1. A method of blade natural frequency identification based on a plurality of tip timing sensors, the method comprising the steps of:

in a first step (S1), acquiring actual arrival times of the rotary blades by using a plurality of blade tip timing sensors, respectively, and converting a difference between a theoretical arrival time and the actual arrival time into displacement data of the blade tips according to the rotational speed of the rotary blades and the blade length;

in a second step (S2), numbering a plurality of tip timing sensors, distinguishing displacement data of each blade based on the numbering for separate analysis;

in the third step (S3), the displacement data of the blade ends of two blades with the same blade length and the same rotation speed of i and j are selectedAnd

in a fourth step (S4), the displacement data is interceptedAndafter mean value is removed, point multiplication is carried out to obtain a multiplied product vector M_i，jFor product vector M_i，jObtaining frequency spectrum data SA by discrete Fourier transform_j，j；

In the fifth step (S5), the third step S3 and the fourth step S4 are repeated for the data of the two blades numbered i and j collected by each sensor, and all the obtained spectrum data are obtainedLinear superposition is carried out, a total amplitude-frequency graph is drawn, and mixed and superposed frequency components of the sum of the natural frequencies of the two blades are extracted from the amplitude-frequency graphAnd a difference frequency component f between the natural frequencies of the two blades_i-jWherein, the frequencies corresponding to the two components with the highest amplitude of the amplitude-frequency diagram are considered asAnd f_i-j；

In the sixth step (S6), the natural frequency range of the blade is determined based on the frequency componentsAnd a natural frequency difference frequency component f_i-jReversely deducing the estimated values of the natural frequencies of the blades i and j;

in the seventh step (S7): combining all the blades in pairs to obtainDifferent combinations, repeating the third step S3 and the sixth step S6 for each combination to obtain the natural frequency estimation values of all the blades, wherein the natural frequency of each blade is 2 (n)_b-1) estimated values clustered according to a predetermined frequency error tolerance G to obtain a class of frequency estimates, the class of frequency estimates being averaged to obtain the natural frequency of the blade, where n_bIs the number of blades in the blisk.

2. The method according to claim 1, wherein preferably in the first step (S1), the arrival time t of each blade is collected by using a plurality of blade end timing sensors arranged arbitrarily and is based on the rotation speed n of the blade_rAnd the blade length R converts the difference between the theoretical arrival time and the actual arrival time into blade end displacement, and the expression is as follows:

where Δ t_i，jRepresents the difference between the actual arrival time and the theoretical arrival time of the ith blade in the jth circle, p (t)_i，j) Indicating the ith vane in the jth turn t_i，jThe displacement of the moment of time, wherein,wherein t is_i，jRepresents the actual arrival time, theta, of the ith blade at the jth turn_iIndicating the angle, alpha, of the ith blade with respect to the mounting position of the rotation speed sensor_kThe angle of the kth sensor is shown with reference to the mounting position of the rotation speed sensor, and n is the rotation speed.

3. The method of claim 2, wherein the rotation process of the blade is a predetermined acceleration process, a predetermined deceleration process or a predetermined uniform speed process, and the gas excitation is simulated by using circumferentially uniformly distributed gas nozzle gas injection during the rotation process.

4. A method according to claim 3, wherein for the acceleration or deceleration process, the displacement data recorded by the integral number of revolutions of the tip timing sensor is selected using the same position interval [ N, M |)]Intercepting the data to obtain displacement data of the same length of the two blades with the numbers i and j under the same rotating speedAndsampling frequency f_sApproximately equal to the average rotational speed of the motor,where M-N +1 is the truncated displacement data length,the rotation speed corresponding to the k-th point.

5. The method of claim 1, wherein in the fourth step (S4), the product vector M_i，jComprises the following steps:whereinWhen the displacement data of the ith blade and the jth blade are subjected to combined analysis, an ith blade displacement data vector is intercepted;average value M of the intercepted displacement data of the ith blade when the displacement data of the ith blade and the jth blade are subjected to combined analysis_i，jThe product vector representing the ith and j blade displacements.

