A global ultra-sensitive rotating body vibration measurement method in a polar coordinate system

Abstract

The present invention discloses a method for measuring the vibration of a rotating body in a full-range ultra-sensitive manner in a polar coordinate system, and relates to the technical field of structural health monitoring. The present invention realizes high-precision vibration monitoring of rotating structures through non-contact optical measurement, including: calibrating scale parameters through known physical dimensions, identifying feature points and calculating homography matrices using SIFT+RANSAC algorithm, and decomposing to obtain the rotation angle and center. The Cartesian coordinate pixel intensity is mapped to polar coordinates using bilinear interpolation, and a singular value decomposition is performed after constructing a spatiotemporal pixel intensity matrix. The top k-order modes are selected based on the cumulative energy proportion of >90% to separate noise. The optical flow algorithm is used to calculate the full-field vibration displacement in polar coordinates, and finally converted into a physical space displacement field through scale parameters. This method effectively separates rotation and vibration, and the vibration measurement accuracy reaches the sub-pixel level. It is suitable for high-precision vibration analysis of complex rotating bodies such as fan blades, and provides a new approach for non-destructive testing of rotating machinery.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural health monitoring, and in particular relates to a global ultra-sensitive rotating body vibration measurement method in a polar coordinate system. Background Art

[0002] Vibration measurement of rotating objects is crucial in modern engineering, particularly in wind turbine structural monitoring and maintenance. During wind turbine operation, the rotational vibration of blades and generators directly impacts their efficiency and safety. Accurate vibration measurement can promptly identify potential faults such as imbalance, resonance, or wear, preventing equipment damage and downtime, thereby extending the wind turbine's service life and reducing maintenance costs. Furthermore, real-time vibration data monitoring helps optimize wind turbine performance, improve energy output efficiency, and support the sustainable development of renewable energy. Therefore, vibration measurement of rotating objects is not only critical to ensuring equipment safety but also an important means of improving wind energy utilization efficiency. Traditional methods for measuring vibration of rotating objects, such as accelerometers, employ sensors placed on the object to acquire real-time acceleration data. This technology rapidly responds to dynamic vibration changes and provides reliable long-term measurement data. However, this method suffers from low-frequency and low-level vibration measurement accuracy, and its spatial resolution depends on the number of sensors deployed, often preventing full-area measurement. Furthermore, the installation, calibration, and maintenance of multiple sensors increase operational costs and complexity.

[0003] Camera-based global measurement technology only requires a consumer-grade camera to capture the measurement object. Each pixel in the camera can be considered a sensor, enabling dense global vibration measurement. Furthermore, since the camera measures displacement changes, it has good measurement accuracy at low frequencies. However, existing camera-based measurement technology is rarely used for vibration measurement of rotating objects. This is because vibration measurement of rotating objects involves complex motion coupling, and traditional vision algorithms cannot directly decouple vibration components from images. Furthermore, because cameras are typically positioned far from the measured object (such as wind turbine blades), the camera's own quantization rounding errors are amplified in the actual physical quantity, resulting in insufficient measurement accuracy.

[0004] In line with the actual needs of the project, when using a camera for measurement, how to extract the vibration component from the response of the rotation and vibration coupling and break through the measurement accuracy limitations of the camera itself is the key to achieving high-precision full-field measurement of the deformation and vibration of rotating structures.

[0005] The present invention overcomes the shortcomings of traditional measurement technology in low-frequency state, such as low measurement accuracy, insufficient spatial resolution and high cost; at the same time, it improves the shortcomings of existing machine vision algorithms, such as the inability to achieve rotating body vibration decoupling and the measurement accuracy being affected by quantization rounding errors. Summary of the Invention

[0006] In order to overcome the shortcomings and deficiencies of the above-mentioned prior art, the present invention adopts the following technical solutions:

[0007] A method for measuring the vibration of a rotating object in a polar coordinate system with ultra-sensitive full-range vibration is described as follows:

[0008] S11, image acquisition: adjusting the camera parameters so that its imaging plane coincides with the rotation plane of the rotating body, and continuously acquiring images of the rotating body;

