Engine rotor blade deformation measurement system and method suitable for continuous wind tunnel

Abstract

The invention relates to an engine rotor blade deformation measurement system and method suitable for a continuous wind tunnel, belonging to the technical field of engine rotor blade deformation measurement. The invention aims to solve the problem of achieving full-surface accurate measurement of high-speed blades. The invention comprises the following steps: installing an engine rotor blade deformation measurement system suitable for a continuous wind tunnel; processing a blade with a speckle texture, adjusting the optical path, and setting the timing to complete phase locking of the blade with the speckle texture; calibrating the first imaging device and the second imaging device to calibrate the internal and external parameters of the camera; conducting experiments to collect test images and reference images; determining the speckle grid and designing a multi-view mask combined synchronization method to determine the three-dimensional coordinates of the speckle grid in the camera coordinate system; calibrating the model coordinate system to obtain the axis system transformation matrix from the camera coordinate system to the model coordinate system; and processing data to calculate the deformation of the blade with the speckle texture.

Description

Technical Field

[0001] The present invention belongs to the technical field of engine rotor blade deformation measurement, and in particular relates to an engine rotor blade deformation measurement system and method suitable for a continuous wind tunnel. Background Art

[0002] Engine rotor blades are key components in aircraft engines, and their deformation characteristics directly affect the engine's performance and safety. In military aircraft, engine rotor blade deformation measurement technology is related to the reliability and stealth performance of the aircraft. High-precision blade deformation measurement can help designers optimize blade structure and improve aircraft engine performance, thereby enhancing the combat effectiveness of aviation weapons. In a combat environment, abnormal deformation of engine blades may cause serious failures. Accurate real-time monitoring can help detect potential problems in advance and ensure the combat capability of the aircraft. From a scientific research perspective, engine rotor blade deformation measurement technology helps to gain a deeper understanding of the mechanical behavior of aircraft engines under high-load working conditions. Through precise monitoring of blade deformation, researchers can better reveal the fatigue characteristics and thermal deformation laws of blade materials, providing valuable data support for the development of aerospace engineering disciplines.

[0003] To ensure engine reliability under extreme operating conditions, accurately measuring rotor blade deformation under aerodynamic loads is crucial. Traditional blade deformation measurement methods typically rely on static laboratory environments or stationary test platforms, but these methods cannot accurately simulate the complex aerodynamic environment of actual flight. As an important aerodynamic testing tool, continuous wind tunnels can provide highly accurate wind tunnel test data under simulated actual flight conditions. Measuring engine rotor blade deformation in a continuous wind tunnel allows blade performance and stability to be evaluated in a more realistic dynamic environment, which has important military and scientific significance.

[0004] However, there are many technical challenges when conducting such measurements in a continuous wind tunnel. First, to ensure the safety of the blades, the test section usually needs to maintain a negative pressure state, which has a significant impact on the stability of the pulsed light source equipment. The negative pressure environment may cause fluctuations in the light source intensity, thereby affecting the measurement accuracy. Secondly, the test section has a complex structure, and the optical path design and equipment installation and commissioning require precise adjustment. Any slight change may have a significant impact on the measurement results. In addition, during the actual test process, errors caused by factors such as unstable light source, camera frame loss or equipment vibration will occur. These factors will affect the synchronization and accuracy of the measurement data. Summary of the Invention

[0005] The problem to be solved by the present invention is to achieve accurate measurement of the entire surface of a high-speed blade, and propose an engine rotor blade deformation measurement system and method suitable for a continuous wind tunnel.

[0006] To achieve the above object, the present invention is implemented through the following technical solutions:

[0007] An engine rotor blade deformation measurement system suitable for a continuous wind tunnel includes a pulsed point light source, a pulsed point light source voltage-stabilized constant temperature chamber, a first reflector device, a second reflector device, a third reflector device, a light source homogenizing and beam expanding device, a first imaging device, a second imaging device, a digital signal generator, and a signal attenuator.

[0008] A pulsed point light source is placed in a pulsed point light source voltage-stabilized constant temperature chamber, and a first reflector assembly is mounted on the top of the pulsed point light source voltage-stabilized constant temperature chamber. Laser light emitted by the pulsed point light source passes through an optical window, is reflected by the first reflector assembly, is then reflected by the second reflector assembly, and then is reflected by the third reflector assembly. The laser light then passes through a light source homogenizing and expanding device and an optical window of a wind tunnel test section to illuminate a blade having a speckle texture. The first and second imaging devices are used to capture images and calibration images of the blade having the speckle texture.

[0009] The first reflector device, the second reflector device, the third reflector device, the light source homogenizing and beam expanding device, the first imaging device, and the second imaging device are respectively fixed near the optical window outside the wind tunnel test section through brackets;

[0010] The pulse point light source is connected to a digital signal generator outside the pulse point light source voltage-stabilized constant temperature chamber, and the digital signal generator is connected to a signal attenuator.

[0011] Furthermore, the pulse point light source voltage-stabilized constant temperature chamber includes a gas nozzle seat, a BNC connector, an electrode, a power socket, an optical glass window, a pulse point light source water cooler, a pulse light source support, a cable sealing component interface, a cooling water outlet, a cooling water inlet, a cooling copper pipe, and a chamber body;

[0012] The left side of the cabin is equipped with a gas nozzle seat, BNC connector, electrode, and power socket. The top of the cabin is equipped with an optical glass window, a cable sealing component interface, a cooling water outlet, and a cooling water inlet. Cooling copper pipes are arranged around the cabin. The cabin also houses a pulsed point light source, a pulsed point light source water cooler, and a pulsed light source support.

[0013] The air nozzle seat is connected to the external normal pressure environment through an air pipe to maintain the normal pressure environment of the pulse point light source constant pressure constant temperature cabin;

[0014] The BNC connector has connectors inside and outside, and the pulse point light source and the digital signal generator are connected via the BNC connector;

[0015] The electrodes are used for external power supply;

[0016] The power socket is used to connect the pulse point light source and the pulse point light source water cooler to electricity;

[0017] The pulse point light source water cooler is used to dissipate heat from the pulse point light source;

[0018] A pulse point light source is placed on the pulse light source support;

[0019] The cable sealing assembly interface is used for connecting cables without affecting the airtightness of the pulsed point light source pressure-stabilized constant temperature chamber;

[0020] The cooling water outlet and cooling water inlet are externally connected to a water chiller for cooling water in and out, and internally connected to a cooling copper pipe. The cooling copper pipe is an auxiliary heat dissipation device for the pulsed point light source voltage-stabilized constant temperature chamber, and real-time heat dissipation is achieved through the cooling water in and out of the cooling water inlet and cooling water outlet.

