Conjugate flow calculation method for fluorescent oil film velocity field

Abstract

The application provides a conjugate optical flow calculation method for a fluorescent oil film velocity field, belongs to the technical field of aerodynamic test, flow display and measurement, and solves the problems of slow convergence and long time consumption caused by the traditional technology using a similar Jacobian iterative form for calculation; the method comprises the following steps: calculating a gray gradient information matrix of a fluorescent oil film image; calculating the weighted velocity of each pixel in the fluorescent oil film image; obtaining a symmetric positive definite matrix after rewriting the obtained calculation equation; using the symmetric positive definite matrix for calculation; creating a velocity iterative formula of the conjugate optical flow method; quickly obtaining the initial value calculation result after iterative calculation; and substituting the initial value calculation result into a traditional optical flow equation, so that the global optimization of the oil film movement is realized, the oil film velocity field with the minimum global energy functional is obtained; and the conjugate iterative method of the optical flow method is derived and created, the required image gray matrix storage amount is small, and the conjugate iterative method has the advantages of high step convergence and stability.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic testing, flow display and measurement technology, specifically a method for calculating the conjugate optical flow of the velocity field of a fluorescent oil film. Background Technology

[0002] The global friction direct measurement technology based on fluorescent oil film has the following advantages:

[0003] 1. The required measuring equipment is simple, requiring only an ultraviolet excitation light source, a camera, and a lens;

[0004] 2. No special requirements are required for the surface of the aircraft model;

[0005] 3. High frictional spatial resolution.

[0006] Based on the above advantages, this technology has become a research hotspot in the fields of global friction measurement and near-wall flow display. This technology involves adding fluorescent molecules to the oil film and describing the relationship between the grayscale of the fluorescent oil film (luminescent imaging excited by ultraviolet light) on the wall of the aircraft model and its velocity through the fluorescent oil film control equation, thereby establishing a measurement equation for the oil film velocity. Because it has a similar form to the optical flow equation, the near-wall flow structure of the test model can be obtained from the time-series images of the fluorescent oil film on the model wall in the wind tunnel test by solving the measurement equation using the optical flow method. This provides an important measurement method and test data for understanding the location, separation mode and characteristics of flow separation on the test model wall and the vortex formation mechanism.

[0007] However, in existing technologies, solving the velocity field of fluorescent oil films using the optical flow method requires complex variational optimization to search for a solution that minimizes the global energy functional, i.e., the following equation:

[0008]

[0009] In the formula, I x I y and I t These represent the gradient information of the grayscale of the oil film image in the spatial domain (x, y coordinate axes) and the temporal domain, respectively; α is the global smoothing parameter, and (u, v) is the oil film velocity vector at a given pixel (x, y) in the spatial domain; after minimizing the Euler-Lagrange equations, we can obtain:

[0010]

[0011]

[0012] In the formula, Given the weighted values ​​of (u,v) within the neighborhood n of a given pixel, the existing iterative formula for optical flow can be obtained as follows:

[0013]

[0014] The above equation is a Jacobi-like iterative form, and its convergence error is as follows:

[0015]

[0016] In the formula, e u and e v These are the residuals of the current step and the previous step, respectively (u,v).

[0017] The optical flow method for solving the velocity field of fluorescent oil film mentioned above uses a Jacobi-like iterative method, which results in slow convergence and long calculation time for the velocity field. It cannot yet measure and display the flow process on the model wall in real time at the fluorescent oil film test site in a production wind tunnel, thus reducing its value for engineering applications.

[0018] Especially with the application of high-resolution (up to 25-65 megapixels) high-speed industrial cameras in fluorescent oil film wind tunnel tests, when using existing optical flow methods to process the massive fluorescent oil film time-series images of such cameras (2GB / s), it takes 1-2 hours after the test to obtain the fine measurement results of the oil film velocity field.

[0019] Therefore, proposing a new and efficient optical flow calculation method is crucial for the application and development of real-time global friction measurement based on fluorescent oil film. Summary of the Invention

[0020] This invention proposes a method for calculating the conjugate optical flow of the velocity field of a fluorescent oil film. Compared with the existing Jacobi-like iterative solution process, this invention derives and creates a conjugate iterative method for optical flow, which requires less image grayscale matrix storage and has the advantages of high step convergence and stability.

[0021] The present invention employs the following technical solutions to achieve its objective:

[0022] A method for calculating the conjugate optical flow of the velocity field of a fluorescent oil film includes the following steps:

[0023] S1. For a given fluorescent oil film image, calculate the gray-level gradient information matrix along the x and y coordinate axes, and calculate the gray-level gradient information matrix of the corresponding pixels in different time frame images.

