Reconstruction Method and System for Timing Undersampled Vibration Signals of Rotating Blades in Aeroengines

Abstract

The present invention relates to the technical field of health monitoring of rotating blades of aero-engines, and provides a method and a system for reconstructing the vibration signal of a rotating blade of an aero-engine with timed undersampling. The method includes: constructing a reconstruction model and a recovery matrix; setting the initial residual and the support set of the recovery matrix; calculating the inner product of the column vectors of the recovery matrix and the initial residual; selecting the column vectors whose absolute value of the inner product exceeds the threshold as matching vectors and combining them to form a first set; projecting the first set into the parameter space; performing clustering by using the K-nearest neighbor algorithm, and retaining the column vector with the largest inner product in each class to form a second set; adding the second set to the support set, and using the least squares method to solve the sparse coefficients with the minimum initial residual as the objective; calculating the new residual, and terminating the iteration until the support set is no longer updated, so as to obtain the sparse coefficients of the final vibration signal; calculating to obtain the reconstructed vibration signal of the tip of the rotating blade of the aero-engine. The present invention can improve the non-contact online real-time health monitoring effect of the blade.

Description

Technical Field

[0001] The present invention relates to the technical field of health monitoring of rotating blades of aero - engines, and particularly to a method and a system for reconstructing the vibration signal of a rotating blade of an aero - engine with time - based undersampling. Background Art

[0002] Aero - engine blades are in a harsh working environment of high speed and high pressure and are at high risk of fatigue or even fracture under the action of complex excitations such as centrifugal loads, high - pressure airflows, and rotor systems. In recent years, the Blade Tip Timing (BTT) method has gradually become a main method for realizing real - time monitoring of the whole - stage blades. According to the principle of blade - tip timing sampling, a single fiber - optic sensor can sample each blade once when the blade rotates one week. Therefore, the sampling frequency of a single blade is related to the number of circumferentially installed fiber - optic sensors and the rotor rotation frequency. Limited by the internal structure of the engine, the number of actually installed fiber - optic sensors is limited, and the natural frequency of the engine blade itself is often much higher than the rotor rotation frequency. Therefore, the blade - tip timing sampling data is undersampled data that does not satisfy the Nyquist sampling theorem. Using traditional signal - processing methods to directly analyze it will result in spectral aliasing, and the dynamic frequency change of the blade cannot be distinguished. At present, the traditional orthogonal matching pursuit algorithm can realize the reconstruction of the undersampled vibration signal of the rotating blade, but complex inner - product calculations are required for each iteration, resulting in problems of low calculation efficiency and poor reconstruction accuracy. Therefore, realizing the reconstruction of the blade - tip timing undersampled vibration signal of the rotating blade of an aero - engine while taking into account the signal reconstruction accuracy and real - time performance is a difficult point in carrying out blade health monitoring. Summary of the Invention

[0003] The purpose of the present invention is to solve at least one technical problem in the background art, and provide a method and a system for reconstructing the vibration signal of a rotating blade of an aero - engine with time - based undersampling.

[0004] To achieve the above purpose, the present invention provides a method for reconstructing the vibration signal of a rotating blade of an aero - engine with time - based undersampling, including:

[0005] S1. Construct a reconstruction model and a recovery matrix for the blade - tip timing undersampled vibration signal of the rotating blade of the aero - engine;

[0006] S2. Set the blade - tip timing undersampled vibration signal as the initial residual of the recovery matrix, and set the support set of the recovery matrix;

[0007] S3. Calculate the inner product of the column vectors of the recovery matrix and the initial residual;

[0008] S4. Select the column vectors of the recovery matrix corresponding to the inner - product values whose absolute values exceed the threshold among all the inner - product values as matching vectors and merge them to form a first set;

[0009] S5. Project the first set onto the parameter space , where , are the amplitudes of the sine and cosine vibration components respectively, is the frequency of the sine and cosine vibration components; Use the nearest neighbor algorithm for clustering, retain the column vector with the largest inner product in each class, and form the second set;

[0010] S6. Add the second set to the support set, and with the goal of minimizing the residual, use the least squares method to solve for the sparse coefficients;

[0011] S7. Calculate the new residual, and repeat steps S3 to S7 until the support set no longer updates, then terminate the iteration. At this time, obtain the final sparse coefficients of the vibration signal;

[0012] S8. Calculate the reconstructed tip vibration signal of the aeroengine rotating blade based on the reconstruction model, the recovery matrix, and the final sparse coefficients of the vibration signal.

