CN109101769A - Leaf end timing sensor number determination method based on compressed sensing - Google Patents
Leaf end timing sensor number determination method based on compressed sensing Download PDFInfo
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Abstract
The application discloses a method for determining the number of leaf end timing sensors based on compressed sensing, which comprises the following steps: step 10, calculating a time difference sequence of the blade passing through a blade end timing sensor, and constructing a blade end timing vibration measurement equivalent model according to the time difference sequence; step 20, constructing a compressed sensing model according to the leaf end timing vibration measurement equivalent model; and step 30, calculating the optimal solution of the leaf end timing sensor number according with the compressed sensing model according to the preset sensor number. Through the technical scheme in this application, improved the accuracy of confirming tip timing sensor quantity, be favorable to improving blade vibration real-time detection's reliability, reduced because of the blade vibration leads to the possibility of rotating vane trouble.
Description
Technical field
This application involves the technical fields of blade vibration non-contact detecting, are based on compressed sensing in particular to one kind
Tip-timing sensor number determine method.
Background technique
Rotating vane is the key that dynamic component in aero-engine, and rotating vane is under extreme Service Environment in operational process
Often transformation operating condition, rotating vane is easy to produce vibration, and then induces rotating vane failure.Apparatus for rotating vane vibration is carried out online
Precise measurement can effectively grasp the Vibration Condition of blade, so that providing for engine blade safety monitoring and fault diagnosis can
By foundation, for guaranteeing that the safe and stable operation of rotating machinery, prevention significant trouble are of great significance.
Contactless tip-timing measurement passes through the one group of Tip-Timing sensing being along the circumferential direction mounted on casing and passes
Sensor records time of the blade by sensor.When blade there is no vibration when, reach sensor fiducial time only with
Revolving speed, blade radius and sensing installation angle are related；And when blade vibrates, reach the real time meeting of sensor
In advance or this fiducial time is lagged behind, generates a time difference.Carrying out processing to the time difference signal sequence can be obtained by
The vibration displacement sequence of rotating vane end of blade, so as to extract every vibration characteristics of blade.
And in actual condition, due to the restriction of the factors such as aero-engine space structure and service requirement, blade tip-timing is passed
Sensor number is generally less, and sample frequency is generally significantly less than the intrinsic frequency of high speed blade, causes measuring signal to belong to and owes to adopt
Sample signal.It is that apparatus for rotating vane vibration blade tip-timing is surveyed that multifrequency vibratory response is obtained by the lack sampling data of Tip-Timing Measurement
The key problem of amount.Therefore, apparatus for rotating vane vibration measurement problem is often closely bound up with Tip-Timing Measurement number of sensors.
And in the prior art, usually assume that blade vibration response is that single-frequency responds, and must accurately obtain blade vibration
Under the premise of prior information, the quantity of Tip-Timing Measurement sensor can be determined.But actual vibration measurement process
In high speed rotational blade vibratory response be closely related with blade state itself and its working condition, on the one hand, due to pivoting leaf
Piece running environment is complicated, causes the factor of blade vibration there are diversity, and single-frequency responds the reality that can not reflect blade vibration
Border situation, leading to the mathematical model of determining Tip-Timing Measurement number of sensors, there are inevitable errors, and then influence passes
The accuracy that sensor quantity determines.On the other hand, rotating vane usually can not accurately be obtained in different shapes during vibration measurement
Vibration prior information under state and running environment.
Summary of the invention
The purpose of the application is at least to solve in the prior art or one of technical problem present in the relevant technologies, to improve
The accuracy of determining tip-timing sensor quantity is conducive to the reliability for improving blade vibration real-time detection, reduce because
Blade vibration leads to a possibility that rotating vane failure.
The technical solution of the application is: providing a kind of compressed sensing based tip-timing sensor number determination side
Method, this method comprises: step 10, calculates the time difference sequence that blade passes through tip-timing sensor, according to time difference sequence, structure
Build blade tip-timing vibration measurement equivalent model；Step 20, according to blade tip-timing vibration measurement equivalent model, compressed sensing mould is constructed
Type；Step 30, according to default number of sensors, the tip-timing sensor quantity optimal solution for meeting compressed sensing model is calculated,
Wherein, in step 30, it specifically includes:
Step 31, the order of the matrix equation of end of blade timing sampling signal spectrum in compressed sensing model is calculated；
Step 32, it according to the relevant sensing matrix of tip-timing sensor quantity in compressed sensing model and position, calculates
Cross-correlation coefficient；
Step 33, according to sum of ranks cross-correlation coefficient, meeting the maximum of default number of sensors just according to preset formula calculating
Integer is denoted as tip-timing sensor quantity optimal solution, wherein default calculation formula are as follows:
In formula, | | Xl(f)||0For multifrequency blade vibration signal spectrum vector Xl(f) number of the non-zero row vector in, W are
Cross-correlation coefficient, Rank (Y (f)) are the order of matrix equation Y (f),Indicate the maximum positive integer smaller than b, giRepresenting matrix Φ
I-th column, gjThe jth of representing matrix Φ arranges.
