CN109583480A - One kind being used for aero-engine anti-asthma control system bathtub curve estimation method - Google Patents
One kind being used for aero-engine anti-asthma control system bathtub curve estimation method Download PDFInfo
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Abstract
The invention discloses one kind to be used for aero-engine anti-asthma control system bathtub curve estimation method, collect multi-aircraft engine anti-asthma control system Complete Sample fault data, assuming that aero-engine anti-asthma control system fault data obeys Weibull distribution, the form parameter m and scale parameter η of Weibull distribution model parameter in the step 1 are estimated based on support vector regression, and optimize the punishment parameter C and loss function ε of the support vector regression in the step 2 based on artificial bee colony algorithm, it is finally completed the estimation of aero-engine anti-asthma control system bathtub curve.Validity of the present invention in terms of improving aeroengine control system bathtub curve estimated accuracy.
Description
Technical field
The present invention is a kind of aero-engine anti-asthma control system bathtub curve estimation method, is related to practical implementation
System reliability field in the process relates more specifically to utilize Weibull distribution, support vector regression and artificial bee colony algorithm
The method combined estimates aero-engine anti-asthma control system bathtub curve.
Background technique
The present invention is used to estimate the bathtub curve of aero-engine anti-asthma control system, estimates failure for existing method
The not high problem of rate curve precision, is proposed and is combined based on Weibull distribution, support vector regression and artificial bee colony algorithm
Aero-engine anti-asthma control system bathtub curve estimation method.
Summary of the invention
In order to solve the above problems existing in the present technology, the invention proposes returned based on Weibull distribution, supporting vector
The aero-engine anti-asthma control system bathtub curve estimation method for returning machine and artificial bee colony algorithm to combine assumes aviation
Engine anti-asthma control system obeys Weibull distribution, estimates Weibull distribution model parameter m, η based on support vector regression
And γ, support vector regression parameter C and ε is optimized based on artificial bee colony algorithm.
The purpose of the present invention is what is be achieved through the following technical solutions:
One kind being used for aero-engine anti-asthma control system bathtub curve estimation method, including following procedure:
Step 1: to estimate bathtub curve, multi-aircraft engine anti-asthma control system Complete Sample number of faults is collected
According to；Assuming that aero-engine anti-asthma control system fault data obeys Weibull distribution, two parameters of Weibull probability density
Function failure rate function isM > 0 is form parameter, and η > 0 is scale parameter；
Step 2: the form parameter of Weibull distribution model parameter in the step 1 is estimated based on support vector regression
M and scale parameter η:
Weibull model parameter is estimated with support vector machines, by a Nonlinear Mapping Φ, by the number of the input space
It is mapped in high-dimensional feature space F according to x, and carries out linear regression in this space；
Given sample data { xi,yi, i=1,2 ..., l, wherein xi∈Rm,yi∈ R, wherein yiFor desired value, l is data
The sum of point；Support vector machines solves regression problem by introducing loss function, using following formula come estimation function:
Y=f (x)=<ω Φ (x)>+b, Φ: Rm→G,ω∈G。
Extreme value is taken to optimization aim:
In formula, C is penalty factor, realizes the compromise in empiric risk and fiducial range；ξiWithFor introducing relaxation because
Son；ε is loss function；
Step 3: based on artificial bee colony algorithm optimize the support vector regression in the step 2 punishment parameter C and
Loss function ε is finally completed the estimation of aero-engine anti-asthma control system bathtub curve.
Described one kind is used for aero-engine anti-asthma control system bathtub curve estimation method, in step 1, it is assumed that
Fault data obeys two parameters of Weibull, carries out Weibull linear transformation, completes the linearisation to Weibull model,
In, accumulated invalid probability F (ti) can use Median rank estimation provide,It is available in this way
One group of ordered series of numbers (t1,F(t1)),(ti,F(ti)),…,(tn,F(tn)), above formula is transformed to (x1,y1),(x2,y2),…,(xn,
yn)。
Described one kind is used for aero-engine anti-asthma control system bathtub curve estimation method, in step 2, loss function
Decision function can be indicated with sparse data point, introduced loss function ε, be defined as
The Lagrange multiplier α of introducingiWithConvex optimization problem is reduced to maximize secondary By the Lagrange multiplier α only not equal to 0iWithWith
It is predicted and is returned, regression function is expressed asWherein,
The problem of solution quadratic programming can be regarded as, finds weight ω and deviates the optimal of b for given training sample
Value, meets Karush-Tucker (KKT) condition, thus regression function isK
(xi, x) and it is kernel function；
Selection uses gaussian radial basis functionσ is the parameter of kernel function.