[0021] Furthermore, the first imaging device and the second imaging device include an industrial camera, a lens and a filter.

[0022] Furthermore, the light source homogenizing and beam expanding device includes a homogenizing device and a beam expanding device, the homogenizing device is a microlens array or an optical fiber cone or frosted glass, and the beam expanding device includes a lens and a lens.

[0023] Furthermore, the blades arranged with the speckle texture are placed in the test section, and fluorescent speckles are arranged on the blades arranged with the speckle texture.

[0024] A method for measuring deformation of an engine rotor blade suitable for a continuous wind tunnel is implemented based on the aforementioned engine rotor blade deformation measurement system suitable for a continuous wind tunnel, and includes the following steps:

[0025] S1. Installing an engine rotor blade deformation measurement system suitable for a continuous wind tunnel;

[0026] S2. Processing the blades with the speckle texture, adjusting the optical path, and then setting the timing to complete phase locking of the blades with the speckle texture;

[0027] S3 performs camera calibration on the first imaging device and the second imaging device to calibrate the internal and external parameters of the camera;

[0028] S4. Conducting a test and collecting test images and reference images;

[0029] S5. Determine the speckle grid: Design a multi-view mask joint synchronization method to determine the 3D coordinates of the speckle grid in the camera coordinate system;

[0030] S6. Calibrate the model coordinate system to obtain the axis transformation matrix from the camera coordinate system to the model coordinate system;

[0031] S7. Data processing, calculating the deformation of the blade with speckle texture.

[0032] Furthermore, in step S3, Zhang's calibration method is used to solve the camera's internal and external parameters.

[0033] Furthermore, the specific implementation method of step S5 includes the following steps:

[0034] S5.1. Determine the first mask region for the leaf region under the perspective of the first imaging device and the second imaging device by manual selection or edge extraction. and the second mask area , the area inside the mask is the leaf speckle area, and the area outside the mask is the background area;

[0035] S5.2. Extract the minimum bounding rectangle surrounding the leaf area based on the first imaging device perspective, and define an equidistant rectangular grid G ​​based on the rectangle, according to Delete the grid points in G that are not in the leaf area to obtain the image captured by the first imaging device , the image coordinates of the speckle grid points corresponding to the first imaging device are ;according to Delete the grid points in G that are not in the leaf area to obtain the image captured by the second imaging device ,in 、 The size is ,but , , for 、 The horizontal resolution size, for 、 The vertical resolution size, i for Any one of j for Any one of the second imaging device corresponds to the speckle grid point image coordinates Combining by image cross-correlation and and get;

[0036] S5.3. According to delete The grid points not in the blade area are obtained , then The points with the same serial number are also deleted to obtain ,according to and As well as the internal and external parameters of the camera obtained in step S3, the three-dimensional coordinates of the blade's speckle grid in the camera coordinate system are obtained by triangulation .

[0037] Furthermore, the specific implementation method of step S6 includes the following steps:

[0038] S6.1. In calm conditions, by rotating a blade having a speckle pattern to a plurality of positions;

[0039] S6.2. The image coordinates of the speckle grid of the image captured by the first imaging device and the second imaging device at the first rotational position of the blade are 、 , the three-dimensional coordinates of the speckle grid of the blade at the first rotation position in the camera coordinate system are ;

[0040] S6.3. Combining Image Cross-Correlation Methods , and images of different rotation positions collected by the first imaging device, and obtaining images of different rotation positions and Image coordinates matching the same name , and different rotation positions and Matching with the same name , , and the three-dimensional coordinates of the speckle grid at different rotation positions of the blade in the camera coordinate system , where mz is the number of rotation positions;

[0041] S6.4. Use the Rodriguez rotation formula to calculate the rotation matrix between different rotation angles ;

[0042] Then convert to multiple axis vector representation , normalize its mean to obtain the standard rotation axis vector ;

[0043] S6.5 Based on the method of steps S6.1-S6.4, obtain the rotation matrix between different pitch angles, and then convert it into multiple pitch axis vectors , normalize its mean to get the standard pitch axis vector ;

[0044] S6.6. Based on , and the yaw axis vector must be orthogonal to it, so the yaw axis vector , and finally get the axis transformation matrix from the camera coordinate system to the model coordinate system .

[0045] Furthermore, the specific implementation method of step S7 includes the following steps:

[0046] S7.1. Data synchronization correction, using multi-view image synchronization and vibration consistency optimization algorithms to obtain a fully synchronized image sequence of the first imaging device and a sequence of images of the second imaging device , nx ​​is the number of images to be matched, is the image sequence of the nxth fully synchronized first imaging device, is the image sequence of the nxth fully synchronized second imaging device;

[0047] S7.2. Obtain the three-dimensional coordinates of the speckle grid in the model coordinate system. Obtain the three-dimensional coordinates of the blade speckle grid in the camera coordinate system at all times by using the image cross-correlation method combined with the inverse transformation of the polynomial transformation. ,in is the three-dimensional coordinate of the blade speckle grid in the camera coordinate system at the nxth moment;

[0048] Then, combined with the results obtained in step S6 , get the three-dimensional coordinates of the blade speckle grid at all times in the model coordinate system ,in, ;

[0049] S7.3. Design a stepwise error screening method to identify grid cells with errors exceeding a set threshold and temporarily fill the data with Nan values.

