CN113504309A - Blade detection method based on single blade end timing sensor - Google Patents

Abstract

The invention discloses a blade detection method based on a single blade end timing sensor, in the method, intercepting two sections of displacement data vectors of the two blades at the same rotating speed in the displacement data, adjusting the intercepted positions of the displacement data vectors based on the included angle of the two blades, the two segments of displacement data vectors are intercepted again, the two segments of the intercepted displacement data vectors are point-multiplied to obtain product data vectors after the multiplication of corresponding serial numbers, the product data vectors are filtered by low frequency, then, discrete Fourier transform is carried out to obtain frequency components, the natural frequency difference of the two blades is extracted from the low-frequency components, and judging the reliability of the frequency difference value through the linear combination of the difference values among different blades so as to correct the frequency difference value matrix, extracting the sum of the natural frequency difference values of each blade based on the coefficient matrix constructed by the frequency difference value matrix, and judging the abnormality of the blade when the sum exceeds the preset frequency difference value and the threshold.

Description

A blade detection method based on a single blade tip timing sensor

technical field

The invention belongs to the field of non-contact non-destructive detection of blades, in particular to a blade detection method based on a single blade end timing sensor.

Background technique

Blades are widely used in rotary fluid machinery equipment such as compressors, gas turbines, and aero-engines. In the use of blades, cracks, block drop, rubbing, blade crown wear, etc. are relatively common failure forms, and once the failure occurs, As the working time gradually deepens, it will cause more failures and safety accidents. Therefore, it is very necessary to carry out online fault diagnosis for the rotating blades of key equipment, and the above-mentioned abnormal conditions of the blades often affect the natural frequency of the blades. Blade Tip Timing (BTT) is a non-contact online method for measuring the vibration of rotating blades, but the sampling rate of blade tip timing is related to the rotation speed and the number of sensors. The data is severely undersampled, and even the installation of a tachometer is not possible. The blade tip displacement measurement with the speed reference method needs to convert the blade arrival time difference into the blade tip displacement by means of the rotation speed. The installation of the sensor and multiple blade-end timing sensors in the actual limited space will cause great trouble and increase the measurement cost. The traditional method is used to identify the modal parameters of the uniform and non-uniform data of the blade-end timing sensors. , such as compressed sensing, subspace methods, least squares iteration. On the one hand, these algorithms involve a large number of operations, and cannot realize online real-time detection and diagnosis. On the other hand, these algorithms directly identify parameters such as the natural frequency of a single blade, and there are large errors.

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.

SUMMARY OF THE INVENTION

In view of the problems existing in the prior art, the present invention proposes a blade detection method based on a single blade tip timing sensor, which provides a faster and more accurate evaluation of the health status of the blade.

The purpose of the present invention is to achieve through the following technical solutions, a blade detection method based on a single blade tip timing sensor includes the following steps:

In the first step, a single blade tip timing sensor is used to obtain the actual reaching time of the rotating blade, and according to the rotating speed of the rotating blade and the blade length, the difference between the theoretical arrival time and the actual reaching time is converted into the displacement data of the blade tip;

In the second step, two segments of displacement data vectors under the same rotational speed of the two blades are intercepted from the displacement data,

In the third step, the position where the displacement data vector is intercepted is adjusted based on the angle between the two blades, so as to re-intercept the two segments of the displacement data vector, and the re-intercepted two segments of the displacement data vector are multiplied to obtain the product data vector;

In the fourth step, the product data vector is filtered by low frequency, and then discrete Fourier transform is performed to obtain frequency components, and the natural frequency difference of the two leaves is extracted from the low frequency components,

In the fifth step, the blades on the blisk are combined in pairs, and the second to fourth steps are repeated to obtain all the natural frequency differences as a frequency difference matrix,

In the sixth step, the reliability of the frequency difference value is judged by the linear combination of the difference values between different blades to correct the frequency difference value matrix,

In the seventh step, based on the coefficient matrix constructed by the frequency difference matrix, the sum of the natural frequency difference of each leaf is extracted, and when the sum of the natural frequency difference exceeds the predetermined frequency difference and threshold, the abnormality of the leaf is judged.

