Structural dynamic load identification method based on dynamic displacement inversion and motion control equation

Abstract

This invention discloses a method for identifying dynamic loads on structures based on dynamic displacement inversion and motion control equations. The method includes: dividing the structure under test into several four-node inverse shell elements; deploying sensors at the centroid positions of the upper and lower surfaces of each element; reconstructing the displacement values ​​of each element node based on the collected strain data; predicting the displacement values ​​at any position of the structure under test using a high-resolution spatial domain reconstruction algorithm based on the reconstructed displacement values ​​of each element node; discretizing the fourth-order spatial deflection derivative of the displacement field of the structure under test using the finite difference method; approximating the second-order derivative of the strain data using the second-order central difference method to obtain the higher-order spatiotemporal deflection derivative; and establishing a model of the relationship between the dynamic displacement and load distribution of the structure under test by combining the motion control equations of the structure under test, thereby achieving dynamic load identification of the structure under test. Given the known geometry and material properties of the structure, this method can not only reconstruct the time history of the dynamic loads on the structure but also simultaneously identify the load application positions.

Description

Technical Field

[0001] This invention relates to a method for identifying structural dynamic loads based on dynamic displacement inversion and motion control equations, belonging to the field of structural health monitoring technology. Background Technology

[0002] In-service loads on aircraft are crucial for structural safety assessments and life predictions, making in-service monitoring of structural loads of paramount importance. Load identification methods are categorized into direct measurement and indirect identification methods. Direct measurement methods, by deploying force sensors at critical structural locations, monitor the loads on the structure in real time, offering advantages such as ease of measurement, rapid response, and reliable results. However, the loads experienced by aircraft during service are highly complex, such as the flutter loads on the vertical tail during high angle-of-attack maneuvers, which are difficult to measure directly. In contrast, indirect identification methods, by acquiring real-time dynamic responses of the structure (such as strain, displacement, and acceleration) and combining them with load identification algorithms to identify external loads, have become a research hotspot in the field of structural health monitoring in recent years.

[0003] Current common frequency domain load identification methods are highly dependent on the accuracy of frequency response function measurements and are prone to matrix ill-posedness or pathological conditions. Time domain load identification methods suffer from error accumulation due to time effects and have difficulty identifying initial loads. Neural network-based load identification methods require extensive pre-experiments and are highly sensitive to the quality of training samples. Therefore, it is urgent to address the limitations of conventional dynamic load identification methods, such as the difficulty in obtaining system parameters and insufficient engineering applicability. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a structural dynamic load identification method based on dynamic displacement inversion and motion control equations. Based on the discrete strain response information that is easy to obtain in actual test scenarios, a theoretical relationship model between structural dynamic displacement and load distribution characteristics is established, which overcomes the shortcomings of conventional load identification methods such as high dependence on system parameters and poor engineering applicability.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] The structural dynamic load identification method based on dynamic displacement inversion and motion control equations includes the following steps:

[0007] Step 1: Divide the structure under test into several four-node inverse shell elements. The four nodes correspond to the four corner points of the neutral surface of each inverse shell element. Strain sensors are placed at the centroid positions of the upper and lower surfaces of each inverse shell element. Based on the strain data collected from the upper and lower surfaces of each inverse shell element, the displacement values ​​of each node of the inverse shell element are reconstructed.

[0008] Step 2: Based on the reconstructed displacement values ​​of each inverse shell element node, the displacement values ​​at any position of the measured structure are predicted using a high-resolution spatial domain reconstruction algorithm, thereby obtaining the displacement field of the measured structure with high spatial resolution.

[0009] Step 3: The fourth spatial deflection derivative of the displacement field of the measured structure with high spatial resolution is discretized and approximated using the finite difference method. At the same time, the second derivative of the strain data collected in Step 1 is approximated using the second-order central difference method to obtain the spatiotemporal high-order deflection derivative.

[0010] Step 4: Based on Steps 1-3, and combined with the motion control equations of the structure under test, establish a relationship model between the dynamic displacement and load distribution of the structure under test, and realize the dynamic load identification of the structure under test.

