear recurrence of certain training entity wherein.To sum up, and the training entity of not all can carry out linear regression modeling, if those state demarcation complete after in 6 groups of data obtaining any one group not than C _minless entity is then trained to carry out linear regression accordingly.

Health factor and 9 sensors tentatively selecting are numbered by 1-10 respectively, grey relational grade between the reading calculating 9 sensors selected in the test entity of 162 groups of health factors and its correspondence is respectively gone forward side by side line ordering, and table 3 provides the calculation of relationship degree result of wherein 5 groups of test entities.

As can be seen from Table 3, with the health factor degree of association the highest be 1, namely itself.Relational degree taxis is that the degree of association size of parameter itself and the health factor of 2-6 is very close, comprise #2, #3, #4, #11, #15 sensor, relational degree taxis be the degree of association of parameter itself and the health factor of 7-10 also relatively, comprise #7, #12, #20, #21 sensor, but relational degree taxis is respectively two its degree of association of parameter changes of 6 and 7 obviously greatly, this also means that the contribution of reading to health factor of reading relative rear 4 kinds of sensors of 5 kinds of sensors is above larger, now can consider that selecting front 5 kinds of sensors carries out new health factor matching, reject rear 4 kinds of sensors.In order to illustrate that this kind of selection mode has versatility to 60 groups of test entities, table 4 will provide the statistical information of the relational degree taxis of all test entities.

The calculation of relationship degree result of 5 groups, table 3 test entity

As shown in Table 4, relational degree taxis be 1 parameter be health factor itself, do not discuss; Relational degree taxis be 2 and 3 the most situation of parameter be respectively #15 and #11 sensor; Relational degree taxis be 4 and 5 the most situation of parameter be #2 and #3 sensor; Relational degree taxis be 6 parameter be essentially #4 sensor.The degree of association size of front 5 sensors is more or less the same, remaining #4, #12, #20, its relational degree taxis of #21 sensor never enters front 6, and according to the observation sequence be 7 the degree of association obvious less on the whole relative to the degree of association of sequence front 6, therefore improved grey correlation analysis can characterize the correlation degree between health factor and sensor preferably, and the subset of sensor selected is { #2, #3, #4, #11, #15}.Certain subset of sensor can about subtract further still have to be discussed, but undue about subtract the loss that can cause some key message, and then cause the reduction of prediction effect.By on the subset of sensor selected through improved grey relational analysis with through tentatively choosing the subset of sensor that obtains experiment Analysis is affected, with the rationality of verificating sensor system of selection for final estimated performance below.

The statistical information of each sensors association degree sequence in all test entities of table 4

1.5 Model Identification

As shown in Figure 9, the trend that health factor is exponentially degenerated in time, therefore adopts Exponential Regression Model to describe the periodic key c after adjustment herein ^adjand the relation between health factor z:

$z=a(e^{b{C}^{\mathrm{adj}}+c}-e^c)+\mathrm{\&epsiv;}$

Wherein a, b, c are the model parameters needing to determine, ε is noise item, e ^cbe used for forcing model through initial point.For each training entity i, need to determine one group of parameter (a _i, b _i, c _i) and noise variance

Function in formula (16) now can be expressed as:

$M_i:y=f_i\left(t\right)=a_i(e^{b_{i}t+c_i}-e^{c_i})+\mathrm{\&epsiv;}$

Certain training entity obtains curve after index return matching, finds that different training entity has different deterioration velocities after index return.

1.6 signal conversion

The object of signal conversion is the data of test entity to be converted to health factor, for the assessment of follow-up distance is prepared.The implementation step of this conversion process is consistent with aforementioned properties evaluation part, and difference is that testing entity directly adopts the parameter of training entity linear regression model (LRM) to calculate health factor.Therefore 1 test entity relatively each linear regression model (LRM) can obtain 1 group of corresponding health factor sequence z, amounts to 162 groups.Certain the test entity HI curve obtained according to the 1st group and the 8th group of linear regression model (LRM) as shown in figure 11.

1.7 distance assessments and RUL estimate

According to the observation to test entity HI sequence, find that its fluctuation of floating is comparatively large, need to adopt running mean method to carry out filtering to it.HI curve, after filtering, assesses certain test entity and model { M _ibetween Euclidean distance and grey relational grade obtain RULs.

The multiple RULs obtained through above-mentioned process can obtain final unique RUL through merging, and are divided into three treatment steps: candidate RUL _iselect, outlier is removed and RUL determines.

