Aero-engine blade damage detection method based on improved ultrasonic sparse reconstruction algorithm

Abstract

The invention provides an aero-engine blade damage detection method based on an improved ultrasonic sparse reconstruction algorithm, and relates to the technical field of aero-engine damage detection positioning, and the method comprises the steps: S1, setting a sensor array and a detection region of a to-be-detected blade, and obtaining an actual measurement damage reflection signal dictionary through a sensor; s2, wave number distribution of a detection area is determined according to a variable thickness structure Lamb wave propagation model, signal reconstruction is carried out, and a theoretical damage reflection signal dictionary is obtained; s3, an aero-engine blade damage detection model is constructed, an improved sparse reconstruction algorithm is adopted to solve and optimize, and damage judgment is carried out; and S4, according to the pixel value distribution condition of the aero-engine blade detection area, generating an aero-engine blade damage detection image, and positioning a damage position. According to the method, the reflected wave amplitude information can be obtained from the array sensor signals, and the reflected wave amplitude information is compared with the reconstructed theoretical reflected signals, so that the damage condition of the aero-engine blade is identified and positioned.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft engine damage detection and positioning, and in particular to an aircraft engine blade damage detection method based on an improved ultrasonic sparse reconstruction algorithm. Background Art

[0002] Variable-thickness structures, such as aircraft engine blades, offer advantages such as lightweight and high aerodynamic efficiency. These structures have been widely used in the aviation, automotive, and marine sectors. For example, variable-thickness structures in aircraft structures, such as engine blades, engine casings, and wing skins, effectively reduce air resistance during operation. The use of variable-thickness plates in automotive structures, such as roofs and crossbeams, effectively expands the design space for automotive parts. Ship hulls also widely utilize variable-thickness structures to reduce fluid resistance during operation. However, these structures are susceptible to damage such as cracks and corrosion under harsh operating conditions, such as high temperature, high pressure, and alternating loads. This directly impacts the safety and lifespan of the structure, hindering its proper operation. Ultrasonic nondestructive testing (NDT), with its superior directional propagation characteristics, strong dielectric penetration, and high sensitivity, holds a significant position in industrial testing. Lamb waves, in particular, have attracted considerable attention due to their reduced propagation attenuation, extended detection range, unique dispersion effects, and multimodal characteristics. With the advancement of array sensing technology, multi-channel detection systems, with their wide-area coverage, precise signal acquisition, and excellent noise immunity, have become a key NDT tool. To address the needs of conventional structural inspection, researchers have developed a variety of classic location algorithms, including time-delayed superposition, minimum variance, and sparse reconstruction. However, it is worth noting that existing methodologies are primarily based on the assumption of uniform cross-section components. When faced with variable-thickness structures such as aviation composites and functionally gradient materials, traditional algorithms are unable to accurately represent the signal propagation characteristics of each part of the variable-thickness structure, resulting in a significant decrease in the algorithm's adaptability. To address this issue, this proposal proposes an aerospace engine blade damage detection method based on an improved ultrasonic sparse reconstruction algorithm, which is crucial for locating damage in complex structures. Summary of the Invention

[0003] In order to address the deficiencies of the above-mentioned prior art, the object of the present invention is to provide an aero-engine blade damage detection method based on an improved ultrasonic sparse reconstruction algorithm. By setting a detection area and a sensor array, the detection sensors are stimulated to obtain corresponding array response signals, and the response signals are obtained and composed of an experimental signal dictionary; the wavenumber distribution of the measurement area is determined according to the Lamb wave propagation model of variable thickness structures, and the theoretical and measured damage reflection signal dictionary of each sensor is calculated; the improved sparse reconstruction algorithm is used to solve the optimization problem, and the pixel value of each grid in the measurement area is calculated. According to the pixel value distribution of the detection area, the damage is located and an image is generated. This improves the traditional imaging method for damage of structures with constant thickness and realizes damage location of variable thickness structures.

