CN108803323A - A kind of particle filter steering engine trend prediction method based on improvement weights generating mode - Google Patents
A kind of particle filter steering engine trend prediction method based on improvement weights generating mode Download PDFInfo
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Abstract
A kind of particle filter steering engine trend prediction method based on improvement weights generating mode.It includes the following steps carried out in order：F distribution of particle filter forecasting frames；F cores construct；Dynamic screening process.Advantage of the present invention：1. even if in the case of not meeting normal System Development trend due to newest measuring value, while obtained current particle collection is not at correct region, but the system mode that prediction obtains also can alleviate the not true property that noisy measuring value is brought by the amendment of weights；2. with traditional particle filter method, this method can obtain preferable failure predication precision.
Description
Technical field
The invention belongs to fault diagnosises and health control (PHM) technical field, more particularly to the rudder based on particle filter
Machine trend prediction method.
Background technology
In automatic flight control system, electro-hydraulic joint steering engine as core execution unit, realize to elevator, aileron and
Three big master control rudder face and wing flap of rudder, slat and trimmer etc. assist the driving of rudder face.Steering engine is as executing agency, property
The quality of energy and reliability directly affects autoflight system or even the performance and reliability of entire aircraft.Fly with automatic
The development of row technology, steering gear system becomes gradually studies focus of attention at present.
It is more mature no matter the research that linear dynamic system is carried out at present all forms in theoretic or practical application
System, and electro-hydraulic joint steering gear system all have very strong nonlinear characteristic.Therefore, it finds a kind of for steering gear system
Method for diagnosing faults is particularly important.Particle filter is as a kind of analytic modell analytical model and the method for data-driven combination to non-linear non-height
The processing of this problem shows apparent superiority, will be to particle filter algorithm and its in fault diagnosis based on this present invention
Using being furtherd investigate.
Numerous studies show that the prediction technique based on particle filter has been able to be used to realize forward status predication,
But in fact, particle filter itself does not have the ability of prediction future state in the case of wantage measured value, but pass through
The process that suitable process just completes prediction is introduced after particle filter state estimation, this status predication process is known as
Prediction process based on particle filter.Fig. 1 summarizes the existing frame based on particle filter prediction technique.It first will be entirely pre-
Survey process is divided into two stages, is estimated using model and historical metrology value to obtain the particle collection at current time by particle filter, this
A part is known as state estimation procedure；The process for predicting end-of-life by the particle collection at current time again is known as forecast period.
In existing research, realizing the forecast period, there are mainly two types of method, particle mapping and measuring value reconstruct.
Particle mapping generates the particle collection of subsequent time and to calculate the state probability density of future time instance, Yi Zhongchang
The particle mapping method of use i.e. by particle by system dynamic model iteration forward, in terms of the computational efficiency for, this is most
Simple and effective way, however the mapping method has an apparent defect, that is, not accounting for noise and mission nonlinear can be with
Time change prediction state probability density, in this method in entire forecast period the weights of particle be always maintained at it is constant.Mesh
The renewal process of preceding particle weights has become a steps necessary of forecast period, but cannot rely on drawing for new measuring value again
Enter, in order to solve this problem, there is researcher newly to define a kind of Epanechnikov kernel functions, the function is in forecast period
The probability density function of each moment reconstituted state can clearly predict the boundary of error and alleviate model and change over time to bring
Error increase, however long-time particle amendment is easy to cause the continuous service of resampling process in particle filter algorithm, to
Generate additional computation burden.Therefore, balance forecast accuracy and computation burden become the one of the research of particle mapping method and choose greatly
War.
Measuring value reconstruct, which is that the another kind of forecast period is typical in based on particle filter prediction algorithm frame, implements hand
Section, using a series of method based on data-driven, such as neural network, Least square support vector regression is required to generate
The measurement value sequence wanted.Historical metrology value is arranged with time series and implements long period prediction iterative calculation and obtains following amount
Measured value sequence, and the input estimated using new measuring value as particle filter is to obtain required future time instance state or ginseng
Number.For observation reconstructing method, in the important uncertainty propagation problem for focusing primarily on data-driven prediction technique of research,
Because the error of reconstruct measuring value can greatly influence the estimation performance of particle filter itself, especially of different nature when being related to
When noise item, it is hardly formed the final error that a standard carrys out control forecasting.For largely carrying the complication system of time-varying parameter
For, parameters of operating part has lasting variation before lifetime of system termination, for needing largely to iterate to calculate using time-varying model
Measuring value reconstructing method, be easy to cause accumulated error.