[0013] According to one aspect of the present invention, the reconstruction model is: , ; The recovery matrix is: ;

[0014] In the formula, is to solve norm, y represents the tip-timing undersampled vibration signal, and the sampled values included in y represent the vibration displacement measured by the pth fiber optic sensor at the nth revolution, x represents the sparse coefficient, represents the time when the blade passes the pth fiber optic sensor at the nth revolution, is the set frequency resolution, N is the number of revolutions of the measured blade rotation, and M is the number of frequency points of the reconstructed signal spectrum.

[0015] According to one aspect of the present invention, the inner product of the column vector of the calculated recovery matrix and the initial residual is: , where r is the initial residual, is the column vector.

[0016] According to one aspect of the present invention, the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all inner product values are selected as matching vectors and combined to form the first set as:

[0017] Select the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all inner product values as matching vectors and combine them to form the first set :

[0018] ;

[0019] wherein, the threshold , T represents the signal length, and s is a coefficient.

[0020] According to one aspect of the present invention, the sparse coefficient is:

[0021]

[0022] wherein, is the sparse coefficient, is the support set, is the transpose of the support set.

[0023] According to one aspect of the present invention, the new residual is .

[0024] According to one aspect of the present invention, the reconstructed tip vibration signal of the rotating blade of the aero-engine calculated based on the reconstruction model, the recovery matrix, and the final sparse coefficient of the vibration signal is:

[0025] According to calculate the reconstructed tip vibration signal of the rotating blade of the aero-engine .

[0026] To achieve the above object, the present invention further provides a system for reconstructing the time-undersampled vibration signal of the rotating blade of an aero-engine, including:

[0027] A reconstruction model and recovery matrix construction module, which constructs a reconstruction model and a recovery matrix for the time-undersampled vibration signal of the tip of the rotating blade of the aero-engine;

[0028] An initial value setting module, which sets the time-undersampled vibration signal of the tip as the initial residual of the recovery matrix and sets the support set of the recovery matrix;

[0029] An inner product value calculation module, which calculates the inner product of the column vector of the recovery matrix and the initial residual;

[0030] A first set acquisition module, which selects the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all the inner product values as matching vectors and combines them to form a first set;

[0031] A second set formation module, which projects the first set into the parameter space , where , are the amplitudes of the sine and cosine vibration components respectively, is the frequency of the sine and cosine vibration components; uses the K-nearest neighbor algorithm for clustering, retains the column vector with the largest inner product in each class, and forms a second set;

[0032] The sparse coefficient solving module adds the second set to the support set, and uses the least squares method to solve the sparse coefficient with the goal of minimizing the residual.

[0033] The sparse coefficient determining module calculates the new residual, and repeatedly executes the inner product value calculation module to the sparse coefficient determining module until the support set is no longer updated and the iteration is terminated. At this time, the final vibration signal sparse coefficient is obtained.

[0034] The reconstructed vibration signal calculation module calculates the reconstructed tip vibration signal of the aero-engine rotating blade based on the reconstruction model, the recovery matrix, and the final vibration signal sparse coefficient.

[0035] To achieve the above object, the present invention also provides an electronic device, including a processor, a memory, and a computer program stored on the memory and executable on the processor. When the computer program is executed by the processor, the above-mentioned method for reconstructing the aero-engine rotating blade timing undersampled vibration signal is implemented.

[0036] To achieve the above object, the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned method for reconstructing the aero-engine rotating blade timing undersampled vibration signal is implemented.

[0037] According to the solution of the present invention, the present invention provides a method for reconstructing the aero-engine rotating blade tip timing undersampled vibration signal based on clustering shrinkage matching pursuit. Compared with the traditional solution, this method can effectively improve the accuracy and real-time performance of reconstructing the aero-engine rotating blade tip timing undersampled vibration signal, and can effectively improve the non-contact online real-time health monitoring effect of the blade.