[0009] S12. Calibrate scale parameters: Determine the scale parameters in millimeters / pixels based on the physical dimensions of the rotating object when not rotating and the number of image pixels, and dynamically update them through fixed markers;

[0010] S13, Feature Recognition and Rotation Parameter Estimation: Apply SIFT algorithm to each frame image to extract feature points, match feature points through BFMatcher and RANSAC, and decompose the homography matrix to obtain the rotation angle and rotation center;

[0011] S14, polar coordinate mapping: based on the rotation center and rotation angle, the Cartesian coordinate pixel intensity is mapped to the polar coordinate system through bilinear interpolation;

[0012] S15, constructing a spatiotemporal pixel intensity matrix: constructing a spatiotemporal matrix from the time series pixel intensities after polar coordinate mapping;

[0013] S16, Singular Value Decomposition and Mode Reconstruction: Perform SVD decomposition on the space-time matrix and select the first k-order singular modes to reconstruct the signal;

[0014] S17, optical flow displacement calculation: the optical flow algorithm is used to calculate the vibration displacement of the reconstructed polar coordinate image;

[0015] S18. Coordinate transformation: transform the displacement field in the polar coordinate system into the physical displacement field in the Cartesian coordinate system by combining the scale parameter.

[0016] Preferably, the calibration scale parameters include:

[0017] The final scale parameter is calculated by measuring the ratio of the physical size of the rotating object when it is not rotated to the number of pixels corresponding to it multiple times. The average value is calculated as the final scale parameter. If the deviation of a measurement value from the average value exceeds 10%, it is discarded and remeasured. When the rotating object is occluded, the scale parameter is updated in real time through fixed markers near the rotation axis.

[0018] Preferably, decomposing the homography matrix comprises:

[0019] Extract the first two column vectors of the homography matrix H , ;

[0020] Calculate the rotation matrix ,in 、 、 To form the rotation matrix Column vector of , , , ;Rotation angle , in radians, and They are and The first element of the vector is used to determine the rotation angle of the rotating body; the center of rotation By solving Obtain; Use the inverse tangent function to calculate the eigenvalues ​​in the homography matrix to obtain the rotation angle ;

[0021] Estimate the center of rotation using the eigenvalues ​​in the homography matrix , .

[0022] Preferably, the conversion formula from Cartesian coordinates to polar coordinates in polar coordinate mapping is:

[0023] ;in, is the rotation angle of the t-th frame, obtained by decomposing the homography matrix, and used to reset the polar coordinates Direction; calculate pixel intensity in polar coordinates using bilinear interpolation : ;in, is the weight coefficient of the four adjacent pixels; the weight coefficient is calculated as follows:

[0024] Let the Cartesian coordinates corresponding to the polar coordinate point be , its four neighboring pixels are , , , , then the weight coefficient is:

[0025] , , , ;in, , .

[0026] Preferably, the condition for selecting the first k-order singular modes is that the cumulative energy ratio of the singular values ​​is greater than 90%.

[0027] Preferably, the displacement calculation in the optical flow algorithm satisfies:

[0028] , which means that in the polar coordinate system, the coordinates are The optical flow displacement of the measuring point at time t reflects the position change of the measuring point over time in polar coordinates; is the pixel intensity value; is the pixel intensity gradient of the measuring point; and is the coordinate of any measuring point in the polar coordinate system; It’s time; The coordinates are The pixel intensity value of the measuring point at the initial time (t=0); The coordinates are The pixel intensity value of the measuring point at time t.

[0029] Preferably, dynamically updating the scale parameter further comprises: adjusting the scale parameter in real time by changing the pixel position of the fixed marker when the rotating body is blocked by blades.

[0030] Preferably, the frame rate and lens focal length among the camera parameters are determined according to the motion characteristics of the measurement object.

[0031] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0032] 1. This invention combines SIFT feature matching, RANSAC mismatch elimination, and homography matrix decomposition to accurately extract the rotation angle and rotation center, reducing image noise and occlusion interference. Furthermore, multiple measurements are used to calibrate scale parameters, and outliers are eliminated (remeasurement is performed if the deviation exceeds 10%). This is combined with comparative verification using a high-precision accelerometer (such as the PCB352C22), thereby improving the measurement accuracy and reliability of vibration displacement.