Invention content
To solve the above-mentioned problems, the purpose of the present invention is to provide one kind under nonlinear system model, and one kind is to portion
Simple, direct, the effective prediction particle filter steering engine trend prediction method in part service life
In order to achieve the above object, provided by the invention a kind of based on the particle filter steering engine shape for improving weights generating mode
State prediction technique (i.e. F distribution of particle filters) includes the following steps carried out in order：
(1) F distribution of particle filter forecasting frame
(2) F cores construct
(3) dynamic screening process
In step (1), the design method of the F distribution of particle filter forecasting frames is：
The prediction framework containment mapping stage of F distribution of particle filtering and more two parts of new stage, in mapping phase, initially
Particle collection p steps are mapped forward by modified system model, the specific step number of prediction determines by remaining life threshold value, and more
New stage, the particle weights for calculating final predicted state are calculated by the F cores constructed,
In order to provide predicted state at (k-1) momentBy (k-1) moment by the modified particle collection of newest measuring valueAs primary collection, while the time-varying parameter θ of modelk-1It is updated as recessive state joint, therefore after update
Model parameter θk-1Can be used for predict before to state then all historical metrology values of (k-1) before the moment are used for
F cores are constructed, and particle weights are calculated, predicted state is finally obtained according to particle weighted sumIt is obtained newly when the k moment
Reliable measuring value when, the model parameter θ of systemkIt will be updated by particle filter with prediction primary collection, with stylish
Measuring value is also added to F cores for updating the particle weights in different moments, and the predicted state of forward direction will all update at this time,
Until the state of prediction reaches remaining life threshold value.
In step (2), the F core building methods are：
In standard particle filtering, the weights of particle are determined according to importance probability function, in general, particle
Weight is according to the measuring value of estimationWith the measuring value obtained by sensorBetween difference calculate, i.e.,
Wherein formula (2) is referred to as Gaussian kernel, and the σ in formula is to measure noise skStandard deviation, the present invention proposes one kind
It improves traditional Gauss core and defines a kind of method that new degree of fitting is measured to calculate particle weights, the thinking of this method is based on F
It examines to reduce global error, combines F distributions and particle filter dynamic prediction residual service life of components, this method are not only inherited
The advantages of conventional particle filter forecasting method, and solve its problem encountered when application is predicted with component life, it is
Improvement based on particle filter prediction technique provides a kind of new thinking,
F inspections are called homogeneity test of variance, and the statistic in F inspections is the ratio between the quadratic sum of two groups of samples, reflection
It is whether two groups of samples have significant difference, in other words, assuming that when two groups of samples variance having the same, what F was examined
Statistic meets F distributions, otherwise when assuming that when invalid, which does not meet F distributions, general two kinds of different degree of freedom then
Chi square distribution come describe F distribution, formula is as follows,
Wherein X1Degree of freedom is represented as d1Chi square distribution, X2Degree of freedom is represented as d2Chi square distribution, in order to ensure F examine
The statistic tested assuming that under meet F distributions, the quadratic sum of each sample data statistical iteration and should obey chi square distribution, card side
This condition is distributed to ensure that sample data independence and meet normal distribution, i.e., whether variance having the same, F examine public affairs
Formula is as follows,
Wherein μi,μ′iFor sample yi,y′iMean value, σi,σ′iFor sample yi,y′iVariance, d1,d2Respectively represent sample
yi,y′iNumber, F distribution of particle filtering in, the historical metrology value of screening is as yi,y′i, desired estimation output is as μi,
μ′i, therefore, when having selected suitable model parameter value, the measuring value of history will be similar to the desired estimation being calculated
Output, while the desired value of the statistic of F inspections is also approximately equal toTherefore two groups of sample datas of molecule denominator are having the same
Variance, that is, exported when the measuring value that sensor obtains on molecule is similar to estimation be calculated, due to two groups of samples
Variance having the same, then the measurement sample on denominator be also similar to estimation output,
In the more new stage, the weight of particle is calculated by new F cores, when the state for needing prediction (k+p) moment
When variable, it is necessary first at the time of initial predicted particle collection is mapped to corresponding forward, reuse the system model without noise
Equation dates back initial time, and the calculation formula is as follows,
WhereinIt represents using the state equation without noise toward the process of inceptive direction iteration, the present invention is directly by xk
Bring formula x intok=f (xk-1,θk) carry out direct solution xk-1, it does not need to specially go to solve inverse function,
Both included the forward direction output valve estimated to construct oneAlso to have and be measured from sensor
Both the statistic of value, i.e., the sample data that difference is constituted, by the forward direction output valve estimated in formula (5) and newest limited
Molecule of the quadratic sum of difference between measuring value as F statistics, at the same it is limited by what is screened in historical metrology value
Denominator before the estimation of a measuring value corresponding thereto to the quadratic sum of output valve difference as F statistics, formula are expressed as follows,
WhereinIndicate that the measuring value of the fixed number screened from historical metrology value, screening measure
The principle of value is：Estimate to obtain system mode more close to actual value, φ using the measuring value chosenjFor the corresponding sampling time
Point, σ are to measure noise skStandard deviation, M and M ' respectively represent the item number of molecule denominator and can be adjusted according to actual demand, because
This, the Gaussian kernel for calculating particle weights is turned into F distribution probability density functions, the F statistics point of the calculation basis of particle weights
The conspicuousness of two groups of samples of sub- denominator, that is to say, that the normal state likelihood function of standard becomes F distribution probability density functions, public
Formula is as follows,
Wherein Γ () is gamma function.