[0004] Specifically, the present invention provides an aero-engine blade damage detection method based on an improved ultrasonic sparse reconstruction algorithm, which comprises the following steps: S1: Set up the sensor array and detection area on the aircraft engine blade to be tested, and stimulate The sensors acquire the response signals and form a dictionary of measured damage reflection signals ; S2: Obtain the sensor array and detection area determined in step S1, determine the wave number distribution of the detection area according to the variable thickness structure Lamb wave propagation model, and obtain the wave number corresponding to each grid thickness in the detection area , thus obtaining the detection area wave number matrix ; Calculate the propagation distance of each sensor-grid path through each grid , forming the distance propagation matrix , get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups , obtain the reconstructed signal parameters ; Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensors , which is converted into a time spectrum signal through inverse Fourier transform , determine the time spectrum signal vector of all grids , and the theoretical damage reflection signal dictionary is obtained by combining ; S3: Based on step S2, an aircraft engine blade damage detection model is constructed, and an improved sparse reconstruction algorithm is used for solution optimization to obtain the pixel value of each grid in the detection area of ​​the aircraft engine blade, specifically: ; in, is the minimum value function; is the dictionary of measured damage reflection signals; is the theoretical impairment reflection signal dictionary; is the pixel value vector The corresponding time spectrum signal vector; is the regularization parameter; For all A vector of pixel values ​​for a grid, , A non-zero value indicates that the grid is damaged. For the The pixel value of a grid; is the L1 norm; is the L2 norm; S4: Obtain pixel value distribution in the aircraft engine blade detection area according to step S3, perform damage judgment, generate an aircraft engine blade damage detection image, and locate the damage position.

[0005] Preferably, step S2 is specifically: S21: According to the sensor array and detection area, it is divided into The thickness of each grid is measured in turn, and the wave number corresponding to each grid thickness is determined according to the Lamb wave propagation model of variable thickness structure. , thus obtaining the detection area wave number matrix ; S22: Calculate the propagation distance of each sensor-grid path through each grid , forming the distance propagation matrix , get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups , obtain the reconstructed signal parameters ; S23: Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensors , which is converted into a time spectrum signal through inverse Fourier transform , and get the time spectrum signal vector , combined into a theoretical damage reflection signal dictionary .

[0006] Preferably, step S22 is specifically as follows: S221: When the sensor-grid path and the Rank The coordinates of the intersection points of the column grids are and , calculate the propagation distance of each sensor-grid path through each grid ; S222: All propagation distances Composition of distance propagation matrix , any two sensor-grid paths Add up to get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups ; S223: Feature distance dictionary The detection area wave number matrix in step S21 Multiply the corresponding elements and add all the internal elements to obtain the reconstructed signal parameters corresponding to each group of stimulus-response detection sensors. .

[0007] Preferably, step S23 is specifically as follows: S231: Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensors ; S232: Use inverse Fourier transform to transform the theoretical damage reflection signals corresponding to all stimulus-response detection sensor groups Converted into time spectrum signal ; S233: Arrange all grids in order Column vector, for the grids, total Group signals into time spectrum signal vectors , all grids corresponding to Combined to obtain the theoretical damage reflection signal dictionary .

[0008] Preferably, step S223 is specifically as follows: The feature distance dictionary The detection area wave number matrix in step S21 Multiply the corresponding elements and add all the internal elements to obtain the reconstructed signal parameters corresponding to each group of stimulus-response detection sensors. for: ; ; in, Reconstructed signal matrix for stimulus-response detection sensor; is the detection area wave number matrix; is the feature distance dictionary; To reconstruct the signal matrix Middle Rank Elements of the column grid; reconstructing signal parameters for the stimulus-response detection sensor; is the dot product operation; is the total number of detection area rows; is the total number of detection area columns.