[0011] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0012] 1. This invention establishes a theoretical model of the dynamic displacement and load distribution characteristics of the tested structure by utilizing readily available discrete strain response information from actual test scenarios and combining it with motion control equations. This method can not only reconstruct the time history of the dynamic loads on the tested structure but also identify the location where the loads are applied. This effectively overcomes the limitations of conventional load identification methods, which require prior information to identify loads at specific locations or are highly dependent on the quality of training samples. It improves the accuracy and reliability of load identification and further achieves collaborative identification of displacement and loads for aircraft structures.

[0013] 2. This invention helps to overcome the limitations of conventional methods that can only identify loads at specific locations or are highly dependent on training samples. It can achieve collaborative identification of displacement and load of the tested structure, and further provide a theoretical basis for structural strength verification, reliability analysis and life prediction in mechanical engineering.

[0014] 3. This invention can effectively invert the load state of a structure under limited measurement information, providing a new technical approach for online monitoring and condition assessment of dynamic loads on aircraft structures in complex service environments, and providing important technical support for aircraft structural safety assessment, life prediction and health management. Attached Figure Description

[0015] Figure 1 This is a flowchart of the structural dynamic load identification method based on dynamic displacement inversion and motion control equations of the present invention;

[0016] Figure 2 This is a schematic diagram of the element mesh generation and strain sensing point layout for dynamic load identification of the structure model under test;

[0017] Figure 3The comparison of the reconstruction effect and absolute error of the periodic sinusoidal load history based on numerical simulation data is shown in (a) and (b), which are the reconstruction effect and absolute error of the periodic sinusoidal load history, respectively.

[0018] Figure 4 The comparison of the reconstruction effect and absolute error of the step load history based on numerical simulation data is shown in (a) and (b), which are the reconstruction effect and reconstruction absolute error of the step load history, respectively.

[0019] Figure 5 The comparison of the reconstruction effect and absolute error of the non-periodic random dynamic load history based on numerical simulation data is shown in (a) and (b), which are the reconstruction effect and absolute error of the non-periodic random dynamic load history, respectively.

[0020] Figure 6 The comparison of the reconstruction effect and absolute error of transient impact load history based on numerical simulation data is shown in (a) and (b), which are the reconstruction effect and absolute error of impact load history, respectively. Detailed Implementation

[0021] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0022] like Figure 1 As shown, based on the easily obtainable discrete strain response information in actual test scenarios, a structural dynamic load identification method based on dynamic displacement inversion and motion control equations is proposed. A theoretical relationship model between structural dynamic displacement and load distribution characteristics is established, overcoming the shortcomings of conventional load identification methods such as high dependence on system parameters and poor engineering applicability. The specific steps are as follows:

[0023] Step 1: Using the measured strain data from the fiber optic sensor at different times as input, reconstruct the dynamic displacement field of the structure under test.

[0024] Taking a rectangular composite material wall panel structure as an example, the lower left vertex of the wall panel is set as the origin. X-axis and Y-axis are established along the horizontal and vertical directions respectively, and the thickness direction is the Z-axis, establishing a global coordinate system O-XYZ for the measured structure. The thickness of the measured structure is... A four-node inverse shell element was constructed, and a local coordinate system o-xyz with the element centroid as the origin was established. Each element node contains six degrees of freedom, namely displacement along the x, y, and z axes. , and rotation angles around the x, y, and z axes , .in, Number the element nodes, and assign degrees of freedom to each element node. for:

[0025] ,

[0026] Displacement of any point on the neutral surface of the element , , and corner , It can be achieved through the unit node degrees of freedom and shape functions , , Interpolation yields the following mathematical expression:

[0027] .

[0028] The displacement of any point within this element can be represented by the degree of freedom and thickness coordinates of the corresponding position on its neutral plane:

[0029] ,

[0030] In the formula, , , This represents the displacement of any point within the element.

[0031] Based on the strain-displacement geometric relationship in linear elasticity theory, the mathematical expression for in-plane strain in the element theory is:

[0032] ,

[0033] In the formula, , The linear strain is along the x and y axes. , These represent displacements along the x and y axes, respectively. Let be the shear strain acting in the xy plane. Based on this, the theoretical membrane strain at the neutral plane of the element is further derived. and bending strain Its mathematical expression is:

[0034] ,

[0035] In the formula, , Let the membrane strain-displacement transformation matrix and the bending strain-displacement transformation matrix be represented respectively. Based on the weighted least squares criterion, an error function is constructed between the theoretical strain and the measured strain of the element. :

[0036] ,

[0037] in, , and These are the weighting coefficients for membrane strain, flexural strain, and shear strain, respectively. , These represent the measured membrane strain and bending strain of the unit, respectively.