In step (3), the dynamic screening process method is：
The purpose of dynamic screening is the sampling of these screenings in order to find out limited time point in window at a fixed time
The estimated value of the system mode at time point is more nearly actual value, before screening process, since historical metrology value is estimated to obtain
System mode obtained, while estimate output valveIt can be obtained, therefore passed through by bringing system state equation into
A kind of performance index is defined to screen sampling instant, what which weighed is the difference between estimation output and measuring value,
Therefore it usually can be used for assessing the result quality of estimation, in the present invention, objective function refers to calculate the performance at k moment
Number, formula is as follows,
Wherein n represents the number of experiment, takes the average value of many experiments to carry out calculating target function in practical application, is come with this
The accidental error that single experiment is brought is reduced, formula (8) can show that performance index is smaller to represent better estimation effect,
Finally obtain a sampling instants filtered out of M ', it is emphasized that, the screening φ of sampling instantjOnly have with the measuring value of history
It closes, and the accuracy rate of predicted state can be reduced with system degradation, therefore propose that one kind can greatly reduce system degradation shadow
Loud class draws window method, and screening process is limited in a regular time window by this method, and window follows newest measurement
The acquisition of value and move.
Particle filter steering engine trend prediction method and the prior art provided by the invention based on improvement weights generating mode
Compared to haing the following advantages：
1. compared with traditional particle filter algorithm, particle can dynamically be calculated in forecast period by F cores by changing method
Weights are solved keeps weights are constant to be easy to cause asking for precision of prediction decline based on particle in particle filter traditional prediction method
Topic.2. this method inherits the advantages of conventional particle filtering method, and solves it applied to different component lifes prediction when institute
The precision of prediction problem faced realizes simple, direct, the effective prediction to component life, to be based on particle filter prediction
The improvement of method provides a kind of new thinking.3. algorithm small scale, operation are simple, it is easy to Project Realization.This technology can be into one
Step is applied to the fault diagnosis of general nonlinearity control system.
Description of the drawings
Fig. 1 is the summary of the existing trend prediction method frame based on particle filter.
Fig. 2 is provided by the invention based on the particle filter steering engine trend prediction method flow for improving weights generating mode
Figure.
Fig. 3 is F distribution of particle filter forecasting frames.
Fig. 4 is that the class in dynamic screening process draws window schematic diagram.
Fig. 5 is F distribution of particle filtering algorithm flow diagrams.
Fig. 6 is electro-hydraulic joint actuator model schematic diagram in experiment.
The change in location track of piston when Fig. 7 is oil leakage fault inside steering engine.
Fig. 8 is prediction and estimated result of three kinds of prediction techniques in scheme 1.
Fig. 9 is prediction and estimated result of three kinds of prediction techniques in scheme 2.
Figure 10 is prediction and estimated result of three kinds of prediction techniques in scheme 3.
Figure 11 is general for the particle number distribution of the fault moment of conventional particle filter forecasting method in the case of scheme 2 and RUL
Rate density function.
Particle number distributions and RUL of the Figure 12 for the fault moment of F distribution of particle filter forecasting methods in the case of scheme 2
Probability density function.
