CN113094950A - Rotor blade damage quantitative identification method based on group sparsity - Google Patents

Rotor blade damage quantitative identification method based on group sparsity Download PDF

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CN113094950A
CN113094950A CN202110358606.2A CN202110358606A CN113094950A CN 113094950 A CN113094950 A CN 113094950A CN 202110358606 A CN202110358606 A CN 202110358606A CN 113094950 A CN113094950 A CN 113094950A
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乔百杰
周凯
朱昱达
曹宏瑞
杨志勃
陈雪峰
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Xian Jiaotong University
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Abstract

The invention discloses a rotor blade damage quantitative identification method based on group sparsity, which comprises the following steps: establishing a three-dimensional model of a single blade, calculating the modal natural frequency of each order of the blade at different rotating speeds through finite element software, taking the difference value of the vibration frequency of the rotor blade measured by a sensor and the modal natural frequency of each order calculated by a finite element model as a target function, taking the material parameters and the geometric parameters of the finite element model as design variables, constructing a finite element model correction equation, and solving by using an evolutionary algorithm to obtain a corrected finite element reference model. Constructing a model update sensitivity matrix to reflect the influence of the change of the unit stiffness matrix on the natural frequency of the rotor blade; the sensitivity matrix is updated based on the model,establishing a finite element model real-time updating equation in a service state; based on the real-time update equation, establishing a base l1，2A group sparse optimization model of the mixed norm; and obtaining the sparse solution of the damage parameters to be identified by a convex optimization method, and judging whether the rotor blade is damaged or not.

Description

Rotor blade damage quantitative identification method based on group sparsity
Technical Field
The invention belongs to the field of mechanical fault diagnosis, and relates to a rotor blade damage quantitative identification method based on group sparsity.
Background
Rotor blades are important components in aircraft engines. The blade is easy to vibrate under severe working conditions of high temperature, high pressure, high rotating speed and the like when the aircraft engine works, and further high-cycle fatigue of the blade is caused, so that the blade is damaged by cracks and the like. Damage to the blade of an aircraft engine often results in changes in some vibration parameters of the blade, such as vibration frequency, amplitude, etc. In the operation process of the blade, the vibration parameter of the blade is accurately monitored, the damage position of the blade is positioned, and the evaluation of the damage condition of the blade plays an important role in reducing the operation and maintenance cost of an engine and guaranteeing the operation safety of an aeroengine.
The high fidelity simulation model is the core of the rotor blade health monitoring implementation. Establishing a multi-physical-field rotor blade simulation model integrating centrifugal load, pneumatic load and temperature load, taking the simulation model as a reference model of an initial state, taking elastic modulus, density and geometric parameters as global correction variables, and researching a rotor blade finite element reference model correction method; on the basis, a model updating strategy based on parameter sensitivity is researched, a model frequency related to updating sensitivity matrix at different rotating speeds is constructed by taking a unit stiffness damage factor as an updating variable, an underdetermined control equation for model updating at an operating state is established, the coefficient characteristic of local damage space distribution is fully utilized, and a model updating strategy based on l is established1，2And updating a group sparse optimization objective function of the model of the finite element model with the mixed norm in real time, updating a stiffness matrix of a potential damage unit, and truly depicting the running state of the rotor blade to realize quantitative identification of the fatigue crack in the service period of the rotor blade.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a rotor blade damage quantitative identification method based on group sparsity, and provides a method based on l through excavating group sparsity characteristics of damage rigidity factors1，2The group sparse optimization method of the mixed norm can obtain the group sparse solution with physical significance of an underdetermined system, and realize real-time update and damage identification of a finite element model of the rotor blade.
