Full-field displacement and rotation angle measurement method for frame structures based on finite element and optical flow method

Abstract

The present invention discloses a method for measuring the full-field displacement and rotation angle of a frame structure based on finite element and optical flow methods. The method comprises the following steps: performing unit segmentation on a target structure image to determine displacement boundary conditions; determining a first relationship between the image displacement of each pixel point within each unit in the target structure image and the corresponding unit node displacement based on the optical flow method and finite element theory; assembling the node displacement vectors of each unit in the overall coordinates into a structure overall node displacement vector using a unit coordinate transformation matrix and an assembly matrix, and determining a vector relationship between the image displacement of each pixel point and the structure overall node displacement at any given time; solving the vector relationship, performing frequency domain decomposition on the time domain displacement of the overall degree of freedom of the structure, obtaining structural modal parameters, and completing full-field displacement and rotation angle measurement of the target structure. The present invention combines finite element and optical flow methods to improve recognition accuracy and can be widely applied in the field of computer technology.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a method for measuring full-field displacement and rotation angle of a frame structure based on finite element and optical flow methods. Background Art

[0002] With the advancement of society and the improvement of people's living standards, the number of buildings, such as bridges and buildings, is increasing. These structures are subject to various environmental influences, such as wind, vehicle traffic, environmental erosion, and natural disasters. These influences can cause changes in structural material parameters and geometric characteristics, leading to damage. To assess their safety, structural health monitoring is necessary. Structural health monitoring encompasses two key areas: "sensing" and "data." Sensing encompasses various sensors and their sensing principles, monitoring structural loads, overall and local responses, and more. Data encompasses the theory, methods, software and hardware for data acquisition and transmission, data analysis, structural identification and damage detection, and structural maintenance decision-making.

[0003] Currently, sensors used for structural health monitoring come in two types: contact and non-contact. Traditional structural health monitoring often relies on contact displacement sensing technology, which offers the advantage of high precision, but also has significant limitations. For example, sensor installation and physical connection to data acquisition and power supply systems require significant effort and time. Sensor installation on long-span bridges or tall structures is extremely difficult and can be dangerous. Furthermore, when continuous displacement data is required, installing a large number, or even an infinite number of sensors, is impractical. With the advancement of technology, non-contact measurement has gradually developed, with the emergence of infinite sensors, fiber optic sensors, and interferometric radar systems.

[0004] However, the related technology has the following disadvantages:

[0005] 1. Most existing vision-based structural displacement measurements target individual points of interest rather than full-field measurements, and usually require the target structure to be marked. The resulting structural modes are discontinuous and cannot provide high-precision structural modal parameters.

[0006] 2. Existing technologies use regularization to deal with the instability of image motion estimation, but rarely consider using the mechanical properties of the structure itself to correct the identified displacements and modes, resulting in the identified displacements being prone to mutations and not conforming to the characteristics of physical structural motion. Summary of the Invention

[0007] In view of this, an embodiment of the present invention provides a full-field displacement and rotation angle measurement method of a frame structure based on finite element and optical flow method to improve recognition accuracy.

[0008] An aspect of an embodiment of the present invention provides a method for measuring full-field displacement and rotation angle of a frame structure based on finite element and optical flow methods, comprising:

[0009] Perform unit division on the target structure image and determine the displacement boundary conditions;

[0010] According to the optical flow method and the finite element theory, for each pixel point in each unit in the target structure image, a first relationship between the image displacement of each pixel point and the displacement of the corresponding unit node is determined;

[0011] Assembling the node displacement vectors of each unit in the global coordinates into the node displacement vector of the overall structure through the unit coordinate transformation matrix and the assembly matrix, and determining the vector relationship between the image displacement of each pixel point and the node displacement of the overall structure at any given time according to the first relationship;

[0012] Solving the vector relationship by the least square method to obtain the global node displacement vector of the target structure at all times;

[0013] According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is decomposed in the frequency domain to obtain the structural modal parameters, thereby completing the full-field displacement and rotation angle measurement of the target structure.

[0014] Optionally, determining, for each pixel point in each unit in the target structure image according to the optical flow method and the finite element theory, a first relationship between the image displacement of each pixel point and the displacement of the corresponding unit node includes:

[0015] Determine the unit degree of freedom of any one-dimensional finite element unit in the target structure image according to the optical flow method and finite element theory, and obtain the unit node displacement vector;

[0016] Determine a unit displacement function based on the unit node displacement vector; the unit displacement function is used to determine a first relationship between the image displacement of each pixel point and the corresponding unit node displacement

[0017] The expression of the unit displacement function is: v(η)=[N]{d} e ,

[0018] v(η) represents the unit displacement function; η is the unit axial coordinate; [N] is the shape function; {d} e represents the unit degrees of freedom.

