Time-frequency rearrangement method for timing signals of aeroengine rotor blade tips

Abstract

A method for time-frequency rearrangement of an aircraft engine rotor blade tip timing signal, wherein the blade dynamic frequency at different rotation speeds is obtained from a Campbell diagram of a rotor blade of an aircraft engine rotor as a priori frequency; a blade tip timing sparse time-frequency reconstruction method is used to obtain a time-frequency representation of rotor blade vibration from an undersampled blade tip timing signal, and a frequency with a maximum amplitude is extracted from the time-frequency representation as a measured frequency; the rotor blade dynamic frequency is estimated based on the priori frequency and the measured frequency, thereby obtaining a posterior frequency; the weight of each time-frequency point is determined according to the size of the time-frequency coefficient, and the time-frequency coefficient is redistributed to the vicinity of the posterior frequency accordingly.

Description

Technical Field

[0001] The present invention relates to the technical field of non-contact testing of rotor blade vibration, and particularly to a time-frequency rearrangement method for tip-timing signals of an aero-engine rotor blade. Background Technique

[0002] Rotating blades are important components in aero-engines. When an aero-engine is operating, the blades will be subjected to harsh working conditions such as high temperature, high pressure, and high rotational speed. And the blades usually vibrate under the excitation of aerodynamic loads, which will cause high-cycle fatigue of the blades and lead to damage such as cracks in the blades. The damage faults of aero-engine blades usually cause some vibration parameters of the blades, such as vibration frequency, amplitude, etc., to change. During the operation of the blades, accurately monitoring their vibration parameters can provide data support for technologies such as blade damage condition assessment and blade remaining life prediction, and plays an important role in reducing the operation and maintenance costs of the engine and ensuring the operation safety of aero-engines.

[0003] Tip-timing technology can perform non-contact measurement of the vibration of rotating blades in an aero-engine, and this feature makes it play an important role in the long-term monitoring of the blade operating state. The tip-timing sensor is installed on the engine casing. By measuring the time when the blade reaches the sensor, the magnitude of the tip vibration displacement is calculated and various parameters of the blade vibration are extracted from it. However, the blade vibration displacement collected by tip-timing is mostly a highly undersampled signal that does not satisfy the Nyquist sampling theorem, and the time-frequency spectrogram obtained by traditional time-frequency analysis methods often has frequency aliasing phenomena. Therefore, undersampled tip-timing signals need to use sparse time-frequency reconstruction methods to obtain an unaliased time-frequency spectrogram, but in a strong noise environment, it is difficult to guarantee the time-frequency concentration and continuity of the sparse time-frequency reconstruction results.

[0004] The above information disclosed in the background technique section is only used to enhance the understanding of the background of the present invention, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] The present invention provides a time-frequency rearrangement method for tip-timing signals of an aero-engine rotor blade, which rearranges the sparse time-frequency spectrum to improve the concentration and continuity of the time-frequency representation of tip-timing signals, and solves the problem of insufficient continuity and concentration of the sparse reconstruction time-frequency spectrogram of tip-timing undersampled signals caused by noise interference.

[0006] A time-frequency rearrangement method for tip-timing signals of an aero-engine rotor blade includes:

[0007] In the first step, according to the finite element model of the rotor blades of an aeroengine, calculate the modal frequencies of the blades at different rotational speeds to obtain the Campbell diagram of the rotor blades, and obtain the blade dynamic frequencies at different rotational speeds from the Campbell diagram of the rotor blades of the aeroengine as prior frequencies;

[0008] In the second step, calculate the inner product of the undersampled blade tip timing signal at a certain moment with each column vector in the dictionary matrix one by one, and take the frequency corresponding to the column vector with the largest absolute value of the inner product as the vibration frequency of the rotor blade at this moment. Calculate the vibration frequencies of the rotor blades at different moments to obtain the time-frequency representation of the rotor blade vibration, and regard the frequency with the largest amplitude at each moment as the measured frequency at this moment;

[0009] In the third step, construct a normal distribution probability density function with the measured frequency as the mean, generate multiple frequency samples from it, assign weights to each sample according to the difference between the frequency sample and the prior frequency, and calculate the weighted average of the weights and frequencies of each sample as the posterior frequency;

[0010] In the fourth step, use the amplitude size of each time-frequency point in the time-frequency representation as the weight. The lower the weight, the greater the probability of assigning the corresponding amplitude to the time-frequency points within the range centered on the posterior frequency, and set the amplitude at the original time-frequency point to zero.