6. The method according to claim 1, wherein in a fifth step (S5), the spectral dataIs linearly superposed into

7. The method of claim 1, wherein in a sixth step (S6), the natural frequencies f of the blades i and j_iAnd f_jComprises the following steps: f. of_i-f_j＝f_i-j，|f_i+f_j-Bf_s|＝f_i+j B∈Z，

Blade natural frequency range f_min，f_max]Obtaining:

from the inequality, the value of B can be determined and the sum f of the natural frequencies of the blades i and j can be estimated_i+jThen, the natural frequencies of the blades i and j are calculated as follows:

wherein Z represents a set of integers, f_i-jRepresenting the difference, f, between the natural frequencies of blades i and j_i+jRepresenting the sum of the natural frequencies of blades i and j, B representing an integer to be determined, by means of an inequalityAnd (4) determining.

8. The method according to claim 1, wherein in a seventh step (S7), clustering is performed according to a predetermined frequency error tolerance G to obtain a class of frequency estimates, which are averaged to obtain the natural frequency of the blade.

Background

Blades are used in a wide variety of rotating machinery, such as gas turbines, aircraft engines, and the like. During the use of the equipment, the blades are impacted by airflow for a long time and are subjected to large centrifugal force, when the blades are impacted by foreign objects, the blades are easy to be injured, and the faults can be mild to severe over time, and finally the equipment can be scrapped or even safety accidents can be caused. On-line fault diagnosis of the blade is necessary. On the one hand, blade vibration is one of the important causes for engine failure; on the other hand, blade faults can be reflected through vibration signals, the natural frequency of the blade is easy to measure in modal parameters of the blade, and the natural frequency of the blade is a parameter capable of reflecting the health condition of the blade, so that the natural frequency of the blade is analyzed by a plurality of existing methods to judge whether the blade has faults or not. The Blade end timing (BTT) collects the arrival time of the rotating Blade through a sensor, compares the arrival time with the ideal arrival time, and converts the time difference into a Blade end displacement method to obtain a Blade end vibration signal so as to realize the online diagnosis of the Blade. However, signals of the blade-end timing sensor are serious undersampled signals, and due to the fact that actual installation space is limited, the number and arrangement of the sensors are strictly limited, and many algorithms which are required for the number and arrangement of the sensors cannot be applied to actual equipment.

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 blade natural frequency identification method based on a plurality of blade end timing sensors, and the method can be used for more quickly and accurately identifying the health state of the blade.

The invention aims to realize the following technical scheme, and the blade natural frequency identification method based on a plurality of blade end timing sensors comprises the following steps:

in the first step, a plurality of blade end timing sensors are used for respectively acquiring the actual reaching time of a rotating blade, and the difference between the theoretical reaching time and the actual reaching time is converted into displacement data of a blade end according to the rotating speed of the rotating blade and the length of the blade;

in the second step, a plurality of blade end timing sensors are numbered, and displacement data of each blade are distinguished based on the numbers to be analyzed respectively;

in the third step, the displacement data of the blade ends of two blades with the same rotating speed and the same blade length are selected, wherein the number of the displacement data is i and jAndboth the sensors and the blades need to be numbered, the sensor numbers are only used for convenience of the subsequent description, and for convenience, the sensor numbers are generally given according to clockwise or anticlockwiseThe sequence numbers are given. The definition of the blade numbers is also arbitrary, only for distinguishing different blades, and providing a basis for the following formulation, and for convenience, the blade numbers are generally given in order of clockwise or counterclockwise. The numbering of the blades is such that no corresponding sensors are required.

In the fourth step, the displacement data is interceptedAndafter mean value is removed, point multiplication is carried out to obtain a multiplied product vector M_i，jFor product vector M_i，jObtaining frequency spectrum data SA by discrete Fourier transform_i，j；

In the fifth step, the third step and the fourth step are repeated for the data of the two blades with the numbers i and j collected by each sensor, and all the obtained frequency spectrum data are obtainedLinear superposition is carried out, a total amplitude-frequency graph is drawn, and mixed and superposed frequency components of the sum of the natural frequencies of the two blades are extracted from the amplitude-frequency graphAnd a difference frequency component f between the natural frequencies of the two blades_i-jThe abscissa of the amplitude-frequency diagram is frequency, the amplitude of the ordinate is extracted, and two components with the highest amplitude are extracted from the amplitude-frequency diagram, and the corresponding frequencies are considered asAnd f_i-j。