The purpose of the invention is realized by the following technical scheme:
a rotor blade damage quantitative identification method based on group sparsity comprises the following steps:
in the first step (S1): establishing a three-dimensional model of a single rotor blade, calculating modal natural frequencies of various orders of the blade at different rotating speeds through finite element software, taking the difference value of the vibration frequency of the rotor blade measured by a sensor and the modal natural frequencies of various orders calculated by a finite element model as a target function, taking the material parameters and the geometric parameters of the finite element model as design variables, constructing a finite element model correction equation, and solving by using an evolutionary algorithm to obtain a corrected finite element reference model;
in the second step (S2): constructing a model update sensitivity matrix to reflect the influence of the change of the unit stiffness matrix on the natural frequency of the rotor blade;
in the third step (S3): establishing a finite element model real-time updating equation under the service state based on the model updating sensitivity matrix;
in the fourth step (S4): based on the real-time updating equation of the model, the method is established based on l1，2A group sparse optimization model of the mixed norm; and obtaining the sparse solution of the damage parameters to be identified by a convex optimization method, and judging whether the rotor blade is damaged or not.
More preferably, it is a mixture of more preferably,
in a first step (S1), a three-dimensional model of the rotor blade is established and a finite element model of the rotor blade is established based on finite element calculationsCalculating the natural frequency f of each order mode of the blade at different rotating speeds through finite elementsFECorrecting the finite element model according to modal information measured in the initial crack-free state of the rotor blade to obtain a finite element reference model, wherein the modal natural frequency f of each orderFEAs an objective function, with the material parameter M ═ E ρ μ of the rotor blade]And the geometric parameter G ═ l w h α]For designing variables, establishing a finite element model correction equation by taking the supremum VHB and the infimum VLB of the material parameters and the geometric parameters as constraint conditions:
Figure BDA0003002800060000021
and E is the elastic modulus of the material, rho is the density, mu is the Poisson ratio, l is the length of the rotor blade, w is the width of the rotor blade, h is the thickness of the rotor blade, and alpha is the attack angle of the rotor blade, and the material parameters and the geometric parameters in the finite element model correction equation are continuously adjusted based on an evolutionary algorithm so as to ensure that the value of the objective function reaches the minimum value, thereby obtaining the finite element reference model.
More preferably, it is a mixture of more preferably,
in the second step (S2), the model update sensitivity matrix is constructed as follows:
Figure BDA0003002800060000031
wherein psijNormalizing the modal shape for the jth order mass of the finite element model,
Figure BDA0003002800060000032
and for the unit stiffness matrix of the ith unit in the finite element reference model, superscript T represents the transposition of a matrix or a vector.
More preferably, it is a mixture of more preferably,
in a third step (S3), a real-time updated model of the rotor blade in service is established based on the model update sensitivity matrix, wherein a parameterized stiffness damage model is established based on the global stiffness matrix and the element stiffness matrix of the finite element reference model:
Figure BDA0003002800060000033
wherein, K (t)s) T-th representing the finite element reference modelsGlobal stiffness matrix, n, corresponding to time of dayeleRepresenting the number of elements in the finite element reference model, i represents the ith element, thetai(ts) Denotes the t-thsThe damage factor of the i-th cell of the rotor blade,
Figure BDA0003002800060000034
a unit stiffness matrix of the ith unit in the finite element reference model;
establishing a model real-time updating equation based on the model updating sensitivity matrix: where Δ f is S θ + e,
Figure BDA0003002800060000035
representing the modal frequency variation before and after damage of the rotor blade; f. ofdAnd fuRespectively representing the actual blade modal frequency measured by the sensor before and after the damage of the rotor blade, S is a sensitivity matrix,
Figure BDA0003002800060000036
is a unit stiffness damage factor vector to be solved, epsilon is a noise vector, nfIs the actual blade modal frequency number, n, measured by the sensoreleIs the number of elements in the finite element reference model.
More preferably, it is a mixture of more preferably,
in a fourth step (S4), the equation is updated in real time based on the model, building a base l1，2Group sparse optimization model of norm:
Figure BDA0003002800060000037
wherein the content of the first and second substances,
Figure BDA0003002800060000038
representing the square of two norms, | ·| non-woven phosphor1，2Denotes the 1, 2 mixed norm, λ denotes the regularization parameter, l of the stiffness impairment factor vector1，2The mixed norm is defined as:
Figure BDA0003002800060000041
wherein the stiffness damage factor vector θ ═ θ1，θ2，...θs]Divided into S sparse groups theta which do not overlap with each otheriSolving the above equation based on l by using convex optimization method1.2Obtaining a uniquely determined unit stiffness damage factor vector by a group sparse optimization model of norm
Figure BDA0003002800060000042
And according to the position of the nonzero element in the theta, the position corresponds to the position of the damaged unit in the three-dimensional model of the rotor blade, and the size of the nonzero element corresponds to the damage severity of the damaged unit.