[0038] According to the solution of the present invention, aiming at the problems of low efficiency and insufficient accuracy of the traditional orthogonal matching pursuit algorithm in reconstructing the aero-engine rotating blade tip timing undersampled vibration signal, the present invention realizes the simultaneous selection of multiple column vectors of the recovery matrix in each iteration process by introducing a threshold criterion and a clustering shrinkage mechanism, and accurately deletes the redundant column vectors among them, significantly improving the algorithm efficiency and reconstruction accuracy. The present invention can realize the efficient and accurate reconstruction of the aero-engine rotating blade tip timing undersampled vibration signal, providing a new solution for the online real-time health monitoring of the aero-engine rotating blade. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematically shows a flowchart of a method for reconstructing the aero-engine rotating blade timing undersampled vibration signal according to an embodiment of the present invention;

[0040] Figure 2Schematically represent the tip-timing undersampled vibration signal data to be analyzed according to Embodiment 1 of the present invention;

[0041] Figure 3 and Figure 4 Schematically represent the reconstruction result diagram of the clustering shrinkage matching pursuit algorithm according to Embodiment 1 of the present invention;

[0042] Figure 5 and Figure 6 Schematically represent the reconstruction result diagram of the orthogonal matching pursuit algorithm according to Embodiment 1 of the present invention;

[0043] Figure 7 Schematically represent the blade vibration Campbell diagram calculated by the finite element method according to Embodiment 1 of the present invention. Detailed implementation manners

[0044] Now, the content of the present invention will be described with reference to exemplary embodiments. It should be understood that the described embodiments are only for enabling those of ordinary skill in the art to better understand and thus implement the content of the present invention, rather than implying any limitation to the scope of the present invention.

[0045] As used herein, the term "comprising" and its variants are to be construed as open-ended terms meaning "including but not limited to". The term "based on" is to be construed as "at least partially based on". The terms "an embodiment" and "a kind of embodiment" are to be construed as "at least one embodiment".

[0046] Figure 1 Schematically represent the flowchart of a method for reconstructing the tip-timing undersampled vibration signal of aeroengine rotating blades according to an embodiment of the present invention. As Figure 1 shown, in this embodiment, the method for reconstructing the tip-timing undersampled vibration signal of aeroengine rotating blades includes:

[0047] S1. Construct a reconstruction model and a recovery matrix for the tip-timing undersampled vibration signal of aeroengine rotating blades;

[0048] S2. Set the tip-timing undersampled vibration signal as the initial residual of the recovery matrix and set the support set of the recovery matrix;

[0049] S3. Calculate the inner product of the column vectors of the recovery matrix and the initial residual (for example: if the recovery matrix has n column vectors, then n inner product values are obtained after taking the inner product with the initial residual respectively);

[0050] S4. Select the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all the inner product values as matching vectors and merge them to form a first set;

[0051] S5. Project the first set into the parameter space , where and are the amplitudes of the sine and cosine vibration components respectively, is the frequency of the sine and cosine vibration components; The nearest neighbor algorithm is used for clustering, and the column vector with the largest inner product in each class is retained to form the second set;

[0052] S6. Add the second set to the support set, and with the goal of minimizing the residual, use the least squares method to solve the sparse coefficients;

[0053] S7. Calculate the new residual, and repeat steps S3 to S7 until the support set is no longer updated, then terminate the iteration. At this time, the final sparse coefficients of the vibration signal are obtained;

[0054] S8. Calculate the reconstructed tip vibration signal of the aeroengine rotating blade based on the reconstruction model, the recovery matrix, and the final sparse coefficients of the vibration signal.

[0055] Furthermore, according to an embodiment of the present invention, the reconstruction model is: , ; The recovery matrix is: ;

[0056] In the formula, is to solve norm, y represents the tip-timing undersampled vibration signal, and the sampled values included in y represent the vibration displacement measured by the p-th fiber optic sensor at the n-th revolution, x represents the sparse coefficient, represents the time when the blade passes through the p-th fiber optic sensor at the n-th revolution, is the set frequency resolution, N is the number of revolutions of the measured blade rotation, and M is the number of frequency points of the reconstructed signal spectrum.

[0057] Furthermore, according to an embodiment of the present invention, the inner product of the column vector of the recovery matrix and the initial residual is calculated as: , where r is the initial residual, is the column vector.

[0058] Furthermore, according to an embodiment of the present invention, select the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all inner product values as matching vectors and combine them to form the first set as:

[0059] Select the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all inner product values as matching vectors and combine them to form the first set :

[0060] ;

[0061] In the formula, the threshold , T represents the signal length, and s is a coefficient.