Figure 13 is close for the particle number distribution of the fault moment of PF-LSSVR prediction techniques in the case of scheme 2 and RUL probability
Spend function.
Figure 14 is general for the particle number distribution of the fault moment of conventional particle filter forecasting method in the case of scheme 3 and RUL
Rate density function.
Particle number distributions and RUL of the Figure 15 for the fault moment of F distribution of particle filter forecasting methods in the case of scheme 3
Probability density function.
Figure 16 is close for the particle number distribution of the fault moment of PF-LSSVR prediction techniques in the case of scheme 3 and RUL probability
Spend function.
Specific implementation mode
In the following with reference to the drawings and specific embodiments to provided by the invention based on the particle filter for improving weights generating mode
Steering engine trend prediction method is described in detail.
As shown in Fig. 2, provided by the invention suitable including pressing based on the F distribution of particle filtering methods for improving weights generating mode
The following steps that sequence carries out：
(1) F distribution of particle filter forecasting frame
As shown in figure 3, the design method of above-described F distribution of particle filter forecasting frame is：
In order to which better descriptive model changes with time, the nonlinear diffusion filtering model table of time-varying parameter is carried
It is shown as
xk=f (xk-1,θk)+vk-1 (1)
zk=h (xk)+sk (2)
WhereinIt is expressed as time-varying parameter vector, which can gradually change in whole system demotion processes, remaining
Parameter have in chapter 2 and specifically make referrals to, enable tk(k=0,1 ...) it is discrete time step number, tkWhat the failure predication at moment referred to
It is to utilize available measuring value z1:kEstimate the state x at current timek, then predict xk+1Moment is to xk+p(p is the state at moment
Need the step number predicted), finally obtain the residual service life of components RUL at current time, that is, when predicting initial time to prediction failure
The difference at quarter,
Before being predicted, estimate in the case where receiving newest measuring value to obtain newest shape using particle filter
State estimatorWith model parameter estimation amountThen new model parameter amount can be used to real-time update in particle mapping phase
Nonlinear model, while the particle after resampling processWill as the primary collection of forecast period,
In standard particle filtering, the weights of particle are determined according to importance probability function, in general, particle
Weight is according to the measuring value of estimationWith the measuring value obtained by sensorBetween difference calculate, i.e.,
Wherein formula (4) is referred to as Gaussian kernel, and the σ in formula is to measure noise skStandard deviation, the present invention proposes one kind
It improves traditional Gauss core and defines a kind of method that new degree of fitting is measured to calculate particle weights, the thinking of this method is based on F
It examines to reduce global error, combines F distributions and particle filter dynamic prediction residual service life of components, this method are not only inherited
The advantages of conventional particle filter forecasting method, and solve its problem encountered when application is predicted with component life, it is
Improvement based on particle filter prediction technique provides a kind of new thinking,
The prediction framework containment mapping stage of F distribution of particle filtering and more two parts of new stage, in mapping phase, initially
Particle collection p steps are mapped forward by modified system model, the specific step number of prediction determines by remaining life threshold value, and more
New stage, the particle weights for calculating final predicted state are calculated by the F cores constructed,
The detailed step at (k-1) moment and k moment is set forth in Fig. 3, in order to provide predicted state at (k-1) momentBy (k-1) moment by the modified particle collection of newest measuring valueAs primary collection, at the same model when
Variable element θk-1It is updated as recessive state joint, therefore updated model parameter θk-1Can be used for predict before to shape
Then by all historical metrology values of (k-1) before the moment for constructing F cores, and particle weights are calculated, last root in state
Predicted state is obtained according to particle weighted sum(the step of 1. line in Fig. 3 represents (k-1) moment), obtains newly when the k moment
Reliable measuring value when, the model parameter θ of systemkIt will be updated by particle filter with prediction primary collection, with stylish
Measuring value is also added to F cores for updating the particle weights in different moments, and the predicted state of forward direction will all update at this time,
Until the state of prediction reaches remaining life threshold value (the step of 2. line in Fig. 3 represents the k moment).