1) candidate RUL _iselect: all RULs of certain test entity are by similarity S _idescending sort, if maximum S _ivalue is S ₁, use restrictive condition S _i>S ₁/ δ, δ >1, meets the RUL of this condition _ican enter next step process, the size of δ is determined by experience, when similarity calculates gained by minimum euclidean distance, and δ=1.05, when similarity is represented by Weighted Grey Incidence Degree, δ=1.1;

2) outlier is removed: the test entity less to history work week issue carries out RUL estimation can produce larger uncertainty or variance, therefore according to the statistical property of training data, if RUL+T _c>350 or RUL+T _c<120, these RULs will be removed, wherein T _crepresent the current operating cycle number of test entity.

3) RUL determines: the method adopting similarity weighting, S remaining after first two steps process _ik the RULs that value is maximum and corresponding similarity are weighted summation.

For each test entity, the many group RUL that do not carry out in the same time along entity lifetime interval predict by we, and often group prediction is all carry out based on all historical datas to corresponding predicted time point.Setting prediction initial time is set to t in this application _s=50, the end time is set to t _f=t _e-10, the predicting interval is set to △ t=5.

(1) grey correlation analysis carries out the impact of sensor selection on estimated performance

What utilize observation initial option to go out all has the sensor of consistance monotonic trend to comprise in all operations state: #2, #3, #4, #7, #11, #12, #15, #20 and #21; Select the subset of sensor higher with the health factor degree of association further through grey correlation analysis to comprise: #2, #3, #4, #11, #15, previous subset set a represents, rear subset set b represents.This experiment adopts minimum euclidean distance to carry out similarity measurement, and selected linear regression threshold value is C _max=-t _e* 10%, C _min=-t _e* 90%.Because the RUL predicted time of single test entity is longer, select 30 test entities at random for the impact of more different set of sensors on estimated performance, comparative result is as shown in table 5.

The estimated performance of DMM method in table 5 different sensors subset situation

As can be seen from Table 5, when the subset of sensor adopting grey correlation analysis to select is applied in DMM method, its estimated performance comparatively sensor has and comparatively significantly promotes before selecting, prediction ratio AP can be accepted and improve 25.9%, relative precision of prediction RA improves 4.3%, convergence CG improves 1.6%, and forecast interval PH large nearly 10 work periods.Therefore employing grey correlation analysis carries out the estimated performance that sensor selects effectively to promote DMM method, and follow-up two groups of experiments are used as linear regression modeling through adopting set b.

(2) linear regression threshold value C _maxand C _minthe impact chosen estimated performance

And the training entity of not all linear recurrence can obtain corresponding health factor, according to C _maxand C _minthe difference of threshold value value, the linear regression model (LRM) that can be formed is also different.This experiment adopts minimum euclidean distance to carry out similarity measurement, and three groups of selected threshold values are respectively C _max=-t _e* 10%, C _min=-t _e* 90%, C _max=-t _e* 5%, C _min=-t _e* 95% and C _max=-20, C _min=-240.30 the test entities adopting first group of experiment to select arrange the impact on estimated performance for more different threshold value, and comparative result is as shown in table 6.

The estimated performance of DMM method under the different threshold condition of table 6

As can be seen from Table 6, C is worked as _max=-t _e* 10%, C _min=-t _e*, when 90%, it can accept prediction ratio AP, relative precision of prediction RA, convergence CG are all arranged much larger than other two kinds of threshold values, and just forecast interval PH is slightly less than C _max=-20, C _min=-240; Work as C _max=-t _e* 5%, C _min=-t _e*, when 95%, its AP, RA and CG are also slightly larger than C _max=-20, C _minmetric when=-240, forecast interval PH is relatively little.This also illustrates that adopting this method of number percent of training entity entire life to arrange threshold value has better effect than fixed threshold, and according to fixed threshold establishing method, all life-spans are less than | C _min| training entity cannot obtain linear regression model (LRM) by training, cause the degree of enriching of types of models in model bank to reduce, if | C _min| value is too small, and training entity over-fitting can occur when training linear regression model, causes the health factor sequence distortion of characterization system degradation trend.Life-span percentage threshold method to set up is obviously more reasonable, also makes DMM method obtain better prediction effect.