其中

表示第j圈时的转速；θ_1，k表示1号叶片和k号叶片静止情况下的角度；t_i，j表示第i个叶片在第j圈的实际到达时间；n_b表示叶片数量，其中

表示第j圈时的转速；θ_1，k表示1号叶片和k号叶片静止情况下的角度；t_i，j表示第i个叶片在第j圈的实际到达时间；n_b表示叶片数量。其中，

其中θ_i表示以转速传感器安装位置为基准，第i个叶片的角度。α_k表示以转速传感器安装位置为基准，第k个传感器的角度，n_j为第j圈时的转速。In the described method, in the first step, a single blade end timing sensor acquires the actual reaching time _t of the rotating blade with uniform speed increase or uniform deceleration, and calculates the difference between the theoretical arrival time and the actual arrival time according to the rotational speed fr of the blade and the blade length R. Converted to tip displacement, the expression is as follows:

in

Represents the rotational speed of the jth circle; θ _{1, k} represents the angle of the 1st blade and the kth blade when the blade is stationary; t _{i, j} represents the actual arrival time of the ith blade in the jth circle; n _b represents the number of blades, in

Represents the rotational speed at the jth turn; θ _{1, k} represents the angle of the No. 1 blade and No. k blade when the blade is stationary; t _{i, j} represents the actual arrival time of the i-th blade in the j-th turn; n _b represents the number of blades. in,

where θ _i represents the angle of the i-th blade based on the installation position of the rotational speed sensor. α _k represents the angle of the k-th sensor based on the installation position of the rotational speed sensor, and n _j is the rotational speed at the j-th turn.

In the method described, the rotation process of the blade is the acceleration or deceleration process of the predetermined acceleration, and the gas nozzles uniformly distributed in the circumferential direction are used to simulate the gas excitation during the rotation process.

其中

为的第k圈对应的转速，M-N+1为所截取的数据长度。In the method described, the interval for the interception of the two displacement data is the same, both are [N, M], and the sampling frequency f _s is:

in

is the rotation speed corresponding to the k-th turn, and M-N+1 is the length of the intercepted data.

In the method described, the two segments of displacement data vectors X _i , X _j under the same rotational speed of the two blades, the intercepted data intervals are all [cN, c+N], and the vector length is 2N+1. Where c is the index number corresponding to a certain position in the two blade displacement data. (How to get the index number)

In the method described, the first blade that reaches the blade end timing sensor is the No. 1 blade. If the angle between the i-th and j-th blades is greater than 180°, the data selection interval of the smaller blade number is shifted forward by 1. units, the data interval becomes [c-N+1, c+N+1].

从频率成分中提取两个叶片的固有频率差值Df_ij，

In the described method, in the third step, the product data vector after multiplying the two displacement data vectors x _i and x _j is:

Extract the natural frequency difference Df _ij of the two leaves from the frequency components,

n是一个迭代数，从0遍历到N-1，即取遍x中的所有元素，k是一个0到N-1整数，X(k)表示离散傅里叶变换后的第k个数据。where x(n) is the sampled signal, i is the imaginary number symbol,

n is an iteration number, traversing from 0 to N-1, that is, traversing all elements in x, k is an integer from 0 to N-1, and X(k) represents the kth data after discrete Fourier transform.

种组合，二步骤至第四步骤得到

个固有频率差值，组成固有频率差值矩阵ΔF，In the described method, in the fifth step, different blade combinations are selected for a total of

kind of combination, the second step to the fourth step obtains

natural frequency difference, forming a natural frequency difference matrix ΔF,

Its impact, Δf _ij =f _i -f _j =sgn(fi -f _j )·Df _ij , sgn(fi -f _j ) represents the symbol of f _i >f _j , when _{f i ≥f j is} extracted as positive sign, otherwise it is a negative sign.

In the described method, in the sixth step, the natural frequency difference is:

Δf _ki -Δf _kj =Δf _ji =-Δf _ij k,i,j=1,2,...,n _b , when the frequency error tolerance ξ ₀ satisfies the following formula, it means that the difference frequency in this area is credible,

固有频率差值矩阵ΔF的可信度L小于0.5时，无法用于故障诊断，频率差值矩阵ΔF的可信度上大于0.5时，通过修正后重新计算频率差值矩阵ΔF的可信度L大于0.8，则矩阵可用于下一步故障诊断。Δk _ij =|Δf _ki -Δf _kj +Δf _ij |≤ξ k=1, 2,...,n _b -2; i=k+1,...,n _b -1; j=i+1,...,n _b , the reliability L expression of the frequency difference matrix ΔF is:

When the reliability L of the natural frequency difference matrix ΔF is less than 0.5, it cannot be used for fault diagnosis. When the reliability of the frequency difference matrix ΔF is greater than 0.5, the reliability L of the frequency difference matrix ΔF is recalculated after correction. greater than 0.8, the matrix can be used for further troubleshooting.

