A liquid surface wave observation system

Abstract

The present application is a liquid surface wave observation system, which corrects the position and posture of a monochrome camera and a regular triangle boundary container, and the radial distortion of the lens combination of the monochrome camera, so that the generated surface wave reaches an ideal state. The monochrome camera captures the current image after the vibration table is driven for 3 minutes and the reference image when it is static, and inputs the images into a computer cluster. The height data containing time evolution is output in binary format. The height data is arranged into a data matrix. The matrix is subjected to singular value decomposition to obtain spatial distribution patterns and time evolution patterns. Each pixel point is differentiated with its neighboring pixel points. The overall height of the pixel points in the image is limited to obtain the gradient distribution of each pixel point. A series of overdetermined equations are converted. The least square solution is taken as the height distribution to obtain the motion information of the corresponding pixel points of any current image and reference image, and the liquid surface wave waveform of a two-dimensional system is reconstructed.

Description

Technical Field

[0001] This invention relates to the field of liquid surface wave observation, and particularly to a two-dimensional liquid surface wave observation system. Background Technology

[0002] Surface waves do not exhibit a fixed or obvious direction of motion. In practical observation systems, it is necessary to record the morphology of surface waves in a two-dimensional region as completely as possible, such as surface waves inside a triangular container. Previous methods for observing and recording such surface waves include direct imaging, collimated refraction imaging, and laser reflection.

[0003] Direct shooting produces results consistent with human observation, roughly reflecting simple information such as the spatial distribution of wave peaks and troughs at the time of shooting. However, it is difficult to perform subsequent processing; for example, it is difficult to obtain accurate wave vector information from the photographs taken.

[0004] Collimated light refraction imaging is the primary liquid surface wave observation method used in the initial stages of this application. This method is mainly influenced by factors such as the collimation characteristics of the light source, lens aperture, and aperture size. The core component of the collimation system is a convex lens, whose accuracy directly affects the collimation characteristics of the light. Its diameter must be at least larger than the longest side of the container to allow collimated light to pass through any point on the container. The relationship between the curvature of the liquid surface at a certain point and the brightness of the image at that location is affected by various factors, such as lens size, lens aperture, aperture size, and the relative positions of different parts. Different sizes and shapes of containers often require different settings. This causes the actual brightness distribution to vary with different settings, making it difficult to ensure that the brightness range exactly matches the dynamic range of the camera. Accuracy and completeness are difficult to balance; the shape of wave crests and troughs and the positional distribution of nodes cannot be recorded simultaneously and accurately. It is difficult to reconstruct the height field from the final recorded surface wave image, and even more difficult to perform further analysis of the waveform.

[0005] Detection methods based on laser refraction and reflection on the liquid surface can only measure the gradient at a certain point or along a certain straight line. It is difficult to measure the gradient at various locations of two-dimensional liquid surface waves at the same time, and it is almost impossible to reconstruct the waveform of the liquid surface wave.

[0006] Therefore, due to the limitations of existing technology, it is impossible to quantitatively measure and record two-dimensional surface waves of liquids. Summary of the Invention

[0007] (I) Purpose of the invention: In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a liquid surface wave observation system to reconstruct the liquid surface wave waveform.

[0008] (II) Technical Solution: In order to solve the above-mentioned technical problems, this technical solution provides a liquid surface wave observation system, including an observation unit, a container, a vibration unit, an image analysis unit, a data processing unit, and a waveform reconstruction unit; The container includes an equilateral triangular boundary container; the vibration unit includes a vibration table, and the equilateral triangular boundary container is placed on the vibration table surface; the observation unit includes a monochrome camera, a first plane mirror, and a tablet computer; the first plane mirror is placed at a 45-degree angle below the container, facing the monochrome camera, and the tablet computer is placed on the container. After being reflected by the first plane mirror, the monochrome camera observes upward from the bottom of the container, passing through the liquid inside the container, and captures a speckle image on the tablet computer. The image analysis unit includes a computer cluster consisting of multiple computers. By inputting an image name, the computer cluster extracts the image of the image name and outputs the height data of each pixel in binary format. The data processing unit arranges the height data of the image analysis unit into a data matrix, performs singular value decomposition on the data matrix to obtain the displacement distribution data of each pixel, differentiates it with its nearest neighbor pixels to obtain the gradient distribution of each pixel, and transforms it into an overdetermined system of equations by limiting the overall height, and uses the least squares solution as the height distribution. The waveform reconstruction unit linearly connects the height distribution of each pixel in the data processing unit within the computer cluster to obtain the liquid surface wave waveform curve.

[0009] The vibration table generates vertical vibration waves, which are transmitted to the liquid inside the container, and liquid surface waves are generated on the surface of the liquid.

[0010] The surface wave of the liquid is obtained by using the free surface synthetic schlieren method.