[0050] S7.3.1. Assume that the , 、 and for The three-dimensional coordinates of and , calculate the difference between each element and the minimum value of the original element, and then divide it by the grid resolution in the corresponding direction to get the normalized Coordinate values ​​and Coordinate values ​​are rounded to obtain normalized and ; then define the grid position of each point ;

[0051] S7.3.2. The three-dimensional coordinates in are converted into matrix form to obtain the three-dimensional coordinate transformation matrix ;

[0052] S7.3.3. For Perform mean filtering and perform difference calculation with the original data to obtain the difference ,in 、 、 Corresponding respectively The data after mean filtering;

[0053] S7.3.4. Set the coarse-grained error to , fine-grained error threshold , ;

[0054] First, perform a preliminary threshold screening to determine the element index that exceeds the coarse-grained error for the overall data. ; Create the first mask , where the data that does not exceed the tolerance is marked as Nan, and the data that exceeds the tolerance is marked as 1. The second mask is obtained by gradually expanding the tolerance area through the corrosion operation ,Will Zhongzai The values ​​marked as 1 are marked as Nan to get the edge data not considered. , then for Using fine-grained error thresholds Perform another screening and determine the index of elements that exceed the fine-grained error , the final super error index ;

[0055] Then based on Will The medium-to-low-tolerance data is set to Nan, and the coordinate transformation matrix of the three dimensions under the final high-to-low index is obtained. ;

[0056] S7.4. For the result obtained in step S7.3 , data interpolation is performed by discretizing the Laplace equation. For Nan in the matrix, the missing value is approximated by the second-order derivative Laplace operator, and the least squares method is used to solve the out-of-tolerance data to obtain the coordinate transformation matrix of the three dimensions after the repair is completed. 、 、 ;

[0057] S7.5. Calculate the blade deformation based on the three-dimensional coordinate transformation matrix after repair.

[0058] Beneficial effects of the present invention:

[0059] The engine rotor blade deformation measurement system described in this invention, suitable for use in continuous wind tunnels, utilizes a specialized pulsed point light source, a constant pressure and constant temperature chamber, to effectively mitigate the effects of the wind tunnel's negative pressure on light source stability. This ensures constant light output throughout the test, thereby guaranteeing high-precision and consistent measurement data. Furthermore, a light path system adapted to the complex structure of the wind tunnel test section was designed, and a rational layout ensured stable operation between the light source and the camera.

[0060] The present invention describes a method for measuring engine rotor blade deformation in a continuous wind tunnel. This method incorporates a multi-view image synchronization and vibration consistency optimization algorithm to address the issue of camera data desynchronization caused by frame loss. Through precise timing control and data correction, the algorithm achieves accurate synchronization of images from different viewpoints, ensuring the timeliness and consistency of deformation data. To further improve measurement accuracy, the present invention proposes a stepwise error screening method that effectively extracts and eliminates erroneous values ​​by setting appropriate thresholds. Furthermore, a simple thin plate model is employed to correct these erroneous values, ensuring that the final measurement results are more consistent with practical physical meaning. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a schematic structural diagram of an engine rotor blade deformation measurement system suitable for a continuous wind tunnel according to the present invention;

[0062] Figure 2 Three views of the pulsed point light source constant pressure constant temperature chamber of the present invention, wherein (a) is the main view, (b) is the side view, and (c) is the top view;

[0063] Figure 3 This is a schematic diagram of the positioning marking points of the present invention;

[0064] Figure 4 This is a flow chart of a method for measuring engine rotor blade deformation in a continuous wind tunnel according to the present invention;

[0065] In the figure, 1 is a pulsed point light source, 2 is a pulsed point light source voltage-stabilized constant temperature chamber, 3 is a first reflector device, 4 is a second reflector device, 5 is a third reflector device, 6 is a light source homogenizing and beam expanding device, 7 is a first imaging device, 8 is a second imaging device, 9 is a blade with a speckle texture, 10 is a digital signal generator, 11 is a signal attenuator, 12 is a nozzle holder, 13 is a BNC connector, 14 is an electrode, 15 is a power socket, 18 is a pulsed point light source water cooler, 19 is a pulsed light source support, 20 is a cable sealing assembly interface, 21 is a cooling water outlet, 22 is a cooling water inlet, 23 is a cooling copper pipe, and 24 is a cabin body. DETAILED DESCRIPTION

[0066] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the specific embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the specific embodiments of the present invention described and illustrated in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0067] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0068] In order to further understand the content, features and effects of the present invention, the following specific embodiments are given as examples, and the attached Figure 1 -Attached Figure 4 The detailed instructions are as follows:

[0069] Example 1:

[0070] An engine rotor blade deformation measurement system suitable for a continuous wind tunnel includes a pulsed point light source 1, a pulsed point light source constant temperature chamber 2, a first reflector device 3, a second reflector device 4, a third reflector device 5, a light source homogenizing and expanding device 6, a first imaging device 7, a second imaging device 8, a digital signal generator 10, and a signal attenuator 11.

[0071] A pulsed point light source 1 is placed in a pulsed point light source pressure-stabilized constant temperature chamber 2, and a first reflector assembly 3 is mounted on top of the pulsed point light source pressure-stabilized constant temperature chamber 2. Laser light emitted by the pulsed point light source 1 passes through an optical window, is reflected by the first reflector assembly 3, is then reflected by the second reflector assembly 4, and then by the third reflector assembly 5. The laser light then passes through a light source homogenizing and expanding device 6 and the optical window of the wind tunnel test section to illuminate a blade 9 having a speckle texture. A first imaging device 7 and a second imaging device 8 are used to capture images and calibration images of the blade 9 having the speckle texture.

[0072] The first reflector device 3, the second reflector device 4, the third reflector device 5, the light source homogenizing and beam expanding device 6, the first imaging device 7, and the second imaging device 8 are respectively fixed near the optical window outside the wind tunnel test section through brackets;

[0073] The pulsed point light source 1 is connected to a digital signal generator 10 outside the pulsed point light source voltage-stabilized constant temperature chamber 2 , and the digital signal generator 10 is connected to a signal attenuator 11 .

[0074] Furthermore, the pulse point light source voltage-stabilized constant temperature chamber 2 includes a gas nozzle seat 12, a BNC connector 13, an electrode 14, a power socket 15, a pulse point light source water cooler 18, a pulse light source support 19, a cable sealing assembly interface 20, a cooling water outlet 21, a cooling water inlet 22, a cooling copper tube 23, and a chamber body 24;

[0075] The left side of the cabin 24 is equipped with a gas nozzle seat 12, a BNC connector 13, an electrode 14, and a power socket 15. The top of the cabin 24 is equipped with an optical glass window, a cable sealing assembly interface 20, a cooling water outlet 21, and a cooling water inlet 22. Cooling copper pipes 23 are arranged around the cabin. The cabin also contains the pulse point light source 1, a pulse point light source water cooler 18, and a pulse light source support 19.