[0011] In the method for time-frequency rearrangement of the blade tip timing signal of an aeroengine rotor described above, in the first step, according to the finite element model of the rotor blade, calculate its modal frequency h(Ω(t j )) at time t j when the rotational speed is Ω(t j ).

[0012] In the method for time-frequency rearrangement of the blade tip timing signal of an aeroengine rotor described above, in the second step, the blade tip timing sensor measures the undersampled displacement d(t j ) of the blade vibration with a data length of L starting from time t j . The time-frequency representation coefficient c(t j ) of the blade vibration with a reconstruction sparsity of η is:

[0013]

[0014] where Φ is the dictionary matrix, d(t j ) is the undersampled displacement of the blade vibration with a data length of L starting from time t j , c(t j ) is the time-frequency representation coefficient of the blade vibration with a sparsity of η to be solved, represents the minimum optimization objective function with c as the independent variable, η is the sparsity of the sparse representation coefficient, s.t. represents the constraint condition, and ||c|| 0 represents the l of c0 Norm:

[0015]

[0016] where Δf is the frequency resolution of the time-frequency representation, I is the upper frequency limit of the time-frequency representation, L is the data length of the signal, t j is the time measured at the j-th blade tip timing, and the obtained time-frequency representation result is denoted as G(t j , f i ), where A i (t j ) and B i (t j ) are the elements at the corresponding positions in c(t j ). The frequency with the largest amplitude at each moment is taken as the measured frequency λ(t j ):

[0017]

[0018] where represents the maximum optimization objective function with f i as the independent variable, f i is the i-th frequency point, t j is the time point measured at the j-th blade tip timing, G(t j , f i ) is the amplitude value of the frequency f j at the moment t i , I is the upper frequency limit of the time-frequency representation, and J is the number of measurement signal data points.

[0019] In the described time-frequency rearrangement method for the blade tip timing signal of an aeroengine rotor, in the third step, a normal distribution with a probability density of q(h j |λ j ) is constructed with the measured frequency λ(t 1:j ) as the mean, where h j represents a random variable of t j at the moment with respect to the prior frequency, λ 1:j represents the set of all measured frequencies from the moment t 1 to the moment t j . The result of the posterior frequency p(h j |λ 1:j ) is expressed as:

[0020]

[0021] where h j represents a random variable of t j at the moment with respect to the prior frequency, λ 1:jDenote the set of all measured frequencies from time t 1 to time t j . Denote the m-th sample extracted at time t j according to the probability density function q(h j |λ 1:j ), where N p is the number of samples extracted, and W j is the weight of the m-th sample at time t

[0022] In the fourth step of the time-frequency rearrangement method for the tip-timing signal of an aero-engine rotor, for each frequency component f j at time t i in the time-frequency representation G(t j , f i ), assign weights as follows:

[0023]

[0024] where I is the upper limit of the frequency of the time-frequency representation, G(t j , f i ) is the amplitude of the frequency f j at time t i . Initialize a rearranged time-frequency representation result G * (t j , f i ) with all coefficients being zero, and generate a random number α in the interval [0, 1]. Then, according to the time-frequency representation G(t j , f i ) and its corresponding weight coefficient W G (t j , f i ), assign values to the rearranged time-frequency representation result:

[0025]

[0026] where s.t. represents the constraint condition, and finally obtain the time-frequency rearrangement result G * (t j , f i ) of the tip-timing.