[0038] Further solve the least squares error functional The minimum value is used to obtain the unit equivalent equilibrium equation in the local coordinate system, and its mathematical expression is:

[0039] ,

[0040] in, , Let represent the pseudo-stiffness matrix and pseudo-load vector of the element, respectively, and their mathematical expressions are as follows:

[0041] ,

[0042] ,

[0043] In the formula, This refers to the shear strain-displacement matrix, which has undergone special interpolation processing to avoid shear locking. It includes the pseudo-stiffness matrices of all inverse elements. and pseudo-load vector After transforming to the global coordinate system, the components are assembled according to the standard finite element method, and boundary conditions are introduced to eliminate rigid body degrees of freedom. Finally, the overall equilibrium equations of the measured structure are established:

[0044] ,

[0045] The displacement vectors of all element nodes can be solved, thereby realizing the reconstruction of the displacement field of the measured structure.

[0046] Step 2: Use a high-resolution spatial domain reconstruction algorithm to supplement the data of the reconstructed discrete displacement field, so as to provide continuous morphological data support for further calculation of higher-order deflection derivatives based on the finite difference method.

[0047] The dynamic displacement response information of the measured structural model is obtained through step 1. The discrete displacement obtained by the spatial domain super-resolution reconstruction algorithm is supplemented with high spatial resolution data, so as to provide continuous morphological data support for further calculation of high-order deflection derivatives based on the finite difference method.

[0048] Construct the squared exponential (SE) kernel function, whose mathematical expression is as follows:

[0049] ,

[0050] In the formula, It is a squared exponential kernel function. These are the spatial coordinates corresponding to the nodes of the measured structural unit obtained from step 1. These are the spatial coordinates of any node in the structure being measured. , is the hyperparameter of the quadratic exponential kernel function. Since step 1 can only reconstruct the displacement values ​​of the element nodes, the element node coordinates and their corresponding reconstructed displacement values ​​are used as the observation dataset. :

[0051] ,

[0052] In the formula, Number the nodes. The total number of nodes in the divided unit. , The first The coordinates of each node and the corresponding reconstructed displacement values. , These are the coordinate matrix and the reconstructed displacement vector, respectively, composed of the nodes of the measured structural unit.

[0053] Assumption The coordinate matrix consisting of all predicted locations. This represents the displacement prediction vector corresponding to the predicted location. It is also the reconstructed displacement vector of the node of the measured structural element. and the displacement vector of the predicted position The distributions should follow a joint Gaussian distribution:

[0054] ,

[0055] In the formula, For the regularization term of the predicted displacement data, It is an identity matrix. , These are the function values ​​of the mean function at the observation point and the prediction point, respectively. The covariance matrix is ​​calculated using the squared exponential kernel function, and its specific mathematical expression is as follows:

[0056] ,

[0057] ,

[0058] In the formula, It is a mean function (usually the prior mean). , Sets 1st, 2nd The spatial coordinate vector of a point, , Sets 1st, 2nd The spatial coordinate vector of a point, The kernel function (covariance function) measures the similarity between two input points. Further... After marginalization, its posterior distribution can be obtained as follows:

[0059] ,

[0060] In the formula, , Let be the mean function and covariance matrix of the posterior distribution, respectively, and their mathematical expressions are:

[0061] ,

[0062] ,

[0063] The logarithmic marginal likelihood function maximization method is used to optimize the kernel function hyperparameters. , Its mathematical expression is:

[0064] ,

[0065] By predicting the reconstructed displacement values ​​at any location of the structure, a high spatial resolution displacement field of the measured structure can be obtained.

[0066] Step 3: To address the discontinuity issue in solving higher-order derivatives of discrete displacement, based on Step 2, the finite difference method is used to discretize and approximate the spatiotemporal higher-order derivatives of the displacement field, providing a data basis for identifying the dynamic loads on the measured structure.