[0076] The air nozzle seat 12 is connected to the external normal pressure environment through an air pipe to maintain the normal pressure environment of the pulse point light source constant pressure constant temperature chamber 2;

[0077] The BNC connector 13 has connectors inside and outside, and the pulse point light source 1 and the digital signal generator 10 are connected via the BNC connector 13;

[0078] The electrode 14 is used for external power supply;

[0079] The power socket 15 is used to connect the pulse point light source 1 and the pulse point light source water cooler 18 to electricity;

[0080] The pulse point light source water cooler 18 is used to dissipate heat from the pulse point light source 1;

[0081] The pulse light source support 19 is placed on the pulse point light source 1;

[0082] The cable sealing assembly interface 20 is used for connecting the cable without affecting the airtightness of the pulsed point light source constant pressure and constant temperature chamber 2;

[0083] The cooling water outlet 21 and the cooling water inlet 22 are externally connected to a water chiller for cooling water in and out, and internally connected to a cooling copper tube 23. The cooling copper tube 23 is an auxiliary heat dissipation device of the pulsed point light source voltage-stabilized constant temperature chamber 2, and real-time heat dissipation is achieved through the cooling water inlet 22 and the cooling water outlet 21.

[0084] Furthermore, the first imaging device 7 and the second imaging device 8 include industrial cameras, lenses and filters.

[0085] Furthermore, the light source homogenizing and beam expanding device 6 includes a homogenizing device and a beam expanding device. The homogenizing device is a microlens array or an optical fiber cone or frosted glass, and the beam expanding device includes a lens and a lens.

[0086] Furthermore, the blade 9 with the speckle texture is placed in the test section, and fluorescent speckles are arranged on the blade 9 with the speckle texture.

[0087] The structure in this embodiment is further described as follows:

[0088] The pulsed point light source 1 is used to provide illumination for the entire measurement system, and is preferably a laser point light source with a wavelength of 532 nm (which is more suitable than lasers of other wavelengths in terms of sensitivity, light source feasibility, detection efficiency, and operational safety);

[0089] The pulse point light source constant pressure chamber 2 is used to provide a normal temperature and pressure environment for the pulse light source, so that the pulse light source can work normally even in a low-pressure or high-pressure wind tunnel test environment.

[0090] The first reflector device 3, the second reflector device 4, and the third reflector device 5 are used to emit the pulsed point light source 1 near the window of the test section;

[0091] The first reflector device 3 , the second reflector device 4 , and the third reflector device 5 include reflectors and mirror frames capable of adjusting the directions and angles of the reflectors.

[0092] The first reflector device 3, the second reflector device 4, and the third reflector device 5 need to be connected to the test section, and no relative displacement must be ensured during the entire test process;

[0093] The first imaging device 7 and the second imaging device 8 are used to capture images of engine rotor blades and calibration images;

[0094] The first imaging device 7 and the second imaging device 8 include industrial cameras, lenses, and filters. The selection of the filters is related to the fluorescence wavelength of the speckle on the blade 9 with the speckle texture. The filters need to filter out stray light. When a laser light source with a wavelength of 532nm is used, the fluorescence wavelength of the speckle on the blade is red light in the range of 620nm-750nm. The selection of the filters needs to filter out green light below 620nm.

[0095] The blades 9 arranged with speckle textures preferably use fluorescent speckles, because stray light can be filtered out by a filter;

[0096] The preferred homogenizer is a microlens array or fiber optic cone. Frosted glass can also be used, but its transmittance is low and will affect the brightness of the light source. Some beam expanders use a variable-focus, large-aperture lens, or a fixed-focus lens or lens. Variable-focus, large-aperture lenses offer low light loss and can dynamically adjust the illumination range.

[0097] The first imaging device 7 and the second imaging device 8 need to be connected to the test section, and no relative displacement must be ensured during the entire test process;

[0098] The light source homogenizing and beam expanding device 6 needs to be fixedly connected to the test section;

[0099] The digital signal generator 10 is used to set the light emission time and timing of the pulsed point light source 1 to trigger the acquisition of the cameras in the first imaging device 7 and the second imaging device 8.

[0100] The signal attenuator 11 is used to filter and attenuate the voltage signal of the speed sensor so that its output signal can normally trigger the digital signal generator 10, thereby triggering the pulsed point light source 1 to emit light and the first imaging device 7 and the second imaging device 8 to synchronously capture images.

[0101] The pulse point light source constant pressure constant temperature chamber 2 is as follows Figure 2 shown.

[0102] Example 2:

[0103] A method for measuring deformation of an engine rotor blade in a continuous wind tunnel is implemented based on the engine rotor blade deformation measurement system in a continuous wind tunnel described in Example 1, and includes the following steps:

[0104] S1. Installing an engine rotor blade deformation measurement system suitable for a continuous wind tunnel;

[0105] S2. The blades 9 with the speckle texture are processed, and then the optical path is adjusted, and then the timing is set to complete the phase locking of the blades 9 with the speckle texture;

[0106] Further, the specific contents are:

[0107] The processing of blades mainly involves the preparation of speckle patterns. If the pulse point light source is normal white light, the generated speckle can appear as black dots on a white background or white dots on a black background; if the light source is a light source of a specific wavelength band, the foreground of the speckle is the fluorescent dots excited by the light source, while the background is not excited by the light source. When making speckles, the spraying method is usually used. The specific method is to first spray a layer of primer on the surface of the blade, and after the primer is completely dry, print or paste hollow stickers, and then spray the foreground paint. In addition, you can also directly paste pre-designed speckle pattern stickers on the surface of the blade, but considering that the stickers are easily damaged during the experiment and the contrast is limited, it is usually not the preferred option. Although the transfer method can improve efficiency, it is usually not preferred due to the poor quality of the speckle.

[0108] In addition, marker points for subsequent image registration need to be evenly arranged on the blade surface.

[0109] The main task of optical path adjustment is to reflect the point light source from the light outlet to the optimal illumination position of the blade through the reflector. The key to adjustment lies in the position and angle of the reflector.