In the described method, in the seventh step, the constructed coefficient matrix is:

sumD _k =ΔF·A _k , if sumD _k <ε, it is determined that the blade is faulty.

The method of the invention only needs a single blade end timing sensor and does not need a rotational speed reference to extract the natural frequency difference between different blades from severely undersampled data, and judge whether there is a fault in the blade according to the natural frequency difference of the different blades. Additional signal reconstruction and more blade-end timing sensors are required, and the operation is fast and stable, simple and feasible, and can realize online fault detection of rotating blades.

The above description is only an overview of the technical solution of the present invention, in order to make the technical means of the present invention clearer, to the extent that those skilled in the art can implement it according to the content of the description, and in order to make the above and other purposes of the present invention, The features and advantages can be more clearly understood, and are exemplified by specific embodiments of the present invention below.

Description of 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 in the description are for the purpose of illustrating the preferred embodiments only, and are not to be considered as limiting the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative effort. Also, the same components are denoted by the same reference numerals throughout the drawings.

In the attached image:

Fig. 1 is a system diagram of a blade detection method based on a single blade tip timing sensor;

Fig. 2 is the displacement graph after the displacement data of No. 1 and No. 2 blades are de-averaged and normalized;

Fig. 3 is the time domain diagram of the product vector X ₁₂ obtained by multiplying the intercepted No. 1 and No. 2 blade data;

Fig. 4 is the spectrogram after product vector X ₁₂ low-pass filtering;

FIG. 5 is a schematic diagram of the triangular combination correction of the frequency difference frequency matrix.

The present invention will be further explained below in conjunction with the accompanying drawings and embodiments.

Detailed ways

Specific embodiments of the present invention will be described in more detail below with reference to FIGS. 1 to 5 . While specific embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present invention will be more thoroughly understood, and will fully convey the scope of the present invention to those skilled in the art.

It should be noted that certain terms are used in the description and claims to refer to specific components. It should be understood by those skilled in the art that the same component may be referred to by different nouns. The description and the claims do not use the difference in terms as a way to distinguish components, but use the difference in function of the components as a criterion for distinguishing. As referred to throughout the specification and claims, "comprising" or "including" is an open-ended term and should be interpreted as "including but not limited to". Subsequent descriptions in the specification are preferred embodiments for implementing the present invention, however, the descriptions are for the purpose of general principles of the specification and are not intended to limit the scope of the present invention. The scope of protection of the present invention should be determined by the appended claims.

To facilitate the understanding of the embodiments of the present invention, the following will take specific embodiments as examples for further explanation and description in conjunction with the accompanying drawings, and each accompanying drawing does not constitute a limitation to the embodiments of the present invention.

Blade detection methods based on a single blade tip timing sensor include,

(1) Use a blade tip timing sensor to obtain the arrival time and speed of the rotating blade, and convert the difference between the theoretical arrival time and the actual arrival time into the blade tip displacement according to the rotation speed and blade length.

In this exemplary example, the single-fiber blade tip timing sensor is fixed on the casing, the initial rotational speed is set to 60 Hz, the rotational speed acceleration is 0.5 Hz/s, and the rotational speed is within the range of 60 Hz-100 Hz-60 Hz, wherein The time of 100Hz constant speed section is 20s. The blisk adopts an integral aluminum alloy blisk with 6 blades, the radius of the blisk is R=68mm, the thickness of the blade is d=1mm, and the width of the blade is w=20mm. Four nozzles are evenly distributed on the casing to spray 0.5Mpa high-pressure gas. The single blade end timing sensor is used to obtain the arrival time and rotation speed of the rotating blade, and according to the rotation speed and blade length, the theoretical arrival time and the actual arrival time difference is converted into blade tip displacement.