[0033] 2. This invention employs polar coordinate mapping (Cartesian coordinates to polar coordinates) and resets the polar coordinate 0° orientation by rotating the angle. This ensures that vibration analysis of rotating bodies is more consistent with their motion characteristics, avoiding the complex deformation calculations caused by rotation in the Cartesian coordinate system. Bilinear interpolation weight optimization and polar coordinate subset sampling strategies further reduce image distortion and ensure the continuity and stability of displacement field reconstruction.

[0034] 3. This method uses singular value decomposition (SVD) to extract the dominant vibration mode (cumulative energy > 90%) and combines it with an optical flow algorithm to directly estimate the displacement field in polar coordinates, achieving efficient conversion from spatiotemporal pixel intensity matrices to physical displacements. This method not only filters out high-frequency noise but also captures global vibration information for rotating bodies in a single measurement. This avoids the limitations of single-point deployment of traditional contact sensors (such as accelerometers) and significantly improves analysis efficiency and coverage. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 A flow chart of a method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to the present invention is shown;

[0037] Figure 2 This is a diagram of the vibration measurement results of the fan blades in Example 1 of the present invention. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] In addition, the described features, structures or characteristics can be combined in any suitable manner in one or more example embodiments. In the following description, many specific details are provided to provide a full understanding of the example embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure can be practiced while omitting one or more of the specific details, or other methods, components, steps, etc. can be adopted. In other cases, well-known structures, methods, implementations or operations are not shown or described in detail to avoid obscuring various aspects of the present disclosure.

[0040] Example 1:

[0041] See Figure 1 As shown, the entire domain ultra-sensitive rotating body vibration measurement method in a polar coordinate system of this embodiment has the following process:

[0042] S11, image acquisition: adjust the camera angle and focal length so that the rotation plane of the structure overlaps with its imaging plane, start the camera, and continuously acquire images of the structure;

[0043] In this embodiment, to measure the blade deformation and vibration of the fan structure during rotation, a camera was fixed in front of the fan structure using a tripod, with the center of the lens aligned with the fan's rotation center. The camera model is SONYNEX-FS700RH, the CMOS imaging chip has a resolution of 1920×1080 pixels, the lens focal length is 24 mm, the acquisition frame rate is 100 frames per second, and the image signal bit depth is 8 bits. Figure 2 To compare and evaluate the measurement results of the present method, an accelerometer was placed on the back of the blade to measure its deformation vibration. This accelerometer, model PCB352C22, uses a high-precision contact-type measurement method, with measurement accuracy and acquisition frequency far exceeding those of conventional vibration measurement sensors.

[0044] S12, calibration scale parameters (Unit: mm / pixel);

[0045] In the case of no rotation, using the known physical size of the wind turbine blades and the number of pixels they occupy in the image, according to the formula Determine the scale parameter; where, Represents the physical size of the fan blade; Indicates the number of pixels occupied by the fan blades in the image.

[0046] Through multiple measurements and the corresponding number of pixels , taking the average value as the final scale parameter value, in this embodiment Millimeters / pixel. If the blades are obstructed during rotation, set fixed marking points on the wind turbine structure (such as near the rotation axis) and update the scale parameters in real time using the marking points. The multiple measurement method is as follows:

[0047] Measure the same leaf 5 times, manually select the leaf edge each time and record the number of pixels, and calculate the average value , the final scale parameter . is the number of pixels measured for the i-th time; if a certain measurement If the deviation from the average value exceeds 10%, the data will be discarded and remeasured.

[0048] S13. Apply the Scale Invariant Feature Transform (SIFT) algorithm to each frame to identify features and determine the center of rotation , and then estimate the rotation angle of each frame relative to the reference frame ;

[0049] The process of identifying features is as follows: use the SIFT algorithm to identify feature points in the image; use the BFMatcher algorithm to match the feature points of the current image with the feature points of the reference image (first frame); based on the matched feature points, use the RANSAC algorithm to eliminate false matches and calculate the optimal homography matrix ; This matrix contains the rotation information.