[0067] Since the displacement field reconstructed in step 1 is in discrete form, it cannot be directly applied to solve continuous differential equations. To address the discontinuity issue in solving higher-order derivatives of discrete displacements, and to simultaneously consider computational efficiency, a high spatial resolution data supplementation method is proposed based on step 2 for the discrete displacement field. On this basis, a discrete approximation of the fourth-order spatial deflection derivative is performed using the finite difference method, and its mathematical expressions are as follows:

[0068] ,

[0069] ,

[0070] In the formula, , The fourth derivative of the lateral deflection. Let be the second-order mixed second-order partial derivative of the lateral deflection with respect to x and y. For the spatial grid points obtained by fitting Lateral deflection at the location, Indicates a time index. , These are the grid step sizes along the X and Y axes of the structure under test, respectively.

[0071] In the time dimension, since the sampling frequency of fiber optic sensors can reach several kilohertz, they can be directly used to sample raw discrete time series data. The second derivative is approximated using the second-order central difference method, and its mathematical expression is:

[0072] ,

[0073] By discretizing the approximate solution of the higher-order derivative of the displacement field obtained by the finite difference method, and combining it with the motion control equation of the measured structure described in step 4, a theoretical relationship model between the dynamic displacement and load distribution characteristics of the structure can be established, thereby realizing the identification of the dynamic load of the measured structure.

[0074] Step 4: Based on the above steps, and combined with the motion control equation of the measured structure, establish a theoretical relationship model between the dynamic displacement of the structure and the load distribution characteristics, thereby realizing the identification of the dynamic load of the measured structure.

[0075] According to the theory of large deflection deformation, the motion control equation of the measured structure can be derived from the transverse deflection function. With Airy stress function Common representation. Under the assumptions of small deflection deformation and linear elasticity, we can let The governing equations are simplified. For the small-deflection lateral vibration of an isotropic structure, the undamped equation of motion is:

[0076] ,

[0077] in, For the Laplace operator, This indicates the bending stiffness of the structure being measured. , , These represent the material density, Young's modulus, and Poisson's ratio of the structure being tested. It is the distributed stiffness coefficient of the elastic foundation on which the structure under test is located. Indicates in Structure under test at all times Lateral deflection at the coordinate position This represents the external load borne by the structure under test. It is assumed that the structure has uniform thickness and... The above undamped motion equations simplify into motion control equations:

[0078] ,

[0079] In the formula, The fourth-order gradient operator is expressed mathematically as follows:

[0080] ,

[0081] If the displacement field of the structure under test is known, the spatiotemporal distribution of the external load on the structure under test can be identified by the above formula.

[0082] Substituting the higher-order spatiotemporal deflection derivative obtained in step 3 into the motion control equation of the structure under test, the dynamic load identification of the structure under test can be achieved. Its mathematical expression is as follows:

[0083] ,

[0084] In the formula, This represents the second derivative with respect to time. For composite laminate structures with symmetrically distributed plylets, the dynamic load identification of the measured structural model can be achieved by synchronously discretizing the spatial and temporal derivatives of its displacement field. Its mathematical expression can be further expanded as follows:

[0085] ,

[0086] In the formula, Here is the bending stiffness matrix of the composite laminate, calculated as follows:

[0087] ,

[0088] In the formula, Let be the off-axis stiffness coefficient of the composite laminate. For the first The boundary coordinates of the layer (i.e., the position of the upper surface of the layer). It is the position of the lower surface. represents the total number of composite material layups, and m represents the current layup number.

[0089] Based on the discrete strain response information that is readily available in real-world testing scenarios, this invention proposes a structural dynamic load identification method based on dynamic displacement inversion and motion control equations. By establishing a theoretical relationship model between structural dynamic displacement and load distribution characteristics, this method helps to overcome the limitations of conventional methods that can only identify loads at specific locations or are highly dependent on training samples. Furthermore, it can achieve collaborative identification of displacement and load for aircraft structures.

[0090] The fuselage panel model is uniformly divided into 10*10 four-node inverse shell elements along the X and Y axes, forming 11*11 element nodes. The centroid of each inverse element is set as a strain sensing point. A schematic diagram of the element mesh generation and strain sensing point layout for dynamic load identification of the fuselage panel model is shown below. Figure 2 As shown. Strain data along the X, Y, and 45° directions were extracted from the sensing points at each time point. , , It is used to simulate the measurement response at actual sensor locations.