[0110] The phase locking of the blades usually needs to be adjusted according to the actual device configuration. For devices equipped with speed sensors and motor encoders, it is recommended to use the output signals of the speed sensors and motor encoders as the phase locking signals. Specifically, each time the blade rotates one circle, the speed sensor and motor encoder will return a voltage signal. These voltage signals usually cannot be used directly as triggers and need to undergo signal processing (such as shaping or amplitude adjustment). The specific method should be determined according to the requirements of the actual device. For devices without speed sensors and motor encoders, photoelectric triggering can be used (setting a reflection or light transmission point on the blade surface, and using a photoelectric sensor or laser sensor to monitor the specific position of the blade).

[0111] The timing setting needs to ensure the following points: the pulsed point light source 1 can emit light stably within the exposure time of the first imaging device 7 and the second imaging device 8; the camera trigger acquisition synchronization of the first imaging device 7 and the second imaging device 8 must be ensured; the camera trigger delay must be adjusted to ensure that the optimal position of the leaf can be captured during image acquisition.

[0112] S3 performs camera calibration on the first imaging device 7 and the second imaging device 8, calibrating the internal and external parameters of the camera;

[0113] Furthermore, in step S3, Zhang's calibration method is used to solve the camera's internal and external parameters.

[0114] Furthermore, the internal parameters are ; The external parameters are ;in is the focal length in the u and v directions, is the radial distortion parameter, are the coordinates of the principal point; R and t are the rotation matrix and translation vector from the world coordinate system to the camera coordinate system, respectively.

[0115] S4. Conducting a test and collecting test images and reference images;

[0116] Furthermore, during the wind tunnel test, the test conditions are first reached, and the trigger delay of the camera is adjusted to ensure that the blade is in the appropriate position (with minimal occlusion and small distortion) in the images captured by the cameras of the first imaging device 7 and the second imaging device 8. The image of the blade at this time is captured. The image sequence captured from the perspective of the camera of the first imaging device 7 is , the image sequence captured from the camera perspective in the second imaging device 8 is , n is the number of images collected during the experiment.

[0117] After the test is over, when the blades have no rotation speed and there is no wind, the position of the blades is adjusted so that the blades in the images captured by the cameras of the first imaging device 7 and the second imaging device 8 are in a position close to that during the test. The images of the blades at this time are captured. The image sequence captured from the perspective of the camera of the first imaging device 7 is: , the image sequence captured from the camera perspective in the second imaging device 8 is , m is the number of collected benchmark images.

[0118] S5. Determine the speckle grid: Design a multi-view mask joint synchronization method to determine the 3D coordinates of the speckle grid in the camera coordinate system;

[0119] Furthermore, the specific implementation method of step S5 includes the following steps:

[0120] For the leaf area under the viewing angle of the first imaging device 7 and the second imaging device 8, the first mask area is determined respectively by manual selection or edge extraction. and the second mask area , the area inside the mask is the leaf speckle area, and the area outside the mask is the background area;

[0121] S5.2. Extract the minimum circumscribed rectangle surrounding the leaf area based on the perspective of the first imaging device 7, and define an equidistant rectangular grid G ​​based on the rectangle, according to Delete the grid points in G that are not in the leaf area to obtain the image captured by the first imaging device 7 , the image coordinates of the speckle grid points corresponding to the first imaging device 7 are ;according to Delete the grid points in G that are not in the leaf area to obtain the image captured by the second imaging device 8 ,in 、 The size is ,but , , for 、 The horizontal resolution size, for 、 The vertical resolution size, i for Any one of j for Any one of the second imaging device 8 corresponds to the speckle grid point image coordinates Combining by image cross-correlation and and get;

[0122] S5.3. According to delete The grid points not in the blade area are obtained , then The points with the same serial number are also deleted to obtain ,according to and As well as the internal and external parameters of the camera obtained in step S3, the three-dimensional coordinates of the blade's speckle grid in the camera coordinate system are obtained by triangulation .

[0123] S6. Calibrate the model coordinate system to obtain the axis transformation matrix from the camera coordinate system to the model coordinate system;

[0124] Furthermore, the specific implementation method of step S6 includes the following steps:

[0125] S6.1. When there is no wind, the blade 9 having the speckle texture is rotated to a plurality of positions;

[0126] S6.2. The image coordinates of the speckle grid of the image captured by the first imaging device 7 and the second imaging device 8 at the first rotational position of the blade are: 、 , the three-dimensional coordinates of the speckle grid of the blade at the first rotation position in the camera coordinate system are ;

[0127] S6.3. Combining Image Cross-Correlation Methods , and the images of different rotation positions collected by the first imaging device 7, and the images of different rotation positions and Image coordinates matching the same name , and different rotation positions and Matching with the same name , , and the three-dimensional coordinates of the speckle grid at different rotation positions of the blade in the camera coordinate system , where mz is the number of rotation positions;

[0128] S6.4. Use the Rodriguez rotation formula to calculate the rotation matrix between different rotation angles ;

[0129] Then convert to multiple axis vector representation , normalize its mean to obtain the standard rotation axis vector ;

[0130] S6.5 Based on the method of steps S6.1-S6.4, obtain the rotation matrix between different pitch angles, and then convert it into multiple pitch axis vectors , normalize its mean to get the standard pitch axis vector ;

[0131] S6.6. Based on , and the yaw axis vector must be orthogonal to it, so the yaw axis vector , and finally get the axis transformation matrix from the camera coordinate system to the model coordinate system .

[0132] S7. Data processing, calculating the deformation of the blade 9 with the speckle texture arranged thereon.

[0133] Furthermore, the specific implementation method of step S7 includes the following steps:

[0134] S7.1. Data synchronization correction, using multi-view image synchronization and vibration consistency optimization algorithm to obtain a fully synchronized image sequence of the first imaging device 7 and the image sequence of the second imaging device 8 , nx ​​is the number of images to be matched, is the image sequence of the nxth completely synchronized first imaging device 7, is the image sequence of the nxth fully synchronized second imaging device 8;

[0135] Furthermore, during experiments, signal interference (caused by factors such as camera acquisition signals and optoelectronic system noise) can affect image data synchronization, resulting in frame loss. Therefore, strategies are needed to minimize the effects of interference and ensure synchronization and accuracy of image data from different viewpoints. A multi-view image synchronization and vibration consistency optimization algorithm was designed to address this issue.

[0136] From step S4, we can see that the image collected during the test is and .