Described one kind is used for aero-engine anti-asthma control system bathtub curve estimation method, in step 3, manually
The basic step that ant colony algorithm is realized is as follows:
3.1) honeybee populations: initial time are initialized, all honeybees do not have any priori knowledge, and role is to scout
Bee；Global random searching nectar source, and nectar source nectar amount, i.e. " the income degree " in nectar source are obtained according to nectar source situation.
Parameter and population has following three:
1. honeybee sum N, defining gathering honey bee and observation bee is respectively N/2；
2. maximum number of iterations maxCycle, all once global search and a local search in each iteration；
3. nectar source stops maximum limitation searching times Limit, local search Limit times, nectar source does not update, then gathering honey bee,
Observation bee is converted into search bee；
3.2) according to the relative size in the 3.1) nectar source " income degree " of all honeybees of step, honeybee is converted into gathering honey bee and sight
Examine two kinds of bee, income degree ranking it is relatively forward become gathering honey bee, income degree ranking relatively rearward become observation bee；Observe bee
It is waited in dancing area, how much knows nectar source nectar amount according to information such as the swings of gathering honey bee, the higher nectar source of nectar amount is recruited
Observation bee it is more；
3.3) for every gathering honey bee, continue the gathering honey near green molasses source, find other new nectar sources, and calculate its fitness
Value, if its income degree is high, honeybee replaces green molasses source by hating to leave criterion, with new nectar source；
3.4) one nectar source is selected according to the probability proportional to nectar source fitness value for every observation bee, and at it
Gathering honey is nearby carried out, other nectar sources are found, it is the same with the gathering honey bee in the 3.3) step, if its income Du Genggao, observes bee and turn
It is changed to gathering honey bee, replaces green molasses source position；
3.5) it is more than to limit number Limit that if gathering honey bee, observation bee, which search number, higher fitness is not still found
The nectar source is then abandoned in nectar source, while the role of honeybee is converted into search bee by gathering honey bee or observation bee, and is randomly generated one
New nectar source；
3.6) the optimal nectar source that current all honeybees are found is recorded, and is adjusted to the 3.2) step, until meeting greatest iteration time
It counts the condition of maxCycle or exports global optimum position when being less than optimization error to get optimized parameter estimated result is arrived.
The present invention has the advantages that
By comparison, it was found that artificial bee colony algorithm optimization support vector regression parameter improves the accuracy of estimation, thus
It can be seen that being estimated based on the method that Weibull distribution, support vector machines combine in raising aeroengine control system bathtub curve
Count the validity of precision aspect.
Detailed description of the invention
The following further describes the present invention with reference to the drawings.
Fig. 1 is bathtub curve estimation method flow chart of the present invention.
Fig. 2 is number of faults strong point distribution map.
Fig. 3 is support vector machines evaluation fitting effect picture.
Fig. 4 is evaluation fitting effect picture after artificial bee colony algorithm Support Vector Machines Optimized parameter.
Fig. 5 is certain type aero-engine anti-asthma control system bathtub curve.
Specific embodiment
Technical solution of the present invention and its effect is discussed in detail below in conjunction with Figure of description:
One kind being used for aero-engine anti-asthma control system bathtub curve estimation method, includes following procedure:
Step 1: present invention assumes that aero-engine anti-asthma control system fault data obeys Weibull distribution.Two parameters
Weibull distribution probability density function failure rate function isM > 0 is form parameter, and η > 0 is scale parameter.
To estimate bathtub curve, the present invention collects the 16 engine anti-asthma control system Complete Samples events of certain 8 airplane of air squadron
Hinder data, as shown in table 1.