[0019] Optionally, the target structure is a plane beam element, and the process of constructing the displacement function and shape function of the plane beam element includes:

[0020] For a plane beam element with plane bending deformation, the element length is l, the displacement in the ζ direction is v(η), the rotation angle is θ(η), and the displacement and rotation angle of the i and j nodes are selected as the unit degrees of freedom. The unit degrees of freedom {d} e Expressed as:

[0021] {d} e =[v i ,θ i ,v j ,θ j ] T

[0022] Based on the number of degrees of freedom being 4, the displacement pattern of the beam element deflection is configured as a cubic polynomial:

[0023] v(η)=a1+a2η+a3η 2 +a4η 3

[0024] Among them, a1, a2, a3, and a4 are four polynomial coefficients;

[0025] The node displacement conditions at both ends of the unit are:

[0026]

[0027] Solve for the coefficients a1, a2, a3, a4, and determine the displacement function expressed by the node displacement and shape function:

[0028] v(η)=[N]{d} e

[0029] Among them, the shape function [N] = [N1, N2, N3, N4], the specific form is:

[0030]

[0031]

[0032]

[0033]

[0034] Among them, N1, N2, N3, N4 represent the corresponding node displacement v i ,θ i ,v j ,θ j The interpolation function of .

[0035] Optionally, the step of determining the unit degrees of freedom of a one-dimensional finite element unit in any plane in the target structure image according to the optical flow method and finite element theory to obtain the unit node displacement vector further includes the step of expressing the displacement of the node using the optical flow method, which step includes:

[0036] According to the target structure unit composed of the pixels in the target structure image, the structural pixel area in the i-th unit in the image is determined as Ω i , the area of ​​all pixels of the target structure is Ω S , and then determine the expression of the displacement of the target structure image.

[0037] Optionally, solving the vector relationship equations according to the least squares method to obtain the overall node displacement vector of the target structure at all times includes:

[0038] For the overall structure of the target structure, performing unit decomposition on the target structure;

[0039] Analyze each unit obtained by segmentation according to the finite element process and determine the coordinate transformation matrix of each unit;

[0040] According to the coordinate transformation matrix of each unit, assembling the node displacement vectors of each unit into the node displacement vector of the entire structure;

[0041] An overdetermined set of equations is solved according to the overall node displacement vector of the structure, and the obtained least square solution is determined as the overall node displacement vector of the target structure.

[0042] Optionally, the structural modal parameters include natural frequency, damping ratio and mode shape, and the frequency domain decomposition of the time domain displacement of the overall degree of freedom of the structure is performed according to the overall node displacement vector to obtain the structural modal parameters, including:

[0043] According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is obtained;

[0044] Determining a power spectrum density matrix of the time domain displacement, performing singular value decomposition on the power spectrum density matrix at any frequency to obtain singular values ​​of each order;

[0045] According to the maximum value of the first-order singular curve at the structural natural frequency, the corresponding structural modal vibration shape is determined;

[0046] Perform inverse Fourier transform on the singular value peak segment to the time domain to calculate the logarithmic attenuation rate to obtain the damping ratio.

[0047] Another aspect of the present invention provides a full-field displacement and rotation angle measurement device for a frame structure based on finite element and optical flow methods, comprising:

[0048] Perform unit division on the target structure image and determine the displacement boundary conditions;

[0049] According to the optical flow method and the finite element theory, for each pixel point in each unit in the target structure image, a first relationship between the image displacement of each pixel point and the displacement of the corresponding unit node is determined;

[0050] Assembling the node displacement vectors of each unit in the global coordinates into the node displacement vector of the overall structure through the unit coordinate transformation matrix and the assembly matrix, and determining the vector relationship between the image displacement of each pixel point and the node displacement of the overall structure at any given time according to the first relationship;

[0051] Solving the vector relationship by the least square method to obtain the global node displacement vector of the target structure at all times;

[0052] According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is decomposed in the frequency domain to obtain the structural modal parameters, thereby completing the full-field displacement and rotation angle measurement of the target structure.

[0053] Another aspect of an embodiment of the present invention further provides an electronic device, including a processor and a memory;

[0054] The memory is used to store programs;

[0055] The processor executes the program to implement the method described above.

[0056] Another aspect of the embodiments of the present invention further provides a computer-readable storage medium, wherein the storage medium stores a program, and the program is executed by a processor to implement the method described above.

[0057] Another aspect of an embodiment of the present invention further provides a computer program product, including a computer program, which implements the above-mentioned method when executed by a processor.

[0058] An embodiment of the present invention performs unit decomposition on a target structure image to determine displacement boundary conditions; based on the optical flow method and finite element theory, for each pixel point in each unit in the target structure image, a first relationship between the image displacement of each pixel point and the corresponding unit node displacement is determined; through the unit coordinate transformation matrix and the assembly matrix, the node displacement vectors of each unit in the overall coordinate are assembled into the overall node displacement vector of the structure, and based on the first relationship, the vector relationship between the image displacement of each pixel point and the overall node displacement of the structure at any given time is determined; the vector relationship is solved by the least squares method for the set of equations to obtain the overall node displacement vector of the target structure at all times; based on the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is decomposed in the frequency domain to obtain the structural modal parameters, thereby completing the full-field displacement and rotation angle measurement of the target structure. The present invention combines the finite element method with the optical flow method to improve the recognition accuracy and make the calculation results closer to the real movement. The displacement of each node of the structure can be obtained. Combined with the finite element shape function expression, the displacement function of each unit can be restored to obtain the global vibration displacement and rotation angle of the structure. It can provide an accurate and effective continuous mode identification method for structures with complex vibration shapes. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0060] Figure 1 An overall step flow chart provided for an embodiment of the present invention;

[0061] Figure 2 This is a flowchart of the implementation of the present invention in a specific scenario.