[0024] S2. Calculate the weighted velocity of each pixel in the fluorescent oil film image to obtain the calculation equation of the oil film velocity field.

[0025] S3. Rewrite the calculation equation as Ax = b to obtain a symmetric positive definite matrix;

[0026] S4. Assemble the obtained symmetric positive definite matrix and use the symmetric positive definite matrix to calculate the velocity iteration formula based on the conjugate optical flow method;

[0027] S5. Calculate the velocity iteration formula based on the conjugate optical flow method, as follows:

[0028]

[0029] S6. Perform iterative calculations according to the velocity iteration formula based on the conjugate optical flow method to obtain the calculation results of the oil film velocity field;

[0030] S7. Take the calculation result of the oil film velocity field in step S6 as the initial value and substitute it into the traditional optical flow equation to achieve global optimization of oil film motion.

[0031] Specifically, in step S1, given two time-series images of fluorescent oil film, image P t and image P t+1 Calculate image P t+1 Gray-level gradient information matrix I along the x and y coordinate axes x and I y Calculate image P t+1 and image P t Gray-level gradient information matrix I of the corresponding pixel t .

[0032] Specifically, step S2 involves: based on the local optical flow theory, for a given pixel (x, y) and its neighboring pixels, the velocities are equal, i.e., (u, v) = the velocity of the point with the largest gray-level gradient in the neighborhood; simultaneously, based on the fact that pixels with large velocity gradients in the oil film velocity field also have large gray-level gradients, a weighted velocity is selected from a neighborhood of n=1:

[0033] The velocity of the point (x,y) and the point with the largest gray-level gradient in its 8-neighborhood is (u,v);

[0034] Based on the above, the calculation equation for the oil film velocity field is derived as follows:

[0035]

[0036]

[0037] In the formula, I x I y and I t These represent the gradient information of the grayscale of the oil film image in the spatial domain (x, y coordinate axes) and the temporal domain, respectively; α is the global smoothing parameter, and (u, v) is the oil film velocity vector at a given pixel (x, y) in the spatial domain; obviously, This reduced the storage requirements of the velocity matrix.

[0038] Specifically, in step S3, the calculation equation for the oil film velocity field is rewritten in the form of Ax = b, as follows:

[0039]

[0040] Based on the rewritten equation, matrix A can be obtained as follows:

[0041]

[0042] Specifically, matrix A is a symmetric positive definite matrix. After assembling matrix A, it is used in the velocity iterative calculation process based on the conjugate optical flow method.

[0043] Specifically, the velocity iteration formula based on the conjugate optical flow method is as follows:

[0044]

[0045] In the formula ɑ k and p k The calculation process is as follows:

[0046] For the matrix A, there must exist a conjugate vector r. i , making

[0047] r i Ar j =0 (i≠j)

[0048] Construct the conjugate iterative formula as follows:

[0049] r k+1 =r k -α k Ap k

[0050] In the formula, p k Let α be the unit residual direction vector. k Representing the step size, after Schmidt orthogonalization, we can obtain:

[0051]

[0052] Continue to solve for a k Let x = (u k ,v k ) T Construct a quadratic form as follows:

[0053]

[0054] The above equation has the same solution as the equation for calculating the oil film velocity field rewritten in the form Ax = b. Therefore, f(x) k +αk p k ) is denoted as g(α) k Let g′(α) k Since ) = 0, we can obtain:

[0055]

[0056] Specifically, in step S7, global optimization of the oil film motion is performed, which involves substituting the calculation results of the oil film velocity field obtained from iterative calculation into the following equation:

[0057]

[0058] This allows for a quick search of the velocity field that minimizes the global energy functional.

[0059] In summary, due to the adoption of this technical solution, the beneficial effects of this invention are as follows:

[0060] Unlike existing iterative methods for solving the velocity field of fluorescent oil films, this invention proposes a conjugate optical flow calculation method for the velocity field of fluorescent oil films. This method derives and creates a conjugate iterative method for optical flow. Compared with the Jacobian iteration of existing optical flow methods, this method requires less storage space and has the advantages of step convergence and high stability. For an n-order matrix, this method only requires n iterations to converge, thus effectively improving the solution speed of the velocity field of fluorescent oil films.