[0137] against For each image in the image, select the local image block at the tail of the leaf in the first image , get the center position of the image , image correlation method based on and Matched , calculate the center position of all image blocks .

[0138] Similarly, we can get The center position of all image blocks .

[0139] If at this time and is a one-to-one correspondence, then and The distribution characteristics of should be consistent. Similarly, the corresponding image sequence can be obtained according to the distribution characteristics of the data.

[0140] The specific method ranges from the following steps:

[0141] Set the sliding window, the sliding window size is , for any ls, lm ,from and Take local data from . Then we have:

[0142] =

[0143] =

[0144] For each and Use normalized cross correlation (NCC) to calculate the correlation of the window NCC . .

[0145] and is the kth center position in the window. and It's a window and The mean of window and If NCC , then it is considered that ls and lm are matched, that is, the ls-th image in the first imaging device 7 and the lm-th image in the second imaging device 8 are matched.

[0146] The above processing is performed on all images to obtain a completely synchronized image sequence of the first imaging device 7 and the second imaging device 8. and , nx ​​is the number of matched images.

[0147] S7.2. Obtain the three-dimensional coordinates of the speckle grid in the model coordinate system. Obtain the three-dimensional coordinates of the blade speckle grid in the camera coordinate system at all times by using the image cross-correlation method combined with the inverse transformation of the polynomial transformation. ,in is the three-dimensional coordinate of the blade speckle grid in the camera coordinate system at the nxth moment;

[0148] Then, combined with the results obtained in step S6 , get the three-dimensional coordinates of the blade speckle grid at all times in the model coordinate system ,in, ;

[0149] Further, the specific steps are as follows:

[0150] S7.2.1. For the results obtained in S4 , take the mean of the series respectively, and get and ;

[0151] S7.2.2. Yes and Using the method in S5, we can get Image coordinates of the speckle grid of the middle leaf 、 Image coordinates of the speckle grid of the middle leaf ;

[0152] S7.2.3. Determine by manual selection or contour extraction combined with contour size screening. and The center coordinates of the positioning markers arranged on the leaves in the image 、 . Select the four outermost marker points as the initial positioning marker coordinates 、 (like Figure 4 The figure shows the distribution of positioning markers, where the “x”-shaped markers are the four outermost markers.

[0153] S7.2.4. For the first set of images in the image sequence for the test state and , determine the coordinates of the four outermost marker points by image cross-correlation or manual selection 、 ;

[0154] S7.2.5. Based on and Combined with the affine transformation method, Coarse registration to Get .based on 、 、 By means of image cross-correlation, we can obtain The image coordinates of the anchor point . Through the inverse transformation of affine transformation, Transformed into , at this time for The image coordinates of the positioning point;

[0155] S7.2.6. Based on 、 、 、 , through the polynomial transformation method, Refine alignment to get ,based on 、 、 (mentioned in the second step), the image cross-correlation method is used to obtain the Speckle grid of the upper blade , then the inverse transformation of the polynomial transformation will be Transformed into ,but ,for The speckle grid of the leaf on the image; similarly, we can get Speckle grid . ,、 and 、 The grids in are completely one-to-one matched;

[0156] S7.2.7. For Each image in can be combined by the method of S6 、 The matched speckle grid is obtained, and then the speckle grids of all the test images in the first imaging device 7 can be obtained. Similarly, the speckle grid of all test images of the second imaging device 8 can be obtained. ,based on and As well as the camera parameters in S3, the three-dimensional coordinates of the blade speckle grid in the camera coordinate system at all times during the test can be obtained by triangulation ;

[0157] S7.2.8. For any , combined with the results obtained in S6 , the three-dimensional coordinates of the speckle grid in the model coordinate system can be obtained Similarly, the three-dimensional coordinates of the blade speckle grid at all times in the model coordinate system can be obtained: Similarly, the three-dimensional coordinates of the blade speckle grid in the model coordinate system when there is no wind and no speed are .

[0158] S7.3. Design a stepwise error screening method to identify grid cells with errors exceeding a set threshold and temporarily fill the data with Nan values.

[0159] S7.3.1. Assume that the , 、 and for The three-dimensional coordinates of and , calculate the difference between each element and the minimum value of the original element, and then divide it by the grid resolution in the corresponding direction to get the normalized Coordinate values ​​and Coordinate values ​​are rounded to obtain normalized and ; then define the grid position of each point ;

[0160] S7.3.2. The three-dimensional coordinates in are converted into matrix form to obtain the three-dimensional coordinate transformation matrix ;

[0161] Furthermore, the point coordinates are converted into matrix form. The three-dimensional coordinates in are converted into matrix form . First initialize All values ​​are "NaN", use the index of coord in 1 to in Fill in In, that is , , ,in , is the number of speckle grids.

[0162] S7.3.3. For Perform mean filtering and perform difference calculation with the original data to obtain the difference ,in 、 、 Corresponding respectively The data after mean filtering;

[0163] S7.3.4. Set the coarse-grained error to , fine-grained error threshold , > ;

[0164] First, perform a preliminary threshold screening to determine the element index that exceeds the coarse-grained error for the overall data. ; Create the first mask , where the data that does not exceed the tolerance is marked as Nan, and the data that exceeds the tolerance is marked as 1. The second mask is obtained by gradually expanding the tolerance area through the corrosion operation ,Will Zhongzai The values ​​marked as 1 are marked as Nan to get the edge data not considered. , then for Using fine-grained error thresholds Perform another screening and determine the index of elements that exceed the fine-grained error , the final super error index ;

[0165] Then based on Will The medium-to-low-tolerance data is set to Nan, and the coordinate transformation matrix of the three dimensions under the final high-to-low index is obtained. ;

[0166] S7.4. For the result obtained in step S7.3 , data interpolation is performed by discretizing the Laplace equation. For Nan in the matrix, the missing value is approximated by the second-order derivative Laplace operator, and the least squares method is used to solve the out-of-tolerance data to obtain the coordinate transformation matrix of the three dimensions after the repair is completed. 、 、 ;

[0167] Furthermore, out-of-tolerance data is corrected primarily through a simple thin plate model approach, primarily by discretizing the Laplace equation (a second-order partial differential equation) for data interpolation. For NaN elements in a given matrix, the missing values ​​are approximated using the second-order derivative (i.e., the Laplace operator), and the linear system is solved using the least squares method. This allows for smooth data repair.