[0009] Preferably, step S231 is specifically as follows: ; in, is the theoretical damage reflection signal; is the spectrum of the excitation signal; is the natural logarithm; is an imaginary unit; is the angular frequency.

[0010] Preferably, step S232 is specifically as follows: ; in, is the time spectrum signal; is the time parameter; is the pi parameter.

[0011] Preferably, the time spectrum signal vector in step S233 is: ; in, For the A time spectrum signal vector; is the time spectrum signal; is the matrix transpose symbol; Number the grid quantities.

[0012] Preferably, the theoretical damage reflection signal dictionary in step S233 is: ; in, is the theoretical impairment reflection signal dictionary.

[0013] Preferably, step S1 is specifically: Sequential excitation sensors, and use the sensors to receive and obtain all response signals, and form a dictionary of measured damage reflection signals from all the response signals obtained. for: ; in, is the dictionary of measured damage reflection signals; for Time A response signal, 1, 2, ..., ; is the time parameter; is the matrix transpose symbol.

[0014] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention reconstructs the theoretical damage reflection signal and establishes a dictionary of theoretical damage reflection signals corresponding to all potential damage locations of all stimulus-response detection sensor groups. The damage location information is extracted from the measured signal obtained from the array sensor and compared with the theoretical damage reflection signal to achieve accurate positioning of the damage on the aircraft engine blade.

[0015] (2) The present invention arranges a small number of sensors to form a sensor array and establishes a theoretical damage reflection signal dictionary that can cover the characteristics of the entire variable thickness aircraft engine blade. This effectively reduces the amount of hardware required and reduces the difficulty of operation without affecting the accuracy of damage location.

[0016] (3) The present invention effectively integrates the Lamb wave propagation information of different parts of the aircraft engine blade through the propagation characteristics of the reflected waves under different thickness structures, improves the traditional damage imaging method of equal thickness structures, realizes the promotion of sparse reconstruction damage imaging from equal thickness structures to variable thickness structures, and expands the application scope of ultrasonic guided wave damage detection methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of the Lamb wave damage location method for aircraft engine blades based on the improved sparse reconstruction algorithm of the present invention; Figure 2 A schematic diagram of the sensor array and proposed point damage and crack damage locations in an embodiment of the present invention; Figure 3 Schematic diagram of the thickness of each grid after the thickness grid is divided in an embodiment of the present invention; Figure 4 Schematic diagram of the wave number of each grid after the thickness grid is divided in an embodiment of the present invention; Figure 5 This is a comparison diagram of the position of the first damage point D1 and the positioning result of the algorithm in an embodiment of the present invention; Figure 6 This is a comparison diagram of the position of the second damage point D2 and the positioning result of the algorithm in an embodiment of the present invention; Figure 7 This is a comparison diagram of the position of the third damage point D3 and the positioning result of the algorithm in an embodiment of the present invention; Figure 8 1 is a comparison diagram of the location of crack damage and the algorithm positioning results in an embodiment of the present invention. DETAILED DESCRIPTION

[0018] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0019] The embodiment of the present invention proposes a Lamb wave damage location method for aircraft engine blades based on an improved sparse reconstruction algorithm. Figure 1 As shown, a sensor array and a detection area are set for the blade to be tested, and a dictionary of measured damage reflection signals is obtained using sensors. The wave number distribution in the detection area is determined based on the variable thickness structure Lamb wave propagation model, and signal reconstruction is performed to obtain a theoretical damage reflection signal dictionary. An aircraft engine blade damage detection model is constructed, and an improved sparse reconstruction algorithm is used to solve and optimize the solution and perform damage judgment. Based on the pixel value distribution of the aircraft engine blade detection area, an aircraft engine blade damage detection image is generated to locate the damage position. The specific steps include: Step S1: a sensor array and a detection area are set on the aero-engine blade to be tested, and the sensors are stimulated in sequence to obtain response signals and form a dictionary of measured damage reflection signals.