[0027] In the time-frequency rearrangement method for the tip-timing signal of an aero-engine rotor, the Campbell diagram of the blade is obtained by using finite element analysis to obtain the blade dynamic frequency results at different rotational speeds.

[0028] Compared with the prior art, the present invention has the following advantages: The present invention obtains the blade dynamic frequencies at different rotational speeds from the Campbell diagram of the rotor blade as prior information, uses the blade tip timing sparse time-frequency reconstruction method to obtain the time-frequency representation of the rotor blade vibration, then extracts the time-frequency ridge line therefrom as the measured frequency, combines the prior frequency and the measured frequency to estimate the dynamic frequency of the rotor blade and further obtain the posterior frequency, and redistributes it near the posterior frequency according to the magnitude of the time-frequency coefficient, improving the time-frequency concentration and continuity of the blade tip timing undersampled signal. Description of the Drawings

[0029] By reading the following detailed description of the preferred specific embodiments, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The accompanying drawings of the specification are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Obviously, the following described drawings are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts. Moreover, throughout the drawings, the same reference numerals are used to represent the same components.

[0030] In the drawings:

[0031] Figure 1 is the flowchart of the method;

[0032] Figure 2 is the schematic diagram of the simulated blade rotational speed and dynamic frequency;

[0033] Figure 3 is the Campbell diagram of the simulated blade;

[0034] Figure 4 is the schematic diagram of the blade tip timing sparse time-frequency representation result;

[0035] Figure 5 is the schematic diagram of the blade vibration time-frequency rearrangement result.

[0036] The following further explains the present invention with reference to the drawings and embodiments. Detailed Embodiments

[0037] The specific embodiments of the present invention will be described in more detail below with reference to the drawings. Although the specific embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0038] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. The specification and claims do not distinguish components by the difference in nouns, but by the difference in the functions of the components. As mentioned throughout the specification and claims, "comprising" or "including" is an open-ended term and should be interpreted as "including but not limited to". The subsequent description in the specification is the preferred implementation manner for implementing the present invention, but the description is for the purpose of the general principles of the specification and is not used to limit the scope of the present invention. The protection scope of the present invention shall be subject to what is defined by the appended claims.

[0039] For the convenience of understanding the embodiments of the present invention, the following will further explain with specific embodiments in conjunction with the drawings, and each drawing does not constitute a limitation on the embodiments of the present invention.

[0040] As Figures 1 to 5 shown, the time-frequency rearrangement method for the tip timing signal of an aero-engine rotor includes the following steps:

[0041] In the first step S1, according to the finite element model of the rotor blade, calculate the modal frequencies of the blade at different rotational speeds, obtain the Campbell diagram of the rotor blade, and obtain the blade dynamic frequencies at different rotational speeds from the Campbell diagram of the rotor blade of the aero-engine rotor as the prior frequencies;

[0042] In the second step S2, calculate the inner product of the undersampled tip timing signal at a certain moment with each column vector in the dictionary matrix one by one, and take the frequency corresponding to the column vector with the largest absolute value of the inner product as the vibration frequency of the rotor blade at this moment. Calculate the vibration frequencies of the rotor blade at different moments to obtain the time-frequency representation of the rotor blade vibration, and regard the frequency with the largest amplitude at each moment as the measured frequency at this moment;

[0043] In the third step S3, construct a normal distribution probability density function with the measured frequency as the mean value, generate multiple frequency samples from it, assign weights to each sample according to the difference between the frequency sample and the prior frequency, and calculate the weighted average of the weights and frequencies of each sample as the posterior frequency;

[0044] In the fourth step S4, use the amplitude size of each time-frequency point in the time-frequency representation as the weight. The lower the weight, the greater the probability of assigning the corresponding amplitude to the time-frequency points within the range centered on the posterior frequency, and set the amplitude at the original time-frequency point to zero.