(2) Select the two displacement data of the two blades to be analyzed at approximately the same rotational speed. If the slow speed-up or speed-down data is selected, the length of the intercepted data should not be too long to meet the requirement of approximately constant sampling frequency.

In this exemplary example, to select the displacement data of blade 1 and blade 2, the intercepted data serial number range is [4786, 5025]. As shown in Figure 2, the corresponding rotational speed variation range estimated by the blade tip timing sensor is: 84.60 Hz to 85.53 Hz, and the approximate sampling frequency f _s =85.06 Hz.

(3) According to the angle between the blades, after adjusting the position where the data vector is intercepted, perform a dot multiplication operation on the two data vectors to obtain the product data vector after the corresponding serial numbers are multiplied;

无需进行数据向量截取位置的调整。In this illustrative example, the angle between blade 1 and blade 2 is

There is no need to adjust the cut-off position of the data vector.

By multiplying the intercepted two vectors x ₁ , x ₂ , a product vector X ₁₂ of leaves 1 and 2 is obtained.

(4) Perform low-pass filtering on the product data vector, obtain frequency components through discrete Fourier transform, and extract the natural frequency difference between the two leaves from the low-frequency components.

In this exemplary example, the cutoff frequency of the low-pass filtering is 40 Hz, and the calculation formula of the discrete Fourier transform is:

N为采集到的信号的长度，x中元素的个数，n是一个迭代数，从0遍历到N-1，即取遍x中的所有元素，k是一个0到N-1整数，X(k)表示离散傅里叶变换后的第k个数据。where x(n) is the sampled signal, i is the imaginary number symbol,

N is the length of the collected signal, the number of elements in x, n is an iteration number, traversing from 0 to N-1, that is, traversing all elements in x, k is an integer from 0 to N-1, X (k) represents the kth data after discrete Fourier transform.

(5) Steps (2) to (4) are repeated, and the blades on the blisk are combined in pairs to obtain all the frequency difference values to form a frequency difference value matrix.

个频率差，得到的频率差值矩阵ΔF为：In this exemplary example, a 6-blade blisk is used, so n _b =6, so it is necessary to calculate

frequency difference, the obtained frequency difference matrix ΔF is:

The frequency error tolerance used in this example is ξ=5Hz, all triangular difference frequency combinations of the frequency difference matrix meet the frequency tolerance condition, and the reliability is 1, so no correction is required.

Six coefficient matrices A ₁ , A ₂ , A ₃ , A ₄ , A ₅ , A ₆ are constructed by the following expressions:

Multiply the frequency difference matrix ΔF by these 6 coefficient matrices to obtain 6 difference frequency sum values sumD _k

sumD _k =ΔF·A _k (19)

sumD=[-102.2 33.6 122.8 42.2 -106 24] ^T

Selecting the threshold ε=-100, it can be seen that the frequencies of the No. 1 blade and No. 5 blade are relatively low, and the following conditions are not met.

sumD _k <ε (20)

Therefore, it is determined that the natural frequencies of the No. 1 blade and No. 5 blade are obviously low, and there is an abnormality.

Using the lead-in slip ring, the natural frequencies of the six blades can be extracted through the strain gauge measurement, and the natural frequencies of the blades are obtained, which is close to the calculation result of the method proposed in this patent, indicating the feasibility of the method.

Table 1 The blade frequency obtained by the strain gauge measurement method

In fact, there are cracks in the No. 1 blade and No. 5 blade in the blisk, and the natural frequency is low.

【Applications】

As shown in Figure 1, the blade end timing test bench is used to fix the single fiber type blade end timing sensor on the casing. 60Hz, of which the 100Hz constant speed period is 20s. The blisk adopts an integral aluminum alloy blisk with 6 blades, the radius of the blisk is R=68mm, the thickness of the blade is d=1mm, and the width of the blade is w=20mm. Four nozzles are evenly distributed on the casing to spray 0.5Mpa high-pressure gas. The single blade end timing sensor is used to obtain the arrival time of the rotating blade, and the difference between the theoretical arrival time and the actual arrival time is converted into the blade tip displacement according to the rotation speed and blade length.

Specifically, the displacement data of blade 1 and blade 2 are selected, and the intercepted data positions are 240 data near the resonance peak of blade 1, and the serial number ranges from [4786, 5025]. As shown in Figure 2, the corresponding rotational speed variation range is: 84.60 Hz to 85.53 Hz, and the approximate sampling frequency f _s =85.06 Hz.