(3) impact chosen estimated performance of similarity estimating method

Between different entities, the prediction effect of definition to DMM method of similarity/distance has a great impact, and the research purpose of this group experiment is for determining which is better similarity expression way for minimum euclidean distance and Weighted Grey Incidence Degree.In the past 2 groups of experiments can be found out, when method for measuring similarity adopts minimum euclidean distance, DMM method has reasonable RUL estimated performance, introduces the situation that Weighted Grey Incidence Degree is used as similarity measurement below.

Adopt and be weighted grey relational grade based on the method for radial basis function, we need to determine that rate of spread ρ is wherein on the impact of final RUL prediction effect.Predict that the time expended is longer because single test entity carries out RUL, the above-mentioned rate of spread all can not be attempted on all test entities.Setting the rate of spread through preliminary experiment is 0.1 and 0.3, and 30 the test entities adopting first group of experiment to select are for the impact of the more different rate of spread on estimated performance, and comparative result is as shown in table 7.

The different rate of spread of table 7 chooses the estimated performance of DMM method in situation

As can be seen from Table 7, when the rate of spread is 0.1, the RUL estimated performance of DMM method is better, be the situation of 0.3 relative to the rate of spread, prediction ratio AP can be accepted and improve 5.2%, relative precision of prediction RA improves 7.2%, convergence CG improves 3.2%, and forecast interval PH large nearly 8 work periods.But compare as measuring similarity with employing minimum euclidean distance, its RUL estimated performance is poor, the former than the performance boost situation of the latter is: can accept prediction ratio AP and improve 19.3%, relative precision of prediction RA improves 8.8%, convergence CG improves 8.7%, but forecast interval PH little 17 work periods.

Comprehensively above-mentioned three groups of experiments can be found out, sensor system of selection adopts improved grey relational analysis, and linear regression threshold value chooses C _max=-t _e* 10%, C _min=-t _e* 90%, during method for measuring similarity employing minimum Eustachian distance, DMM method can obtain best RUL estimated performance.Adopt minimum euclidean distance and Weighted Grey Incidence Degree as measuring similarity standard respectively.

DMM method does not rely on fault mechanism, failure mode, the priori such as failure criteria and background information of system, the prediction of RUL only relies on the Degradation path information obtained from the Condition Monitoring Data of system, simultaneously because it is to the imparametrization expression way of degenerated form, no longer need to suppose the form of degradation trend, therefore DMM method is for obtaining the application of continuous Monitoring Data as aeromotor from the Different Individual of same model system, can good prediction effect be obtained, there is certain actual application value.

Claims (4)

1., based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling, it is as follows that it comprises concrete steps:

Step one, data prediction: extract from the raw data collected and determine turbine engine running status variable: c ₁for height, c ₂for Mach number and c ₃for gasoline throttle angle; The numerical value composition set c=(c of described running status variable ₁, c ₂, c ₃) ^t; c _irepresent that c is at moment t _ithe value of corresponding height, Mach number and gasoline throttle angle, c _i=(c _1i, c _2i, c _3i) ^t, wherein i is positive integer;

The sensor being positioned at turbine engine diverse location from 21 collects the numerical value that can characterize turbine engine degenerative process, and described numerical value forms 21 dimensional feature vectors: x=(x ₁, x ₂..., x ₂₁) ^t, x _irepresent that x is at moment t _ithe temperature of the engine difference that corresponding 21 sensors collect, pressure and velocity amplitude;

At moment t _iby described running status variable c _iwith proper vector x _i, obtain the tlv triple (c of measuring period _i, x _i, t _i); By c _iand x _imerge and obtain health factor z _i;

Step 2, set up degradation model storehouse: utilize and merge that form can the health factor z of characterization system degradation trend _idegradation model is set up for training entity accordingly; Multiple degradation model composition degradation model storehouses of described foundation;

Step 3, similarity assessment: models all in the health factor sequence of certain test turbine engine and model bank is carried out Similarity matching, and each model provides a RUL to this test turbine engine and estimates;

Step 4, RUL merge: according to the height of model matching in test turbine engine and model bank, adopt the method for Similarity-Weighted to merge the RUL predicted value obtaining final remaining life,

It is characterized in that, step one data prediction detailed process is:

Set c=(the c of step one by one, to decision turbine engine running status variable ₁, c ₂, c ₃) ^tk-means algorithm cluster is adopted to obtain p class running status Ω={ O ₁, O ₂..., O _p, p is positive integer;