[0011] Specifically, radial distortion is corrected at a position consistent with the distance between the monochrome camera and the equilateral triangular boundary container; the sub-region marking function of the acquisition card is used to adjust the position and orientation of the monochrome camera to obtain ideal observation conditions.

[0012] The computer cluster of the image analysis unit simultaneously calculates the height data of a current image relative to a reference image, and the height data is the data of surface wave evolution over time.

[0013] The image analysis unit performs binary encoding on the calculation of eight consecutive pixels in the image and uses an unsigned integer variable to store the encoded height data.

[0014] The horizontal and vertical components of the height data are stored in two separate binary files.

[0015] The data processing unit arranges the height data obtained by the image analysis unit from left to right, column by column, in the original order from top to bottom into a data matrix. Each column contains all the height data information at a certain moment, and different columns correspond to different moments. Each row corresponds to the change of the height of a certain pixel in the region over time.

[0016] The gradient distribution of an internal pixel in the data processing unit corresponds to two overdetermined equations, which embody the differential information of each pixel and its nearest neighbor pixels.

[0017] The waveform reconstruction unit obtains a smooth two-dimensional liquid surface wave waveform curve.

[0018] (III) Beneficial Effects: This invention provides a liquid surface wave observation system and establishes a liquid surface wave observation and surface wave reconstruction method, which can obtain the expected surface wave waveform under relatively ideal conditions. It links the height change of the liquid surface wave with the change of the background image. Through a computer cluster, C++ code is written to convert the pixels of any image into data to obtain the height data of the liquid surface wave. The height data is arranged into a matrix, singular value decomposition is performed to obtain the corresponding spatial distribution pattern and temporal evolution pattern, and the displacement distribution is obtained. The differential of any pixel with its nearest neighbor pixels is used to limit the overall height. The gradient distribution is transformed into an overdetermined equation system problem. The least squares solution of the overdetermined equation system is used as the height distribution of the corresponding pixel. The height distribution is linearly connected to obtain the two-dimensional liquid surface wave waveform curve. Attached Figure Description

[0019] Figure 1 This is a flowchart of a liquid surface wave observation system according to the present invention; Figure 2 This is a diagram of the observation device of a liquid surface wave observation system according to the present invention; Figure 3 This invention relates to a checkerboard pattern created to correct radial distortion in monochrome cameras. Figure 4 These are the corner points and coordinate axes identified in a checkerboard image captured by a monochrome camera; Figure 5 This is a distribution chart of the first 100 singular values; Figure 6 It is the first-time evolutionary pattern curve; Figure 7 It is the waveform curve of the left cross section of the reconstructed stereo image of the liquid surface wave; Figure 8 It is the bottom cross-sectional waveform curve of the reconstructed three-dimensional image of the liquid surface wave.

[0020] Reference numerals: 1-Equilateral triangle boundary container, 2-First acrylic plate, 3-First plane mirror, 4-Acrylic box equipped with 45-degree tilted first plane mirror 3, 5-Vibration table, 6-Monochrome camera, 7-Second plane mirror, 8-Second acrylic plate, 9-Checkerboard pattern, 10-Third acrylic plate, 11-Tablet computer. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to preferred embodiments. More details are set forth in the following description in order to provide a full understanding of the present invention. However, the present invention can obviously be implemented in many other ways different from those described herein. Those skilled in the art can make similar extensions and derivations based on actual application situations without departing from the spirit of the present invention. Therefore, the scope of protection of the present invention should not be limited by the content of this specific embodiment.

[0022] The accompanying drawings are schematic diagrams of embodiments of the present invention. It should be noted that these drawings are for illustrative purposes only and are not drawn to scale, and should not be construed as limiting the actual scope of protection of the present invention.

[0023] A liquid surface wave observation system, such as Figure 1 As shown, it includes a container, a vibration unit, and an observation unit. The container includes an equilateral triangular boundary container, the vibration unit includes a vibration table, and the observation unit includes a monochrome camera, a first plane mirror, and a tablet computer.

[0024] A liquid surface wave observation system further includes an image analysis unit, a data processing unit, and a waveform reconstruction unit. The image analysis unit comprises a computer cluster consisting of multiple computers. By inputting an image name, the computer cluster extracts an image of that name and outputs the height data of each pixel in binary format. The data processing unit arranges the height data of the image analysis unit into a data matrix, performs singular value decomposition on the data matrix to obtain the displacement distribution data of each pixel, differentiates it with its nearest neighbor pixels to obtain the gradient distribution of each pixel, and transforms it into an overdetermined system of equations by limiting the overall height, and uses the least squares solution as the height distribution. The waveform reconstruction unit linearly connects the height distribution of each pixel in the data processing unit within the computer cluster to obtain the liquid surface wave waveform curve.