[0091] Loading points (283.33mm, 288.33mm) were randomly selected on the upper surface of the tested structural model. A periodic sinusoidal load F1=10sin(10*t) with an amplitude of 10N and an angular frequency of 10rad / s was applied at these locations. The reconstruction effect of the periodic sinusoidal load history based on the numerical simulation data and the corresponding absolute error curves are shown below. Figure 3 As shown in (a) and (b) in the figure, the root mean square error of the periodic sinusoidal load history reconstructed by the Tikhonov regularization method is 1.54N, the average relative error is 23.85%, and the consistency correlation coefficient is 0.9666.

[0092] In comparison, the root mean square error of the periodic sinusoidal load history reconstructed by this invention is reduced to 0.52 N, the average relative error is reduced to 7.56%, and the consistency correlation coefficient is increased to 0.9968. Meanwhile, the identified load application location is (290.86 mm, 292.45 mm), and the Euclidean distance between this location and the actual loading location is 8.58 mm.

[0093] It should be noted that traditional load identification methods require prior pre-impact experiments to obtain the structure's frequency response function and can only identify the load history at preset locations, failing to pinpoint the load location. In contrast, the load identification method in this invention, based on known structural geometry and material properties, and combined with discrete strain measurement data, can not only reconstruct the time history of the dynamic loads on the structure but also simultaneously identify the load application location.

[0094] Loading points (150.00 mm, 316.67 mm) were randomly selected on the upper surface of the tested structural model, and a step load with an amplitude of 10 N and a period of 0.5 s was applied at these locations. The reconstruction effect and absolute error of the step load history based on numerical simulation data are compared as follows: Figure 4 As shown in (a) and (b) in the figure. Figure 4 It can be seen that the root mean square error of the step load history reconstructed by the Tikhonov regularization method is 1.32N, the consistency correlation coefficient is 0.9605, and the load application location cannot be identified.

[0095] In comparison, the root mean square error of the step load history reconstructed by this invention is reduced to 0.72 N, and the consistency correlation coefficient is increased to 0.9887. Meanwhile, the load application location identified by this invention is (148.70 mm, 306.83 mm), and the Euclidean distance between this location and the actual loading location is 9.93 mm.

[0096] Loading points (250.00 mm, 250.00 mm) were randomly selected on the upper surface of the tested structural model, and a non-periodic random dynamic load was applied at these locations. The reconstruction effect of the non-periodic random dynamic load history based on numerical simulation data and the corresponding absolute error curves are shown below. Figure 5 As shown in (a) and (b) in the figure. Figure 5 It can be seen that the root mean square error of the non-periodic random dynamic load history reconstructed by the Tikhonov regularization method is 1.92N, the average relative error is 31.13%, the consistency correlation coefficient is 0.9392, and the load application location cannot be identified.

[0097] In comparison, the root mean square error of the non-periodic random dynamic load history reconstructed by this invention is reduced to 0.91 N, the average relative error is reduced to 17.64%, and the consistency correlation coefficient is increased to 0.9871. Meanwhile, the load application location identified by this invention is (235.79 mm, 250.76 mm), and the Euclidean distance between this location and the actual loading location is 14.23 mm.

[0098] A loading point (233.33 mm, 233.33 mm) was randomly selected on the upper surface of the tested structural model, and a transient impact load with an amplitude of 20 N was applied at this location. The reconstruction effect of the transient impact load history based on the numerical simulation data and the corresponding absolute error curves are shown below. Figure 6 As shown in (a) and (b) in the figure. Figure 6 It can be seen that the root mean square error of the transient impact load history reconstructed by the Tikhonov regularization method is 1.98N, the consistency correlation coefficient is 0.9998, and the impact load loading location cannot be identified.

[0099] In comparison, the root mean square error of the transient impact load history reconstructed by this invention is reduced to 0.98 N, and the consistency correlation coefficient is increased to 1.0000. Meanwhile, the load application location identified by this invention is (223.01 mm, 232.34 mm), and the Euclidean distance between this location and the actual loading location is 10.37 mm.