Table 1
| Serial number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Fault time | 511.35 | 103.46 | 263.47 | 119.25 | 139.53 | 119.25 | 29.01 | 120.53 |
| Serial number | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Fault time | 69.49 | 211.06 | 344.33 | 583.56 | 514.25 | 244.01 | 198.24 | 391.31 |
As described in step 1: assuming that fault data obeys two parameters of Weibull, carrying out Weibull linear transformation, essence
On complete linearisation to Weibull model.Wherein, accumulated invalid probability F (ti) can use Median rank estimation provide,One group of ordered series of numbers (t available in this way1,F(t1)),(ti,F(ti)),…,(tn,F(tn)),
Above formula can be transformed to, (x1,y1),(x2,y2),…,(xn,yn), fault point distribution is as shown in Figure 2.
Step 2: the present invention is based on support vector regressions to estimate Weibull distribution model parameter m and η.
2.1) it introduces support vector machines and carrys out estimation method.Weibull model parameter is estimated with support vector machines, it is basic to think
Think it is the data x of the input space to be mapped in high-dimensional feature space F, and by a Nonlinear Mapping Φ in this space
Carry out linear regression.Given sample data { xi,yi, i=1,2 ..., l, wherein xi∈Rm,yi∈ R, wherein yiFor desired value, l
For the sum of data point.Support vector machines solves regression problem by introducing loss function.Letter is generally estimated using following formula
Number y=f (x)=<ω Φ (x)>+b, Φ: Rm→G,ω∈G。
Extreme value is taken to optimization aim:
C is penalty factor, realizes the compromise in empiric risk and fiducial range；ξiWithFor the relaxation factor of introducing；ε is loss letter
Number.
Loss function can indicate decision function with sparse data point.Introduce the ε loss function with good nature, definition
ForThe Lagrange multiplier α of introducingiWithConvex optimization problem is reduced to most
Change greatly secondary By the Lagrange multiplier α only not equal to 0iWithWith
It is predicted and is returned, regression function is expressed asWherein,The problem of solution quadratic programming can be regarded as.For given training
Sample finds weight ω and deviates the optimal value of b, meets Karush-Tucker (KKT) condition, thus regression function isK(xi, x) and it is kernel function, present invention selection uses gaussian radial basis functionσ is the parameter of kernel function.
In the present embodiment, sample average is acquired using training sampleSample standard deviation σY standard deviation=
0.9639, estimate punishment parameterIt is true in punishment parameter
Determine in situation, with root-mean-square error σY root-mean-square errorMinimum criterion finds insensitive loss function of ε using iterative algorithm, finally
σY root-mean-square error is minimum=0.0460, corresponding insensitive loss function of ε=0.3280.In punishment parameter C=3.3421 and insensitive loss
In the case where function of ε=0.3280, linear equation y=a+bx slope and intercept are solved using the method for supporting vector linear regression
Estimated value, wherein a=-mln η, b=m, after calculating Support vector regression evaluation fitting effect is as shown in Figure 3.
Step 3: support vector regression punishment parameter C and loss function ε is optimized based on artificial bee colony algorithm.
Introduce artificial bee colony method.Artificial bee colony method is a kind of new swarm intelligence optimization method, to its theoretical research
New hot spot is had become with application, due to its very various excellent performances, has become the one of bionic intelligence calculating field
Kind important optimization algorithm.
The basic step that artificial bee colony algorithm is realized is as follows.
3.1) honeybee populations are initialized.Initial time, all honeybees do not have any priori knowledge, and role is to scout
Bee.Global random searching nectar source, and nectar source nectar amount, i.e. " the income degree " in nectar source are obtained according to nectar source situation.
Parameter and population has following three:
1. honeybee sum N (general definition gathering honey bee is respectively N/2 with observation bee)；
2. maximum number of iterations maxCycle (in each iteration all once global search and a local search)；
3. nectar source stop maximum limitation searching times Limit (local search Limit times, nectar source do not update, then gathering honey bee,
Observation bee is converted into search bee).