[0062] Figure 3 A schematic structural diagram of a plane beam unit provided in an embodiment of the present invention;

[0063] Figure 4 A schematic diagram of a cantilever beam model unit provided in an embodiment of the present invention;

[0064] Figure 5 A schematic diagram of a plane beam element in a global coordinate system provided by an embodiment of the present invention;

[0065] Figure 6 A schematic diagram illustrating a specific scenario of the finite element structural continuous modal identification method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of the present application. They are merely examples of devices and methods consistent with some aspects of the embodiments of the present application as detailed in the appended claims.

[0067] It will be understood that the terms "first", "second", etc. used in this application may be used herein to describe various concepts, but unless otherwise specified, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the words "if" and "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0068] The terms "at least one", "plurality", "each", "any", etc. used in this application include "at least one", "two" or more, "plurality" or "each", "any" or "any one", "each" or "any one" as used herein.

[0069] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application pertains. The terms used herein are for the purpose of describing the embodiments of this application only and are not intended to limit this application.

[0070] Before describing the embodiments of the present application in detail, some of the related technologies involved in the embodiments of the present application are first described as follows:

[0071] Structural health monitoring (SHM) refers to strategies and processes for identifying and characterizing damage in engineering structures. Structural damage refers to changes in the structural material parameters and geometric characteristics. The SHM process involves acquiring the structural response using a periodically sampled sensor array, extracting damage-sensitive indicators, and performing statistical analysis of these indicators to determine the current structural health.

[0072] Optical flow: Optical flow is the instantaneous speed of pixel motion of a moving object on the observation imaging plane. Optical flow uses the temporal changes in pixels in an image sequence and the correlation between adjacent frames to find the correspondence between the previous and current frames, thereby calculating the motion information of objects between adjacent frames.

[0073] Finite element analysis: A method used to analyze static or dynamic physical systems. In this method, an object or system is decomposed into a geometric model consisting of a number of interconnected, simple, independent points. The number of these independent points is limited, hence the term "finite element" analysis. Equilibrium equations derived from the actual physical model are applied to each point, resulting in a system of equations that can be solved using linear algebra.

[0074] Structural modal parameters: These are the natural vibration characteristics of a structure. Each mode has a specific natural frequency, damping ratio, and modal shape. These modal parameters can be obtained by performing modal analysis on the structural vibration input and output signals. Structural modal parameters are important parameters in structural health monitoring and damage identification.

[0075] In response to the shortcomings of the related prior art, the embodiments of the present invention provide a method for measuring the full-field displacement and rotation angle of a frame structure based on finite element and optical flow methods to improve the related technical means. Specifically, the related prior art has the following shortcomings:

[0076] 1. Vision-based structural displacement measurements are targeted at individual points of interest rather than full-field measurements, and usually require the target structure to be marked. The resulting structural modes are discontinuous and cannot provide high-precision structural modal parameters.

[0077] 2. Existing technologies use regularization to deal with the instability of image motion estimation, but rarely consider using the mechanical properties of the structure itself to correct the identified displacements and modes, resulting in the identified displacements being prone to mutations and not conforming to the characteristics of physical structural motion.

[0078] Accordingly, an object of the present invention is to provide a full-field displacement and rotation angle measurement technology that conforms to the inherent mechanical properties of the structure.

[0079] This technology has the following characteristics:

[0080] 1. This technology uses the optical flow method to achieve full-field recognition of markerless structures. Combined with subsequent operations and modal analysis, it can realize continuous modal recognition of structures and obtain high-precision continuous modal parameters;

[0081] 2. This technology utilizes finite element theory to modify displacement identification, enabling the measurement of displacement and rotation angles. This also ensures that identification results are more consistent with the inherent mechanical properties and motion characteristics of the structure, effectively reducing sudden changes that are inconsistent with physical motion. For practical engineering problems, this technology's identification results can be directly input into the finite element model parameter correction process.

[0082] It should be noted that the full-field displacement and rotation angle measurement method of the frame structure based on the finite element and optical flow method provided in the embodiment of the present application relates to the field of computer technology. The full-field displacement and rotation angle measurement method of the frame structure based on the finite element and optical flow method provided in the embodiment of the present application can be applied to a terminal, can also be applied to a server, and can also be software running in a terminal or a server. In some embodiments, the terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, and a car terminal, etc., but is not limited to this; the server side can be configured as an independent physical server, or can be configured as a server cluster or distributed system composed of multiple physical servers, and can also be configured as a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network; the software can be an application that implements the full-field displacement and rotation angle measurement method of the frame structure based on the finite element and optical flow method, etc., but is not limited to the above forms.

[0083] The present application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like. The present application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, and the like that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments in which tasks are performed by remote processing devices connected via a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media, including storage devices.

[0084] like Figure 1 As shown, a method for measuring full-field displacement and rotation angle of a frame structure based on finite element and optical flow method according to an embodiment of the present invention specifically includes the following steps:

[0085] S1. Divide the target structure image into units and determine displacement boundary conditions. For example, the displacement boundary conditions of the embodiment of the present invention may include fixed end constraints, simply supported constraints, etc.

[0086] S2. Determine, for each pixel point in each unit of the target structure image, a first relationship between the image displacement of each pixel point and the displacement of the corresponding unit node based on the optical flow method and finite element theory;

[0087] S3. Assembling the node displacement vectors of each unit in the global coordinates into the node displacement vector of the overall structure through the unit coordinate transformation matrix and the assembly matrix, and determining the vector relationship between the image displacement of each pixel point and the node displacement of the overall structure at any given time according to the first relationship;

[0088] S4. Solving the vector relationship equations according to the least squares method to obtain the overall node displacement vector of the target structure at all times;

[0089] S5. Based on the overall node displacement vector, perform frequency domain decomposition on the time domain displacement of the overall degree of freedom of the structure to obtain structural modal parameters, and complete full-field displacement and rotation angle measurement of the target structure.