[0045] In the preferred implementation manner of the time-frequency rearrangement method for the tip timing signal of an aero-engine rotor, in the first step S1, according to the finite element model of the rotor blade, calculate its rotational speed at time t j at the moment, which is Ω(t j) modal frequency h(Ω(t j ))

[0046] In the preferred embodiment of the time-frequency rearrangement method for the tip-timing signal of an aero-engine rotor, in the second step S2, starting from time t j , the tip-timing sensor measures the undersampled displacement d(t j ) of the blade vibration with a data length of L, and the time-frequency representation coefficient c(t j ) of the blade vibration with a reconstruction sparsity of η is:

[0047]

[0048] where Φ is the dictionary matrix, d(t j ) is the undersampled displacement of the blade vibration with a data length of L starting from time t j , c(t j ) is the time-frequency representation coefficient of the blade vibration with a sparsity of η to be solved, represents the minimum optimization objective function with c as the independent variable, η is the sparsity of the sparse representation coefficient, s.t. represents the constraint condition, and ||c|| 0 represents the l 0 norm of c:

[0049]

[0050] where Δf is the frequency resolution of the time-frequency representation, I is the upper frequency limit of the time-frequency representation, L is the data length of the signal, t j is the time measured by the j-th tip-timing, and the obtained time-frequency representation result is denoted as G(t j , f i ), where, A i (t j ) and B i (t j ) are the elements at the corresponding positions in c(t j ), and the frequency with the largest amplitude at each moment is taken as the measured frequency λ(t j ):

[0051]

[0052] where, represents the maximum optimization objective function with f i as the independent variable, f i is the i-th frequency point, t j is the time point measured by the j-th tip-timing, and G(t j , f i ) is at time t j , frequency f iThe amplitude value, I is the upper limit of the frequency of the time-frequency representation, and J is the number of measurement signal data points.

[0053] In the preferred embodiment of the time-frequency rearrangement method for the tip-timing signal of an aero-engine rotor, in the third step S3, with the measured frequency λ(t j ) as the mean, construct a normal distribution with a probability density of q(h j |λ 1:j ), where h j represents a random variable of the prior frequency at time t j , λ 1:j represents the set of all measured frequencies from time t 1 to t j , and the result of the posterior frequency p(h j |λ 1:j ) is expressed as:

[0054]

[0055] where h j represents a random variable of the prior frequency at time t j , λ 1:j represents the set of all measured frequencies from time t 1 to t j , represents the m-th sample extracted at time t j according to the probability density function q(h j |λ 1:j ), N p is the number of extracted samples, is the weight of the m-th sample at time t j .

[0056] In the preferred embodiment of the time-frequency rearrangement method for the tip-timing signal of an aero-engine rotor, in the fourth step S4, for each frequency component f j at time t i in the time-frequency representation G(t j , f i ), assign weights:

[0057]

[0058] where I is the upper limit of the frequency of the time-frequency representation, G(t j , f i ) is the amplitude value of the frequency f j at time t i , initialize a rearranged time-frequency representation result G * (t j , f i), and generate a random number α within the interval [0, 1]. Then, according to the time-frequency representation G(t j , f i ) and its corresponding weight coefficient W G (t j , f i ), assign values to the rearranged time-frequency representation result:

[0059]

[0060] Among them, s.t. represents the constraint condition, and finally obtain the time-frequency rearrangement result G * (t j , f i ).

[0061] In the preferred implementation manner of the time-frequency rearrangement method for the tip-timing signal of an aero-engine rotor, the Campbell diagram of the blade is obtained by using finite element analysis to obtain the blade dynamic frequency results at different speeds.

[0062] In one embodiment, a tip-timing measurement system is used to measure the blade vibration displacement, so as to obtain the Campbell diagram of the rotor blades of the aero-engine rotor. Further, the tip-timing measurement system includes tip-timing sensors.