3.2) according to the relative size in the 3.1) nectar source " income degree " of all honeybees of step (being all search bee role), honeybee
Be converted into two kinds of bee of gathering honey bee and observation, income degree ranking it is relatively forward become gathering honey bee, income degree ranking is relatively rearward
As observation bee.It observes bee to wait in dancing area, how much knows nectar source nectar amount according to information such as the swings of gathering honey bee, nectar
It is more (process is recruited with probability completion) to measure the observation bee that higher nectar source is recruited.
3.3) for every gathering honey bee, continue gathering honey (local search procedure) near green molasses source, find other new nectar sources,
And its fitness value (the nectar amount in nectar source or " income degree ") is calculated, if its income degree is high, honeybee is by hating to leave criterion, with new
Nectar source replaces green molasses source.
3.4) one nectar source is selected according to the probability proportional to nectar source fitness value for every observation bee, and at it
Gathering honey is nearby carried out, other nectar sources are found, it is the same with the gathering honey bee in the 3.3) step, if its income Du Genggao, observes bee and turn
It is changed to gathering honey bee, replaces green molasses source position.
3.5) it is more than to limit number Limit that if gathering honey bee, observation bee, which search number (nectar source stop), still do not find more
The nectar source of high fitness, then abandon the nectar source, while the role of honeybee is converted into search bee by gathering honey bee or observation bee, and with
Machine generates a new nectar source.
3.6) the optimal nectar source (i.e. globally optimal solution) that current all honeybees are found is recorded, and is adjusted to the 3.2) step, until
Meet the condition of maximum number of iterations maxCycle or exports global optimum position when being less than optimization error.Above-mentioned parameter optimization side
The available optimized parameter estimated result of method.
It is as described above, the present invention be arranged population size be 50, setting limits number be 5, be arranged the number of iterations be 50.It is logical
Iterative calculation is crossed close to optimal result, at this time punishment parameter C=0.6011 and insensitive loss function of ε=0.0112,
σY root-mean-square error is minimum=0.0439.The method for recycling supporting vector linear regression solves above formula linear equation y=a+bx slope and cuts
Away from estimated value, wherein a=-mln η, b=m, after calculating Fitting effect is as shown in Figure 4 after artificial bee colony algorithm optimization.
Artificial bee colony algorithm optimization front and back comparison is as shown in table 2.
Table 2
By comparison, it was found that artificial bee colony algorithm optimization support vector regression parameter improves the accuracy of estimation, thus
It can be seen that being estimated based on the method that Weibull distribution, support vector machines combine in raising aeroengine control system bathtub curve
Count the validity of precision aspect.
As shown in figure 5, finally obtaining certain type aero-engine anti-asthma control system Weibull distribution mould by above-mentioned analysis
Type, failure rate function λ (t)=0.00065062t0.3610。
Claims (4)
1. one kind is used for aero-engine anti-asthma control system bathtub curve estimation method, which is characterized in that including following mistake
Journey:
Step 1: to estimate bathtub curve, multi-aircraft engine anti-asthma control system Complete Sample fault data is collected；It is false
If aero-engine anti-asthma control system fault data obeys Weibull distribution, the event of two parameters of Weibull probability density functions
Barrier rate function isM > 0 is form parameter, and η > 0 is scale parameter；
Step 2: based on support vector regression estimate Weibull distribution model parameter in the step 1 form parameter m and
Scale parameter η:
Weibull model parameter is estimated with support vector machines, and by a Nonlinear Mapping Φ, the data x of the input space is reflected
It is mapped in high-dimensional feature space F, and carries out linear regression in this space；
Given sample data { xi,yi, i=1,2 ..., l, wherein xi∈Rm,yi∈ R, wherein yiFor desired value, l is data point
Sum；Support vector machines solves regression problem by introducing loss function, using following formula come estimation function:
Y=f (x)=<ω Φ (x)>+b, Φ: Rm→G,ω∈G。
Extreme value is taken to optimization aim:
In formula, C is penalty factor, realizes the compromise in empiric risk and fiducial range；ξiWithFor the relaxation factor of introducing；ε is
Loss function；
Step 3: optimize punishment parameter C and the loss of the support vector regression in the step 2 based on artificial bee colony algorithm
Function of ε is finally completed the estimation of aero-engine anti-asthma control system bathtub curve.