[0020] In a specific embodiment of the present invention, Figure 2 The sensor array and the proposed damage location diagram in the embodiment of the present invention are shown as follows: = 12 sensor arrays, 12 sensors are marked as R1-R12, forming a 275mm×225mm rectangular detection area; circular damage with a diameter of 20mm is set at the upper, middle and lower positions of the detection area, respectively marked as the first damage point D1, the second damage point D2 and the third damage point D3. Detection sensors are formed into an array, and the number of received detection signals is: ; in, The number of received detection signals; To detect the number of sensors.

[0021] Sequential excitation Sensors are used to receive and obtain all response signals and form a dictionary of measured damage reflection signals. The order of the sensor groups represented by the response signals is used to form a dictionary of measured damage reflection signals. , specifically: ; in, is the dictionary of measured damage reflection signals; for For time A response signal, 1, 2, ..., ; is the time parameter; is the matrix transpose symbol.

[0022] In a specific embodiment of the present invention, a detection sensor is used to obtain the reflected signal amplitude of the detection area of ​​the aircraft engine blade, specifically: measuring the received signal of the damaged aircraft engine blade to obtain The damage signals of the groups are ; The entire test system is replaced by a linear system, and the excited guided wave signal is only the A0 mode.

[0023] Step S2: Obtain the sensor array and detection area determined in step S1, determine the wave number distribution of the detection area according to the variable thickness structure Lamb wave propagation model, and calculate the theoretical damage reflection signal dictionary of each sensor.

[0024] Step S21: Divide the detection area of ​​the aero-engine blade into The thickness of each grid is measured in turn to determine the excitation signal type and frequency. Based on the relevant parameters of the aircraft engine blade material, the dispersion curve (the relationship between wave number and frequency thickness) is obtained. The specific process is as follows: , symmetric mode; , antisymmetric mode; ; ; in, Half the thickness of an aircraft engine blade; is the first auxiliary parameter; is the second auxiliary parameter; is the angular frequency, ; is the frequency; is the pi parameter; is the longitudinal wave velocity, determined experimentally; is the shear wave velocity, determined experimentally; is a sine function; is the wave number corresponding to the grid thickness.

[0025] The wave number corresponding to each grid thickness in the detection area is obtained by the above formula , thus obtaining the detection area wave number matrix for: ; in, is the detection area wave number matrix; is the total number of detection area rows; is the total number of detection area columns; For the Rank The wave number corresponding to the column grid thickness; Number the detection area rows; Number the detection area columns.

[0026] In the specific embodiment of the present invention, the grid is set to be a square with a side length of 25 mm. , There are a total of Measure the thickness of the 99 grid center points, and the distribution diagram is as follows: Figure 3 As shown. Based on the material and thickness of the aircraft engine blade, the wave dispersion curve is solved, that is, the curve showing the relationship between the dispersion wave frequency and the wave number. The wave number distribution diagram is shown in Figure 4 The excitation signal frequency is set to 100kHz, and the wave number corresponding to each grid is obtained according to the dispersion curve and the excitation signal frequency to form the detection area wave number matrix .

[0027] Step S22: Calculate the propagation distance of each sensor-grid path through each grid , forming the distance propagation matrix , get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups , obtain the reconstructed signal parameters , specifically including the following steps: Step S221: When the sensor-grid path and the Rank The coordinates of the intersection points of the column grids are and , then the propagation distance of the path through the grid for: ; in, The sensor-grid path passes through Rank propagation distance of the column grid; is the horizontal coordinate of the second grid intersection point; is the horizontal coordinate of the first grid intersection point; is the column coordinate of the second grid intersection point; is the column coordinate of the first grid intersection point.

[0028] All propagation distances Composition of distance propagation matrix for: ; in, is the distance propagation matrix.

[0029] Step S222: Under the same grid condition, two pairs of sensor-grid paths of any two groups Add up to get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups According to step S1, there are Group stimulus-response detection sensor group, each sensor group corresponds to Feature distance dictionary .