[0168] The specific steps are as follows: For any grid point to be repaired , perform interpolation repair on its neighborhood by performing second-order difference, and establish the equation by calculating the difference between it and the neighborhood point , are the values ​​of the upper, lower, left and right areas of the current point respectively. Then the sparse matrix of the current point can be expressed as: ;

[0169] Then all the points that need to be repaired are added to the sparse matrix above to form a large sparse matrix that represents the relationship between all missing values ​​and the surrounding known values. Let this matrix be A. Then by You can solve The repair value of the nan value is obtained. , similarly, we can get of and .

[0170] Then , , Based on the data restored to the three-dimensional grid form in corrd in S7.3, let it be , then:

[0171]

[0172]

[0173] ;

[0174] S7.5. Calculate the blade deformation based on the three-dimensional coordinate transformation matrix after repair.

[0175] Furthermore, in the model coordinate system, the deformation in the three directions is :Assume that the three-dimensional coordinates of the repaired speckle grid under no wind and no speed are , for any repaired speckle grid in the test process .

[0176] but , , , the Euclidean distance is .

[0177] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0178] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and components may be substituted with equivalents without departing from the scope of the present application. In particular, as long as there are no structural conflicts, the various features of the embodiments disclosed herein may be combined with each other in any manner, and the omission of an exhaustive description of these combinations in this specification is solely for the sake of space and resource conservation. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions within the scope of the claims.

Claims

1. An engine rotor blade deformation measurement system suitable for a continuous wind tunnel, characterized in that: It comprises a pulsed point light source (1), a pulsed point light source voltage-stabilized constant temperature chamber (2), a first reflector device (3), a second reflector device (4), a third reflector device (5), a light source homogenizing and beam expanding device (6), a first imaging device (7), a second imaging device (8), a digital signal generator (10), and a signal attenuator (11); The pulsed point light source (1) is placed in a pulsed point light source constant pressure and constant temperature chamber (2), and the first reflector device (3) is installed on the top of the pulsed point light source constant pressure and constant temperature chamber (2); the laser light emitted by the pulsed point light source (1) passes through the optical window, is reflected by the first reflector device (3) to the second reflector device (4), and then is reflected to the third reflector device (5), and then passes through the light source homogenizing and expanding device (6) and the optical window of the wind tunnel test section to illuminate the blade (9) arranged with a speckle texture; the first imaging device (7) and the second imaging device (8) are used to collect an image and a calibration image of the blade (9) arranged with the speckle texture; The first reflector device (3), the second reflector device (4), the third reflector device (5), the light source homogenizing and beam expanding device (6), the first imaging device (7), and the second imaging device (8) are respectively fixed near the optical window outside the wind tunnel test section via brackets; The pulsed point light source (1) is connected to a digital signal generator (10) outside the pulsed point light source voltage-stabilized constant temperature chamber (2), and the digital signal generator (10) is connected to a signal attenuator (11).

2. The engine rotor blade deformation measurement system suitable for a continuous wind tunnel according to claim 1, characterized in that: The pulse point light source constant pressure constant temperature chamber (2) comprises a nozzle seat (12), a BNC connector (13), an electrode (14), a power socket (15), a pulse point light source water cooler (18), a pulse light source support (19), a cable sealing component interface (20), a cooling water outlet (21), a cooling water inlet (22), a cooling copper pipe (23), and a chamber body (24); The left side of the cabin (24) is equipped with a gas nozzle seat (12), a BNC connector (13), an electrode (14), and a power socket (15); the top of the cabin (24) is equipped with an optical glass window, a cable sealing component interface (20), a cooling water outlet (21), and a cooling water inlet (22); cooling copper pipes (23) are arranged around the cabin; and a pulse point light source (1), a pulse point light source water cooler (18), and a pulse light source support (19) are placed in the cabin; The air nozzle seat (12) is connected to the external normal pressure environment through an air pipe to maintain the normal pressure environment of the pulse point light source constant pressure constant temperature chamber (2); The BNC connector (13) has connectors inside and outside, and the pulse point light source (1) and the digital signal generator (10) are connected via the BNC connector (13); The electrode (14) is used for external power supply; The power socket (15) is used to connect the pulse point light source (1) and the pulse point light source water cooler (18) to electricity; The pulse point light source water cooler (18) is used for dissipating heat from the pulse point light source (1); A pulsed point light source (1) is placed on the pulse light source support (19); The cable sealing assembly interface (20) is used for connecting cables without affecting the airtightness of the pulsed point light source constant pressure and constant temperature chamber (2); The cooling water outlet (21) and the cooling water inlet (22) are externally connected to a water chiller for cooling water inlet and outlet, and are internally connected to a cooling copper tube (23). The cooling copper tube (23) is an auxiliary heat dissipation device of the pulse-type point light source voltage-stabilized constant temperature chamber (2), and achieves real-time heat dissipation through the cooling water inlet (22) and the cooling water outlet (21).

3. The engine rotor blade deformation measurement system suitable for a continuous wind tunnel according to claim 2, characterized in that: The first imaging device (7) and the second imaging device (8) include an industrial camera, a lens, and a filter.

4. The engine rotor blade deformation measurement system suitable for a continuous wind tunnel according to claim 3, characterized in that: The light source homogenizing and beam expanding device (6) comprises a homogenizing device and a beam expanding device, the homogenizing device is a microlens array or an optical fiber cone or frosted glass, and the beam expanding device comprises a lens and a lens.

5. The engine rotor blade deformation measurement system suitable for a continuous wind tunnel according to claim 4, characterized in that: The blade (9) with the speckle texture is placed in the test section, and fluorescent speckles are arranged on the blade (9) with the speckle texture.

6. A method for measuring deformation of an engine rotor blade in a continuous wind tunnel, implemented by a system for measuring deformation of an engine rotor blade in a continuous wind tunnel according to any one of claims 1 to 5, characterized in that: The steps include: S1. Installing an engine rotor blade deformation measurement system suitable for a continuous wind tunnel; S2. Processing the blade (9) with the speckle texture, adjusting the optical path, and then performing timing setting to complete phase locking of the blade (9) with the speckle texture; S3. Calibrate the first imaging device (7) and the second imaging device (8) to calibrate the internal and external parameters of the cameras; S4. Conducting a test and collecting test images and reference images; S5. Determine the speckle grid: Design a multi-view mask joint synchronization method to determine the 3D coordinates of the speckle grid in the camera coordinate system; S6. Calibrate the model coordinate system to obtain the axis transformation matrix from the camera coordinate system to the model coordinate system; S7. Data processing, calculating the deformation of the blade (9) with the speckle texture arranged.