[0025] The liquid surface wave observation system described above can convert the liquid surface wave of a microscopic two-dimensional wave system into a macroscopic image for display. The image is then processed by singular value decomposition to obtain displacement distribution data. Based on the displacement distribution data, the gradient distribution data of the liquid surface wave is obtained. By limiting the overall height, the height distribution data of the liquid surface wave is obtained. By linearly fitting the height distribution data, the waveform of the liquid surface wave can be reconstructed.

[0026] In this application, the free surface synthetic schlieren method is used to obtain liquid surface waves, and the observation device used is as follows: Figure 2 As shown. A container 1 with an equilateral triangular boundary is attached to a first acrylic plate 2. This assembly is then placed on an acrylic box 4 equipped with a first plane mirror 3 tilted at 45 degrees. The acrylic box 4 with the first plane mirror 3 tilted at 45 degrees is then placed on the vibration table 5. Metal strips are used to fix the first acrylic plate 2 with the equilateral triangular boundary container 1 and the acrylic box 4 with the first plane mirror 3 tilted at 45 degrees to the vibration table 5. The monochrome camera 6 takes pictures horizontally, and after reflection by the first plane mirror 3, captures an image of the tablet computer 11 viewed from the bottom center of the container 1 with the equilateral triangular boundary, looking upwards.

[0027] The preferred container in this application is an equilateral triangular boundary container 1, with a side length of 104 mm and a height of 12.5 mm. Because existing technologies have provided sufficient theoretical research on the equilateral triangular case, and equilateral triangles correspond to integrable systems, the Helmholtz equations for this shape have been extensively studied. Multiple methods from different perspectives have been used to derive analytical solutions, and the structure of the solutions is well understood. The results can be compared with these existing theories to verify the rationality of the observation system and data processing methods.

[0028] The images captured by the monochrome camera 6 deviate from the real world. The simplest camera model is the pinhole camera model, but its exposure is too small. Therefore, to increase the exposure, a lens combination is used instead of a pinhole. On the one hand, the lens combination increases the brightness of the image, which helps to reduce the actual exposure. On the other hand, the introduction of the lens combination also brings image distortion. Among these, the most important is geometric aberration, which is divided into monochrome aberration and chromatic aberration. The camera in this application is preferably a monochrome camera 6, which can avoid the influence of chromatic aberration. Therefore, only the influence of monochrome aberration on the results of this application needs to be considered.

[0029] To eliminate monochrome aberration, the spatial position and orientation of the monochrome camera 6 should be adjusted to ensure that the principal optical axis of the lens of the monochrome camera 6 is perpendicular to the plane. In this way, the imaging pattern near the principal optical axis is the same as that of pinhole imaging, ensuring that the image captured near the principal optical axis is a direct projection. This can eliminate the influence of monochrome aberration of the monochrome camera 6 near the principal optical axis on the result, and thus eliminate the influence of geometric aberration on the result.

[0030] Adjusting the spatial position and orientation of the monochrome camera 6 involves correcting the relative position and angle between the monochrome camera 6 and the equilateral triangular boundary container 1. To ensure accurate location of the center of the field of view, the sub-region marking function of the acquisition card is used. The acrylic box 4 equipped with the first plane mirror 3 at a 45-degree angle is placed on the vibration table 5. The second acrylic plate 8 with the second plane mirror 7 is placed flat on top of the acrylic box 4 equipped with the first plane mirror 3 at a 45-degree angle. The position and orientation of the monochrome camera 6 are adjusted so that the monochrome camera 6 captures its own image after reflection from the first plane mirror 3 at a 45-degree angle inside the acrylic box 4 and the second plane mirror 7 on top of the acrylic box, ensuring that the lens of the monochrome camera 6 is centered in the field of view in the current image captured by the monochrome camera 6. Based on the current image size captured by the monochrome camera 6 and the distance of the monochrome camera 6 from the first plane mirror 3, a sub-region is drawn at the center of the field of view of the monochrome camera 6. After successful configuration, a red rectangle will appear in the center of the field of view of the monochrome camera 6, so that after reflection by the first plane mirror 3 and the second plane mirror 7, the lens of the monochrome camera 6 is located in the red rectangle, which can ensure that the optical axis of the lens of the monochrome camera 6 is perpendicular to the first plane mirror 3.

[0031] Replace the second acrylic plate 8 with the second plane mirror 7 on the acrylic box 4 containing the first plane mirror 3 at a 45-degree angle with the first acrylic plate 2 with the equilateral triangular boundary container 1 attached to it. Adjust the overall position of the monochrome camera 6 so that the equilateral triangular boundary container 1 is in the center of the image. When adjusting the position of the monochrome camera 6, it should be moved as a whole, and the angle of the monochrome camera 6 should not be changed.