[0090] Specifically, the determining of a first relationship between the image displacement of each pixel point and the corresponding unit node displacement for each pixel point in each unit in the target structure image based on the optical flow method and the finite element theory includes:

[0091] Determine the unit degree of freedom of any one-dimensional finite element unit in the target structure image according to the optical flow method and finite element theory, and obtain the unit node displacement vector;

[0092] Determine a unit displacement function based on the unit node displacement vector; the unit displacement function is used to determine a first relationship between the image displacement of each pixel point and the corresponding unit node displacement

[0093] The expression of the unit displacement function is: v(η)=[N]{d} e ,

[0094] v(η) represents the unit displacement function; η is the unit axial coordinate; [N] is the shape function; {d} e represents the unit degrees of freedom.

[0095] Specifically, the target structure is a plane beam element, and the process of constructing the displacement function and shape function of the plane beam element includes:

[0096] For a plane beam element with plane bending deformation, the element length is l, the displacement in the ζ direction is v(η), the rotation angle is θ(η), and the displacement and rotation angle of the i and j nodes are selected as the unit degrees of freedom. The unit degrees of freedom {d} e Expressed as:

[0097]

[0098] Based on the number of degrees of freedom being 4, the displacement pattern of the beam element deflection is configured as a cubic polynomial:

[0099] v(η)=a1+a2η+a3η2 +a4η 3

[0100] Among them, a1, a2, a3, and a4 are four unknown polynomial coefficients;

[0101] The node displacement conditions at both ends of the unit are:

[0102]

[0103] Solve for the coefficients a1, a2, a3, a4, and determine the displacement function expressed by the node displacement and shape function:

[0104] v(η)=[N]{d} e

[0105] Among them, the shape function [N] = [N1, N2, N3, N4], the specific form is:

[0106]

[0107]

[0108]

[0109]

[0110] Among them, N1, N2, N3, N4 represent the corresponding node displacement v i ,θ i ,v j ,θ j The interpolation function of .

[0111] Specifically, the step of determining the unit degrees of freedom of the one-dimensional finite element unit of any plane in the target structure image according to the optical flow method and the finite element theory to obtain the unit node displacement vector also includes the step of expressing the displacement of the node using the optical flow method, which step includes:

[0112] According to the target structure unit composed of the pixels in the target structure image, the structural pixel area in the i-th unit in the image is determined as Ω i , the area of ​​all pixels of the target structure is Ω S , and then determine the expression of the displacement of the target structure image.

[0113] Specifically, the vector relationship is solved by the least square method to obtain the overall node displacement vector of the target structure at all times, including:

[0114] For the overall structure of the target structure, performing unit decomposition on the target structure;

[0115] Analyze each unit obtained by segmentation according to the finite element process and determine the coordinate transformation matrix of each unit;

[0116] According to the coordinate transformation matrix of each unit, assembling the node displacement vectors of each unit into the node displacement vector of the entire structure;

[0117] An overdetermined set of equations is solved according to the overall node displacement vector of the structure, and the obtained least square solution is determined as the overall node displacement vector of the target structure.

[0118] Specifically, the structural modal parameters include natural frequency, damping ratio and mode shape. The structural modal parameters are obtained by performing frequency domain decomposition on the time domain displacement of the overall degree of freedom of the structure according to the overall node displacement vector, including:

[0119] According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is obtained;

[0120] Determining a power spectrum density matrix of the time domain displacement, performing singular value decomposition on the power spectrum density matrix at any frequency to obtain singular values ​​of each order;

[0121] According to the maximum value of the first-order singular curve at the structural natural frequency, the corresponding structural modal vibration shape is determined;

[0122] Perform inverse Fourier transform on the singular value peak segment to the time domain to calculate the logarithmic attenuation rate to obtain the damping ratio.

[0123] Another aspect of the present invention provides a full-field displacement and rotation angle measurement device for a frame structure based on finite element and optical flow methods, comprising:

[0124] Perform unit division on the target structure image and determine the displacement boundary conditions;

[0125] According to the optical flow method and the finite element theory, for each pixel point in each unit in the target structure image, a first relationship between the image displacement of each pixel point and the displacement of the corresponding unit node is determined;

[0126] Assembling the node displacement vectors of each unit in the global coordinates into the node displacement vector of the overall structure through the unit coordinate transformation matrix and the assembly matrix, and determining the vector relationship between the image displacement of each pixel point and the node displacement of the overall structure at any given time according to the first relationship;

[0127] Solving the vector relationship by the least square method to obtain the global node displacement vector of the target structure at all times;

[0128] According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is decomposed in the frequency domain to obtain the structural modal parameters, thereby completing the full-field displacement and rotation angle measurement of the target structure.

[0129] The specific implementation process of the present invention is described in detail below. The overall implementation process is as follows: Figure 2 As shown:

[0130] The core steps are as follows:

[0131] 1) Perform unit decomposition on the structure and determine the displacement boundary conditions. For example, the displacement boundary conditions of the embodiment of the present invention may be, for example, fixed end constraints, simply supported constraints, etc.