In the sixth step, according to the natural frequency range of the blade, based on the frequency componentsAnd a natural frequency difference frequency component f_i-jReversely deducing the estimated values of the natural frequencies of the blades i and j;

in the seventh step: combining all the blades in pairs to obtainDifferent combinations, repeating the third step S3 to the sixth step S6 for each combination to obtain the natural frequency estimation values of all the blades, wherein the natural frequency of each blade is 2 (n)_b-1) estimated values clustered according to a predetermined frequency error tolerance G to obtain a class of frequency estimates, the class of frequency estimates being averaged to obtain the natural frequency of the blade, wherein n_bIs the number of blades in the blisk. The method adopted by the clustering mode is essentially K-means clustering, each natural frequency estimated value of the blades is arranged on a digit axis, a first natural frequency value is selected as a clustering center, when the natural frequency estimated value which is not beyond G and is close to the blade is taken as a class, the distance from the clustering center to the nearest point is calculated, if the natural frequency estimated value is not beyond G, the blade is considered as a class, and the clustering center is recalculated, and if the natural frequency estimated value is beyond G, the blade is not considered as a class. And taking each inherent frequency value as a clustering center, respectively clustering, selecting the class with the largest quantity from the clustering results, and selecting the class with the highest aggregation degree in the classes, namely the class with small variance, when the quantity in the classes is the same. And clustering to obtain a result class, namely a frequency estimation class of the blade, and averaging the result class to obtain the natural frequency of the blade.

In the method, in the first step, a plurality of randomly arranged blade end timing sensors are used for receiving the reaching time t of each blade and the reaching time t is determined according to the rotating speed n of the blade_rAnd the blade length R converts the difference between the theoretical arrival time and the actual arrival time into blade end displacement, and the expression is as follows:

where Δ t_i，jRepresents the difference between the actual arrival time and the theoretical arrival time of the ith blade in the jth circle, p (t)_i，j) Indicating the ith vane in the jth turn t_i，jThe displacement of the moment of time, wherein,

wherein t is_i，jRepresents the actual arrival time, theta, of the ith blade at the jth turn_iThe angle of the ith vane is shown with reference to the rotational speed sensor mounting position. Alpha is alpha_kThe angle of the kth sensor is shown with reference to the mounting position of the rotation speed sensor, and n is the rotation speed.

In the method, the rotation process of the blades is a predetermined acceleration process, a predetermined deceleration process or a predetermined uniform speed process, and the rotation process is stimulated by gas injection simulation gas with circumferentially uniformly distributed gas nozzles.

In the method, for the speed increasing or reducing process, the displacement data recorded by integral circles of the timing sensor at the leaf end is selected, and the same position interval [ N, M ] is utilized]Intercepting the data to obtain displacement data of the same length of the two blades with the numbers i and j under the same rotating speedAndsampling frequency f_sApproximately equal to the average rotational speed of the motor,where M-N +1 is the truncated displacement data length,the rotation speed corresponding to the k-th point.

In the method, in the fourth step, the product vector M_i，jComprises the following steps:wherein, thereinFor displacement of the ith and jth vanesWhen the data are subjected to combined analysis, the ith blade displacement data vector is intercepted;and when the ith blade and the jth blade displacement data are subjected to combined analysis, the average value of the ith blade displacement data is intercepted. M_i，jThe product vector representing the ith and j blade displacements.

In the method, in the fifth step, the spectrum dataIs linearly superposed into

In the method, in the sixth step, the natural frequencies f of the blades i and j_iAnd f_jComprises the following steps: f. of_i-f_j＝f_i-j，|f_i+f_j-Bf_s|＝f_i+j B∈Z，

Blade natural frequency range f_min，f_max]Obtaining:

from the inequality, the value of B can be determined and the sum f of the natural frequencies of the blades i and j can be estimated_i+jThen, the natural frequencies of the blades i and j are calculated as follows:

wherein Z represents a set of integers, f_i-jRepresenting the difference, f, between the natural frequencies of blades i and j_i+jRepresenting the sum of the natural frequencies of blades i and j. B represents an integer to be determined and can be represented by an inequalityAnd (4) determining.