[0032] However, during operation, the angle of the monochrome camera 6 inevitably changes. Therefore, the second acrylic plate 8 with the second plane mirror 7 attached is placed on top of the acrylic box 4 containing the first plane mirror 3 tilted at 45 degrees. The angle of the monochrome camera 6 is adjusted so that the lens of the monochrome camera 6 is centered in the image. Since it has already been adjusted once, the adjustment this time is smaller than before. Similarly, adjusting the angle of the monochrome camera 6 inevitably changes its spatial position. Therefore, the second acrylic plate 8 with the second plane mirror 7 attached to the top of the acrylic box 4 containing the first plane mirror 3 tilted at 45 degrees should be replaced with the first acrylic plate 2 with the equilateral triangular boundary container 1 attached, and the spatial position of the monochrome camera 6 should be adjusted. Through multiple alternating adjustments of the first acrylic plate 2 with the equilateral triangular boundary container 1 and the second acrylic plate 8 with the second plane mirror 7 attached, the principal optical axis of the lens of the monochrome camera 6 is made perpendicular to the equilateral triangular boundary container 1 and passes through its center.

[0033] By adjusting the spatial position and orientation of the monochrome camera 6, it can be ensured that the lens of the monochrome camera 6 is facing the equilateral triangular boundary container 1. Therefore, theoretically, the monochrome camera 6 can eliminate the influence of monochrome aberration.

[0034] However, it was found that the lens of the monochrome camera 6 uses a lens combination, which improves the brightness of the formed image and helps reduce actual exposure. But on the other hand, the introduction of the lens combination also brings image distortion. Among these, the most important is monochrome aberration, a geometric aberration. Monochrome aberration, mainly radial distortion, refers to the fact that the image has different magnifications in the region near the center and the region far from the center, causing straight lines in the real world to bend in the image.

[0035] In this application, the Camera Calibrator tool in MATLAB is used to correct the radial distortion of the monochrome camera 6. For example... Figure 3 As shown, a chessboard grid 9 with a fixed spacing is used as the actual calibration object. The size of a single grid 9 is 7mm×7mm, and the spatial arrangement is 7×10.

[0036] During calibration, the distance between the monochrome camera 6 and the checkerboard 9 should be consistent with the distance between the monochrome camera 6 and the equilateral triangular boundary container 1. In this application, the monochrome camera 6 is approximately 60cm away from the object being photographed. Therefore, when calibrating the monochrome camera 6, we should also take pictures of the checkerboard 9 at a position approximately 60cm away from the monochrome camera 6. During sampling, different positions should be selected within the field of view of the monochrome camera 6 for shooting, and the captured checkerboard 9 should have different tilt directions. Figure 4As shown, corner points in the acquired chessboard 9 image are identified and located to obtain the position information of each corner point in the image. By comparing the actual size of the chessboard 9 image with its position in the captured image, the actual position and angle of the chessboard 9 calibration object in real space can be calculated. Seventy images of the chessboard 9 were actually acquired, and for each image, the actual size of the chessboard 9 was compared with its position in the captured image to obtain the position and angle of the chessboard 9 image relative to the camera in the real world. By analyzing the deformation of the images captured by the monochrome camera 6 at different positions of the chessboard 9, the radial distortion correction parameters of the monochrome camera 6 can be obtained. The radial distortion correction parameters are different at different positions; the closer to the lens optical axis of the monochrome camera 6, the smaller the radial distortion correction parameter; conversely, the closer to the edge, the larger the radial distortion correction parameter.

[0037] A measured amount of liquid is poured into the equilateral triangular boundary container 1, and a third acrylic plate 10 is placed on top. A tablet computer 11 is then placed on the third acrylic plate 10, and the tablet computer 11 and the third acrylic plate 10 are fixed to the equilateral triangular boundary container 1 using acrylic strips. The liquid can be water, silicone oil, or alcohol, etc. In this application, silicone oil with a viscosity of 0.65 cSt is preferred. The surface tension of silicone oil with a viscosity of 0.65 cSt is very small, so the influence of the surface tension of silicone oil with a viscosity of 0.65 cSt on the results of this application can be ignored.

[0038] The monochrome camera 6 captures a still image of the vibration table 5 before it is driven: a reference image. The vibration table 5 is driven at a frequency between 63.00 Hz and 63.40 Hz, with a step size of 0.01 Hz. At each driving frequency, the driving amplitude gradually increases from low to high in steps of 0.0001 mm. During this time, the liquid surface changes. After two strong surface waves appear, the driving frequency is changed. The monochrome camera 6 captures an image of the liquid surface after 3 minutes of driving, obtaining the current image. The frame rate during capture is 369.5 fps, and the fixed number of frames is 1000.