In any of the above-described technical solution, further, in step 10, specifically includes: step 11, being reached according to blade
The theoretical arrival time of tip-timing sensor and actual time of arrival calculate time difference sequence；Step 12, according to time difference sequence
Column and lack sampling principle construct blade tip-timing vibration measurement equivalent model.
In any of the above-described technical solution, further, in step 20, specifically include: step 21, according to blade tip-timing
Vibration measurement equivalent model calculates corresponding matrix equation；Step 22, it is shown in a frequency domain according to blade vibration signal dilute
Characteristic is dredged, calculating matrix non trivial solution is denoted as compressed sensing model.
The beneficial effect of the application is: by constructing compressed sensing model, determining the quantity of tip-timing sensor, improves
The accuracy and reliability of determining tip-timing sensor quantity improves identification and reconstruct multifrequency end of blade combination of vibrations signal
Frequency accuracy, be conducive to improve blade vibration real-time detection measurement accuracy, reduce because blade vibration causes to rotate
A possibility that blade fault.
Detailed description of the invention
The advantages of above-mentioned and/or additional aspect of the application, will become bright in combining description of the following accompanying drawings to embodiment
It shows and is readily appreciated that, in which:
Fig. 1 is to determine method according to the compressed sensing based tip-timing sensor number of one embodiment of the application
Schematic flow diagram；
Fig. 2 is the tip-timing sensor schematic view of the mounting position according to one embodiment of the application.
Specific embodiment
It is with reference to the accompanying drawing and specific real in order to be more clearly understood that the above objects, features, and advantages of the application
Mode is applied the application is further described in detail.It should be noted that in the absence of conflict, the implementation of the application
Feature in example and embodiment can be combined with each other.
In the following description, many details are elaborated in order to fully understand the application, still, the application may be used also
To be implemented using other than the one described here other modes, therefore, the protection scope of the application is not by described below
Specific embodiment limitation.
Presently filed embodiment is illustrated hereinafter with reference to Fig. 1-2.
As shown in Figure 1, compressed sensing based tip-timing sensor number determines that method includes the following steps:
Step 10, the time difference sequence that blade passes through tip-timing sensor is calculated, according to time difference sequence construct end of blade
Timing vibration measures equivalent model；
In the step 10, specifically include:
Step 11, the theoretical arrival time and actual time of arrival that tip-timing sensor is reached according to blade, when calculating
Between difference sequence；
Specifically, it as shown in Fig. 2, I tip-timing sensor 22 is installed on the surrounding of machine circle 21, is equipped in rotor leaf dish
M rotating vane 23, the vibration displacement d (t) of each rotating vane can be measured by I tip-timing sensor 22,
Setting refers to tip-timing sensor r0The surface of installation and shaft middle line, and a reflective position is set in shaft, with
Just a rotary speed reference signal is obtained in each swing circle, wherein tip-timing sensor 22 is circumferentially relative to reference
Sensor r0Angle be αi, i=1,2 ..., I, the relative angle of blade in rotational direction is θkK=1,2 ..., M, time
Difference sequenceCorresponding calculation formula are as follows:
In formula, R is vane pivot radius, and n is the rotating cycle of blade, frFor the constant speed of blade,It is
K blade passes through the actual time of arrival of i-th of tip-timing sensor in the n-th circle,Sample bits are vibrated for end of blade
It moves,Pass through the theoretical arrival time of i-th of tip-timing sensor in the n-th circle for k-th of blade.
Step 12, according to time difference sequence and lack sampling principle, blade tip-timing vibration measurement equivalent model is constructed.