[0132] 2) According to the optical flow method, the relationship between the image displacement and image brightness of each pixel within each unit satisfies the optical flow equation. According to the finite element displacement function and shape function theory, the unit displacement function can be expressed using node displacement and shape functions. Therefore, at any given time, for each pixel within each unit in the image, the relationship between its image displacement and the corresponding unit node displacement can be found.

[0133] 3) Through the unit coordinate transformation matrix and the assembly matrix, the node displacement vectors of each unit in the global coordinate are assembled into the overall node displacement vector of the structure. Combined with step 2), the relationship between the image displacement of each pixel point and the overall node displacement vector of the structure at any given time can be obtained.

[0134] 4) Establish a system of equations based on the relationship in step 3). The number of unknowns in the system of equations is the number of degrees of freedom of the structure as a whole, and the number of equations is the number of pixels in the structure. The number of unknowns is much smaller than the number of equations. The system of equations can be solved using the least squares method to obtain the displacement vectors of the structure's nodes at all times.

[0135] 5) Perform frequency domain decomposition on the time domain displacement of the overall degree of freedom of the structure to obtain the structural modal parameters.

[0136] The optical flow method mentioned in the embodiment of the present invention is introduced and explained below:

[0137] Optical flow theory explains the relationship between image motion and image intensity. The two basic assumptions are as follows:

[0138] 1) Spatial smoothness. That is, the visual data should be smooth enough in space without mutation. In practical applications, the image can be preprocessed by Gaussian smoothing to achieve the smoothness requirement. The Gaussian kernel K with a standard deviation of σ is used. σ (x) Perform convolution on each frame of image:

[0139]

[0140] 2) Consistent brightness. That is, the brightness value of the same target point does not change over time.

[0141] I(x+u(x,t),t)=I0(x)(2)

[0142] The optical flow equation can be expressed as:

[0143]

[0144] Where: I0(x) is the reference image of the structure at zero displacement; is the reference image gradient; is the image speed.

[0145] After integrating formula (3), the relationship between brightness and displacement can be obtained:

[0146]

[0147] Where ΔI(x, t) is the brightness difference between the current image and the reference image; u(x, t) = [Δx, Δy] T is the image displacement.

[0148] The finite element theory mentioned in the present invention is described below:

[0149] The general process of the finite element method is as follows:

[0150] 1) Establish a variational principle description of the problem. For mechanical problems, the variational principle is mainly manifested as the potential energy principle or the virtual displacement principle, which not only includes external loads but also determines deformation constraints, continuity requirements, and boundary conditions;

[0151] 2) Unitize the spatial domain of the problem. Divide any spatial domain into a series of simple-shaped units to facilitate subsequent interpolation function construction and integral calculation;

[0152] 3) Interpolate on the element to construct a displacement function of any complex geometry. The displacement function should satisfy continuity and displacement boundary conditions, and its unknown coefficients are exactly the node displacements;

[0153] 4) Substitute the displacement function into the variational principle (potential energy functional or virtual displacement equation) to obtain the nodal displacements. Since the potential energy functional for the entire spatial domain is equal to the sum of the potential energy functionals for all elements, each element can be analyzed first to obtain the element stiffness matrix and element load vector. Then, according to the potential energy superposition principle, the element stiffness matrix and element load vector are assembled to obtain the global stiffness matrix and global load vector. Finally, the stiffness equation is solved to obtain the global nodal displacement vector.

[0154] The focus of this study is to combine the finite element unit displacement function expression with the optical flow method, and to achieve the displacement identification of all unit nodes after the finite element segmentation of the bar structure through visual methods. For any planar one-dimensional finite element unit, its unit degree of freedom is recorded as {d} e , which is the unit node displacement vector, and its unit displacement function is recorded as v(η). In finite element, the unit node displacement is usually used to express the unit displacement function:

[0155] v(η)=[N]{d} e (5)

[0156] Among them, [N] is the shape function, which is the interpolation function corresponding to the displacement component of the unit node. The shape function [N] has different forms for different types of units.

[0157] Consider Figure 3 The plane beam element shown has an element length of l and two nodes i and j, whose corresponding η-axis coordinates are 0 and l respectively. The following is a detailed description of the construction process of its displacement function and shape function:

[0158] 1) For a beam with plane bending deformation, the displacement in the ζ direction, i.e., the deflection, is v(η), and the angular displacement, i.e., the rotation angle, is Therefore, its deflection v must satisfy C 1 Continuity and displacement boundary conditions; select the displacement and rotation of nodes i and j as unit degrees of freedom (such as Figure 1 ), the unit node displacement is expressed as:

[0159] {d} e =[v i ,θ i ,v j ,θ j ] T (6)

[0160] 2) Assuming the number of degrees of freedom is 4, the displacement mode of the beam element deflection is a cubic polynomial:

[0161] v(η)=a1+a2η+a3η 2 +a4η 3 (7)

[0162] Among them, a1, a2, a3, and a4 are four unknown polynomial coefficients;

[0163] 3) Based on the node displacement conditions at both ends of the unit:

[0164]

[0165] Solve for the coefficients a1, a2, a3, and a4. Substituting them into equation (6) yields the displacement function expressed by the node displacement and shape function:

[0166] v(η)=[N]{d} e

[0167] The specific form of the shape function [N] is:

[0168] [N]=[N1,N2,N3,N4]

[0169]

[0170]

[0171]

[0172]

[0173] Among them, N1, N2, N3, N4 represent the corresponding node displacement v i ,θ i ,v j ,θ j The interpolation function of .