[0039] By adjusting the spatial position and angle of the monochrome camera 6 and the equilateral triangular boundary container 1, the observation conditions can be made ideal, meaning that the captured image can be multiplied by the radial distortion correction parameter at each position to obtain the true image. Liquid is added into the equilateral triangular boundary container 1, and the vibration table 5 is driven, generating surface waves on the liquid surface. The monochrome camera 6 captures a speckle image of the tablet computer after reflection from the first plane mirror 3, presenting the microscopic surface waves in a macroscopic image format.

[0040] Images captured at a certain driving frequency often range from 1000 to 5000. To separate a good temporal evolution pattern, 1000 images actually need to be processed. This significantly increases the processing time for images at the driving frequency. The data processing time is much longer than the time it takes for the monochrome camera 6 to capture images. Therefore, it is necessary to improve data processing efficiency and reduce data processing time. On the one hand, we can upgrade computers to increase the computing power of a single computer; on the other hand, we can also build a cluster to enable multiple computers to collaboratively process computing tasks. This application adopts both solutions. Upgrading computers to increase the computing power of a single computer node is still insufficient to meet the processing speed requirements; therefore, multiple high-performance computers must be used to form a cluster.

[0041] A self-built computer cluster management system based on SLURM was adopted, which has good robustness and scalability, as well as a parallel environment and DIC environment built on the cluster. All computers participating in the cluster are equipped with the CentoOS operating system, with CentoOS 7 being the preferred system in this application. The installation type is all compute nodes, sharing storage and account information. The computers do not need to install large-capacity hard drives, nor do they need to create new ordinary users.

[0042] Data processing using the aforementioned computer cluster, including batch DIC calculations, typically lacks a graphical user interface; therefore, this application utilizes only a C++ interface. The Ncorr program is installed, and subsequent C++ code calls relevant functions to process the data and obtain the displacement distribution of the liquid surface waves. Data processing on the computer cluster allows the program to process the displacement distribution of only one current image relative to a reference image at a time, facilitating task allocation and scheduling.

[0043] Considering that the current image acquired after the vibration table 5 drives for 3 minutes is about 1000 frames, that is, each task needs to process about 1000 images and obtain 1000 displacement distributions, this application adds binary format data output code, so that we can save the lateral and longitudinal components of the displacement distribution to two binary files respectively.

[0044] For a specific pixel in an image, the Ncorr program may not always be able to calculate the height data; that is, the calculated data may not cover all image pixels. Therefore, a variable is needed to store information about whether the calculation for a particular pixel was successful. This success / failure information is suitable for storing a logical variable, but C++ does not have 1-bit logical variables; instead, integer variables are used to implement the functionality of logical variables. Using integer variables to implement the logical variable function has no impact on the operation, but it increases the amount of data stored to eight times the original amount.

[0045] In this application, the monochrome camera 6 is configured such that the width of the captured image must be a multiple of 8. Therefore, the calculation of 8 consecutive pixels of the image is binary encoded, and the encoded data is stored in an unsigned integer variable. By modifying the code and organizing the file, the binary encoding can be used to process an image and obtain its height distribution.

[0046] Since the monochrome camera 6 captures images of the vibration table 5 at different driving frequencies, the image size and the number of pixels in the successfully processed area will both change. Therefore, the sed tool is used to replace specific characters with the required numbers before compiling the source code.

[0047] For different nodes in the computer cluster, different folders are created, and the executable file is copied to the corresponding folder. When executed, the target image is copied from the specified node to the current folder, and the displacement distribution is calculated and saved in binary file format to the current folder. The displacement distribution data file is named according to the file name of the original target image.

[0048] Based on the cluster configuration, write a SHEEL script to submit tasks. The number of images can be passed in. The image processing tasks in the current directory are submitted to the computer cluster management system in sequence, and wait to be scheduled to obtain the height data of each 8 pixels of the image in binary format.

[0049] At this time, the image captured by the monochrome camera 6 changes with the driving of the vibration table 5, and the tablet computer 11 displays the changes in the speckle image captured by the monochrome camera 6. By comparing any current image captured by the monochrome camera 6 after 3 minutes of driving on the vibration table 5 with a reference image, a correspondence between the pixels of the reference image and the current image is established, and the motion information of each pixel in the reference image and the current image is obtained.

[0050] The correspondence between the pixels can be represented using either an Eulerian or a Lagrange representation. An Eulerian representation focuses on a specific location in the image, describing the change of a sub-image at that location when the image changes; a Lagrange representation focuses on a specific sub-image, describing the change of the position of that sub-image when the image changes. Specifically, regarding the reference image and the current image, the Eulerian representation describes which sub-image in the reference image will move to that location in the current image, while the Lagrange representation describes which sub-image in the reference image will move to that location in the current image. In practice, this difference mainly lies in the selection of the reference and current images. Simply swapping the reference and current images allows for the conversion between the two representation methods. This application does not impose specific restrictions on which method is used for pixel correspondence.