In the method, in the seventh step, clustering is carried out according to the preset frequency error tolerance G to obtain a frequency estimation class, and the average value of the frequency estimation class is obtained to obtain the natural frequency of the blade.

The method can extract the inherent frequency difference between different blades from the seriously undersampled data only by randomly arranging the blade end timing sensors, does not need additional signal reconstruction and more blade end timing sensors, has quick and stable operation, is simple and feasible, and can realize the real-time health monitoring of the rotating blades.

The above description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly apparent, and to make the implementation of the content of the description possible for those skilled in the art, and to make the above and other objects, features and advantages of the present invention more obvious, the following description is given by way of example of the specific embodiments of the present invention.

Drawings

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 schematic diagram of a mirror folding based process for identifying the natural frequency of an arbitrarily arranged tip timing sensor blade;

FIG. 2 is a graph of the displacement of blade numbers 1 and 2 taken from sensor 1;

FIG. 3 is a vector M of the product of the displacement of blade No. 1 and blade No. 2 extracted by sensor 1_1，2A time domain graph;

FIG. 4 is a graph of the intercepted displacement of blade numbers 1 and 2 from sensor 2;

FIG. 5 is a vector M of the product of the displacement of blade No. 1 and blade No. 2 extracted by sensor 2_1，2A time domain graph;

FIG. 6 is a graph of the intercepted displacement of blade numbers 1 and 2 from sensor 3;

FIG. 7 is a vector M of the product of the displacement of blade No. 1 and blade No. 2 extracted by sensor 3 and taken out_1，2A time domain graph;

FIG. 8 shows sensor 1 obtaining product vector M_1，2An amplitude-frequency diagram after discrete Fourier transform;

FIG. 9 shows sensor 2 obtaining product vector M_1，2An amplitude-frequency diagram after discrete Fourier transform;

FIG. 10 shows the sensor 3 obtaining the product vector M_1，2An amplitude-frequency diagram after discrete Fourier transform;

FIG. 11 shows the product vector M extracted by 3 sensors_1，2And (4) a total amplitude-frequency graph after the frequency spectrum data are superposed.

The invention is further explained below with reference to the figures and examples.

Detailed Description

Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings fig. 1 to 11. 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.

A method of blade natural frequency identification based on a plurality of tip timing sensors includes,

(1) the arrival time of the rotating blade is obtained by using a blade end timing sensor at any position, and the difference between the theoretical arrival time and the actual arrival time is converted into blade end displacement according to the rotating speed and the length of the blade.

In the present exemplary embodiment, specifically, 3 optical fiber type blade end timing sensors are fixed at random positions on the casing, and the installation angles of the sensors are measured after the fact: 58 degrees, 108 degrees and 158 degrees, and the method designed by the invention patent does not use specific installation angle information, so that no requirement is made on the installation position of the sensor. Setting the initial rotating speed to be 60Hz, the rotating speed acceleration to be 0.5Hz/s, and the rotating speed variation range to be 60Hz-100Hz-60Hz, wherein the time of the 100Hz constant speed section is 20 s. The blade disc adopts a 3-blade integral aluminum alloy blade disc, the radius of the blade disc is 68mm, the thickness d of the blade is 1mm, and the width w of the blade is 20 mm. 4 nozzles are uniformly distributed on a casing, high-pressure gas of 0.5Mpa is sprayed, the reaching time of the rotating blade is obtained by using a timing sensor at the blade end which is randomly arranged, and the difference between the theoretical reaching time and the actual reaching time is converted into blade end displacement according to the rotating speed and the length of the blade.

(2) And separating the displacement data of each blade according to the sensor number, and analyzing the displacement data of each sensor.

The blade end timing system used in the embodiment can directly output the actual reaching time of the blade of each sensor channel, the difference between the actual reaching time and the theoretical reaching time is converted into displacement by using the rotating speed and the blade radius information, and the vibration displacement of all the blade ends measured by each sensor channel is obtained through the process.

(3) By using a data alignment mode, if the displacement data of the blades under the same narrow window is selected to be slow speed-up or slow speed-down data, the length of the intercepted data is not too long, so as to meet the requirement of approximate constant sampling frequency.