[0030] In a specific embodiment of the present invention, taking the grid where the sensor group and the first damage point D1 are located in step S1 as an example, the intercept of the path of the stimulus-response sensor group passing through the damage position of the first damage point D1 in each grid is calculated. , and form a feature distance dictionary Correspondingly, the sensor group and 99 grids have a total of 99 distance propagation matrices There are 66 sensor groups in total, corresponding to Feature distance dictionary .

[0031] Step S223: The feature distance dictionary The detection area wave number matrix in step S21 Multiply the corresponding elements and add all the internal elements to obtain the reconstructed signal parameters corresponding to each group of stimulus-response detection sensors. : ; ; in, Reconstructed signal matrix for stimulus-response detection sensor; is the feature distance dictionary; To reconstruct the signal matrix Middle Rank Elements of the column grid; reconstructing signal parameters for the stimulus-response detection sensor; is the dot product operation.

[0032] Each group of stimulus-response detection sensors also corresponds to The reconstructed signal matrix of the grid and reconstructed signal parameters ; Combine them with the detection area wave number matrix By multiplying the corresponding elements of , 66 groups of stimulus-response detection sensor groups and 99 grids can obtain a total of 6534 groups of reconstructed signal parameters. .

[0033] Step S23: Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensor groups , which is converted into a time spectrum signal through inverse Fourier transform , and get the time spectrum signal vector , combined into a theoretical damage reflection signal dictionary , specifically including the following steps: Step S231: Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensors: ; in, is the theoretical damage reflection signal; is the spectrum of the excitation signal; is the natural logarithm; is an imaginary unit; is the angular frequency.

[0034] Step S232: The theoretical damage reflection signals corresponding to all stimulus-response detection sensor groups are Converted into time spectrum signal The inverse Fourier transform formula is: ; in, is the time spectrum signal; is the time parameter; is the pi parameter.

[0035] Step S233: Arrange all grids in order from left to right and from top to bottom. Column vector, for the grids, total The time spectrum signal vector composed of group signals is: ; in, For the time spectrum signal vectors, a total of indivual; is the time spectrum signal; is the matrix transpose symbol; Number the grid quantities.

[0036] All grids corresponding The theoretical damage reflection signal dictionary obtained by combination is: ; in, is the theoretical impairment reflection signal dictionary.

[0037] In a specific embodiment of the present invention, the excitation signal The toneburst signal with a frequency of 100 kHz is set, and the reconstructed signal parameters calculated in step S22 are 6534 time spectrum signals were obtained , and form a theoretical damage reflection signal dictionary in sequence .

[0038] Step S3: using an improved sparse reconstruction algorithm to solve the optimization problem, and calculating the pixel value of each grid in the detection area of ​​the aero-engine blade, that is, the coincidence of the theoretical damage reflection signal and the measured signal at that point.

[0039] The aero-engine blade damage detection model established based on the improved sparse reconstruction algorithm is: ; in, is the minimum value function; is the pixel value vector The corresponding time spectrum signal vector; is the regularization parameter; For all A vector of pixel values ​​for a grid, , a non-zero value means that the theoretical damage reflection signal passing through the grid coincides with the measured damage reflection signal, that is, there is damage in the grid; is the L1 norm, which is the Manhattan norm; is the L2 norm, which is the Euclidean norm.

[0040] In a specific embodiment of the present invention, the regularization parameter , the optimization problem is calculated on MATLAB using the CVX convex optimization problem solving toolbox to find all non-zero pixel value vectors Chinese elements The location of the value.

[0041] Step S4: According to the pixel value distribution of the aircraft engine blade detection area obtained in step S3, determine A non-zero value indicates that the theoretical damage reflection signal passing through the grid coincides with the measured damage reflection signal, indicating that damage exists. After all grids are judged, an aircraft engine blade damage detection image is generated, and the damage position is located.