[0100] Based on the same inventive concept, this application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the aforementioned structural dynamic load identification method based on dynamic displacement inversion and motion control equations.

[0101] Based on the same inventive concept, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the aforementioned structural dynamic load identification method based on dynamic displacement inversion and motion control equations.

[0102] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0103] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0104] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0105] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0106] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A structural dynamic load identification method based on dynamic displacement inversion and motion control equation, characterized in that, Includes the following steps: Step 1: Divide the structure under test into several four-node inverse shell elements. The four nodes correspond to the four corner points of the neutral surface of each inverse shell element. Strain sensors are placed at the centroid positions of the upper and lower surfaces of each inverse shell element. Based on the strain data collected from the upper and lower surfaces of each inverse shell element, the displacement values ​​of each node of the inverse shell element are reconstructed. Step 2: Based on the reconstructed displacement values ​​of each inverse shell element node, a high-resolution spatial domain reconstruction algorithm is used to predict the displacement values ​​at any location of the measured structure, thus obtaining the high spatial resolution displacement field of the measured structure. The specific process is as follows: All inverse shell element node coordinates and corresponding reconstructed displacement values are taken as the observation dataset : ， in, , The first The coordinates and reconstructed displacement values ​​of each node. The total number of nodes in all inverse shell elements is given. , These are the coordinate matrix and reconstructed displacement vector, respectively, composed of the nodes of all inverse shell elements of the structure under test; Setting a coordinate matrix of all predicted positions for the structure under test, a displacement prediction vector for all predicted positions of the structure under test, and subject to a Gaussian distribution: ， where is a regularization term, is an identity matrix, denotes a normal distribution, , are the function values of the mean function at the observation points and the prediction point, respectively, is a covariance matrix calculated by a squared exponential kernel function Covariance matrix ， ， in, , It is a mean function. , , Sets 1st, 2nd The spatial coordinate vector of a point, , Sets 1st, 2nd The spatial coordinate vector of a point, , , These are all hyperparameters of the squared exponential kernel function. , ; right After marginalization, its posterior distribution is obtained as follows: ， in, , Let be the mean function and covariance matrix of the posterior distribution, respectively; The hyperparameters of the squared exponential kernel function are optimized using the log-marginal likelihood maximization method. , : ， in, It represents the probability density function of displacement observation under given coordinate conditions; by predicting the reconstructed displacement value at any position of the structure, a high spatial resolution displacement field of the measured structure can be obtained. Step 3: The fourth-order spatial deflection derivative of the displacement field of the measured structure with high spatial resolution is discretized and approximated using the finite difference method. Simultaneously, the second-order central difference method is used to approximate the second-order derivative of the strain data acquired in Step 1, thus obtaining the higher-order spatiotemporal deflection derivative. The specific process is as follows: The fourth-order spatial deflection derivative of the displacement field of the measured structure with high spatial resolution is discretized and approximated using the finite difference method, and the expression is as follows: ， ， in, , The fourth derivative of the lateral deflection. Let be the second-order mixed second-order partial derivative of the lateral deflection with respect to x and y. For the predicted spatial grid points Lateral deflection, Let k represent the time index, where k is the index of the discrete time step, and satisfy the following conditions: , For the sampling time step, , These are the grid step sizes along the X and Y axes of the structure under test, respectively. In the time dimension, the second derivative of the strain data acquired in step 1 is approximated using the second-order central difference method, and the expression is: ， in, Indicates at spatial grid points The second partial derivative of the lateral deflection with respect to time at the point; Step 4: Based on Steps 1-3, and combined with the motion control equations of the structure under test, establish a relationship model between the dynamic displacement and load distribution of the structure under test, and realize the dynamic load identification of the structure under test.