In the present exemplary embodiment, specifically, the displacement data of the blade 1 and the blade 2 are selected, both are one-dimensional vectors, the length is 7823, and the range of the serial numbers in the displacement data of the blade 1 and the blade 2 is cut to [4740, 4980 ]]As shown in fig. 2, two one-dimensional vectors with length 241 are obtained:andaverage frequency conversion f in the 241 data length_r85Hz, average sampling rate f_s≈f_r。

(4) For two intercepted data vectorsAndremoving the mean value, and then performing dot multiplication to obtain a multiplied product vector M_i，jFor product vector M_i，jDirectly carrying out discrete Fourier transform to obtain frequency spectrum data SA_i，j。

In the present exemplary example, the data for blade 1 and blade 2 within the narrow window are respectively:andcarrying out mean value removing operation on the two displacement data and multiplying to obtain a product vector M of the blades 1 and 2_1，2The time domain diagram is shown in fig. 3. For product vector M_1，2Direct discrete Fourier transformObtaining spectral data SA_1，2The amplitude-frequency diagram is shown in fig. 8.

(5) Repeating (3) and (4) on the data of the blades i and j acquired by each sensor, and obtaining frequency spectrum data SA_i，jPerforming linear superposition, drawing a total amplitude-frequency diagram, and extracting the frequency components of the mixture of the natural frequencies of the two blades from the total amplitude-frequency diagramAnd a difference frequency component f between the natural frequencies of the two blades_i-j。

Specifically, step (3) and step (4) are repeated for the displacement data of the blade 1 and the blade 2 acquired by the 3 sensors in the present example, and 3 pieces of frequency spectrum data obtained by processing the displacement data acquired by different sensors are obtained in totalAnd the 3 frequency spectrum data are linearly superposed to obtain a total amplitude-frequency diagram of the blade 1 and the blade 2, and as shown in fig. 11, the frequency components obtained by mixing and superposing the sum of the natural frequencies of the two blades are extracted from the diagramAnd a difference frequency component f between the natural frequencies of the two blades_1-2. From fig. 11, it is apparent that two frequency components of 16.26Hz and 19.45Hz are present, so that the following two possibilities are made:

(6) according to the prior information of the natural frequency range of the blade, the frequency components mixed and overlapped by the sum of the natural frequencies of the blades i and jAnd a bladei and j natural frequency difference frequency f_i-jInformation, reverse-deducing the natural frequencies f of the blades i and j_iAnd f_j。

In the present exemplary embodiment, the following steps are specifically included:

a) through finite element analysis and engineering experience, the natural frequency range [340Hz, 365Hz ] of each blade of the selected 3-blade disc is known]Sampling frequency f_s85 Hz. The following expression can be obtained according to equation (6):

b) the natural frequency range of the blade is known a priori:

680≤f₁+f₂≤730 (11)

from this, it can be estimated that B is 8When, | f₁₊₂-8 × 85| ═ 16.26, and thus f can be obtained₁₊₂696.26Hz, at this time:

when in useWhen, | f₁₊₂-8 × 85| ═ 19.45, and thus f can be obtained₁₊₂699.45Hz, at this time:

this gives the natural frequency possibilities of the two blades when the blade 1 and blade 2 are analyzed in combination:

	f1	f2
			possibility of 1	338.4Hz	357.9Hz
Possibility 2	341.6Hz	357.9Hz

Combining all the blades in pairs to obtainRepeating the steps (2) to (5) for each combination to obtain natural frequency estimated values of all the blades, wherein the natural frequency of each blade is 2 (n)_bAnd-1) estimating values, and after removing abnormal values, calculating an average value as the natural frequency of each blade.