(2) F is examined constructs with F cores
Above-described F is examined with F core building methods：
F inspections are called homogeneity test of variance, and the statistic in F inspections is the ratio between the quadratic sum of two groups of samples, reflection
It is whether two groups of samples have significant difference, in other words, assuming that when two groups of samples variance having the same, what F was examined
Statistic meets F distributions, otherwise when assuming that when invalid, which does not meet F distributions then,
F distributions generally are described with the chi square distribution of two kinds of different degree of freedom, formula is as follows,
Wherein X1Degree of freedom is represented as d1Chi square distribution, X2Degree of freedom is represented as d2Chi square distribution, in order to ensure F examine
The statistic tested assuming that under meet F distributions, the quadratic sum of each sample data statistical iteration and should obey chi square distribution, card side
This condition is distributed to ensure that sample data independence and meet normal distribution, i.e., whether variance having the same, F examine public affairs
Formula is as follows,
Wherein μi,μ′iFor sample yi,y′iMean value, σi,σ′iFor sample yi,y′iVariance, d1,d2Respectively represent sample
yi,y′iNumber, F distribution of particle filtering in, the historical metrology value of screening is as yi,y′i, desired estimation output is as μi,
μ′i, therefore, when having selected suitable model parameter value, the measuring value of history will be similar to the desired estimation being calculated
Output, while the desired value of the statistic of F inspections is also approximately equal toTherefore two groups of sample datas of molecule denominator are having the same
Variance, that is, exported when the measuring value that sensor obtains on molecule is similar to estimation be calculated, due to two groups of samples
Variance having the same, then the measurement sample on denominator be also similar to estimation output,
In the more new stage, the weight of particle is calculated by new F cores, when the state for needing prediction (k+p) moment
When variable, it is necessary first at the time of initial predicted particle collection is mapped to corresponding forward, reuse the system model without noise
Equation dates back initial time, and the calculation formula is as follows,
WhereinIt represents using the state equation without noise toward the process of inceptive direction iteration, the present invention is directly by xk
Bring formula x intok=f (xk-1,θk) carry out direct solution xk-1, it does not need to specially go to solve inverse function,
Both included the forward direction output valve estimated to construct oneAlso to have and be measured from sensor
Both the statistic of value, i.e., the sample data that difference is constituted, by the forward direction output valve estimated in formula (7) and newest limited
Molecule of the quadratic sum of difference between measuring value as F statistics, at the same it is limited by what is screened in historical metrology value
Denominator before the estimation of a measuring value corresponding thereto to the quadratic sum of output valve difference as F statistics, formula are expressed as follows,
WhereinIndicate that the measuring value of the fixed number screened from historical metrology value, screening measure
The principle of value is：Estimate to obtain system mode more close to actual value, φ using the measuring value chosenjFor the corresponding sampling time
Point, σ are to measure noise skStandard deviation, M and M ' respectively represent the item number of molecule denominator and can be adjusted according to actual demand, because
This, the Gaussian kernel for calculating particle weights is turned into F distribution probability density functions, the F statistics point of the calculation basis of particle weights
The conspicuousness of two groups of samples of sub- denominator, that is to say, that the normal state likelihood function of standard becomes F distribution probability density functions, public
Formula is as follows,
Wherein Γ () is gamma function.
(3) dynamic screening process
As shown in figure 3, above-described dynamic screening process method is：
The purpose of dynamic screening is the sampling of these screenings in order to find out limited time point in window at a fixed time
The estimated value of the system mode at time point is more nearly actual value, before screening process, since historical metrology value is estimated to obtain
System mode obtained, while estimate output valveIt can be obtained, therefore passed through by bringing system state equation into
A kind of performance index is defined to screen sampling instant, what which weighed is the difference between estimation output and measuring value,
Therefore the result that usually can be used for assessing estimation is fine or not, and herein, objective function calculates the performance index at k moment,
Formula is as follows,
Wherein n represents the number of experiment, takes the average value of many experiments to carry out calculating target function in practical application, is come with this
The accidental error that single experiment is brought is reduced, formula (8) can show that performance index is smaller to represent better estimation effect,
Finally obtain a sampling instants filtered out of M ', it is emphasized that, the screening φ of sampling instantjOnly have with the measuring value of history
It closes, and the accuracy rate of predicted state can be reduced with system degradation, therefore propose that one kind can greatly reduce system degradation shadow
Loud class draws window method, and screening process is limited in a regular time window by this method, and window follows newest measurement
The acquisition of value and move,
In Fig. 4, the width of each window is L, and the selection of window width is determined according to the susceptibility of data processing,
Such as similar two windows Data Representation be similar object function as a result, then width can be reduced, so as to not
Same time serial ports will not obtain similar the selection result, and in an actual situation, especially steering engine, typically no condition obtain
The quality data in whole service stage, getable Data Representation is the shortage of data of diastem, and the screening process can
It is not limited by case above.