[0042] In a specific embodiment of the present invention, Figure 5 This is a comparison diagram of the position of the first damage point D1 and the positioning result of the algorithm in an embodiment of the present invention. The damage point is a circular damage with a diameter of 20 mm in the upper part of the detection area; Figure 6 This is a comparison diagram of the position of the second damage point D2 and the positioning result of the algorithm in an embodiment of the present invention. The damage point is a circular damage with a diameter of 20 mm in the middle of the detection area; Figure 7 This is a comparison diagram of the position of the third damage point D3 and the positioning result of the algorithm in an embodiment of the present invention. The damage point is a circular damage with a diameter of 20 mm in the lower part of the detection area; Figure 8 This figure compares the location of crack damage and the algorithm's positioning results in an embodiment of the present invention. The crack endpoint coordinates are (0, -10) and (25, 10), respectively. The imaging results of point-like damage at the top, middle, and bottom positions, along with the corresponding crack damage, show that the damage location identification results largely coincide with the actual prefabricated damage, demonstrating the effectiveness of this method and its accuracy and robustness in damage positioning.

[0043] The beneficial effects of the present invention are as follows: by reconstructing the theoretical damage reflection signal, a dictionary of theoretical damage reflection signals corresponding to all potential damage positions of all excitation-response detection sensor groups is established, and the damage position information is extracted from the measured signal obtained from the array sensor and compared with the theoretical damage reflection signal to achieve accurate positioning of the damage on the aircraft engine blade; through the propagation characteristics of the reflected wave under different thickness structures, the Lamb wave propagation information of different parts of the aircraft engine blade is effectively integrated, the traditional imaging method of damage of equal thickness structure is improved, and the sparse reconstruction damage imaging is promoted from equal thickness structure to variable thickness structure, which expands the application scope of the ultrasonic guided wave damage detection method.

[0044] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for detecting damage to aircraft engine blades based on an improved ultrasonic sparse reconstruction algorithm, characterized in that: It includes: S1: Set up the sensor array and detection area on the aircraft engine blade to be tested, and stimulate The sensors acquire the response signals and form a dictionary of measured damage reflection signals ; S2: Obtain the sensor array and detection area determined in step S1, determine the wave number distribution of the detection area according to the variable thickness structure Lamb wave propagation model, and obtain the wave number corresponding to each grid thickness in the detection area , thus obtaining the detection area wave number matrix ; Calculate the propagation distance of each sensor-grid path through each grid , forming the distance propagation matrix , get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups , obtain the reconstructed signal parameters ; Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensors , which is converted into a time spectrum signal through inverse Fourier transform , determine the time spectrum signal vector of all grids , and the theoretical damage reflection signal dictionary is obtained by combining ; S3: Based on step S2, an aircraft engine blade damage detection model is constructed, and an improved sparse reconstruction algorithm is used for solution optimization to obtain the pixel value of each grid in the detection area of ​​the aircraft engine blade, specifically: ； in, is the minimum value function; is the dictionary of measured damage reflection signals; is the theoretical impairment reflection signal dictionary; is the pixel value vector The corresponding time spectrum signal vector; is the regularization parameter; For all A vector of pixel values ​​for a grid, , A non-zero value indicates that the grid is damaged. For the The pixel value of a grid; is the L1 norm; is the L2 norm; S4: Obtain pixel value distribution in the aircraft engine blade detection area according to step S3, perform damage judgment, generate an aircraft engine blade damage detection image, and locate the damage position.

2. The method for detecting damage to an aero-engine blade based on an improved ultrasonic sparse reconstruction algorithm according to claim 1, characterized in that: Step S2 is specifically as follows: S21: According to the sensor array and detection area, it is divided into The thickness of each grid is measured in turn, and the wave number corresponding to each grid thickness is determined according to the Lamb wave propagation model of variable thickness structure. , thus obtaining the detection area wave number matrix ; S22: Calculate the propagation distance of each sensor-grid path through each grid , forming the distance propagation matrix , get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups , obtain the reconstructed signal parameters ; S23: Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensors , which is converted into a time spectrum signal through inverse Fourier transform , and get the time spectrum signal vector , combined into a theoretical damage reflection signal dictionary .