[0061] On the other hand, this invention utilizes the theory of local optical flow, which "reasonably assumes that the velocities of a given pixel (x,y) and its neighboring points are equal." Simultaneously, considering that pixels with large velocity gradients in the oil film velocity field also have large grayscale gradients, a fast and efficient conjugate optical flow velocity iteration formula is cleverly derived and constructed. This formula can quickly obtain large flow structures in the oil film velocity field. Using these as initial values ​​for global velocity field optimization, the fine flow structures can be accurately captured, significantly improving the solution speed of the fluorescent oil film velocity field. Therefore, the method of this invention has great potential for engineering applications. Attached Figure Description

[0062] Figure 1 This is a schematic flowchart of the method of the present invention;

[0063] Figure 2 Image of the wall jet;

[0064] Figure 3 For comparison of experimental results under the same error limit. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0066] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0067] like Figure 1 The diagram illustrates a method for calculating the conjugate optical flow of a fluorescent oil film velocity field, comprising the following steps:

[0068] S1. For a given fluorescent oil film image, calculate the gray-level gradient information matrix along the x and y coordinate axes, and calculate the gray-level gradient information matrix of the corresponding pixels in different time frame images.

[0069] S2. Calculate the weighted velocity of each pixel in the fluorescent oil film image to obtain the calculation equation of the oil film velocity field.

[0070] S3. Rewrite the calculation equation in the form of Ax = b to obtain a symmetric positive definite matrix;

[0071] S4. Assemble the obtained symmetric positive definite matrix and use the symmetric positive definite matrix to calculate the velocity iteration formula based on the conjugate optical flow method;

[0072] S5. Calculate the velocity iteration formula based on the conjugate optical flow method, as follows:

[0073]

[0074] S6. Perform iterative calculations according to the velocity iteration formula based on the conjugate optical flow method to obtain the calculation results of the oil film velocity field;

[0075] S7. Take the calculation result of the oil film velocity field in step S6 as the initial value and substitute it into the traditional optical flow equation to achieve global optimization of oil film motion.

[0076] In step S1, given two frames of time-series fluorescent oil film images, let image P be... t and image P t+1 Calculate image P t+1 Gray-level gradient information matrix I along the x and y coordinate axes x and I y Calculate image Pt+1 and image P t Gray-level gradient information matrix I of the corresponding pixel t .

[0077] In this embodiment, step S2 specifically involves: based on the local optical flow theory, for a given pixel (x, y) and its neighboring pixels, the velocities are equal, i.e., (u, v) = the velocity of the pixel with the largest gray-level gradient in the neighborhood; simultaneously, based on the fact that pixels with large velocity gradients in the oil film velocity field also have large gray-level gradients, a weighted velocity is selected from a neighborhood of n=1:

[0078] The velocity of the point (x,y) and the point with the largest gray-level gradient in its 8-neighborhood is (u,v);

[0079] Based on the above, the calculation equation for the oil film velocity field is derived as follows:

[0080]

[0081]

[0082] In the formula, I x I y and I t These represent the gradient information of the grayscale of the oil film image in the spatial domain (x, y coordinate axes) and the temporal domain, respectively; α is the global smoothing parameter, and (u, v) is the oil film velocity vector at a given pixel (x, y) in the spatial domain; obviously, This reduced the storage requirements of the velocity matrix.

[0083] In step S3, the calculation equation for the oil film velocity field is rewritten in the form of Ax = b, as follows:

[0084]

[0085] Based on the rewritten equation, matrix A can be obtained as follows:

[0086]

[0087] Clearly, matrix A is a symmetric positive definite matrix. After assembling matrix A, it is used in the velocity iterative calculation process based on the conjugate optical flow method.

[0088] The velocity iteration formula based on the conjugate optical flow method is as follows:

[0089]

[0090] In the formula ɑ k and p k The calculation process is as follows:

[0091] For a matrix A, there must exist a conjugate vector r.i , making

[0092] r i Ar j =0 (i≠j)

[0093] Construct the conjugate iterative formula as follows:

[0094] r k+1 =r k -α k Ap k

[0095] In the formula, p k Let α be the unit residual direction vector. k Representing the step size, after Schmidt orthogonalization, we can obtain:

[0096]

[0097] Continue to solve for a k Let x = (u k ,v k ) T Construct a quadratic form as follows:

[0098]

[0099] The above equation has the same solution as the equation for calculating the oil film velocity field rewritten in the form Ax = b. Therefore, f(x) k +α k p k ) is denoted as g(α) k Let g′(α) k Since ) = 0, we can obtain:

[0100]

[0101] In this embodiment, step S7 involves global optimization of the oil film motion, specifically by substituting the calculated results of the oil film velocity field obtained through iterative calculation into the following equation:

[0102]

[0103] This allows for a quick search of the velocity field that minimizes the global energy functional.

[0104] The following section presents an example of wall jet velocity field calculation performed according to the method of this embodiment.