(4) residual Life Calculation
Above-described residual Life Calculation method is：
The final purpose of prediction is to obtain the remaining life of component, and the filtering of F distribution of particle can not only obtain current time
The remaining life of system, moreover it is possible to provide the probability density distribution of remaining life, this makes the accuracy and redundancy of fault pre-alarming
It greatly promotes, when predicted state reaches scheduled fault threshold, prediction process terminates, and can provide residual service life of components at this time
Probability density distribution, formula is as follows
Wherein int represents integer field, and inf represents the infimum for taking set, and λ is scheduled fault threshold, etching system when k
The probability density distribution of the remaining life of component is,
As shown in figure 5, to be provided by the present invention based on the particle filter steering engine status predication for improving weights generating mode
Method flow schematic diagram.
In order to verify the particle filter steering engine trend prediction method provided by the invention based on improvement weights generating mode
Validity, the present inventor test it, and process is as follows：
It is provided by the invention based on the particle filter steering engine status predication for improving weights generating mode in order to further prove
The performance of method chooses electro-hydraulic joint steering engine as experiment porch, according to the motion data prediction rudder of rudder face in following experiment
The standard of machine inside oil leakage fault and the remaining life for providing steering engine, this experiment vacuum metrics steering engine oil leak is oil leak hole area
aleak。
Fig. 6 gives the electro-hydraulic joint actuator model after a kind of typical simplification, is provided based on electro-hydraulic joint actuator model
Nonlinear system equation,
Z (k)=x (k)+sk
Wherein
This tests state variable X=[x a to be estimatedleak], wherein x is the position for connecting steering engine start cylinder piston, sampling interval Δ T
277 milliseconds are taken, flight control input is SIN function u=Asin (2 π at), vk-1For zero-mean gaussian system noise, variance is
Nonsingular matrix Qk-1=diag [0.11] measures noise and meets sk~N (0, σ), it is X that estimation stages, which obtain original state,0=
[0.12.0], the particle number of sampling are 100, due to the variation compared to piston position, internal hydraulic pressure cylinder oil leak rate of change compared with
Slowly, the data while in hydraulic cylinder can not remove measurement in practical applications, the sampling interval of oil leak hole area is set as 5 ×
Δ T, i.e. r=5, M and M ' are defined as 10, and it is 30 × Δ T that class, which draws window width, the position of piston when Fig. 7 is hydraulic cylinder gradual oil leak
Set variation track schematic diagram, it can be seen that the flexible amplitude of pressurized strut can be because the leakage of hydraulic oil continuously decreases.
1 electro-hydraulic joint actuator model parameter value of table
(note：sq.in:Square inch in:Inch psi:Ft lbf/square inch)
Predicted state reach fault threshold then decision-making system break down, in this experiment fault threshold take λ=
4.14sq.in defines original state and predicts that the entire period to fault threshold is true lifetime value (TL), and TL is set in this experiment
390* Δ T are set to, it is superior compared to conventional particle filter forecasting method in order to comprehensively verify the filtering of F distribution of particle
Property, three kinds of different prediction initial points are set herein, are respectively to predict oil leakage fault, 3 kinds of algorithms with 3 kinds of different algorithms
Particle filter-Least square support vector regression (PF-LSSVR) prediction technique, conventional particle filter forecasting method, F are distributed grain
The experiment prediction result under different schemes is set forth in sub- filter forecasting method, Fig. 7.
Scheme 1：Predict starting point in 20%TL
Scheme 2：Predict starting point in 50%TL
Scheme 3：Predict starting point in 80%TL
Green dotted line in Fig. 8 to Figure 10 is distinguishing the estimation stages and forecast period of algorithm flow, purple dotted line generation
Table fault threshold.It can be seen that although can maintain within 12 seconds before the prediction locus of three kinds of algorithms and true oil leaking hole areal sampling
Data are coincide, however, for traditional particle filter prediction algorithm, subsequent prediction locus begins to deviate from real trace, especially
It is in the case of scheme 1 and scheme 2, when the time phase of prediction is elongated, the prediction locus of PF-LSSVR can not be maintained at
The state of one tenacious tracking real trace, and set forth herein F distribution of particle filter forecastings algorithms still to have higher prediction
Precision, therefore, the estimated performance of algorithm proposed in this paper have higher stability compared to other two kinds of algorithms.It is worth noting
, in scheme 3, ideally 3 kinds of algorithms all should have similar prediction locus, but glassy yellow represent traditional grain
The prediction locus of sub- filter forecasting method is but in the starting stage of the prediction serious true state trajectory of deviation, it means that
The primary of forecast period has just been not at true region, on the contrary since utilize is previous to the filtering of F distribution of particle
Multiple measuring values calculate the weights of particle, and the measurement disturbance even for estimation stages single point in time can also keep predicting
Stability.