[0062] Further, according to an embodiment of the present invention, the sparse coefficient is:

[0063] ;

[0064] In the formula, is the sparse coefficient, is the support set, is the transpose of the support set.

[0065] Further, according to an embodiment of the present invention, the new residual is .

[0066] Further, according to an embodiment of the present invention, the reconstructed tip vibration signal of the aeroengine rotating blade is calculated based on the reconstruction model, the recovery matrix, and the final sparse coefficient of the vibration signal:

[0067] According to calculate the reconstructed tip vibration signal of the aeroengine rotating blade .

[0068] According to the above solution of the present invention, the present invention provides a method for reconstructing the tip timing undersampled vibration signal of an aeroengine rotating blade based on clustering shrinkage matching pursuit. Compared with the traditional solution, this method can effectively improve the accuracy and real-time performance of reconstructing the tip timing undersampled vibration signal of an aeroengine rotating blade, and can effectively improve the non-contact online real-time health monitoring effect of the blade.

[0069] According to the above solution of the present invention, aiming at the problems of low efficiency and insufficient accuracy of the traditional orthogonal matching pursuit algorithm in reconstructing the tip timing undersampled vibration signal of an aeroengine rotating blade, the present invention realizes the simultaneous selection of multiple column vectors of the recovery matrix in each iteration process by introducing a threshold criterion and a clustering shrinkage mechanism, and accurately deletes the redundant column vectors among them, significantly improving the algorithm efficiency and reconstruction accuracy. The present invention can realize the efficient and accurate reconstruction of the tip timing undersampled vibration signal of an aeroengine rotating blade, providing a new solution for the online real-time health monitoring of an aeroengine rotating blade.

[0070] Further, to achieve the above object, the present invention also provides a system for reconstructing the tip timing undersampled vibration signal of an aeroengine rotating blade, including:

[0071] A reconstruction model and recovery matrix construction module, which constructs a reconstruction model and a recovery matrix for the tip timing undersampled vibration signal of an aeroengine rotating blade;

[0072] An initial value setting module sets the tip timing undersampled vibration signal as the initial residual of the recovery matrix and sets the support set of the recovery matrix;

[0073] An inner product value calculation module calculates the inner product of the column vectors of the recovery matrix and the initial residual;

[0074] A first set acquisition module selects the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all the inner product values as matching vectors and combines them to form a first set;

[0075] A second set formation module projects the first set into the parameter space , where and are the amplitudes of the sine and cosine vibration components respectively, and is the frequency of the sine and cosine vibration components; the K-nearest neighbor algorithm is used for clustering, and the column vector with the largest inner product in each class is retained to form a second set;

[0076] A sparse coefficient solving module adds the second set to the support set and uses the least squares method to solve the sparse coefficient with the goal of minimizing the residual;

[0077] A sparse coefficient determination module calculates the new residual and repeatedly executes the inner product value calculation module to the sparse coefficient determination module until the support set is no longer updated, then the iteration is terminated, and the final vibration signal sparse coefficient is obtained at this time;

[0078] A reconstructed vibration signal calculation module calculates the reconstructed tip vibration signal of the aero-engine rotating blade based on the reconstruction model, the recovery matrix, and the final vibration signal sparse coefficient.

[0079] Furthermore, according to an embodiment of the present invention, the reconstruction model is: , ; the recovery matrix is: ;

[0080] In the formula, is to solve norm, y represents the tip timing undersampled vibration signal, the sampling values included in y represent the vibration displacement measured by the p-th fiber optic sensor at the n-th revolution, x represents the sparse coefficient, represents the time when the blade passes through the p-th fiber optic sensor at the n-th revolution, is the set frequency resolution, N is the number of measured revolutions of the blade rotation, and M is the number of frequency points of the reconstructed signal spectrum.

[0081] Further, according to an embodiment of the present invention, the inner product of the column vector of the recovery matrix and the initial residual is calculated as: , where r is the initial residual, is the column vector.

[0082] Further, according to an embodiment of the present invention, select the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all the inner product values as matching vectors and combine them to form the first set as:

[0083] Select the inner product values whose absolute values exceed the threshold among all the inner product values and the column vectors of the recovery matrix corresponding to the inner product values are used as matching vectors and combined to form the first set

[0084] ;

[0085] where the threshold , T represents the signal length, and s is a coefficient.