Specifically, according to time difference sequence, end of blade vibration sample shift is obtainedCalculation formula, corresponding calculating
Formula are as follows:
Since blade tip-timing vibration measuring signal is typical undersampled signal, sets L and put as machine circle is circumferentially distributed
The quantity of tip-timing sensor position 24 is set, I is the number of tip-timing sensor 22, and C indicates I tip-timing sensor
22 layout on casing 21.I position installation blade tip-timing is chosen in L mountable tip-timing sensor positions 24 to pass
Sensor 22, therefore, the road I sample sequence C={ ci: 1≤i≤I }, wherein 1≤c1< c2... < cI≤ L, ciIt is fixed for i-th of end of blade
When sensor position, so the sampling of practical blade tip-timing may be defined as (L, I, C) sampling configuration, for example, mountable end of blade is fixed
When sensor position quantity L=20, the number of sensors I of actual installation is 4, selected position C=1,5,11,
17 }, i.e., tip-timing sensor is placed at the 1st, the 5th, the 11st and the 17th 4 position.Therefore, actual sampling sequence number is n
× L+C, i.e., as n=0, the sampling sequence number of first lap is C(0)={ 1,5,11,17 }, as n=1, the sampling sequence number of the second circle
For C(1)={ 1+20,5+20,11+20,17+20 }, that is to say, that the sampling of tip-timing sensor can be equivalent to adopts from the road L
The resampling on the road I is carried out in sample data.
Therefore, k-th of blade passes through the theoretical arrival time of i-th of tip-timing sensor in the n-th circleAnd the setting angle of tip-timing sensor i is αi, therefore, k-th of blade passes through in the n-th circle
The theoretical arrival time of i-th of tip-timing sensor are as follows:
The vibration signal of blade k is set as x (t), obtains blade tip-timing vibration measurement equivalent model yi(n), corresponding meter
Calculate formula are as follows:
In formula, i=1,2 ..., I, n ∈ Z, δ are dirichlet functions.
Step 20, according to blade tip-timing vibration measurement equivalent model, compressed sensing model is constructed；
In the step 20, specifically include:
Step 21, according to blade tip-timing vibration measurement equivalent model, corresponding matrix equation is calculated；
Specifically, compressed sensing model is set as P0, to blade tip-timing vibration measurement equivalent model yi(n) Fourier is carried out
Transformation, corresponding calculation formula are as follows:
In formula, fRFor fundamental frequency section [- fr/ 2, fr/ 2], the frequency separation of blade vibration signal spectrum X (f) is [- fmin,
fmax], and according to tip-timing sensor position L can be placed, the entire frequency separation of X (f) is averaged and is divided into L son frequency
Band, the frequency bandwidth of sub-band are fr, the definition of first of sub-band is Xl(f)=X (fR+(l-(L+1)/2)fr), l=1,
2 ..., L.
According to compressed sensing basic theory, by the blade tip-timing vibration measurement equivalent model Y after Fourier transformi(f), turn
It is changed to matrix equation, corresponding matrix equation Y (f) are as follows:
Y (f)=Φ Xl(f),
In formula, Y (f)=[Y1(f), Y2(f) ..., YI(f)]T, Y (f) is the matrix side of blade tip-timing sampled signal frequency spectrum
Journey,Xl(f) be multifrequency blade vibration signal spectrum vector, Φ be with
The relevant sensing matrix of tip-timing sensor quantity and position, corresponding formula are as follows:
Step 22, the sparse characteristic shown in a frequency domain according to blade vibration signal, calculating matrix non trivial solution, is denoted as
Compressed sensing model；
Specifically, according to sparse characteristic, signal spectrum X (f) just has spectrum only in frequency range, is felt according to compression
Know theory, the solution X of calculating matrix equation Y (f)l(f)。
According to the basic theories and formula of compressed sensing, the specific observation expression formula of compressive sensing theory is y=Θ x=Θ
Ψ θ=Φ θ, signal accuracy, which restores problem, can be expressed as l0Norm minimum problem,Wherein, Θ
For observing matrix, Ψ is the rarefaction representation matrix of signal, and θ is sparse vector of the original signal x in sparse transform-domain, and Φ is to pass
Feel matrix.Xl(f) be matrix equation Y (f) most sparse solution, the minimum model that solution matrix equation Y (f) can be expressed as
Number l0Vibration measurement process based on blade tip-timing is converted to the sparse Solve problems of compressed sensing model P0 by problem, compression
The corresponding calculation formula of sensor model P0 are as follows:
Step 30, according to default number of sensors, calculating meets the tip-timing sensor quantity of compressed sensing model most
Excellent solution,
Wherein, in step 30, it specifically includes:
Step 31, the order of the matrix equation of end of blade timing sampling signal spectrum in compressed sensing model is calculated；
Step 32, it according to the relevant sensing matrix of tip-timing sensor quantity in compressed sensing model and position, calculates
Cross-correlation coefficient；
Step 33, according to the sum of ranks cross-correlation coefficient of matrix equation, meet default sensor number according to preset formula calculating
The maximum positive integer of amount is denoted as tip-timing sensor quantity optimal solution, wherein default calculation formula are as follows:
In formula, | | Xl(f)||0For multifrequency blade vibration signal spectrum vector Xl(f) number of the non-zero row vector in, W are
Cross-correlation coefficient, Rank (Y (f)) are the order of matrix equation Y (f),Indicate the maximum positive integer smaller than b, giRepresenting matrix Φ
I-th column, gjThe jth of representing matrix Φ arranges.