无需进行数据向量截取位置的调整。通过将所截取的两个向量x₁，X₂相乘，得到叶片1和2的乘积向量X₁₂。The angle between blades 1 and 2 is

There is no need to adjust the cut-off position of the data vector. By multiplying the two intercepted vectors x ₁ , X ₂ , a product vector X ₁₂ of leaves 1 and 2 is obtained.

Low-pass filtering is performed on the product data vector, frequency components are obtained by discrete Fourier transform, and the natural frequency difference between the two leaves is extracted from the low-frequency components. In this illustrative example, the cutoff frequency of the low pass filtering is 40 Hz. The amplitude-frequency diagram of the signal after the low-frequency filtering of the product vector X ₁₂ is drawn, as shown in Figure 4, in which it can be seen that the obvious frequency component is 11.7Hz, and 11.7Hz is the frequency difference frequency calculated by the patent method. It can be considered that blade 1 and blade The natural frequency difference of 2 is Δf ₁₂ =−11.7 Hz.

Using the lead slip ring and strain gauge to analyze the rotating blade, it can be seen that the first-order natural frequencies of the six blades of the aluminum alloy blisk are: 341.95Hz, 354.32Hz, 361.29Hz, 354.02Hz, 341.97Hz, 351.53Hz, No. 1 The natural frequency difference between the blade and No. 2 blade is 12.37Hz. The natural frequency difference extracted by the method in this paper, as shown in Figure 4, is 11.7Hz, and the difference is only 0.67Hz. Continue to use this method to calculate the frequency between the blades difference, and the frequency difference matrix ΔF is obtained, as shown in the following formula:

The frequency error tolerance used in this example is ξ=5Hz, all triangular difference frequency combinations of the frequency difference matrix meet the frequency tolerance condition, and the reliability is 1, so no correction is required.

Construct 6 coefficient matrices A ₁ , A ₂ , A ₃ , A ₄ , A ₅ , A ₆ by the following expressions, and multiply the frequency difference matrix ΔF by these 6 coefficient matrices to obtain 6 difference frequency sums sumD _k , after 6 operations, we get

sumD=[-102.2 33.6 122.8 42.2 -106 24] ^T .

Selecting the threshold ε=-100, it can be seen that the frequencies of the No. 1 blade and No. 5 blade are relatively low, and the following conditions are not met.

SumD _k <ε (20)

Therefore, it is determined that the natural frequencies of the No. 1 blade and No. 5 blade are obviously low, and there is an abnormality.

In fact, there are cracks in the No. 1 blade and No. 5 blade in the blisk, and the natural frequency is low. This example illustrates the effectiveness of the blade detection method proposed by the present invention with no speed reference single blade end timing sensor.

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-mentioned specific embodiments and application fields, and the above-mentioned specific embodiments are only illustrative and instructive, rather than restrictive . Those of ordinary skill in the art can also make many forms under the inspiration of this specification and without departing from the scope of protection of the claims of the present invention, which all belong to the protection of the present invention.

Claims (10)

1. A blade detection method based on a single blade tip timing sensor, the method comprising the steps of: In the first step (S1), a single blade tip timing sensor is used to obtain the actual reaching time of the rotating blade, and according to the rotating speed of the rotating blade and the blade length, the difference between the theoretical reaching time and the actual reaching time is converted into the displacement data of the blade tip; In the second step (S2), two segments of displacement data vectors under the same rotational speed of the two blades are intercepted from the displacement data, In the third step (S3), the position where the displacement data vector is intercepted is adjusted based on the included angle of the two blades, so as to re-intercept the two segments of the displacement data vector. the multiplied product data vector; In the fourth step (S4), the product data vector is filtered at a low frequency, and then a discrete Fourier transform is performed to obtain a frequency component, and the natural frequency difference of the two leaves is extracted from the low frequency component, In the fifth step (S5), the blades on the blisk are combined in pairs, and the second step to the fourth step are repeated to obtain all the natural frequency difference values as a frequency difference value matrix, In the sixth step (S6), the reliability of the frequency difference value is judged by the linear combination of the difference values between different blades to correct the frequency difference value matrix, In the seventh step (S7), based on the coefficient matrix constructed by the frequency difference matrix, the natural frequency difference sum of each leaf is extracted, and the leaf is abnormal when it exceeds a predetermined frequency difference sum and a threshold. 2. The method according to claim 1, wherein, preferably, in the first step (S1), a single blade end timing sensor acquires the actual reaching time t of the rotating blade with uniform acceleration or uniform deceleration, and according to the rotation speed of the blade f _r and blade length R convert the difference between the theoretical arrival time and the actual arrival time into the blade tip displacement, which is expressed as:

in

Represents the rotational speed of the jth circle; θ _{1, k} represents the angle of the 1st blade and the kth blade when the blade is stationary; t _{i, j} represents the actual arrival time of the ith blade in the jth circle; n _b represents the number of blades, in

Represents the rotational speed of the jth circle; θ _{1, k} represents the angle of the 1st blade and the kth blade when the blade is stationary; t _{i, j} represents the actual arrival time of the ith blade in the jth circle; n _b represents the number of blades, in,

where θ _i represents the angle of the i-th blade based on the installation position of the speed sensor, α _k represents the angle of the k-th sensor based on the installation position of the speed sensor, and n _j is the rotational speed at the j-th turn. 3 . The method according to claim 2 , wherein the rotation process of the blade is a speed-up or deceleration process of a predetermined acceleration, and gas excitation is simulated by using gas nozzles uniformly distributed in the circumferential direction during the rotation process. 4. The method according to claim 1, wherein, the intervals of two displacement data interception are the same, both are [N, M], and the sampling frequency f _s is:

in

is the rotation speed corresponding to the k-th turn, and M-N+1 is the length of the intercepted data. 5. The method according to claim 1, wherein, the two segments of displacement data vectors X _i , X _j under the same rotational speed of the two blades, the intercepted data intervals are [cN, c+N], and the vector length is 2N +1, where c is the index number corresponding to a certain position in the two blade displacement data. 6. The method according to claim 5, wherein the first blade that reaches the blade end timing sensor is the No. 1 blade, and if the angle between the i-th and j-th blades is greater than 180°, the blade with the smaller blade number is set. The data selection interval is shifted forward by ₁ unit, and the data interval becomes [c-N+1, c+N+1]. 7. The method according to claim 4, wherein, in the third step (S3), the product data vector after the multiplication of two displacement data vectors X _i and X _j is:

Extract the natural frequency difference Df _ij of the two leaves from the frequency components,

where x(n) is the sampled signal, i is the imaginary number symbol,

n is an iteration number, traversing from 0 to N-1, that is, traversing all elements in x, k is an integer from 0 to N-1, and X(k) represents the kth data after discrete Fourier transform. 8. The method according to claim 1, wherein, in the fifth step (S5), different blade combinations are selected to

kind of combination, the second step to the fourth step obtains

natural frequency difference, forming a natural frequency difference matrix ΔF,

Among them, Δf _ij =f _i -f _j =sgn(fi -f _j )·Df _ij , sgn(fi -f _j ) represents the sign of f _i >f _j , when _{f i ≥f j is} extracted as a positive sign , otherwise it is a negative sign. 9. The method according to claim 1, wherein, in the sixth step (S6), the natural frequency difference is: Δf _ki -Δf _kj =Δf _ji =-Δf _ij k,i,j=1,2,..., n _b , when the frequency error tolerance ξ ₀ satisfies the following formula, it means that the difference frequency in this region is credible, Δ _kij =|Δf _ki -Δf _kj +Δf _ij |≤ξ k=1, 2,...,n _b -2 ; i=k+1,...,n _b -1; j=i+1,...,n _b , the reliability L expression of the frequency difference matrix ΔF is:

When the reliability L of the natural frequency difference matrix ΔF is less than 0.5, it cannot be used for fault diagnosis. When the reliability L of the frequency difference matrix ΔF is greater than 0.5, recalculate the reliability L of the frequency difference matrix ΔF after correction. greater than 0.8, the matrix can be used for further troubleshooting. 10. The method according to claim 1, wherein, in the seventh step (S7), the constructed coefficient matrix is:

in

sumD _k =ΔF·A _k , if sumD _k <ε, it is determined that the blade is faulty.

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