[0086] Further, according to an embodiment of the present invention, the sparse coefficient is:

[0087] ;

[0088] where is the sparse coefficient, is the support set, is the transpose of the support set.

[0089] Further, according to an embodiment of the present invention, the new residual is .

[0090] Further, according to an embodiment of the present invention, the reconstructed tip vibration signal of the aeroengine rotating blade is calculated based on the reconstruction model, the recovery matrix, and the final sparse coefficient of the vibration signal as:

[0091] According to calculate the reconstructed tip vibration signal of the aeroengine rotating blade .

[0092] According to the above solution of the present invention, the present invention provides a method for reconstructing the tip timing undersampled vibration signal of an aeroengine rotating blade based on clustering shrinkage matching pursuit. Compared with the traditional solution, this method can effectively improve the accuracy and real-time performance of reconstructing the tip timing undersampled vibration signal of an aeroengine rotating blade, and can effectively improve the non-contact on-line real-time health monitoring effect of the blade.

[0093] According to the above solution of the present invention, aiming at the problems of low efficiency and insufficient accuracy of the traditional orthogonal matching pursuit algorithm in the reconstruction of the undersampled vibration signals of the rotating blades of aeroengines, the present invention realizes the simultaneous selection of multiple column vectors of the recovery matrix in each iteration process by introducing a threshold criterion and a clustering shrinkage mechanism, and accurately deletes the redundant column vectors among them, significantly improving the algorithm efficiency and reconstruction accuracy. The present invention can realize the efficient and accurate reconstruction of the undersampled vibration signals of the rotating blades of aeroengines, providing a new solution for the online real-time health monitoring of the rotating blades of aeroengines.

[0094] Furthermore, to achieve the above object, the present invention also provides an electronic device, including a processor, a memory, and a computer program stored on the memory and executable on the processor. When the computer program is executed by the processor, it realizes the method for reconstructing the undersampled vibration signals of the rotating blades of aeroengines as described above.

[0095] Furthermore, to achieve the above object, the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by the processor, it realizes the method for reconstructing the undersampled vibration signals of the rotating blades of aeroengines as described above.

[0096] To make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only the best embodiments of the present invention, only for explaining the present invention, and do not limit the protection scope of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0097] Embodiment 1

[0098] Taking a scaled test piece of the compressor rotor disk of a certain type of aeroengine as the research object, an experimental analysis of the reconstruction of the undersampled vibration signals of the rotating blades of aeroengines is carried out by using a high-speed rotating blade tip timing vibration measurement test bench. The entire disk is made of 7050 aluminum alloy material. The disk contains 34 blades with complex curved surface configurations. Its overall radius is 113.5 mm, the disk radius is 63.5 mm, and the blade length is 50 mm. A through crack with a width of 1 mm and a depth of 4.5 mm is prefabricated at a position 11 mm from the root of the leading edge of the 15th blade of the disk. The parameters of the disk test piece are shown in Table 1 below.

[0099] Table 1 Parameters of the disk test piece:

[0100]

[0101] The clustering shrinkage matching pursuit algorithm (i.e., the method for reconstructing the time-undersampled vibration signals of the rotating blades of an aero-engine based on clustering shrinkage matching pursuit) and the orthogonal matching pursuit algorithm are used to reconstruct the tip-timing measurement data of each blade in the resonance section. Taking the No. 15 blade as an example for analysis, its tip-timing vibration data is as Figure 2 shown, and the results of solving and reconstructing using the clustering shrinkage matching pursuit algorithm and the orthogonal matching pursuit algorithm are respectively as Figure 3 and Figure 4 as well as Figure 5 and Figure 6 shown. As Figure 4 and Figure 6 shown, the first-order dynamic frequencies of the blade reconstructed by the two algorithms are 752.4 Hz and 752.3 Hz respectively.