[0105] like Figure 2 As shown, two images of the wall jet were selected to simulate the motion of the fluid oil film in a simulation experiment. Figure 2 In the image, a represents the initial image and b represents the evolved image. To verify and compare the convergence speed, the number of iterations required for the two methods to converge to a given error limit is counted.

[0106] Three error limits were set for the wall jet experiment: 1.0 × 10⁻⁶ -6 5.0×10 -7 and 1.0×10 -7 The number of iterations required for existing optical flow methods and the method of this invention to converge to the error limit, as well as the iteration time, were statistically analyzed. The statistical results are shown in Table 1 below.

[0107] Table 1. Number of iterations for convergence in wall jet experiments under different error limits.

[0108]

[0109] It can be seen that the error limit is 1.0×10 -6 Under the standard, the method in this embodiment achieves a maximum speed increase of 40.7%; within an error limit of 5.0 × 10⁻⁶. -7 The speed increased by 26% at 1.0×10 -7 The speedup is increased by 5.7% below the error limit. Since the subsequent global optimization algorithm of this invention is the same as the traditional algorithm, the speedup is further increased as the error limit is reduced from 1.0 × 10⁻⁶. -6 Increased to 1.0×10 -7 As the weight of global optimization gradually increases, the acceleration of iterative calculation of the entire velocity field slows down.

[0110] like Figure 3 As shown, a represents the flow field characteristics of the existing optical flow method, and b represents the flow field characteristics of the method in this embodiment; under the same global convergence error limit of 1.0 × 10⁻⁶. -7 Under these conditions, the flow field characteristics obtained by the method in this embodiment will be more obvious.

Claims

1. A method for calculating the conjugate optical flow of fluorescent oil film velocity fields, characterized in that, The method comprises the following steps: S1, for a given fluorescent oil film image, calculate the gray scale gradient information matrix along , coordinate axis direction and , calculate the gray scale gradient information matrix of the corresponding pixels in different time sequence frame images ; S2. Calculate the weighted velocity of each pixel in the fluorescent oil film image to derive the calculation equation for the oil film velocity field, including: based on the local optical flow theory, for a given pixel... The velocities of the points and their neighboring points are equal, that is The velocity of the point with the largest gray-level gradient in the neighborhood; simultaneously, based on the fact that pixels with large velocity gradients in the oil film velocity field also have large gray-level gradients, a neighborhood is selected. Weighted velocity: ← point and the velocity of the point with the maximum gray level gradient in the 8-neighborhood of the point ; According to the above basis, the calculation equation of the oil film velocity field is obtained, as shown in the following formula: wherein is a global smoothing parameter, is the oil film velocity vector at a given pixel point on the spatial domain; S3. rewriting the computational equation into the form of equation of a symmetric positive definite matrix as follows: S4. computing a symmetric positive definite matrix Assembling is completed, using the symmetric positive definite matrix Computing the velocity iteration formula based on the conjugate optical flow method S5, the velocity iteration formula based on the conjugate optical flow method is calculated, as shown in the following formula: wherein represents a step size, is a unit residual direction vector; and The calculation process is as follows: For symmetric positive definite matrices there certainly exist conjugate vectors such that The conjugate iteration formula is constructed, as shown in the following formula: Through Schmidt orthogonalization, the following formula is obtained: continuing to solve , let , construct a quadratic form as follows: The above equation is rewritten as The calculation equation of the oil film velocity field in the form of is solved, and is obtained. , and S6, according to the velocity iteration formula based on the conjugate optical flow method, iterative calculation is performed to obtain the calculation result of the oil film velocity field; S7, the calculation result of the oil film velocity field in step S6 is taken as an initial value and substituted into a traditional optical flow equation to realize global optimization of the oil film movement.

2. The method of claim 1, wherein: In step S1, two frames of time-sequential fluorescent oil film images are given, as image and image . The gray gradient information matrix of image along , the coordinate axis direction is calculated and . The gray gradient information matrix of image and image corresponding pixels is calculated .

3. The method of fluorescent oil film velocity field's conjugate optical flow calculation according to claim 2, characterized in that: In step S3, the calculation equation of the oil film velocity field is rewritten as in the form of the equation as follows: According to the modified equation, a symmetric positive definite matrix .

4. The method of fluorescent oil film velocity field's conjugate optical flow calculation according to claim 3, characterized in that, In the step S7, the global optimization of the oil film movement is performed, specifically, the calculation result of the oil film velocity field obtained through the iterative calculation is substituted into the following formula: The oil film velocity field of the global energy functional minimization is obtained.

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