[0051] In this application, the assumptions of irrotation and sourcelessness are used to treat the liquid. Considering the wave velocity u of the liquid in the equilateral triangular boundary container 1, a velocity potential is introduced. , Considering only the smaller amplitude of the liquid surface, a linear approximation is made to the amplitude of the liquid surface, then... Satisfies the Laplace equation, And the boundary conditions at z=0, Where G(k) is the wavenumber dependence. The function, Here, g is the acceleration due to gravity, ρ is the density of the liquid, and T is the surface tension coefficient of the liquid.

[0052] Let ξ be the z-coordinate of the liquid surface. Then, for the stationary liquid surface when the vibration table 5 is not driven, it can be expressed as ξ = 0. ξ can be derived from the velocity potential. We further assume that the system is variable-separable. Considering the boundary conditions, we have The Helmholtz equation can then be obtained by solving the Laplace equation.

[0053] The liquid surface ξ is That is, for any given moment, ξ and They differ only by a coefficient independent of x and y, and they have the same morphological characteristics. Therefore, the study of ξ can be transformed into the study of... The research.

[0054] To The definition of the separated variables is in X Functions in the Y-plane Indicates different The relative amplitude at different points. For different Each has a corresponding and ,constitute The complete movement of the liquid can be caused by 1, 2,…, n,…expand.

[0055] Therefore, this application only explores the spatial structure of ξ, i.e., f(x, y). In this application, the current image captured by the monochrome camera 6 is a sequence of surface wave evolution over time. Figure 8As shown, each image in the sequence represents the height distribution of the liquid surface at a certain moment. To obtain the information corresponding to f(x, y), the amplitude distribution that best characterizes the surface wave properties, i.e., the most dominant spatial distribution pattern, should be obtained from this time-dependent evolution sequence. Therefore, it is necessary to extract the spatial distribution pattern from the time-dependent evolution data and use singular value decomposition in the fluid to explore its pattern composition.

[0056] Each image captured by the monochrome camera 6 represents the height data of the pixels at the current moment. The height data is processed column by column from left to right, with the elements in each column rearranged from top to bottom according to their original order. This rearranges the height distribution into a column vector. After processing all columns, the height data distributed within the two-dimensional region acquired at a certain time t is obtained. Convert to a column vector The above operations are performed on the height data at all times obtained by the image analysis unit to obtain the data matrix X.

[0057] Any column in the matrix Each matrix X contains all the information about the height field at a given moment, with different columns corresponding to different moments; each row represents the change in height over time at a specific location within the region. Performing singular value decomposition on the matrix X yields the left singular vector. Represents spatial distribution patterns, right singular vectors Represents a pattern of temporal evolution. For example... Figure 5 The figure shows the distribution of the first 100 singular values. All subsequent singular values ​​are smaller than the singular values ​​shown in the figure.

[0058] Consider matrix If n≥m, its singular value decomposition is: .in, , All are unitary matrices, and each column of U... , 1≤i≤n, each column in V , 1≤i≤m, Let V be the transpose of the complex conjugate matrix; It is a real matrix, and it is required that... That is, all diagonal elements of Σ are not less than 0 and are arranged in descending order, while the remaining positions are 0.

[0059] In the least squares sense, the optimal approximation of matrix X with rank r is truncated by the singular value decomposition of matrix X with rank r. Give, that is

[0060] in, and Let U and V be matrices consisting of the first r columns of each matrix. Let Frobenius norm be the matrix. Let Σ be the submatrix formed by the first r rows and the first r columns, i.e.

[0061] therefore, It can be seen that, considering matrix approximation in the least squares sense, to make the rank of the target matrix r, we should multiply the complex conjugate matrix of the transpose of the matrix formed by the first r left singular vectors obtained from singular value decomposition and the matrix formed by the first r right singular vectors, and then multiply it by the submatrix formed by the first r rows and first r columns of the corresponding singular value matrix. Since U and V are both unitary matrices, the rank of the sum of the first r terms is r. As r increases, The difference from X gradually decreases in the least squares sense. Since the singular values ​​are arranged in descending order, the influence of later terms on matrix approximation also gradually weakens. Any Represents spatial distribution patterns According to the time evolution model The evolved spatiotemporal pattern, σi, represents the components or weights of the data within this pattern. Therefore, from a matrix approximation perspective, if r spatiotemporal patterns are used to approximate the data, the best approximation in the least squares sense is: From the perspective of matrix factorization, the spatiotemporal pattern with the highest component or weight in the data is... , followed by , wait.