[0174] The following describes in detail the specific implementation process of the present invention using the optical flow method to achieve node displacement expression:

[0175] like Figure 4 As shown, Figure 4 As shown in the figure, the unit of the structure in the image is composed of pixels. Let the structural pixel area in the i∈[1,2,…,m]th unit in the image be Ω i , the area of ​​all pixels in the structure is Ω s =Ω1∪Ω2∪…∪Ω m According to formula (4), the relationship between the image displacement and brightness of each pixel satisfies the optical flow equation. Similarly, each pixel can also be regarded as a point in the finite element unit. According to formula (8), the relationship between the image displacement of each pixel and the node displacement satisfies the finite element displacement function expression. At this time, for any given time t, given pixel position x0 ∈ Ω i CΩ S , the image displacement can be expressed by u(x0,t) in equation (4) or by the unit displacement function in equation (8) Indicates that is the η-axis coordinate corresponding to x0 in its finite element unit. That is:

[0176]

[0177] Among them, {d i} e is the unit node displacement vector of the i-th unit.

[0178] The process of recovering the displacement vector of the entire structure node of the present invention is described in detail below:

[0179] For the overall structure, firstly, the structure is divided into units; secondly, each unit is analyzed according to the finite element process to determine its coordinate transformation matrix; then, the node displacement vectors of each unit are assembled into the overall node displacement vector of the structure; finally, the overdetermined equations are solved, and its least squares solution is the overall node displacement vector of the structure. Figure 5 The specific steps are as follows:

[0180] 1) Divide the structure into units. Divide the structure into m units, n nodes, and the degree of freedom of each unit is n e , the overall degree of freedom of the structure is n G ;

[0181] 2) Determine the coordinate transformation matrix [T]. Since the unit displacement function and unit degree of freedom are defined according to the coordinate axis components of the unit local coordinate system, and the directions of different units are not necessarily the same, when performing structural system analysis, it is necessary to express the unit displacement degrees of freedom according to the unified global coordinate axis components so that the overall analysis of different units at the same node can be performed. Construct the coordinate transformation matrix [T] so that it satisfies the coordinate transformation form:

[0182]

[0183] in, It is the unit degree of freedom in the global coordinate system, that is, the representation of the unit displacement degree of freedom under the unified global coordinate axis component.

[0184] The following is Figure 5 Taking the plane beam element in the global coordinate system as an example, the process of constructing the element coordinate transformation matrix is ​​described in detail. The angle between the local coordinate x-axis and the global coordinate X-axis is α. For this element, the unit degrees of freedom in the local coordinate system are:

[0185]

[0186] The degrees of freedom of the element in the global coordinate system are:

[0187]

[0188] Obviously, they satisfy the following coordinate transformation:

[0189]

[0190]

[0191] Written in coordinate transformation form Then the coordinate transformation matrix [T] is:

[0192]

[0193] 3) Assemble the node displacement vectors of each unit in the global coordinates into the overall node displacement vector of the structure. For any unit, its (global coordinate) unit degree of freedom is part of the overall degree of freedom of the structure, that is, there is an assembly matrix [A] e , such that:

[0194]

[0195] Where {d} G is the overall node displacement vector of the structure, which is an n G dimensional vector; assemble matrix dimensional matrix, where It is the unit degree of freedom in the global coordinate system. In each row, only one element is 1, and the rest are all 0. The position of element 1 is the corresponding global degree of freedom number.

[0196] 4) Establish a set of equations and obtain the least squares solution to obtain the overall node displacement vector of the structure.

[0197] Substituting equations (11) and (16) into equation (10), we can obtain the overall node displacement vector of the structure at a given time t as follows: Solution:

[0198]

[0199] in, are the coordinate transformation matrix, assembly matrix and unit node displacement vector of the i-th unit in the global coordinate system; η x ∈[0,l] is the η-axis coordinate of the pixel position x in its unit, which corresponds one-to-one to x.

[0200] At time t, the number of unknowns in equation (17) is the number of overall degrees of freedom of the structure n G The number of equations is the sum of the number of pixels in each unit, which is much larger than the number of unknowns. It is an overdetermined system of equations. The least squares method is used to solve the system of equations to obtain the overall node displacement vector {d(t)} at time t. G :

[0201]

[0202] [F] G =[N(η x )] G [T] G [A] G (18)

[0203] Among them, N iis the number of structural pixels in the i-th unit; [N(η)] G is the overall shape function formed by integrating the shape functions of each unit:

[0204]

[0205] in, η ij is the η coordinate value of the jth pixel in the i-th unit.

[0206] [T] G is the overall coordinate transformation matrix formed by integrating the coordinate transformation matrices of each unit, and its diagonal element a ii is the coordinate transformation matrix of the i-th unit.

[0207] Likewise, [A] G is the overall assembly matrix formed by integrating the unit assembly matrices, and its diagonal element a ii Assemble the matrix for the cell of the i-th unit.