[0102] Figure 7 is the Campbell diagram of blade vibration calculated by the finite element method for the bladed disk model, Figure 7 in which EO represents the blade vibration order. Further, as Figure 7 shown, when the rotational speed is 7503 revolutions per minute (125.05 Hz), the first-order natural frequency line of the blade intersects with the 6-fold excitation frequency line, exciting the resonance of the first-order mode of the blade, and the corresponding first-order dynamic frequency of the blade is 750.3 Hz. Comparing the first-order dynamic frequencies (752.4 Hz and 752.3 Hz) calculated by the clustering shrinkage matching pursuit algorithm and the orthogonal matching pursuit algorithm with the first-order dynamic frequency (750.3 Hz) analyzed by the Campbell diagram, the deviations of the first-order dynamic frequencies are 2.1 Hz and 2 Hz respectively, and the deviation rates are 0.28% and 0.27% respectively, and the deviation is very small. Due to the manufacturing errors of each blade, there will be a small deviation between the actual first-order dynamic frequency of each blade and the analysis result of the Campbell diagram. Therefore, it can be considered that both algorithms have achieved accurate reconstruction of blade vibration. Further comparative analysis of the performance of the clustering shrinkage matching pursuit algorithm and the orthogonal matching pursuit algorithm shows that when the blade resonates, the excited first-order dynamic frequency energy amplitude should be the largest component in the signal spectrum. However, from Figure 5 and Figure 6 the reconstructed signal spectrogram of the orthogonal matching pursuit algorithm shown, the vibration amplitude at the first-order dynamic frequency is significantly low, indicating that the orthogonal matching pursuit algorithm underestimates the reconstruction of the blade vibration component amplitude, while Figure 3 and Figure 4 the reconstruction results of the clustering shrinkage matching pursuit algorithm shown are more in line with the actual situation. In addition, the reconstruction time of the orthogonal matching pursuit algorithm is 0.16 s, and the reconstruction time of the clustering shrinkage matching pursuit algorithm is 0.06 s, saving 62.5% in time. In summary, compared with the orthogonal matching pursuit algorithm, the tip-timing undersampled vibration signal reconstruction based on the clustering shrinkage matching pursuit algorithm has a greater improvement in both accuracy and efficiency, and can improve the non-contact online real-time health monitoring effect of the blade.

[0103] Those of ordinary skill in the art can realize that the modules and algorithm steps described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0104] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described devices and equipment can refer to the corresponding processes in the foregoing method embodiments, and will not be elaborated herein.

[0105] In the embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the modules is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces. The indirect couplings or communication connections of the devices or modules can be electrical, mechanical or other forms.

[0106] The modules described as separate components may or may not be physically separated. The components shown as modules may or may not be physical modules, that is, they may be located in one place, or may be distributed to multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the embodiments of the present invention.

[0107] In addition, the various functional modules in the embodiments of the present invention can be integrated into one processing module, or each module can exist physically alone, or two or more modules can be integrated into one module.

[0108] When the above-mentioned functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method for sending / receiving energy-saving signals in various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, ROM, RAM, magnetic disks, or optical discs that can store program codes.

[0109] The above description is only a preferred embodiment of the present application and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of the invention involved in the present application is not limited to the technical solution formed by the specific combination of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. For example, the technical solution formed by mutually replacing the above features with the (but not limited to) technical features having similar functions disclosed in the present application.

[0110] It should be understood that the magnitudes of the sequence numbers of the steps in the content and embodiments of the present invention do not absolutely mean the sequence of execution. The execution sequence of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

Claims

1. A method for reconstructing the vibration signal of a rotating blade of an aeroengine by undersampling in time domain, characterized in that, Including: S1. Construct a reconstruction model and a recovery matrix for the undersampled vibration signal of the tip-timing of an aero-engine rotating blade; S2. Set the undersampled vibration signal of the tip-timing as the initial residual of the recovery matrix, and set the support set of the recovery matrix; S3. Calculate the inner product of the column vectors of the recovery matrix and the initial residual; S4. Select the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all the inner product values as matching vectors and merge them to form the first set; S5. Project the first set onto the parameter space , where and are the amplitudes of the sine and cosine vibration components respectively, is the frequency of the sine and cosine vibration components; Use the K-nearest neighbor algorithm for clustering, retain the column vector with the largest inner product in each class, and form the second set; S6. Add the second set to the support set, and with the goal of minimizing the residual, use the least squares method to solve for the sparse coefficients; S7. Calculate the new residual, and repeat steps S3 to S7 until the support set is no longer updated and the iteration is terminated. At this time, the final sparse coefficients of the vibration signal are obtained; S8. Calculate the reconstructed tip vibration signal of the aero-engine rotating blade based on the reconstruction model, the recovery matrix, and the final sparse coefficients of the vibration signal; The reconstruction model is as follows: , ; The recovery matrix is as follows: ; In the formula, is to solve the 1-norm, y represents the vibration signal of the tip timing undersampling, and the sampled values included in y represent the vibration displacement measured by the p-th fiber optic sensor at the n-th revolution, x represents the sparse coefficient, represents the time when the blade passes through the p-th fiber optic sensor at the n-th revolution, is the set frequency resolution, N is the number of revolutions of the measured blade rotation, and M is the number of frequency points of the reconstructed signal spectrum.