[0062] The left singular vector Represents the spatial distribution pattern, indicating the displacement distribution of each pixel in any image at the current moment; such as Figure 6 As shown, the right singular vector This represents the temporal evolution pattern, indicating the displacement change of any pixel in any image at any given time. Superimposing both yields the displacement distribution of each pixel in the image of the liquid surface wave at any given time.

[0063] The image is processed by a computer cluster to obtain highly distributed binary format data. The binary data is arranged into a data matrix from left to right according to the order of each pixel. The data matrix is ​​decomposed by singular value decomposition to separate the left singular vector representing the spatial distribution pattern and the right singular vector representing the temporal evolution pattern. The spatial distribution pattern is the displacement distribution of each pixel of the liquid surface wave.

[0064] After obtaining the displacement distribution of each pixel of the liquid surface wave, it is necessary to further calculate the gradient distribution of each pixel of the liquid surface wave in the image. The gradient distribution is the differential relationship between a pixel in the image and its nearest neighbor pixels. The gradient information of each internal pixel leads to two equations. Roughly speaking, the number of equations is almost twice the number of pixels that need to be solved. These equations are contradictory equations without solutions, therefore the system of equations formed by these equations is called an overdetermined system of equations. Since the overdetermined system of equations is a contradictory system without solutions, the least squares solution of the overdetermined system of equations is used as the height distribution of the pixels in the image. The gradient equation of the image pixels reflects the differential information of the image pixels, and the overall increase or decrease of the height distribution will not affect the gradient distribution of the image pixels. Therefore, we should add constraints to these differential information to determine the overall height of the height distribution.

[0065] The overall height of the defined height distribution can be determined by pre-specifying the height at a certain pixel point, or by setting the average height of the overall height distribution to zero; no specific restrictions are imposed here.

[0066] After defining the overall image height, the gradient distribution of the image pixels becomes a problem of solving an overdetermined system of equations. Each internal pixel corresponds to two overdetermined equations, and all pixels form a system of overdetermined equations with twice the number of pixels. The least-squares solution of the overdetermined system of equations is used as the height distribution of the pixels in the image. The height distribution of each pixel is output to the waveform reconstruction unit, and arranged sequentially to obtain the waveform curve of the liquid surface wave in the image.

[0067] The gradient distribution of each pixel in the image, that is, the differential information of each pixel and its nearest neighbor, is converted into the solution of the overdetermined system of equations. By adding constraints, the height distribution of the entire image is limited, and the least squares solution is obtained as the height distribution data of each pixel in the image. Thus, each pixel in the image is converted into a numerical value, and the numerical value is output to the waveform reconstruction unit to obtain the waveform of the liquid surface wave.

[0068] The waveform reconstruction unit uses the least-squares solution obtained by the data processing unit input into the computer cluster as the height distribution, and connects the height distribution of each pixel through linear connections, such as... Figure 7 , 8 As shown, the waveform curve of the liquid surface wave at the corresponding moment in the current image is obtained; the reconstructed waveform curve is smooth, and the amplitude gradually decreases from the container boundary to the center. The waveform curves of the liquid surface wave in all images at each moment captured by the monochrome camera 6 are superimposed to obtain a smooth waveform curve of the entire two-dimensional liquid surface wave.

[0069] The waveform reconstruction unit reconstructs the liquid surface wave waveform curve at a certain moment by arranging the height data of each pixel in the image corresponding to a certain moment according to the pixel order of the image based on the height data of each pixel in the image obtained by the data processing unit; and superimposes the liquid surface wave waveform curves reconstructed from any image at the same driving frequency of the vibration table to reconstruct the two-dimensional liquid surface wave waveform curve at the driving frequency.

[0070] The free-surface synthetic schlieren method of this invention corrects the spatial position and angle of the monochrome camera by alternating the equilateral triangular boundary container 1 and the second acrylic plate 8 with the second plane mirror 7 in the observation system. This allows the monochrome camera lens to refract light through the first plane mirror 3 and observe upwards through the bottom of the container. However, due to the lens combination, the monochrome camera is prone to radial distortion. To correct this, a 7×10 checkerboard pattern 9 is used. The checkerboard pattern 9 is placed at the location of the equilateral triangular boundary container 1 for imaging. By comparing the image position and angle of each corner point of the checkerboard pattern 9 with the real-world position and angle of each corner point, radial distortion correction parameters are obtained, thus achieving ideal conditions. An image of a stationary liquid surface is captured under these ideal conditions as a reference image. Then, the vibration table 5 is driven, and imaging begins after 3 minutes, resulting in multiple current images. The image analysis unit processes the reference image and each current image through the computer cluster, writing C++ code. By modifying the source code in the C++ code test example and fixing the name of the input image, the height distribution of each pixel in any image is output to the data processing unit in binary format. The data processing unit arranges the binary data in left-to-right order of the pixels to obtain a data matrix. This data matrix is ​​a sequence of time-dependent evolution data of the surface wave. Singular value decomposition is performed on the data matrix to obtain the displacement distribution of each pixel, which consists of a left singular vector and a right singular vector. The left singular vector represents the spatial distribution pattern, and the right singular vector represents the temporal evolution pattern. Differentiating each pixel with its nearest neighbors yields the gradient distribution of each pixel. This limits the overall height of the liquid surface wave, resulting in a series of overdetermined equations. Solving these equations yields a least-squares solution, which is used as the height distribution of each pixel in the liquid surface wave. The waveform reconstruction unit inputs the pixel height distribution sequentially into the computer cluster, and a smooth curve connects the data points to obtain the waveform curve of the current image at a specific moment. The waveform reconstruction unit connects the height distribution of each pixel at different times to obtain the waveform motion curve of a certain pixel over the entire time.