More preferably, it is a mixture of more preferably,
in a first step (S1), establishing a finite element reference model of the rotor blade, and modifying the model comprises the steps of:
s101, carrying out equal-proportion three-dimensional modeling according to the shape of the rotor blade in actual use to obtain a three-dimensional model of the rotor blade, establishing a finite element model of the rotor blade based on finite element calculation,
s102, determining the highest rotating speed Rm reached in the actual operation process of the rotor blade, calculating the modal natural frequency of each order of the three-dimensional model of the rotor blade at the rotating speed of 0-Rm by utilizing a finite element,
s103, detecting the rotor blade before the rotor blade runs to ensure that no fault exists before the actual blade runs,
s104, mounting sensors in the actual rotor blade casing and the surrounding operating environment, enabling the rotating speed of the rotor blade to run from 0-Rm and then reduce to 0, obtaining data measured by all the sensors,
and S105, after the operation of the rotor blade is finished, checking the blade, and if the actual blade is checked to have a fault after operation, replacing the blade and repeating the steps S103, S104 and S105 until the actual blade does not have the fault after operation.
More preferably, it is a mixture of more preferably,
in step S104, the sensor for measuring the blade vibration parameter is a blade tip timing sensor, and the step of measuring the blade vibration frequency includes the following steps:
s1041, installing the blade end timing sensor on an engine casing, measuring the time when the blade reaches the sensor, and calculating the vibration displacement of the blade end by taking a time signal measured by the rotating speed sensor as a reference standard:
y＝2πfrRtipΔ t, wherein Δ t ═ texpected-tactual，frIs the blade frequency rotation; rtipIs the distance from the rotor axis of rotation to the blade tip; t is texpectedThe time when the blade reaches the sensor under the ideal state; t is tactualIs the time that the tip timing system measures when the blade actually reaches the sensor,
s1042, constructing a compressed sensing reconstruction model according to the measured blade vibration displacement y:
Figure BDA0003002800060000051
the non-undersampled reconstructed signal is obtained as follows: d is a discrete cosine dictionary, alpha is sparse representation of the non-undersampled reconstructed signal Y under the discrete cosine dictionary D, phi is installation position parameters of an observation matrix and a leaf end timing sensor, epsilon is an allowable error,
s1043, calculating actual blade vibration frequency f according to the non-undersampled reconstructed signal Ym：
fmFFT (y), where FFT (·) denotes a discrete fourier transform.
More preferably, it is a mixture of more preferably,
the ideal situation is that the blade does not vibrate.
More preferably, it is a mixture of more preferably,
when theta isiWhen the value is 0, the i-th unit of the rotor blade is not damaged, and when theta is equal toiWhen the value is 1, the ith unit of the rotor blade is completely damaged.
More preferably, it is a mixture of more preferably,
in the third step (S3), the noise vector ∈ includes a modal frequency measurement error and a model numerical calculation error.
Advantageous effects
The method provided by the invention has the advantages that through an optimization algorithm pairCorrecting the finite element model to obtain a finite element reference model corresponding to the physical entity, constructing a model updating sensitivity matrix, establishing a real-time updating model of the rotor blade in the service state, and utilizing the matrix l1，2Compared with the traditional manual detection, the method provided by the invention can realize real-time monitoring of the health condition of the blade and quantitative identification of the damage, reduce the shutdown maintenance time, reduce the maintenance cost and provide guarantee for the flight safety of the aero-engine.
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Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a flow chart of a method for quantitative identification of rotor blade damage based on group sparsity.
The invention is further explained below with reference to the figures and examples.