[0050] The homography matrix H is decomposed into the rotation matrix R and the translation vector t by the following steps: Extract the first two column vectors of H , ;

[0051] Calculate the rotation matrix ,in , , ;Rotation angle , in radians; the center of rotation By solving Obtain. Use the inverse tangent function to calculate the eigenvalues ​​in the homography matrix to obtain the rotation angle .

[0052] Estimate the center of rotation using the eigenvalues ​​in the homography matrix , .

[0053] S14, perform interpolation sampling based on the rotation center and the estimated rotation angle by solving the equation Map pixel intensities from Cartesian coordinates to polar coordinates. This subset of polar coordinates is for every integer radius use The rotation angle is subtracted from the sampling points to reset the polar coordinates to 0°.

[0054] The mapping formula from Cartesian coordinates to polar coordinates is:

[0055] ;in, is the rotation angle (in radians) of the t-th frame, obtained by decomposing the homography matrix and used to reset the polar coordinates direction.

[0056] Calculate pixel intensity in polar coordinates using bilinear interpolation : ;in is the weight coefficient of the four adjacent pixels.

[0057] The weight coefficient is calculated as follows:

[0058] Let the Cartesian coordinates corresponding to the polar coordinate point be , its four neighboring pixels are , , , , then the weight coefficient is:

[0059] , , , ;in, , .

[0060] S15. The time series of polar coordinate pixel intensity samples after conversion can form a spatiotemporal pixel intensity matrix , whose size is ,in and are the number of spatial samples and temporal samples of the spatiotemporal pixel intensity matrix, respectively;

[0061] S16, spatiotemporal pixel intensity matrix Do singular value decomposition to get the left singular matrix , singular value diagonal matrix and right singular matrices ;

[0062] S17, select the front according to the singular value cumulative energy ratio greater than 90% order singular modes; and reconstruct the singular values ​​by using the singular value modes ;

[0063] S18. Apply an optical flow algorithm to each frame of the polar coordinate space image after reconstruction (filtering) to estimate the full-field vibration displacement of the structure in the polar coordinate system.

[0064] Specifically, the displacement is obtained by interpolating the pixel intensity of the image frame t in the polar coordinate system and the pixel intensity of the original frame (frame 0) and dividing it by the gradient at that position. ,in is the pixel intensity value; is the pixel intensity gradient of the measuring point; and is the coordinate of any measuring point in the polar coordinate system; It's time.

[0065] S19, through the scale parameter The space-time displacement field of the physical space in the Cartesian coordinate system is calculated by the coordinate transformation relationship .

[0066] The beneficial effects of this embodiment include: non-contact full-field measurement, avoiding interference from the sensor's additional mass, and realizing non-destructive monitoring of rotating bodies; polar coordinate transformation combined with bilinear interpolation, effectively avoiding large displacement measurement inaccuracies caused by rotation, and improving the sensitivity of small vibration detection; SIFT+RANSAC feature matching and homography matrix decomposition, accurately estimating rotation parameters, and strong anti-occlusion ability; spatiotemporal matrix SVD denoising and modal reconstruction, effectively separating noise from real vibration signals; optical flow algorithm realizes full-field displacement solution in polar coordinate system, with spatial resolution reaching pixel level; dynamic update mechanism of calibration parameters ensures long-term measurement accuracy; comparison and verification with high-precision accelerometers ensure the credibility of the results, and is suitable for ultra-sensitive vibration analysis of complex rotating structures such as wind blades.

[0067] The weighting coefficients of the present invention are used to measure the degree of influence of different factors or variables on a particular outcome or decision. A weighting coefficient is defined as a numerical value assigned to each factor when comparing and evaluating multiple factors to reflect its importance or priority. These weighting coefficients can be determined based on specific circumstances and needs, and are typically developed and confirmed by professionals or relevant stakeholders. By properly setting weighting coefficients, programs or systems can be helped to make more accurate decisions or predictions.