[0063] In one embodiment, Figure 1 is the flowchart of a time-frequency rearrangement method for the tip-timing signal of an aero-engine rotor completed by the present invention. This method obtains the blade dynamic frequencies at different speeds from the Campbell diagram of the rotor blades as prior information; uses the tip-timing sparse time-frequency reconstruction method to obtain the time-frequency representation of the rotor blade vibration from the undersampled tip-timing signal, and then extracts the frequency with the largest amplitude as the measured frequency; combines the prior frequency and the measured frequency to estimate the dynamic frequency of the rotor blade and then obtain the posterior estimated frequency; determines the weights of each time-frequency point according to the magnitude of the time-frequency coefficient, and accordingly redistributes the time-frequency coefficients near the posterior frequency. The specific steps are as follows:

[0064] 1) Analyze the simulated blade operating speed and blade vibration frequency as shown in Figure 2 . The blade speed rises from 3000 RPM to 6000 RPM and then drops to 3000 RPM within 2.5 seconds, and the blade dynamic frequency changes with the speed. First, use finite element analysis to obtain the blade dynamic frequency results at different speeds to obtain the blade Campbell diagram, and its result is as shown in Figure 3 . The blade speed Ω(t j ) at time t j can be obtained through Figure 2 , then the prior modal frequency h(Ω(t j )) is to substitute the blade speed Ω(t j ) into Figure 3Obtained by calculating the Campbell diagram.

[0065] 2) According to Figure 2 the simulated blade vibration signal shown, the maximum analysis time of data analysis is max(t j ) = 5, the sparsity η = 10 is set, and the data length L for each analysis is such that t j+L-1 -t j < 0.5 and when t j+L -t j ≥ 0.5, the frequency resolution Δf of the time-frequency representation is 1 Hz, and the upper limit of the analysis frequency I = 1000 Hz. Then the dictionary matrix is:

[0066] Use the orthogonal matching pursuit method to solve the sparse time-frequency representation coefficients:

[0067]

[0068] where d(t j ) is the under-sampled displacement of the blade vibration with a data length of L starting from time t j , c(t j ) is the sparse time-frequency representation coefficient of the blade vibration with a sparsity of 10 to be solved, represents the minimum optimization objective function with c as the independent variable, s.t. represents the constraint condition, and ||c|| 0 represents the l 0 norm of c.

[0069] According to the elements A j (t i ) and B j (t i ) in c(t j ), calculate the coefficients of each frequency component in the time-frequency representation:

[0070]

[0071] Obtain the sparse time-frequency representation result of the tip timing signal as shown in Figure 4 . Take the frequency with the largest amplitude at each moment as the measurement frequency λ(t j ):

[0072]

[0073] where represents the maximum optimization objective function with f i as the independent variable, f i is the i-th frequency point, t j is the time point measured at the j-th tip timing, and G(t j , f i) is t j At time t, the amplitude of frequency f i , and J is the number of measurement signal data points.

[0074] 3) Construct a normal distribution function with a mean of the measured frequency λ(t j ), a variance of 1, and extract 100 sample data points from it Calculate the weight coefficient of the m-th sample Then normalize each sample weight to obtain the weight coefficient of the m-th sample The post-verification estimated frequency determined by 100 sample points is:

[0075]

[0076] where h j represents a random variable of t j at time t with respect to the prior frequency, and λ 1:j represents the set of all measured frequencies from t 1 to t j ; represents the m-th sample extracted at time t j according to the probability density function q(h j |λ 1:j ), and j is the weight of the m-th sample at time t.

[0077] 4) Initialize a rearranged time-frequency representation result G * (t j , f i ) with all coefficients being zero, and generate a random number α within the interval [0, 1]. According to the magnitudes of the elements at time t j in the time-frequency representation G(t i , f j ), assign weights to each frequency component f i :

[0078]

[0079] Then, in the rearranged time-frequency representation result, assign a value to the f j -th frequency component at time t i to satisfy:

[0080]

[0081] where s.t. represents the constraint condition, and the rearranged time-frequency representation result of the blade tip timing signal is as shown in Figure 5 . Compare Figure 4 and Figure 5It can be seen that, compared with the sparse time-frequency representation of the classical blade tip timing signal, the rearranged time-frequency spectrogram obtained by the proposed method has higher time-frequency concentration and better time-frequency continuity.