Detailed Description
A specific embodiment of the present invention will be described in more detail below with reference to fig. 1. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a flowchart of a group sparsity-based quantitative identification method for rotor blade damage, as shown in fig. 1, the group sparsity-based quantitative identification method for rotor blade damage includes the following steps:
in the first step, a three-dimensional finite element model of the rotor blade is established, modal natural frequencies of various orders of the blade at different rotating speeds are calculated through finite elements, and the finite element model is corrected according to modal information measured in the initial crack-free state of the rotor blade;
in the second step, a model is constructed to update a sensitivity matrix;
in the third step, a real-time updating model of the rotor blade in the service state is established;
in a fourth step, the establishment is based on1，2Solving the group sparse optimization model of the mixed norm by using a convex optimization method;
in the method, in the first step, establishing a reference model for health monitoring of the rotor blade, and correcting the model comprises the following steps:
and S101, carrying out equal-proportion three-dimensional modeling according to the shape of the rotor blade in actual use. And scanning the actual blade by using the contact type aspheric surface measuring instrument to obtain a more accurate three-dimensional model of the rotor blade, and establishing a finite element model of the rotor blade in ANSYS.
S102, determining the highest rotating speed Rm which can be reached in the actual operation process of the rotor blade, and calculating the modal natural frequency of each order of the three-dimensional model of the rotor blade at the rotating speed of 0-Rm by using a finite element.
S103, detecting the rotor blade before the rotor blade runs to ensure that no fault exists before the actual blade runs.
S104, mounting sensors in the actual rotor blade casing and the surrounding operating environment, and enabling the rotating speed of the rotor blade to run from 0-Rm in an increasing speed mode and then to be reduced to 0, so that data measured by all the sensors are obtained.
And S105, after the operation of the rotor blade is finished, checking the blade. If the fault is generated after the actual blade is checked to operate, the steps S103, S104 and S105 are repeated until the actual blade does not contain the fault after the actual blade operates.
S106, calculating the natural frequency f of each order of modes of the finite elementFEWith actual blade vibration frequency f measured by the sensormAs an objective function, with the material parameter M ═ E ρ μ of the rotor blade]And the geometric parameter G ═ l w h α]For designing variables, establishing a finite element model correction equation by taking the supremum VHB and the infimum VLB of the material parameters and the geometric parameters as constraint conditions:
Figure BDA0003002800060000071
subjected to VLB≤{M，G}≤VHB
wherein E is the elastic modulus of the material, rho is the density, mu is the Poisson's ratio, l is the blade length, w is the blade width, h is the blade thickness, and alpha is the blade attack angle. And continuously adjusting the material parameters and the geometric parameters in the finite element model correction equation by using an evolutionary algorithm to minimize the value of the target function, thereby obtaining the finite element reference model of the rotor blade.
In the method, in step S104, the sensor for measuring the blade vibration parameter is a blade tip timing sensor, and the step of measuring the blade vibration frequency includes the following steps:
s1041, installing the blade end timing sensor on an engine casing, measuring the time when the blade reaches the sensor, and calculating the vibration displacement of the blade end by taking a time signal measured by the rotating speed sensor as a reference standard:
y＝2πfrRtipΔt
where, t isexpected-tactual，frIs the blade frequency rotation; rtipIs the distance from the rotor axis of rotation to the blade tip; t is texpectedIs the time that the blade reaches the sensor under ideal conditions (i.e., the blade does not vibrate); t is tactualIs the time that the blade actually reaches the sensor as measured by the tip timing system.
S1042, constructing a compressed sensing reconstruction model according to the measured blade vibration displacement y:
Figure BDA0003002800060000081
the non-undersampled reconstructed signal is obtained as follows:
Y＝Dα
d is a discrete cosine dictionary, alpha is sparse representation of the non-undersampled reconstructed signal Y under the discrete cosine dictionary D, phi is correlation of an observation matrix and the installation position of a leaf end timing sensor, and epsilon is an allowable error.
S1043, calculating actual blade vibration frequency f according to the non-undersampled reconstructed signal Ym：
fm＝FFT(Y)
Where FFT (.) represents a discrete fourier transform.
In the method, in the second step, the model update sensitivity matrix is constructed as follows:
Figure BDA0003002800060000082
wherein psijIs the j-th order mass normalized mode shape of the finite element model of the rotor blade,
Figure BDA0003002800060000083
for the unit stiffness matrix of the ith unit in the finite element reference model in step S106, the superscript T represents the transpose of the matrix or vector.