Step one two, the reading of sensor in each training entity extracted to be divided by p class running status Ω, be divided into p group altogether;

Step one three, detect reading time dependent situation under each running status of each sensor in all training entities, select set of sensors Α={ X that reading under all operating conditions all has consistance monotonic trend ₁, X ₂..., X _m, wherein m is positive integer;

Step one four, certain group training entity divide by limited running status Ω the reading of the set of sensors Α selected, and according to carry out linear regression and obtain p group health factor time series;

After step First Five-Year Plan, p group health factor time series press the time-sequencing before state demarcation, be reduced into one group of complete health factor time series X ₀={ X ₀(k) | k=1,2 ..., n}, wherein n is positive integer;

Step one six, determine the health factor time series X reflecting system degradation behavioural characteristic ₀for reference sequences, the sensor time sequence X of influential system behavior _i={ X _i(k) | } be comparative sequences, i=1,2 ..., m;

Step one seven, just value is adopted to carry out nondimensionalization process to reference sequences and comparative sequences, by all data of original data series first value divided by sequence, namely

Step one eight, calculate the reference sequences x after nondimensionalization process ₀with comparative sequences x _ibetween some correlation coefficient be $r(x_0\left(k\right),x_i\left(k\right))=\frac{\underset{i}{\min }\underset{k}{\min }|x_0\left(k\right)-x_i\left(k\right)|+\mathrm{\&zeta;}\underset{i}{\max }\underset{k}{\max }|x_0\left(k\right)-x_i\left(k\right)|}{|x_0\left(k\right)-x_i\left(k\right)|+\mathrm{\&zeta;}\underset{i}{\max }\underset{k}{\max }|x_0\left(k\right)-x_i\left(k\right)|},$ Wherein ζ ∈ (0, ∞) is called resolution ratio, gets ζ=0.5;

Step one nine, the degree of association between computing reference sequence and comparative sequences, represent at the mean value of the correlation coefficient in each moment with reference sequences and comparative sequences, that is:

The degree of stability of step one ten, calculation level inteerelated order Number Sequence

Grey relational grade after step one 11, computed improved

Step one 12, the degree of association calculated to be sorted from big to small;

Step one 13, step one four to step 12 is repeated to all training entities, obtain the statistical information of each sensor reading and corresponding health factor relational degree taxis in all training turbine engines, select the subset of sensor B={X that the degree of association is high ₁, X ₂..., X _t.

2., according to claim 1 based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling, it is characterized in that, the detailed process that step 2 sets up degradation model storehouse is:

Step 2 one, the reading of the set of sensors B selected divided by running status Ω and according to carry out linear regression and obtain p group health factor time series;

Step 2 two, p group health factor time series are by being reduced into one group of complete health factor time series X after the time-sequencing before state demarcation ₀={ X ₀(k) | };

Step 2 three, step 2 one and step 2 two are repeated to all training entities, make each training entity have one group of corresponding health factor time series;

Step 2 four, employing Exponential Regression Model matching is carried out to the health factor time series often organizing training entity corresponding, obtains degradation model storehouse.

3., according to claim 2 based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling, it is characterized in that, the concrete steps that step 3 comprises are:

Step 3 one, test turbine engine directly adopt the linear regression model (LRM) in step 2 one calculate health factor, 1 relatively each linear regression model (LRM) of test turbine engine has 1 group of corresponding health factor sequence Z=z ₁, z ₂..., z _r;

Step 3 two, will test turbine engine health factor sequence Z=z ₁, z ₂..., z _rthe model corresponding with Exponential Regression Model storehouse carries out Similarity matching, namely calculates minimum euclidean distance d (τ, Z, M between test turbine engine health factor sequence and corresponding Exponential Regression Model respectively _i) and maximum grey relational grade S (τ, Z, M _i), this two indices corresponding, in model bank, each model can provide 1 RUL to this test turbine engine respectively and estimates.

4. according to claim 3 based on the Forecasting Methodology of the turbine engine residual life of degradation model coupling, it is characterized in that, the RUL predicted value of testing the final residual life of turbine engine described in step 4 adopts expression formula: calculating obtains, and wherein L represents the number of degradation model in model bank, ^lrUL _rrepresent the estimated value of l degradation model for test turbine engine residual life, ^ls represents the maximum similarity between l degradation model and test turbine engine, respectively with maximum grey relational grade S (τ, Z, M _i) and exp (-d (τ, Z, M _i)) represent.