In addition, in order to further verify the difference of algorithms of different prediction result, experiment gives φ under 3 kinds of algorithmsRULWhen
The particle distribution situation inscribed, since the prediction of longer cycle can be easy to cause the deviation of prediction, we only have chosen scheme 2
It is studied with scheme 3, Fig. 8 to Figure 10 is that scheme 2 predicts that particle distribution situation under end time, Figure 11 to Figure 13 are scheme 1
Predict that particle distribution situation under end time, jade-green block diagram represent the number distribution of particle.
As can be seen that compared to other two kinds of prediction algorithms, the overwhelming majority of the F distribution of particle filtering in prediction end time
ParticleAll concentrate on the position of fault threshold, it means that the anticipation trend of proposed algorithm has preferable steady
It is qualitative, while the RUL probability density distribution situations provided also comply with the distribution situation of particle, more demonstrate the filter of F distribution of particle
Advantage of the wave algorithm in prediction stability.
It is square used here as a kind of common judge criterion for the accuracy of each algorithm predicting residual useful life of quantitative comparison
Root error (RMSE) assesses the precision of prediction under different schemes,
From the point of view of analysis of experimental results before, PF-LSSVR prediction techniques be not appropriate for long period prediction, therefore to
Go out φRULThis method is not accounted for when the number of particles at moment, is held under three kinds of different schemes using different prediction algorithms
The data result that the experiment that row is 100 times obtains is as shown in table 2.Due to the introducing of F cores and dynamic screening process, particle obtains base
It is modified in the particle weights that a large amount of historical metrology information calculate, the precision of prediction and stability of the filtering of F distribution of particle are passing
It is obtained for promotion on the basis of system particle filter prediction technique.
2 predicting residual useful life precision of table compares
Claims (3)
1. based on the particle filter steering engine trend prediction method for improving weights generating mode comprising the following step carried out in order
Suddenly：
(1) F distribution of particle filter forecasting frame；
(2) F cores construct；
(3) dynamic screening process；
It is characterized in that：In step (1), the F distribution of particle filter forecasting frames are：
The prediction framework containment mapping stage of F distribution of particle filtering and more two parts of new stage；In mapping phase, initial grain
Subset maps forward p steps by modified system model, and the specific step number of prediction is determined by remaining life threshold value, and in update rank
Section, the particle weights for calculating final predicted state are calculated by the F cores constructed,
In order to provide predicted state at (k-1) momentBy (k-1) moment by the modified particle collection of newest measuring valueAs primary collection, while the time-varying parameter θ of modelk-1It is updated as recessive state joint, therefore after update
Model parameter θk-1Can be used for predict before to state then all historical metrology values of (k-1) before the moment are used for
F cores are constructed, and particle weights are calculated, predicted state is finally obtained according to particle weighted sumIt is obtained newly when the k moment
Reliable measuring value when, the model parameter θ of systemkIt will be updated by particle filter with prediction primary collection, with stylish
Measuring value is also added to F cores for updating the particle weights in different moments, and the predicted state of forward direction will all update at this time,
Until the state of prediction reaches remaining life threshold value.