In the method, in the third step, a real-time update model of the rotor blade in the service state is established, which mainly comprises the following steps:
s301, reflecting the damage condition of the blade by using the change of the overall stiffness matrix K in the finite element reference model. Establishing a parameterized stiffness damage model based on the overall stiffness matrix and the unit stiffness matrix of the rotor blade finite element reference model:
Figure BDA0003002800060000091
wherein, K (t)s) Representing the rotor blade finite element model tsGlobal stiffness matrix, n, corresponding to time of dayeleRepresenting the number of elements in the finite element model, i representing the ith element, θi(ts) Denotes the t-thsAt the moment, the damage factor of the ith unit of the rotor blade is thetaiWhen the value is 0, the i-th unit of the rotor blade is not damaged, and when theta is equal toiWhen the number is 1, the ith unit of the rotor blade is completely damaged,
Figure BDA0003002800060000092
the element stiffness matrix of the ith element in the finite element reference model.
S302, establishing a sensitivity matrix-based model real-time updating equation:
Δf＝Sθ+ε
wherein the content of the first and second substances,
Figure BDA0003002800060000093
the modal frequency variation before and after the damage of the rotor blade is represented, and the modal frequency variation can be used for judging whether the rotor blade is damaged or not; f. ofdAnd fuRespectively representing the actual blade modal frequencies measured by the sensor before and after damage to the rotor blade, S being the system of claim 3The sensitivity matrix is used to determine the sensitivity of the sensor,
Figure BDA0003002800060000094
is a unit stiffness damage factor vector to be solved and can represent the unit damage position and degree, a noise vector epsilon comprises a modal frequency measurement error and a model numerical value calculation error, nfIs the actual blade modal frequency number, n, measured by the sensoreleIs the number of elements in the finite element model.
In the fourth step, the establishment is based on l1，2Group sparse optimization model of mixed norm:
Figure BDA0003002800060000095
wherein the content of the first and second substances,
Figure BDA0003002800060000096
representing the square of two norms, | ·| non-woven phosphor1，2Representing a 1, 2 mixed norm and lambda represents a regularization parameter. Solving the above equation based on l by convex optimization method1，2The group sparse optimization model of the mixed norm can obtain the uniquely determined unit stiffness damage factor vector
Figure BDA0003002800060000097
And according to the position of the nonzero element in the theta, the position of the damage unit in the finite element model of the rotor blade can be corresponded, and the size of the nonzero element corresponds to the damage severity of the damage unit.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (10)

1. A quantitative identification method of rotor blade damage based on group sparsity, the method comprising the steps of:
in the first step (S1): establishing a three-dimensional model of a single rotor blade, calculating modal natural frequencies of various orders of the blade at different rotating speeds through finite element software, taking the difference value of the vibration frequency of the rotor blade measured by a sensor and the modal natural frequencies of various orders calculated by a finite element model as a target function, taking the material parameters and the geometric parameters of the finite element model as design variables, constructing a finite element model correction equation, and solving by using an evolutionary algorithm to obtain a corrected finite element reference model;
in the second step (S2): constructing a model update sensitivity matrix to reflect the influence of the change of the unit stiffness matrix on the natural frequency of the rotor blade;
in the third step (S3): establishing a finite element model real-time updating equation under the service state based on the model updating sensitivity matrix;
in the fourth step (S4): based on the real-time updating equation of the model, the method is established based on l1，2A group sparse optimization model of the mixed norm; and obtaining the sparse solution of the damage parameters to be identified by a convex optimization method, and judging whether the rotor blade is damaged or not.