2. The method for reconstructing the vibration signal of the rotating blade of an aero-engine by undersampling in time according to claim 1, wherein, The inner product of the column vector of the calculated recovery matrix and the initial residual is: , where r is the initial residual, is the column vector.

3. The method for reconstructing the vibration signal of the rotating blade of an aeroengine by undersampling in time according to claim 2, characterized in that The step of selecting the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all the inner product values as matching vectors and merging them to form the first set is: Select the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all inner product values and combine them as matching vectors to form the first set J: ​ ； In the formula, the threshold value , T represents the signal length, and s is a coefficient.

4. The method for reconstructing the vibration signal of the rotating blade of an aero-engine with undersampling in time according to claim 3, characterized in that, The sparse coefficients are: ； wherein, is the sparse coefficient, is the support set, is the transpose of the support set.

5. The method for reconstructing the vibration signal of the rotating blade of an aero-engine by timed undersampling according to claim 4, characterized in that The new residual is .

6. The method for reconstructing the vibration signal of the rotating blade of an aeroengine by timed undersampling according to claim 5, wherein The step of calculating the reconstructed tip vibration signal of the aero-engine rotating blade based on the reconstruction model, the recovery matrix, and the final sparse coefficients of the vibration signal is: According to the reconstructed aero-engine rotating blade tip vibration signal is calculated .

7. A system for reconstructing the vibration signal of a rotating blade of an aero-engine with undersampling in time domain, characterized in that Including: A reconstruction model and recovery matrix construction module, which constructs a reconstruction model and a recovery matrix for the undersampled vibration signal of the tip-timing of an aero-engine rotating blade; An initial value setting module, which sets the undersampled vibration signal of the tip-timing as the initial residual of the recovery matrix and sets the support set of the recovery matrix; An inner product value calculation module, which calculates the inner product of the column vectors of the recovery matrix and the initial residual; A first set obtaining module, which selects the column vectors of the recovery matrix corresponding to the inner product values whose absolute values exceed the threshold among all the inner product values as matching vectors and merges them to form the first set; The second set formation module projects the first set into the parameter space , where and are the amplitudes of the sine and cosine vibration components respectively, is the frequency of the sine and cosine vibration components; the K-nearest neighbor algorithm is used for clustering, and the column vector with the largest inner product in each class is retained to form the second set; A sparse coefficient solving module, which adds the second set to the support set and uses the least squares method to solve for the sparse coefficients with the goal of minimizing the residual; A sparse coefficient determination module, which calculates the new residual and repeats the execution of the inner product value calculation module to the sparse coefficient determination module until the support set is no longer updated and the iteration is terminated. At this time, the final sparse coefficients of the vibration signal are obtained; A reconstructed vibration signal calculation module, which calculates the reconstructed tip vibration signal of the aero-engine rotating blade based on the reconstruction model, the recovery matrix, and the final sparse coefficients of the vibration signal; The reconstruction model is as follows: , ; The recovery matrix is as follows: ; In the formula, is used to solve the 1-norm. y represents the tip-timing undersampled vibration signal, and the sampled values included in y represent the vibration displacement measured by the p-th fiber optic sensor at the n-th revolution. x represents the sparse coefficient, represents the time when the blade passes the p-th fiber optic sensor at the n-th revolution, is the set frequency resolution, N is the number of revolutions of the measured blade rotation, and M is the number of frequency points of the reconstructed signal spectrum.

8. An electronic device, characterized in that, Including a processor, a memory, and a computer program stored on the memory and executable on the processor. When the computer program is executed by the processor, it implements the method for reconstructing the undersampled vibration signal of the tip-timing of an aero-engine rotating blade as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium. When the computer program is executed by the processor, it implements the method for reconstructing the undersampled vibration signal of the tip-timing of an aero-engine rotating blade as described in any one of claims 1-6.

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