[0208] right Solving equation (18) yields the time domain displacement of the overall degree of freedom of the structure:

[0209]

[0210] The following describes in detail the process of obtaining structural modal parameters by frequency domain decomposition in the present invention:

[0211] After obtaining the time domain displacement of the overall degree of freedom of the structure, the present invention introduces the frequency domain decomposition (FDD) method to analyze the time domain information to obtain the structural modal parameters, including the natural frequency ω k , damping ratio ξ k Harmonic vibration mode φ k , where k = 1, 2, ..., n is the modal order of the structure. The power spectrum density matrix of the time domain displacement d(t) in equation (20) is denoted as S dd (ω), the power spectrum density matrix at any frequency ω is subjected to singular value decomposition (SVD) to obtain:

[0212]

[0213] Where: s1, s2 are the first and second order singular values; v1, v2 are the first and second order singular vectors; the superscript H indicates the conjugate transpose.

[0214] The first-order singular curve is at the structural natural frequency ω=ω kThere is a maximum value at , and the first-order singular vector at the maximum point is the corresponding structural mode vibration shape:

[0215] φ k =v1, in ω=ω k Department (22)

[0216] The variation of the first- and second-order singular values ​​at different frequencies can be used to determine whether a structure has a near-frequency problem. If there is no near-frequency problem, s1>>s2≈0 at the maximum value. If there is a near-frequency problem, s1 and s2 are of the same magnitude. In this case, FDD cannot accurately identify the modal shape, and additional conditions must be introduced to improve the FDD method.

[0217] Damping ratios ξ1,ξ2,…,ξ n The logarithmic decay rate can be obtained by performing an inverse Fourier transform on the peak segment of the singular value s1 to the time domain.

[0218] like Figure 6 As shown in FIG, in the full-field displacement and rotation angle measurement technology of the structure implemented by this method, by combining the finite element method with the optical flow method, the mechanical correction of the displacement and rotation angle measurement is realized, and the continuous modal parameters of the structure with higher precision are obtained.

[0219] Specifically, the present invention has the following two characteristics:

[0220] 1. Finite element unit decomposition of the structural image: Similar to the finite element method analysis process, the structural image is divided into different units for analysis and processing. Each unit contains its own node, and the overall node displacement of the structure is realized through steps such as unit coordinate transformation and overall assembly.

[0221] 2. Combining finite element analysis with optical flow: The interpolation shape function of the finite element unit is applied to image displacement recognition, thereby achieving unit node displacement calculation (including displacement and rotation) similar to finite element analysis. The mechanical properties of the structure are corrected to make the recognition results more accurate.

[0222] Compared with the prior art, the advantages of the present invention are:

[0223] 1) Combining the finite element method with the optical flow method is equivalent to adding corrections to the mechanical properties of the structure itself to the visual method, making the calculation results closer to the real movement. At the same time, the calculation results can be directly added to the finite element correction step, facilitating the updating of the finite element model and the construction of the structural dynamics model;

[0224] 2) By combining the finite element method with the optical flow method, the displacement of each node in the structure can be obtained. Combined with the finite element shape function expression, the displacement function of each unit can be recovered, and the global vibration displacement and rotation angle of the structure can be obtained. This technology can provide an accurate and effective continuous mode identification method for structures with complex vibration shapes.

[0225] Another aspect of the present invention provides a full-field displacement and rotation angle measurement device for a frame structure based on finite element and optical flow methods, comprising:

[0226] Perform unit division on the target structure image and determine the displacement boundary conditions;

[0227] According to the optical flow method and the finite element theory, for each pixel point in each unit in the target structure image, a first relationship between the image displacement of each pixel point and the displacement of the corresponding unit node is determined;

[0228] Assembling the node displacement vectors of each unit in the global coordinates into the node displacement vector of the overall structure through the unit coordinate transformation matrix and the assembly matrix, and determining the vector relationship between the image displacement of each pixel point and the node displacement of the overall structure at any given time according to the first relationship;

[0229] Solving the vector relationship by the least square method to obtain the global node displacement vector of the target structure at all times;

[0230] According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is decomposed in the frequency domain to obtain the structural modal parameters, thereby completing the full-field displacement and rotation angle measurement of the target structure.

[0231] It can be understood that the contents of the above method embodiments are all applicable to the present device embodiments, the functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0232] Another aspect of an embodiment of the present invention further provides an electronic device, including a processor and a memory;

[0233] The memory is used to store programs;

[0234] The processor executes the program to implement the method described above.

[0235] It can be understood that the contents of the above method embodiments are applicable to the present device embodiments, the functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0236] Another aspect of the embodiments of the present invention further provides a computer-readable storage medium, wherein the storage medium stores a program, and the program is executed by a processor to implement the method described above.

[0237] It can be understood that the contents of the above method embodiments are all applicable to the present storage medium embodiment, the functions specifically implemented by the present storage medium embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0238] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0239] Another aspect of an embodiment of the present invention further provides a computer program product, including a computer program, which implements the above-mentioned method when executed by a processor.

[0240] In some optional embodiments, the function / operation mentioned in the block diagram may not occur in the order mentioned in the operation diagram. For example, depending on the function / operation involved, the two boxes shown in succession can actually be executed substantially simultaneously or the boxes can sometimes be executed in reverse order. In addition, the embodiment presented and described in the flow chart of the present invention is provided in an exemplary manner for the purpose of providing a more comprehensive understanding of the technology. The disclosed method is not limited to the operation and logic flow presented herein. Optional embodiments are contemplated in which the order of the various operations is changed and the sub-operations described as a part of a larger operation are performed independently.