2. The structural dynamic load identification method based on dynamic displacement inversion and motion control equations according to claim 1, characterized in that, The specific process of step 1 is as follows: A global coordinate system O-XYZ is established with the lower left corner of the structure being measured as the origin, the horizontal and vertical directions as the X-axis and Y-axis respectively, and the thickness direction as the Z-axis. The thickness of the structure being measured is... ,definition The time is the neutral surface of the structure under test; for each inverse shell element, a local coordinate system o-xyz is established with the centroid of the inverse shell element as the origin and the X, Y, and Z axes of the global coordinate system as the x, y, and z axes, respectively. The degrees of freedom of each node are: ， in, For the first The degrees of freedom of each node, and The first The displacement of each node along the x, y, and z axes of the local coordinate system. and The first The rotation angle of each node around the x, y, and z axes of the local coordinate system. The node number of the inverse shell element; any point on the neutral surface of the inverse shell element displacement , , and corner , Through the nodal degrees of freedom and the shape function of the inverse shell element , , The interpolation is obtained using the following expression: ， any point within the inverse shell element displacement , , Degrees of freedom and thickness coordinates of the corresponding position of the neutral plane of the inverse shell element express: ， According to the strain-displacement geometry of linear elasticity theory, the expression for in-plane strain in the inverse shell element theory is as follows: ， in, , These represent the linear strains along the x and y axes, respectively. This refers to the shear strain acting in the xy plane. , These represent displacements along the x and y axes, respectively. , These are the rotation angles along the x and y axes, respectively. , These represent the distances the measured structure moves in the x and y directions within the neutral plane, respectively. The theoretical membrane strain at the neutral surface of the inverse shell element. and bending strain The expression is: ， in, , Let these represent the membrane strain-displacement transformation matrix and the bending strain-displacement transformation matrix, respectively. For each node of the inverse shell element, there are degrees of freedom. Based on the weighted least squares criterion, an error function is constructed between the theoretical strain and the measured strain of the inverse shell element. : ， in, , and These are the weighting coefficients for membrane strain, flexural strain, and shear strain, respectively. , These are the measured membrane strain and bending strain of the inverted shell element, respectively. The shear strain of the inverse shell element; Solving the error function The minimum value of is used to obtain the equivalent equilibrium equation of the inverse shell element in the local coordinate system, which is expressed as: ， ， ， in, , These are the pseudo-stiffness matrix and pseudo-load vector of the inverse shell element, respectively. Let be the geometric area of ​​the inverse shell element. The shear strain-displacement matrix is ​​used to avoid shear lock-up; T denotes transpose. The pseudo-stiffness matrix of all inverse shell elements and pseudo-load vector After transforming to the global coordinate system, the components are assembled according to the standard finite element method, and boundary conditions are introduced to eliminate rigid body degrees of freedom. Finally, the overall equilibrium equations of the measured structure are established: ， in, The pseudo-stiffness matrix of the structure under test. For the displacement values ​​of all nodes of the inverse shell element, This is the pseudo-load vector of the structure under test; through The displacement values ​​of all nodes of the inverse shell element are obtained by solving.

3. The structural dynamic load identification method based on dynamic displacement inversion and motion control equations according to claim 2, characterized in that, The specific process of step 4 is as follows: Under the assumptions of small deflection and linear elasticity, the equation of motion for the measured structure without damping is: ， in, For the Laplace operator, This is a fourth-order partial differential operator used to describe the additional bending term generated when the bending stiffness is spatially unevenly distributed. This indicates the bending stiffness of the structure being measured. , , , These represent the material density, Young's modulus, and Poisson's ratio of the structure being tested. This is the distributed stiffness coefficient of the elastic foundation on which the structure under test is located. Indicates the coordinate position of the measured structure at time t. Lateral deflection at the location, This indicates the external load borne by the structure under test; When the thickness of the structure being measured is uniform and At this point, the above undamped motion equations simplify into motion control equations: ， in, It is a fourth-order gradient operator. ; Substituting the higher-order spatiotemporal deflection derivatives into the above motion control equations, dynamic load identification of the measured structure is achieved, as shown in the following expression: ， Expanding further: ， in, Right now , Right now , Right now , Right now , Here is the bending stiffness matrix of the structure under test. Let be the third-order mixed partial derivative of the lateral deflection with respect to x and the first-order partial derivative with respect to y. Let be the mixed partial derivative of the lateral deflection with respect to x and y.

4. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the structural dynamic load identification method based on dynamic displacement inversion and motion control equations as described in any one of claims 1 to 3.

5. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the structural dynamic load identification method based on dynamic displacement inversion and motion control equations as described in any one of claims 1 to 3.

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