[0071] The above description illustrates preferred embodiments of the present invention and helps those skilled in the art to more fully understand the technical solution of the present invention. However, these embodiments are merely illustrative and should not be construed as limiting the specific implementation of the present invention to these embodiments. For those skilled in the art, several simple deductions and modifications can be made without departing from the inventive concept, and all such modifications should be considered within the protection scope of the present invention.

Claims

1. A liquid surface wave observation system, characterized in that, It includes an observation unit, a container, a vibration unit, an image analysis unit, a data processing unit, and a waveform reconstruction unit; The container includes an equilateral triangular boundary container; the vibration unit includes a vibration table, and the equilateral triangular boundary container is placed on the vibration table surface; the observation unit includes a monochrome camera, a first plane mirror, and a tablet computer; the first plane mirror is placed at a 45-degree angle below the container, facing the monochrome camera, and the tablet computer is placed on the container. After being reflected by the first plane mirror, the monochrome camera observes upward from the bottom of the container, passing through the liquid inside the container, and captures a speckle image of the tablet computer; the monochrome camera lens uses a lens combination to adjust the position and direction of the monochrome camera, and the principal optical axis of the monochrome camera lens is perpendicular to the first plane mirror; The image analysis unit includes a computer cluster consisting of multiple computers. By inputting an image name, the computer cluster extracts the image of the image name and outputs the height data of each pixel in binary format. The data processing unit arranges the height data of the image analysis unit into a data matrix, performs singular value decomposition on the data matrix to decompose the spatial distribution pattern, and obtains the spatial distribution pattern of each pixel. The data of the spatial distribution pattern is differentiated with its nearest neighbor pixels to obtain the gradient distribution of each pixel. By limiting the overall height, it is transformed into an overdetermined system of equations for solution. The least squares solution of the overdetermined system of equations is used as the height distribution of each pixel of the liquid surface wave. The waveform reconstruction unit linearly connects the height distribution of each pixel in the data processing unit according to the original arrangement order to obtain the liquid surface wave waveform curve.

2. The liquid surface wave observation system according to claim 1, characterized in that, The vibration table generates vertical vibration waves, which are transmitted to the liquid inside the container, and liquid surface waves are generated on the surface of the liquid.

3. The liquid surface wave observation system according to claim 1, characterized in that, The surface waves of the liquid were obtained using the free surface synthetic schlieren method.

4. A liquid surface wave observation system according to claim 3, characterized in that, Radial distortion is corrected at a position consistent with the distance between the monochrome camera and the equilateral triangular boundary container; the position and orientation of the monochrome camera are adjusted using the sub-region marking function of the acquisition card to obtain an ideal liquid surface wave.

5. A liquid surface wave observation system according to claim 1, characterized in that, The computer cluster of the image analysis unit simultaneously calculates the height data of a current image relative to a reference image, and the height data is the data of surface wave evolution over time.

6. A liquid surface wave observation system according to claim 5, characterized in that, The computer cluster performs binary encoding of the calculation results for eight consecutive pixels of the image and stores the encoded height data using an unsigned integer variable.

7. A liquid surface wave observation system according to claim 6, characterized in that, The horizontal and vertical components of the height data are saved to two separate binary files.

8. A liquid surface wave observation system according to claim 1, characterized in that, The data processing unit arranges the height data obtained by the image analysis unit into a data matrix from left to right, column by column, and top to bottom. Each column contains all the height data information at a certain moment, and different columns correspond to different moments. Each row corresponds to the change of the height of a certain pixel in all current images captured by the monochrome camera at a certain driving frequency of the vibration table over time.

9. A liquid surface wave observation system according to claim 1, characterized in that, The gradient distribution of an internal pixel in the data processing unit corresponds to two overdetermined equations, which embody the differential information of each pixel and its nearest neighbor pixels.

10. A liquid surface wave observation system according to claim 1, characterized in that, The waveform reconstruction unit obtains a smooth two-dimensional liquid surface wave waveform curve.

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