2. it is according to claim 1 based on the particle filter steering engine trend prediction method for improving weights generating mode, it is special
Sign is：In step (2), F cores construction is：
In standard particle filtering, the weights of particle are determined according to importance probability function, in general, particle weights
According to the measuring value of estimationWith the measuring value obtained by sensorBetween difference calculate, i.e.,
Wherein formula (2) is referred to as Gaussian kernel, and the σ in formula is to measure noise skStandard deviation；The present invention proposes a kind of improvement biography
System Gaussian kernel simultaneously defines a kind of method that new degree of fitting is measured to calculate particle weights, the thinking of this method based on F inspections come
Global error is reduced, F distributions is combined and particle filter dynamic prediction residual service life of components, this method not only inherits tradition
The advantages of particle filter prediction technique, and solve its problem encountered when application is predicted with component life, to be based on grain
The improvement of sub- filter forecasting method provides a kind of new thinking,
F inspections are called homogeneity test of variance, and the statistic in F inspections is the ratio between the quadratic sum of two groups of samples, and reflection is two
Whether group sample has significant difference, in other words, in the statistics that assuming that when two groups of samples variance having the same, F is examined
Amount meets F distributions, otherwise when assuming that when invalid, which does not meet F distributions, the general card with two kinds of different degree of freedom then
Side's distribution is distributed to describe F, and formula is as follows,
Wherein X1Degree of freedom is represented as d1Chi square distribution, X2Degree of freedom is represented as d2Chi square distribution, in order to ensure F examine system
Metering assuming that under meet F distributions, the quadratic sum of each sample data statistical iteration and should obey chi square distribution, chi square distribution this
A condition ensure that sample data independence and meets normal distribution, i.e., whether variance having the same, the formula that F is examined is such as
Under,
Wherein μi,μ′iFor sample yi,y′iMean value, σi,σ′iFor sample yi,y′iVariance, d1,d2Respectively represent sample yi,y′i
Number, F distribution of particle filtering in, the historical metrology value of screening is as yi,y′i, desired estimation output is as μi,μ′i,
Therefore, when having selected suitable model parameter value, the measuring value of history will be similar to the desired estimation being calculated output,
The desired value for the statistic that F is examined simultaneously is also approximately equal toTherefore two groups of sample data variances having the same of molecule denominator,
It is namely exported when the measuring value that sensor obtains on molecule is similar to estimation be calculated, since two groups of samples have phase
With variance, then the measurement sample on denominator be also similar to estimation output,
In the more new stage, the weight of particle is calculated by new F cores, when the state variable for needing prediction (k+p) moment
When, it is necessary first at the time of initial predicted particle collection is mapped to corresponding forward, reuse the system model equation without noise
Initial time is dateed back, the calculation formula is as follows,
WhereinIt represents using the state equation without noise toward the process of inceptive direction iteration, the present invention is directly by xkIt brings into
Formula xk=f (xk-1,θk) carry out direct solution xk-1, it does not need to specially go to solve inverse function,
Both included the forward direction output valve estimated to construct oneAlso there is the system from sensor measuring value
Metering, i.e., the sample data that the difference of the two is constituted will the middle forward direction output valve estimated of formula (5) and newest limited a measuring value
Between difference molecule of the quadratic sum as F statistics, while will be screened in historical metrology value limited measures
Denominator before the estimation of value corresponding thereto to the quadratic sum of output valve difference as F statistics, formula are expressed as follows,
WhereinThe measuring value for indicating the fixed number screened from historical metrology value, screens measuring value
Principle is：Estimate to obtain system mode more close to actual value, φ using the measuring value chosenjFor corresponding sampling time point, σ
To measure noise skStandard deviation, M and M ' respectively represent the item number of molecule denominator and can be adjusted according to actual demand, therefore,
The Gaussian kernel for calculating particle weights is turned into F distribution probability density functions, the F statistic molecules point of the calculation basis of particle weights
The conspicuousness of female two groups of samples, that is to say, that the normal state likelihood function of standard becomes F distribution probability density functions, and formula is such as
Under,
Wherein Γ () is gamma function.
3. it is according to claim 1 based on the particle filter steering engine trend prediction method for improving weights generating mode, it is special
Sign is：In step (3), the dynamic screening process is：
The purpose of dynamic screening is the sampling time of these screenings in order to find out limited time point in window at a fixed time
The estimated value of the system mode of point is more nearly actual value, before screening process, since what historical metrology value was estimated is
System state has obtained, while the output valve estimatedIt can be obtained by bringing system state equation into, therefore by fixed
A kind of performance index of justice screens sampling instant, and what which weighed is the difference between estimation output and measuring value, because
Result that this usually can be used for assessing estimation is fine or not, and in the present invention, objective function calculates the performance index at k moment,
Formula is as follows,
Wherein n represents the number of experiment, take the average value of many experiments to carry out calculating target function in practical application, is reduced with this
The accidental error that single experiment is brought, formula (8) can show that performance index is smaller to represent better estimation effect, finally
Obtain a sampling instants filtered out of M ', it is emphasized that, the screening φ of sampling instantjIt is only related with the measuring value of history,
And the accuracy rate of predicted state can be reduced with system degradation, therefore propose it is a kind of can greatly reduce system degradation influence
Class draws window method, and screening process is limited in a regular time window by this method, and window follows newest measuring value
It obtains and moves.
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