Setting the natural frequency error tolerance G to be 2Hz, arranging each natural frequency estimated value of the blade on a digit axis, selecting a first natural frequency value as a cluster center, taking the natural frequency estimated value which is not beyond G and is close to the cluster center as a class, calculating the distance from the cluster center to the nearest point, if not beyond G, determining the cluster center as a class, and recalculating the cluster center, if beyond G, determining the cluster center as a class. And taking each inherent frequency value as a clustering center, respectively clustering, selecting the class with the largest quantity from clustering results, selecting the class with the highest degree of aggregation in the classes, namely the class with small variance, when the quantity in the classes is the same, and taking the average value in the classes as the inherent frequency. When the number and variance in the clusters are the same, the clusters are all used as frequency estimation clusters, and the average value of the frequency estimation clusters is used as the natural frequency. This clustering process will be described below by taking the estimated natural frequency of the blade 1 as an example.

a. Choose 338.41Hz as the initial cluster center, 338.77 as the nearest point, their distance D₁₂0.36 < G, so 338.41 and 338.77 are one class, where the cluster centers are updated to their mean 338.59, the closest point to the cluster center is 341.24, and their distance is D₂₃2.65 > G, 341.24 is not classified as 338.77 or 338.41. Clustering is finished, the obtained results are 338.41 and 338.77, and the variance of the category is

b. Selecting 341.60Hz as an initial clustering center, repeating the above process to obtain a clustering result of 341.60 and 341.24 as a class,

c. selecting 338.41Hz as an initial clustering center, repeating the above process to obtain a clustering result of 338.41 and 338.77 as a class,

d. selecting 341.24Hz as an initial clustering center, repeating the above process to obtain a clustering result of 341.60 and 341.24 as a class,

selecting different initial clustering centers to obtain two clustering results, wherein the first clustering result is 338.41 and 338.77, the second clustering result is 341.60 and 341.24, the two clustering results have the same number of clusters, are both 2, have the same variance, and are both 0.0648, so that the two clusters are both used as the frequency estimation class of the blade 1, and the average value isThe natural frequency of the blade 1 is 340 Hz.

The natural frequencies of the blades 1, 2 and 3 obtained by the method are respectively as follows: 340Hz, 361.1Hz, 351.6 Hz.

The natural frequency of the rotating blade is measured through the electric leading slip ring and the strain gauge, and the natural frequencies of the blades 1, 2 and 3 are respectively obtained as follows: 341.9Hz, 363.1Hz and 353.3Hz, which are relatively close to the natural frequency obtained by the method, thereby illustrating the effectiveness of the method.

[ application example ]

As shown in fig. 1, the blade end timing test stand fixes 3 optical fiber type blade end timing sensors at random positions on the casing, and the installation angles of the sensors are measured and known as follows: 58 degrees, 108 degrees and 158 degrees, and the method designed by the invention patent does not use specific installation angle information, so that no requirement is made on the installation position of the sensor. Setting the initial rotating speed to be 60Hz, the rotating speed acceleration to be 0.5Hz/s, and the rotating speed variation range to be 60Hz-100Hz-60Hz, wherein the time of the 100Hz constant speed section is 20 s. The blade disc adopts a 3-blade integral aluminum alloy blade disc, the radius of the blade disc is 68mm, the thickness d of the blade is 1mm, and the width w of the blade is 20 mm. 4 nozzles are uniformly distributed on a casing, high-pressure gas of 0.5Mpa is sprayed, the reaching time of the rotating blade is obtained by using a timing sensor at the blade end which is randomly arranged, and the difference between the theoretical reaching time and the actual reaching time is converted into blade end displacement according to the rotating speed and the length of the blade.

Selecting displacement data of the blade 1 and the blade 2, wherein the displacement data are one-dimensional vectors, the length of the vectors is 7823, and the range of sequence numbers in the displacement data of the blade 1 and the blade 2 is intercepted to be [4740, 4980 ]]As shown in fig. 2, two one-dimensional vectors with length 241 are obtained:andaverage frequency conversion f in the 241 data length_r85Hz, average sampling rate f_s≈f_r。

Carrying out mean value removing operation on the two displacement data and multiplying to obtain a product vector M of the blades 1 and 2_1，2The time domain diagram is shown in fig. 3. For product vector M_1，2Directly carrying out discrete Fourier transform to obtain frequency spectrum data SA_1，2The amplitude-frequency diagram is shown in fig. 8.