[0241] Furthermore, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise indicated, one or more of the functions and / or features described may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in separate physical devices or software modules. It will also be understood that a detailed discussion of the actual implementation of each module is not necessary for understanding the present invention. More specifically, given the properties, functions, and internal relationships of the various functional modules in the devices disclosed herein, the actual implementation of the module will be understood within the ordinary skill of an engineer. Therefore, a person skilled in the art using ordinary skill will be able to implement the present invention set forth in the claims without undue experimentation. It will also be understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present invention, which is determined by the full scope of the appended claims and their equivalents.

[0242] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0243] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0244] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0245] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0246] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0247] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

[0248] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for measuring full-field displacement and rotation angle of a frame structure based on finite element and optical flow method, characterized in that: include: Perform unit division on the target structure image and determine the displacement boundary conditions; According to the optical flow method and the finite element theory, for each pixel point in each unit in the target structure image, a first relationship between the image displacement of each pixel point and the corresponding unit node displacement is determined, including: according to the optical flow method and the finite element theory, determining the unit degree of freedom of any plane one-dimensional finite element unit in the target structure image to obtain a unit node displacement vector; determining a unit displacement function according to the unit node displacement vector; the unit displacement function is used to determine the first relationship between the image displacement of each pixel point and the corresponding unit node displacement; wherein the expression of the unit displacement function is: , represents the unit displacement function; is the unit axial coordinate; is the shape function; represents the unit degree of freedom; Assembling the node displacement vectors of each unit in the global coordinate into the node displacement vector of the structure as a whole through the unit coordinate transformation matrix and the assembly matrix, and determining the vector relationship between the image displacement of each pixel point and the node displacement of the structure as a whole at any given time according to the first relationship; Solving the vector relationship equations according to the least squares method to obtain the overall node displacement vectors of the target structure at all times, including: dividing the overall structure of the target structure into units; analyzing each unit obtained by the division according to the finite element process to determine the coordinate transformation matrix of each unit; assembling the node displacement vectors of each unit into the overall node displacement vector of the structure according to the coordinate transformation matrix of each unit; solving the overdetermined equations according to the overall node displacement vector of the structure, and determining the obtained least squares solution as the overall node displacement vector of the target structure; According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is decomposed in the frequency domain to obtain the structural modal parameters, and the full-field displacement and rotation angle measurement of the target structure is completed, including: according to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is solved; the power spectrum density matrix of the time domain displacement is determined, and the power spectrum density matrix at any frequency is decomposed in the singular value to obtain the singular values ​​of each order; according to the maximum value of the first-order singular curve at the natural frequency of the structure, the corresponding structural modal vibration shape is determined; according to the singular value peak segment, the inverse Fourier transform is performed to the time domain to calculate the logarithmic attenuation rate to obtain the damping ratio, wherein the structural modal parameters include the natural frequency, the damping ratio and the vibration shape.

2. The method for measuring full-field displacement and rotation angle of a frame structure based on finite element and optical flow method according to claim 1, characterized in that: The target structure is a plane beam element, and the process of constructing the displacement function and shape function of the plane beam element includes: For a plane beam element with plane bending deformation, the element length is ,exist The displacement in the direction of , the corner is ,choose The displacement and rotation of the nodes are used as unit degrees of freedom. Expressed as: Based on the number of degrees of freedom being 4, the displacement pattern of the beam element deflection is configured as a cubic polynomial: in, are 4 polynomial coefficients; The node displacement conditions at both ends of the unit are: Solving for coefficients , and determine the displacement function expressed by the node displacement and shape function as: ; Among them, the shape function , Represent the corresponding node displacements The interpolation function is as follows: in, Represent the corresponding node displacements The interpolation function of .

3. The method for measuring full-field displacement and rotation angle of a frame structure based on finite element and optical flow method according to claim 2, characterized in that: The step of determining the unit degrees of freedom of the one-dimensional finite element unit of any plane in the target structure image according to the optical flow method and the finite element theory to obtain the unit node displacement vector also includes the step of expressing the displacement of the node using the optical flow method, which step includes: According to the target structure unit composed of the pixels in the target structure image, the first pixel in the image is determined. The structural pixel area within a unit is , the area of ​​all pixels of the target structure is , and then determine the expression of the displacement of the target structure image.

4. A device for implementing the full-field displacement and rotation angle measurement method of a frame structure based on finite element and optical flow method as described in any one of claims 1 to 3, characterized in that: include: Perform unit division on the target structure image and determine the displacement boundary conditions; According to the optical flow method and the finite element theory, for each pixel point in each unit in the target structure image, a first relationship between the image displacement of each pixel point and the displacement of the corresponding unit node is determined; Assembling the node displacement vectors of each unit in the global coordinate into the node displacement vector of the structure as a whole through the unit coordinate transformation matrix and the assembly matrix, and determining the vector relationship between the image displacement of each pixel point and the node displacement of the structure as a whole at any given time according to the first relationship; Solving the vector relationship by the least square method to obtain the global node displacement vector of the target structure at all times; According to the overall node displacement vector, the time domain displacement of the overall degree of freedom of the structure is decomposed in the frequency domain to obtain the structural modal parameters, thereby completing the full-field displacement and rotation angle measurement of the target structure.

5. An electronic device, characterized in that: including a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method according to any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that The storage medium stores a program, and the program is executed by a processor to implement the method according to any one of claims 1 to 3.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 3 is implemented.

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