2. The method according to claim 1, wherein, preferably,
in the first step (S1), a three-dimensional model of the rotor blade is established, a finite element model of the rotor blade is established based on finite element calculation, and the modal natural frequency f of each order of the blade at different rotating speeds is calculated through the finite elementFECorrecting the finite element model according to modal information measured in the initial crack-free state of the rotor blade to obtain a finite element reference model, wherein the modal natural frequency f of each orderFEAs an objective function, with the material parameter M ═ E ρ μ of the rotor blade]And the geometric parameter G ═ l w h α]For designing variables, establishing a finite element model correction equation by taking the supremum VHB and the infimum VLB of the material parameters and the geometric parameters as constraint conditions:
Figure FDA0003002800050000011
and E is the elastic modulus of the material, rho is the density, mu is the Poisson ratio, l is the length of the rotor blade, w is the width of the rotor blade, h is the thickness of the rotor blade, and alpha is the attack angle of the rotor blade, and the material parameters and the geometric parameters in the finite element model correction equation are continuously adjusted based on an evolutionary algorithm so as to ensure that the value of the objective function reaches the minimum value, thereby obtaining the finite element reference model.
3. The method of claim 1, wherein,
in the second step (S2), the model update sensitivity matrix is constructed as follows:
Figure FDA0003002800050000021
wherein psijNormalizing the modal shape for the jth order mass of the finite element model,
Figure FDA0003002800050000022
and for the unit stiffness matrix of the ith unit in the finite element reference model, superscript T represents the transposition of a matrix or a vector.
4. The method of claim 1, wherein,
in a third step (S3), a real-time updated model of the rotor blade in service is established based on the model update sensitivity matrix, wherein a parameterized stiffness damage model is established based on the global stiffness matrix and the element stiffness matrix of the finite element reference model:
Figure FDA0003002800050000023
wherein, K (t)s) T-th representing the finite element reference modelsGlobal stiffness matrix, n, corresponding to time of dayeleRepresenting the number of elements in the finite element reference model, i represents the ith element, thetai(ts) Denotes the t-thsTime of day, rotor blade ithThe damage factor of each of the units is,
Figure FDA0003002800050000024
a unit stiffness matrix of the ith unit in the finite element reference model;
establishing a model real-time updating equation based on the model updating sensitivity matrix: where Δ f is S θ + e,
Figure FDA0003002800050000025
representing the modal frequency variation before and after damage of the rotor blade; f. ofdAnd fuRespectively representing the actual blade modal frequency measured by the sensor before and after the damage of the rotor blade, S is a sensitivity matrix,
Figure FDA0003002800050000026
is a unit stiffness damage factor vector to be solved, epsilon is a noise vector, nfIs the actual blade modal frequency number, n, measured by the sensoreleIs the number of elements in the finite element reference model.
5. The method of claim 1, wherein,
in a fourth step (S4), the equation is updated in real time based on the model, building a base l1，2Group sparse optimization model of norm:
Figure FDA0003002800050000027
wherein the content of the first and second substances,
Figure FDA0003002800050000028
representing the square of two norms, | ·| non-woven phosphor1，2Denotes the 1, 2 mixed norm, λ denotes the regularization parameter, l of the stiffness impairment factor vector1，2The mixed norm is defined as:
Figure FDA0003002800050000031
wherein the stiffness damage factor vector θ ═ θ1，θ2，...θs]Is divided intoAre S sparse groups theta which are not coincident with each otheriSolving the above equation based on l by using convex optimization method1，2Obtaining a uniquely determined unit stiffness damage factor vector by a group sparse optimization model of norm
Figure FDA0003002800050000032
And according to the position of the nonzero element in the theta, the position corresponds to the position of the damaged unit in the three-dimensional model of the rotor blade, and the size of the nonzero element corresponds to the damage severity of the damaged unit.
6. The method of claim 2, wherein in the first step (S1), establishing a finite element reference model of the rotor blade, and modifying the model comprises the steps of:
s101, carrying out equal-proportion three-dimensional modeling according to the shape of the rotor blade in actual use to obtain a three-dimensional model of the rotor blade, establishing a finite element model of the rotor blade based on finite element calculation,
s102, determining the highest rotating speed Rm reached in the actual operation process of the rotor blade, calculating the modal natural frequency of each order of the three-dimensional model of the rotor blade at the rotating speed of 0-Rm by utilizing a finite element,
s103, detecting the rotor blade before the rotor blade runs to ensure that no fault exists before the actual blade runs,
s104, mounting sensors in the actual rotor blade casing and the surrounding operating environment, enabling the rotating speed of the rotor blade to run from 0-Rm and then reduce to 0, obtaining data measured by all the sensors,
and S105, after the operation of the rotor blade is finished, checking the blade, and if the actual blade is checked to have a fault after operation, replacing the blade and repeating the steps S103, S104 and S105 until the actual blade does not have the fault after operation.