Repeating the step (3) and the step (4) on the displacement data of the blade 1 and the blade 2 acquired by the 3 sensors in the example, and obtaining 3 frequency spectrum data obtained by processing the displacement data acquired by different sensors in totalAnd the 3 frequency spectrum data are linearly superposed to obtain a total amplitude-frequency diagram of the blade 1 and the blade 2, and as shown in fig. 11, the frequency components obtained by mixing and superposing the sum of the natural frequencies of the two blades are extracted from the diagramAnd a difference frequency component f between the natural frequencies of the two blades_1-2. From fig. 11, it is apparent that two frequency components of 16.26Hz and 19.45Hz are present, so that the following two possibilities are made:

deducing from the prior information of the natural frequency range of the bladeNatural frequency f of blade 1 and blade 2₁And f₂。

In the present exemplary embodiment, the following steps are specifically included:

a) through finite element analysis and engineering experience, the natural frequency range [340Hz, 365Hz ] of each blade of the selected 3-blade disc is known]Sampling frequency f_s85 Hz. The following expression can be obtained according to equation (6):

b) the natural frequency range of the blade is known a priori:

680≤f₁+f₂≤730 (16)

from this, it can be estimated that B is 8When, | f₁₊₂-8 × 85| ═ 16.26, and thus f can be obtained₁₊₂696.26Hz, at this time:

when in useWhen, | f₁₊₂-8 × 85| ═ 19.45, and thus f can be obtained₁₊₂699.45Hz, at this time:

this gives the natural frequency possibilities of the two blades when the blade 1 and blade 2 are analyzed in combination:

	f1	f2
			possibility of 1	338.4Hz	357.9Hz
Possibility 2	341.6Hz	357.9Hz

Combining all the blades in pairs to obtainRepeating the steps (2) to (5) for each combination to obtain natural frequency estimated values of all the blades, wherein the natural frequency of each blade is 2 (n)_bAnd-1) estimating values, and after removing abnormal values, calculating an average value as the natural frequency of each blade.

Setting the natural frequency error tolerance G to be 2Hz, arranging each natural frequency estimated value of the blade on a digit axis, selecting a first natural frequency value as a cluster center, taking the natural frequency estimated value which is not beyond G and is close to the cluster center as a class, calculating the distance from the cluster center to the nearest point, if not beyond G, determining the cluster center as a class, and recalculating the cluster center, if beyond G, determining the cluster center as a class. And taking each inherent frequency value as a clustering center, respectively clustering, selecting the class with the largest quantity from clustering results, selecting the class with the highest degree of aggregation in the classes, namely the class with small variance, when the quantity in the classes is the same, and taking the average value in the classes as the inherent frequency. When the number and variance in the clusters are the same, the clusters are all used as frequency estimation clusters, and the average value of the frequency estimation clusters is used as the natural frequency. This clustering process will be described below by taking the estimated natural frequency of the blade 1 as an example.

a. Choose 338.41Hz as the initial cluster center, 338.77 as the nearest point, their distance D₁₂0.36 < G, so 338.41 and 338.77 are one class, where the cluster centers are updated to their mean 338.59, the closest point to the cluster center is 341.24, and their distance is D₂₃2.65 > G, 341.24 is not classified as 338.77 or 338.41. Clustering is finished, the obtained results are 338.41 and 338.77, and the variance of the category is

b. Selecting 341.60Hz as an initial clustering center, repeating the above process to obtain a clustering result of 341.60 and 341.24 as a class,

c. selecting 338.41Hz as an initial clustering center, repeating the above process to obtain a clustering result of 338.41 and 338.77 as a class,

d. selecting 341.24Hz as an initial clustering center, repeating the above process to obtain a clustering result of 341.60 and 341.24 as a class,

selecting different initial clustering centers to obtain two clustering results, wherein the first clustering result is 338.41 and 338.77, the second clustering result is 341.60 and 341.24, the two clustering results have the same number of clusters, are both 2, have the same variance, and are both 0.0648, so that the two clusters are both used as the frequency estimation class of the blade 1, and the average value isThe natural frequency of the blade 1 is 340 Hz.

The natural frequencies of the blades 1, 2 and 3 obtained by the method are respectively as follows: 340Hz, 361.1Hz, 351.6 Hz.

The natural frequency of the rotating blade is measured through the electric leading slip ring and the strain gauge, and the natural frequencies of the blades 1, 2 and 3 are respectively obtained as follows: 341.9Hz, 363.1Hz and 353.3Hz, which are relatively close to the natural frequencies obtained by the method, thereby illustrating the effectiveness of the method.

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.