2. as described in claim 1 a kind of for aero-engine anti-asthma control system bathtub curve estimation method, feature
It is, in the step 1, it is assumed that fault data obeys two parameters of Weibull, carries out Weibull linear transformation, completes to prestige
The linearisation of Boolean Model, wherein accumulated invalid probability F (ti) can use Median rank estimation provide, One group of ordered series of numbers (t available in this way1,F(t1)),(ti,F(ti)),…,(tn,F(tn)), above formula is transformed to
(x1,y1),(x2,y2),…,(xn,yn)。
3. as described in claim 1 a kind of for aero-engine anti-asthma control system bathtub curve estimation method, feature
It is, in the step 2, loss function can indicate decision function with sparse data point, introduce loss function ε, be defined asThe Lagrange multiplier α of introducingiWithConvex optimization problem is reduced to
It maximizes secondary By the Lagrange multiplier α only not equal to 0iWithWith
It is predicted and is returned, regression function is expressed asWherein,
The problem of solution quadratic programming can be regarded as, finds weight ω and deviates the optimal value of b for given training sample,
Meet Karush-Tucker (KKT) condition, thus regression function isK(xi,x)
It is kernel function；
Selection uses gaussian radial basis functionσ is the parameter of kernel function.
4. it is as described in claim 1 a kind of for aero-engine anti-asthma control system bathtub curve estimation method, it is special
Sign is, in the step 3, the basic step that artificial bee colony algorithm is realized is as follows:
3.1) initialize honeybee populations: initial time, all honeybees do not have any priori knowledge, and role is search bee；Entirely
Office's random search nectar source, and nectar source nectar amount, i.e. " the income degree " in nectar source are obtained according to nectar source situation；
Parameter and population has following three:
1. honeybee sum N, defining gathering honey bee and observation bee is respectively N/2；
2. maximum number of iterations maxCycle, all once global search and a local search in each iteration；
3. nectar source stops maximum limitation searching times Limit, local search Limit times, nectar source does not update, then gathering honey bee, observation
Bee is converted into search bee；
3.2) according to the relative size in the 3.1) nectar source " income degree " of all honeybees of step, honeybee is converted into gathering honey bee and observation bee
Two kinds, income degree ranking it is relatively forward become gathering honey bee, income degree ranking relatively rearward become observation bee；Observation bee is being waved
Area's waiting is stepped, how much knows nectar source nectar amount according to information such as the swings of gathering honey bee, the sight that the higher nectar source of nectar amount is recruited
It is more to examine bee；
3.3) for every gathering honey bee, continue the gathering honey near green molasses source, find other new nectar sources, and calculate its fitness value,
If its income degree is high, honeybee replaces green molasses source by hating to leave criterion, with new nectar source；
3.4) one nectar source is selected according to the probability proportional to nectar source fitness value for every observation bee, and in its vicinity
Gathering honey is carried out, other nectar sources are found, it is the same with the gathering honey bee in the 3.3) step, if its income Du Genggao, observes bee and be converted to
Gathering honey bee replaces green molasses source position；
3.5) it is more than to limit number Limit that if gathering honey bee, observation bee, which search number, the honey of higher fitness is not still found
The nectar source is then abandoned in source, while the role of honeybee is converted into search bee by gathering honey bee or observation bee, and is randomly generated one newly
Nectar source；
3.6) the optimal nectar source that current all honeybees are found is recorded, and is adjusted to the 3.2) step, until meeting maximum number of iterations
The condition of maxCycle or be less than optimization error when export global optimum position to get arrive optimized parameter estimated result.
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| CN110503632A (en) * | 2019-07-26 | 2019-11-26 | 南昌大学 | SVR parameter optimization method in a kind of blind image quality evaluation algorithm |
| CN111459094A (en) * | 2020-03-09 | 2020-07-28 | 西南交通大学 | Regional selection method for temperature sensitive point combination in machine tool spindle thermal error modeling |
| CN111914891A (en) * | 2020-06-23 | 2020-11-10 | 国网天津市电力公司电力科学研究院 | Fault data-based electric energy meter service life prediction method |
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