[0068] The above embodiments can be implemented in whole or in part via software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions or computer programs. When loaded or executed on a computer, the processes or functions described in the embodiments of this application are fully or partially generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, tapes), optical media (e.g., DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0069] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0070] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0071] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is only for some logical functions. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0072] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0073] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A global ultra-sensitive rotating body vibration measurement method in a polar coordinate system, characterized in that: The method flow is as follows: S11, image acquisition: adjusting the camera parameters so that its imaging plane coincides with the rotation plane of the rotating body, and continuously acquiring images of the rotating body; S12. Calibrate scale parameters: Determine the scale parameter in millimeters per pixel based on the physical dimensions of the rotating object when not rotating and the number of image pixels, and dynamically update it through fixed markers; millimeters per pixel represents the actual physical length corresponding to each pixel; S13, Feature Recognition and Rotation Parameter Estimation: Apply SIFT algorithm to each frame image to extract feature points, match feature points through BFMatcher and RANSAC, and decompose the homography matrix to obtain the rotation angle and rotation center; S14, polar coordinate mapping: based on the rotation center and rotation angle, the Cartesian coordinate pixel intensity is mapped to the polar coordinate system through bilinear interpolation; S15, constructing a spatiotemporal pixel intensity matrix: constructing a spatiotemporal matrix from the time series pixel intensities after polar coordinate mapping; S16, Singular Value Decomposition and Mode Reconstruction: Perform SVD decomposition on the space-time matrix and select the first k-order singular modes to reconstruct the signal; S17, optical flow displacement calculation: the optical flow algorithm is used to calculate the vibration displacement of the reconstructed polar coordinate image; S18. Coordinate transformation: transform the displacement field in the polar coordinate system into the physical displacement field in the Cartesian coordinate system by combining the scale parameter.

2. The method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to claim 1, characterized in that: The calibration scale parameters include: The final scale parameter is calculated by measuring the ratio of the physical size of the rotating object when it is not rotated to the number of pixels corresponding to it multiple times. The average value is calculated as the final scale parameter. If the deviation of a measurement value from the average value exceeds 10%, it is discarded and remeasured. When the rotating object is occluded, the scale parameter is updated in real time through fixed markers near the rotation axis.

3. The method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to claim 1, characterized in that: The decomposed homography matrix includes: Extract the first two column vectors of the homography matrix H , ; Calculate the rotation matrix ,in 、 、 To form the rotation matrix Column vector of , , , ;Rotation angle , in radians, and They are and The first element of the vector is used to determine the rotation angle of the rotating body; the center of rotation By solving Obtain; Use the inverse tangent function to calculate the eigenvalues ​​in the homography matrix to obtain the rotation angle ; Estimate the center of rotation using the eigenvalues ​​in the homography matrix , .

4. The method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to claim 3, wherein: The conversion formula from Cartesian coordinates to polar coordinates of the polar coordinate mapping is: ;in, is the rotation angle of the t-th frame, obtained by decomposing the homography matrix, and used to reset the polar coordinates Direction; calculate pixel intensity in polar coordinates using bilinear interpolation : ;in, is the weight coefficient of the four adjacent pixels; the weight coefficient is calculated as follows: Let the Cartesian coordinates corresponding to the polar coordinate point be , and its four neighboring pixels are , , , , then the weight coefficient is: , , , ;in, , .

5. The method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to claim 1, characterized in that: The condition for selecting the first k-order singular modes is that the cumulative energy ratio of the singular values ​​is greater than 90%.

6. The method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to claim 1, characterized in that: The displacement calculation in the optical flow algorithm satisfies: , which means that in the polar coordinate system, the coordinates are The optical flow displacement of the measuring point at time t reflects the position change of the measuring point over time in polar coordinates; is the pixel intensity value; is the pixel intensity gradient of the measuring point; and is the coordinate of any measuring point in the polar coordinate system; It’s time; The coordinates are The pixel intensity value of the measuring point at the initial time t=0; The coordinates are The pixel intensity value of the measuring point at time t.

7. The method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to claim 1, wherein: It also includes dynamic updating of scale parameters: when the rotating body is blocked by leaves, the scale parameters are adjusted in real time by changing the pixel position of fixed markers.

8. The method for measuring global ultra-sensitive rotating body vibration in a polar coordinate system according to claim 1, wherein: The frame rate and lens focal length of the camera parameters are determined according to the motion characteristics of the measurement object.

Images