7. The method of claim 6, wherein in step S104, the sensor for measuring the blade vibration parameter is an end-of-blade timing sensor, and measuring the blade vibration frequency comprises the steps of:
s1041, installing a timing sensor at the leaf endOn an engine casing, measuring the time of a blade reaching a sensor, and calculating the vibration displacement of a blade end by taking a time signal measured by a rotating speed sensor as a reference standard: y 2 pi frRtipΔ t, wherein Δ t ═ texpected-tactual，frIs the blade frequency rotation; rtipIs the distance from the rotor axis of rotation to the blade tip; t is texpectedThe time when the blade reaches the sensor under the ideal state; t is tactualIs the time that the tip timing system measures when the blade actually reaches the sensor,
s1042, constructing a compressed sensing reconstruction model according to the measured blade vibration displacement y: arg min alpha Y1，
Figure FDA0003002800050000041
The non-undersampled reconstructed signal is obtained as follows: d is a discrete cosine dictionary, alpha is sparse representation of the non-undersampled reconstructed signal Y under the discrete cosine dictionary D, phi is installation position parameters of an observation matrix and a leaf end timing sensor, epsilon is an allowable error,
s1043, calculating actual blade vibration frequency f according to the non-undersampled reconstructed signal Ym：
fmFFT (y), where FFT (·) denotes a discrete fourier transform.
8. The method of claim 7, wherein the ideal condition is that the blade does not vibrate.
9. The method of claim 5, wherein θ is measured asiWhen the value is 0, the i-th unit of the rotor blade is not damaged, and when theta is equal toiWhen the value is 1, the ith unit of the rotor blade is completely damaged.
10. The method according to claim 4, wherein in the third step (S3), the noise vector ε contains modal frequency measurement errors and model numerical calculation errors.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113987871A (en) * 2021-10-19 2022-01-28 中国航发沈阳黎明航空发动机有限责任公司 Online recognition method for blade damage of aircraft engine
CN117076992A (en) * 2023-10-16 2023-11-17 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) Structural member damage detection method and system based on signal processing

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10065314A1 (en) * 2000-12-30 2002-07-18 Igus Ingenieurgemeinschaft Umw Method for condition monitoring of wind turbine rotor blades in which sound and vibration sensors are used to generate signals that can be compared with an existing database of signals so that rapid damage assessment can be made
WO2020192621A1 (en) * 2019-03-22 2020-10-01 西安交通大学 Measurement method for rotor blade dynamic strain field based on blade tip timing and system thereof
CN112100874A (en) * 2020-07-24 2020-12-18 西安交通大学 Rotor blade health monitoring method and monitoring system based on digital twinning

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10065314A1 (en) * 2000-12-30 2002-07-18 Igus Ingenieurgemeinschaft Umw Method for condition monitoring of wind turbine rotor blades in which sound and vibration sensors are used to generate signals that can be compared with an existing database of signals so that rapid damage assessment can be made
WO2020192621A1 (en) * 2019-03-22 2020-10-01 西安交通大学 Measurement method for rotor blade dynamic strain field based on blade tip timing and system thereof
CN112100874A (en) * 2020-07-24 2020-12-18 西安交通大学 Rotor blade health monitoring method and monitoring system based on digital twinning

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
邱飞力;张立民;张卫华;: "基于模态柔度矩阵的结构损伤识别", 噪声与振动控制, no. 04 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113987871A (en) * 2021-10-19 2022-01-28 中国航发沈阳黎明航空发动机有限责任公司 Online recognition method for blade damage of aircraft engine
CN113987871B (en) * 2021-10-19 2024-04-16 中国航发沈阳黎明航空发动机有限责任公司 Online identification method for damage of aero-engine blade
CN117076992A (en) * 2023-10-16 2023-11-17 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) Structural member damage detection method and system based on signal processing
CN117076992B (en) * 2023-10-16 2024-01-19 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) Structural member damage detection method and system based on signal processing

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