Specifically, it is assumed that multifrequency blade vibration signal spectrum vector Xl(f) be compressed sensing model P0 solution, work as Xl(f) full
Foot | | Xl(f)||0When < spark (Φ)/2, then Xl(f) be compressed sensing model P0 most sparse solution, wherein | | Xl(f)||0For
Multifrequency blade vibration signal spectrum vector Xl(f) number of the non-zero row vector in, i.e. the frequency-domain sparse degree of blade vibration signal,
Linear relevant minimum column vector number in spark (Φ) representing matrix Φ.
Xl(f) non-zero row only a small number of in, extracts Xl(f) the non-zero row in, is denoted as supported collection IM, multifrequency blade is shaken
Dynamic spectral matrix Xl(f) supported collection IMGesture be denoted as p, that is to say, that as supported collection IMGesture p be less than spark (Φ)/2 when,
The most sparse solution of compressed sensing model P0 can then be found out.
Further, according to the property Rank (Y (f))≤1 of rank of matrix, therefore, if XlIt (f) is compressed sensing mould
Unique sparse solution of type P0, then meet:
In view of being difficult to determination when spark (Φ), therefore, spark (Φ) is replaced to be counted by cross-correlation coefficient W
It calculates.The calculation formula of cross-correlation coefficient W are as follows:
In formula, Φ is sensing matrix, giThe i-th column of representing matrix Φ, gjThe jth of representing matrix Φ arranges.
Therefore, it in conjunction with default number of sensors, can use preset formula, show that tip-timing sensor quantity is optimal
Solution, the i.e. number of tip-timing sensor, preset formula are as follows:
In formula, operationExpression takes the maximum positive integer smaller than b.
In the present embodiment, the Parameter Conditions of blade vibration signal x (t): maximum frequency f are setmax=790Hz, blade turn
Speed is 5000r/min, and sensor position is installed in Tip-Timing Measurement and meets Lfr≥2fmax, mountable blade tip-timing sensing
The quantity L=19 of device position can be calculated under multiple-frequency signal vibration blade difference degree of rarefication, blade tip-timing by the above method
Tip-timing sensor number required for measuring, as shown in table 1.
Table 1
From table 1 it follows that setting end of blade when the spectrum sparse degree value for choosing multifrequency blade vibration signal is 6
Time Pick-off Units number is 9, be may be implemented to apparatus for rotating vane vibration blade tip-timing precise measurement.
The technical solution for having been described in detail above with reference to the accompanying drawings the application, present applicant proposes a kind of compressed sensing based
Tip-timing sensor number determines method, this method comprises: step 10, calculates time of the blade by tip-timing sensor
Difference sequence constructs blade tip-timing vibration measurement equivalent model according to time difference sequence；Step 20, it is vibrated and is surveyed according to blade tip-timing
Equivalent model is measured, compressed sensing model is constructed；Step 30, according to default number of sensors, calculating meets compressed sensing model
Tip-timing sensor quantity optimal solution.The accuracy for improving determining tip-timing sensor quantity is conducive to improve blade
The reliability for vibrating real-time detection, reduces a possibility that leading to rotating vane failure because of blade vibration.
Step in the application can be sequentially adjusted, combined, and deleted according to actual needs.
Unit in the application device can be combined, divided and deleted according to actual needs.
Although disclosing the application in detail with reference to attached drawing, it will be appreciated that, these descriptions are only exemplary, not
For limiting the application of the application.The protection scope of the application may include not departing from this Shen by appended claims
It please be in the case where protection scope and spirit for various modifications, remodeling and equivalent scheme made by inventing.