7. The method for measuring engine rotor blade deformation in a continuous wind tunnel according to claim 6, characterized in that: In step S3, Zhang's calibration method is used to solve the camera's internal and external parameters.

8. The method for measuring deformation of an engine rotor blade in a continuous wind tunnel according to claim 7, characterized in that: The specific implementation method of step S5 includes the following steps: S5.

1. For the leaf area under the viewing angle of the first imaging device (7) and the second imaging device (8), determine the first mask area by manual selection or edge extraction respectively. and the second mask area , the area inside the mask is the leaf speckle area, and the area outside the mask is the background area; S5.

2. Extract the minimum bounding rectangle surrounding the leaf area based on the perspective of the first imaging device (7), and define an equidistant rectangular grid G ​​based on the rectangle, according to Delete the grid points in G that are not in the leaf area to obtain the image captured by the first imaging device (7) , the image coordinates of the speckle grid points corresponding to the first imaging device (7) are ;according to Delete the grid points in G that are not in the leaf area to obtain the image captured by the second imaging device (8) ,in 、 The size is ,but , , for 、 The horizontal resolution size, for 、 The vertical resolution size; i for Any one of j for Any one of the following; the second imaging device (8) corresponds to the speckle grid point image coordinates Combining by image cross-correlation and and get; S5.

3. According to delete The grid points not in the blade area are obtained , then The points with the same serial number are also deleted to obtain ,according to and As well as the internal and external parameters of the camera obtained in step S3, the three-dimensional coordinates of the blade's speckle grid in the camera coordinate system are obtained by triangulation .

9. The method for measuring deformation of an engine rotor blade in a continuous wind tunnel according to claim 8, characterized in that: The specific implementation method of step S6 includes the following steps: S6.

1. In a calm state, the blade (9) having the speckle texture is rotated to a plurality of positions; S6.

2. The image coordinates of the speckle grid of the image captured by the first imaging device (7) and the second imaging device (8) at the first rotation position of the blade are 、 , the three-dimensional coordinates of the speckle grid of the blade at the first rotation position in the camera coordinate system are ; S6.

3. Combining Image Cross-Correlation Methods , and the images at different rotation positions collected by the first imaging device (7), and the images at different rotation positions and Image coordinates matching the same name , and different rotation positions and Matching with the same name , , and the three-dimensional coordinates of the speckle grid at different rotation positions of the blade in the camera coordinate system , where mz is the number of rotation positions; S6.

4. Use the Rodriguez rotation formula to calculate the rotation matrix between different rotation angles ; Then convert to multiple axis vector representation , normalize its mean to obtain the standard rotation axis vector ; S6.5 Based on the method of steps S6.1-S6.4, obtain the rotation matrix between different pitch angles, and then convert it into multiple pitch axis vectors , normalize its mean to get the standard pitch axis vector ; S6.

6. Based on , and the yaw axis vector must be orthogonal to it, so the yaw axis vector , and finally get the axis transformation matrix from the camera coordinate system to the model coordinate system .

10. The method for measuring engine rotor blade deformation in a continuous wind tunnel according to claim 9, characterized in that: The specific implementation method of step S7 includes the following steps: S7.

1. Data synchronization correction, using multi-view image synchronization and vibration consistency optimization algorithm to obtain a fully synchronized image sequence of the first imaging device (7) and a sequence of images of the second imaging device (8) , nx ​​is the number of images to be matched, is the image sequence of the nxth fully synchronized first imaging device (7), is the image sequence of the nxth fully synchronized second imaging device (8); S7.

2. Obtain the three-dimensional coordinates of the speckle grid in the model coordinate system. Obtain the three-dimensional coordinates of the blade speckle grid in the camera coordinate system at all times by using the image cross-correlation method combined with the inverse transformation of the polynomial transformation. ,in is the three-dimensional coordinate of the blade speckle grid in the camera coordinate system at the nxth moment; Then, combined with the results obtained in step S6 , get the three-dimensional coordinates of the blade speckle grid at all times in the model coordinate system ,in, ; S7.

3. Design a stepwise error screening method to identify grid cells with errors exceeding a set threshold and temporarily fill the data with Nan values. S7.3.

1. Assume that the , 、 and for The three-dimensional coordinates of and , calculate the difference between each element and the minimum value of the original element, and then divide it by the grid resolution in the corresponding direction to get the normalized Coordinate values ​​and Coordinate values ​​are rounded to obtain normalized and ; then define the grid position of each point ; S7.3.

2. The three-dimensional coordinates in are converted into matrix form to obtain the three-dimensional coordinate transformation matrix ; S7.3.

3. For Perform mean filtering and perform difference calculation with the original data to obtain the difference ,in 、 、 Corresponding respectively The data after mean filtering; S7.3.

4. Set the coarse-grained error to , fine-grained error threshold , ; First, perform a preliminary threshold screening to determine the element index that exceeds the coarse-grained error for the overall data. ; Create the first mask , where the data that does not exceed the tolerance is marked as Nan, and the data that exceeds the tolerance is marked as 1. The second mask is obtained by gradually expanding the tolerance area through the corrosion operation ,Will Zhongzai The values ​​marked as 1 are marked as Nan to get the edge data not considered. , then for Using fine-grained error thresholds Perform another screening and determine the index of elements that exceed the fine-grained error , the final super error index ; Then based on Will The medium-to-low-tolerance data is set to Nan, and the coordinate transformation matrix of the three dimensions under the final high-to-low index is obtained. ; S7.

4. For the result obtained in step S7.3 , data interpolation is performed by discretizing the Laplace equation. For Nan in the matrix, the missing value is approximated by the second-order derivative Laplace operator, and the least squares method is used to solve the out-of-tolerance data to obtain the coordinate transformation matrix of the three dimensions after the repair is completed. 、 、 ; S7.

5. Calculate the blade deformation based on the three-dimensional coordinate transformation matrix after repair.

Images