3. The method for detecting damage to an aero-engine blade based on an improved ultrasonic sparse reconstruction algorithm according to claim 2, characterized in that: Step S22 is specifically as follows: S221: When the sensor-grid path and the Rank The coordinates of the intersection points of the column grids are and , calculate the propagation distance of each sensor-grid path through each grid ; S222: All propagation distances Composition of distance propagation matrix , any two sensor-grid paths Add up to get the feature distance dictionary corresponding to each group of stimulus-response detection sensor groups ; S223: Feature distance dictionary The detection area wave number matrix in step S21 Multiply the corresponding elements and add all the internal elements to obtain the reconstructed signal parameters corresponding to each group of stimulus-response detection sensors. .

4. The method for detecting damage to an aero-engine blade based on an improved ultrasonic sparse reconstruction algorithm according to claim 2, wherein: Step S23 is specifically as follows: S231: Determine the theoretical damage reflection signal corresponding to each group of stimulus-response detection sensors ; S232: Use inverse Fourier transform to transform the theoretical damage reflection signals corresponding to all stimulus-response detection sensor groups Converted into time spectrum signal ; S233: Arrange all grids in order Column vector, for the grids, total Group signals into time spectrum signal vectors , all grids corresponding to Combined to obtain the theoretical damage reflection signal dictionary .

5. The method for detecting damage to aero-engine blades based on an improved ultrasonic sparse reconstruction algorithm according to claim 3, characterized in that: Step S223 is specifically as follows: The feature distance dictionary The detection area wave number matrix in step S21 Multiply the corresponding elements and add all the internal elements to obtain the reconstructed signal parameters corresponding to each group of stimulus-response detection sensors. for: ； ； in, Reconstructed signal matrix for stimulus-response detection sensor; is the detection area wave number matrix; is the feature distance dictionary; To reconstruct the signal matrix Middle Rank Elements of the column grid; reconstructing signal parameters for the stimulus-response detection sensor; is the dot product operation; is the total number of detection area rows; is the total number of detection area columns.

6. The method for detecting damage to aero-engine blades based on an improved ultrasonic sparse reconstruction algorithm according to claim 4, characterized in that: Step S231 is specifically as follows: ； in, is the theoretical damage reflection signal; is the spectrum of the excitation signal; is the natural logarithm; is an imaginary unit; is the angular frequency.

7. The method for detecting damage to aircraft engine blades based on an improved ultrasonic sparse reconstruction algorithm according to claim 4, characterized in that: Step S232 is specifically as follows: ； in, is the time spectrum signal; is the time parameter; is the pi parameter.

8. The method for detecting damage to aero-engine blades based on an improved ultrasonic sparse reconstruction algorithm according to claim 4, characterized in that: The time spectrum signal vector in step S233 is: ； in, For the A time spectrum signal vector; is the time spectrum signal; is the matrix transpose symbol; Number the grid quantities.

9. The method for detecting damage to aircraft engine blades based on an improved ultrasonic sparse reconstruction algorithm according to claim 4, characterized in that: The theoretical damage reflection signal dictionary in step S233 is: ； in, is the theoretical impairment reflection signal dictionary.

10. The method for detecting damage to aircraft engine blades based on an improved ultrasonic sparse reconstruction algorithm according to claim 1, characterized in that: Step S1 is specifically as follows: Sequential excitation sensors, and use the sensors to receive and obtain all response signals, and form a dictionary of measured damage reflection signals from all the response signals obtained. for: ； in, is the dictionary of measured damage reflection signals; for Time A response signal, 1, 2, ..., ; is the time parameter; is the matrix transpose symbol.

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