Claims (3)
1. a kind of compressed sensing based tip-timing sensor number determines method, which is characterized in that this method comprises:
Step 10, the time difference sequence that blade passes through tip-timing sensor is calculated, according to the time difference sequence, building
Blade tip-timing vibration measurement equivalent model；
Step 20, according to the blade tip-timing vibration measurement equivalent model, compressed sensing model is constructed；
Step 30, according to default number of sensors, calculating meets the tip-timing sensor quantity of the compressed sensing model most
Excellent solution,
Wherein, in step 30, it specifically includes:
Step 31, the order of the matrix equation of end of blade timing sampling signal spectrum in the compressed sensing model is calculated；
Step 32, it according to the relevant sensing matrix of tip-timing sensor quantity and position in the compressed sensing model, calculates
Cross-correlation coefficient；
Step 33, the cross-correlation coefficient according to the sum of ranks, according to preset formula, calculating meets the default number of sensors
Maximum positive integer, be denoted as the tip-timing sensor quantity optimal solution, wherein default calculation formula are as follows:
In formula, ‖ Xl(f)‖0For multifrequency blade vibration signal spectrum vector Xl(f) number of the non-zero row vector in, W are described mutual
Related coefficient, Rank (Y (f)) are the order of the matrix equation Y (f),Indicate the maximum positive integer smaller than b, giIt indicates
The i-th column of matrix Φ, gjThe jth of representing matrix Φ arranges.
2. compressed sensing based tip-timing sensor number as described in claim 1 determines method, which is characterized in that its
It is characterized in that, in step 10, specifically includes:
Step 11, the theoretical arrival time and actual time of arrival of the tip-timing sensor are reached according to the blade, are counted
Evaluation time difference sequence；
Step 12, according to the time difference sequence and lack sampling principle, the blade tip-timing vibration measurement equivalent model is constructed.
3. compressed sensing based tip-timing sensor number as described in claim 1 determines method, which is characterized in that
In step 20, specifically include:
Step 21, according to the blade tip-timing vibration measurement equivalent model, corresponding matrix equation is calculated；
Step 22, the sparse characteristic shown in a frequency domain according to blade vibration signal calculates the solution of the matrix equation, is denoted as
The compressed sensing model.
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| CN109870282A (en) * | 2019-03-26 | 2019-06-11 | 西安交通大学 | Compressed sensing based blade vibration feature identification method and system |
| CN109883380A (en) * | 2019-03-22 | 2019-06-14 | 西安交通大学 | A kind of rotor blade displacement field measurement method and its system based on blade tip-timing |
| CN109883379A (en) * | 2019-03-22 | 2019-06-14 | 西安交通大学 | Blade displacement strain measurement method based on Mode Shape |
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| CN110896308A (en) * | 2019-10-31 | 2020-03-20 | 中国工程物理研究院电子工程研究所 | Single tone signal reconstruction method |
| CN111353129A (en) * | 2020-02-10 | 2020-06-30 | 西安交通大学 | Leaf-end timing data storage matrixing processing method |
| CN112362275A (en) * | 2020-10-27 | 2021-02-12 | 湖南工业大学 | Method and device for reducing timing measurement deviation of blade vibration blade end under variable rotating speed |
| CN113340244A (en) * | 2021-03-04 | 2021-09-03 | 北京化工大学 | Non-contact type turbine machinery blade vibration displacement monitoring method and device |
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| CN109883389A (en) * | 2019-03-22 | 2019-06-14 | 西安交通大学 | A kind of rotating vane dynamic strain field measurement method and its system |
| CN109870282A (en) * | 2019-03-26 | 2019-06-11 | 西安交通大学 | Compressed sensing based blade vibration feature identification method and system |
| CN110896308A (en) * | 2019-10-31 | 2020-03-20 | 中国工程物理研究院电子工程研究所 | Single tone signal reconstruction method |
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| CN111353129B (en) * | 2020-02-10 | 2021-12-28 | 西安交通大学 | Leaf-end timing data storage matrixing processing method |
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| CN112362275B (en) * | 2020-10-27 | 2021-08-13 | 湖南工业大学 | Method and device for reducing timing measurement deviation of blade vibration blade end under variable rotating speed |
| CN113340244A (en) * | 2021-03-04 | 2021-09-03 | 北京化工大学 | Non-contact type turbine machinery blade vibration displacement monitoring method and device |
| CN113340244B (en) * | 2021-03-04 | 2023-06-13 | 北京化工大学 | Non-contact turbine mechanical blade vibration displacement monitoring method and device |
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