[0082] Although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields. The above specific embodiments are merely illustrative and guiding, 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 protected by the claims of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for time-frequency rearrangement of timing signals of an aircraft engine rotor blade tip, characterized in that: The steps include: In the first step (S1), according to the finite element model of the rotor blade of the aircraft engine rotor, the modal frequency of the blade at different rotational speeds is calculated to obtain the Campbell diagram of the rotor blade, and the blade dynamic frequency at different rotational speeds is obtained from the Campbell diagram of the rotor blade of the aircraft engine rotor as a priori frequency; In the second step (S2), the inner product of the undersampled blade tip timing signal at a certain moment and each column vector in the dictionary matrix is ​​calculated one by one, and the frequency corresponding to the column vector with the largest absolute value of the inner product is taken as the vibration frequency of the rotor blade at that moment. The vibration frequencies of the rotor blades at different moments are calculated to obtain the time-frequency representation of the vibration of the rotor blades, and the frequency with the largest amplitude at each moment is taken as the measured frequency at that moment; In the third step (S3), a normal distribution probability density function is constructed with the measured frequency as the mean, a plurality of frequency samples are generated therefrom, a weight is assigned to each sample according to the difference between the frequency sample and the prior frequency, and a weighted average of the weights and frequencies of each sample is calculated as the posterior frequency; In the fourth step (S4), the amplitude of each time-frequency point in the time-frequency representation is used as a weight. The lower the weight, the greater the probability that the corresponding amplitude is assigned to the time-frequency point within the range centered on the a posteriori frequency, and the amplitude at the original time-frequency point is set to zero; In the second step (S2), the blade tip timing sensor is From the moment, the measured data length is The blade vibration under-sampled displacement , and its reconstruction sparsity is The blade vibration time-frequency representation coefficient for: ， in, is the dictionary matrix, for The data length from time The blade vibration undersampled displacement, The sparsity to be sought is The blade vibration time-frequency representation coefficient, Representative is the minimum optimization objective function of the independent variable, is the sparsity of the sparse representation coefficient, represents the constraints, represent of Norm: in, is the frequency resolution of the time-frequency representation, is the upper frequency limit of the time-frequency representation, is the data length of the signal, For the The time measured by the leaf end is recorded as ,in, , and for The element at the corresponding position in the , takes out the frequency with the largest amplitude at each moment as the measured frequency : ， in, Representative is the maximum optimization objective function of the independent variable, For the frequency points, For the The time point measured by the leaf tip timing, for At this moment, the frequency The magnitude of is the upper frequency limit of the time-frequency representation, is the number of measurement signal data points.

2. The method for time-frequency rearrangement of the timing signal of the rotor blade tip of an aircraft engine according to claim 1, characterized in that: In the first step (S1), the rotor blade finite element model is used to calculate its At time, the speed is The modal frequency at .

3. The method for time-frequency rearrangement of the timing signal of the rotor blade tip of an aircraft engine according to claim 1, characterized in that: In the third step (S3), the measured frequency Construct a probability density for the mean The normal distribution of represent A random variable with a prior frequency at time, Representative from arrive At this moment, the set of all measured frequencies, the posterior frequency The result is expressed as: ， in, represent A random variable with a prior frequency at time, Representative from arrive At this moment, the set of all measured frequencies, represent The probability density function The extracted samples, is the number of samples drawn, for Moment The weight of the samples.

4. The method for time-frequency rearrangement of the timing signal of the rotor blade tip of an aircraft engine according to claim 3, characterized in that: In the fourth step (S4), the time-frequency representation middle Each frequency component at a time Assign weights: ， in, is the upper frequency limit of the time-frequency representation, for At this moment, the frequency The amplitude of the initialization is a rearranged time-frequency representation with all coefficients zero. , and in the interval Generate a random number , and then according to the time-frequency representation and its corresponding weight coefficient Assign the rearranged time-frequency representation result: ， in, Represents the constraint condition, and finally obtains the time-frequency rearrangement result of the leaf end timing .

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