Method for locating concentrated load based on principal stress constraint and strain gradient trajectory identification

Abstract

The application belongs to the technical field of load identification of structural health monitoring, and provides a concentrated load positioning method based on principal stress constraint and strain gradient trajectory identification, which comprises the following steps: arranging strain sensors in a monitoring area of a planar structure plate and collecting strain data of measuring points, constructing a strain field inversion function based on a radial basis function and establishing an error optimization function containing a fitting error term and a smooth constraint, introducing a principal stress direction constraint and a gradient projection smooth constraint to form a comprehensive error function and solving to obtain an optimal strain field distribution, then calculating strain gradient vectors of each grid node and tracking a gradient trajectory through a gradient descent method, and finally performing an iterative clustering analysis based on distance statistics on a trajectory end point to output a cluster center as a concentrated load application position identification result. The application can improve the concentrated load positioning accuracy, enhance the anti-noise capability, and realize fast, stable and large-sample-free load position identification.

Description

Technical Field

[0001] This application belongs to the field of load identification technology for structural health monitoring, and particularly relates to a concentrated load location method, terminal equipment and storage medium based on principal stress constraints and strain gradient trajectory identification. Background Technology

[0002] Structural health monitoring is a crucial means of ensuring the safe operation of critical components in aerospace and other fields. Aircraft structures are subjected to complex alternating loads during service, and concentrated loads (such as impact loads) are key factors leading to the initiation of localized structural damage and the propagation of fatigue cracks. Accurately identifying the location of these concentrated loads is of great significance for structural damage assessment and proactive health monitoring. Currently, concentrated load location methods mainly fall into two categories: one is based on strain field reconstruction, which inverts the full-field strain distribution through sparse measurement points, but often uses linear interpolation or radial basis function interpolation, only considering geometric smoothness constraints; the other is based on machine learning, which constructs complex mapping models through neural networks, but relies on a large number of training samples. However, existing methods suffer from reliance on a large amount of prior knowledge and insufficient location accuracy. Summary of the Invention

[0003] This application provides a concentrated load positioning method based on principal stress constraints and strain gradient trajectory identification, which can solve the problems of existing methods relying on a large amount of prior knowledge and having insufficient positioning accuracy.

[0004] In a first aspect, embodiments of this application provide a concentrated load positioning method based on principal stress constraints and strain gradient trajectory identification, comprising: S1, determining a structural monitoring area on a planar structural plate and arranging strain sensors within the monitoring area to acquire the position coordinates of multiple strain measurement points; S2, applying a concentrated load within the monitoring area and collecting and recording strain data at each strain measurement point through strain sensors; S3, constructing a strain field inversion function to describe the strain distribution in the monitoring area based on the position coordinates of the strain measurement points, the strain data of the strain measurement points, and the radial basis function, and establishing an error optimization function including fitting error terms and strain field smoothing constraints; S4, applying the principal stress constraints based on the principal stress direction and the gradient projection smoothing constraints... S5. Input the error optimization function to correct the strain field inversion function; S6. Solve the error optimization function after introducing principal stress constraints and gradient projection smoothing constraints in the principal stress direction to obtain the optimal strain field inversion function, and calculate the strain value of each grid node in the monitoring area based on the optimal strain field inversion function to obtain the strain field distribution in the monitoring area; S7. Based on the strain field distribution in the monitoring area, calculate the strain gradient vector of each grid node, and iteratively track the strain gradient descent trajectory of each grid node through the gradient descent method to form a set of trajectory endpoints; S8. Perform iterative cluster analysis based on distance statistics on the set of trajectory endpoints, calculate the cluster center coordinates of all trajectory endpoints, and output the cluster center coordinates as the identification result of the application position of the concentrated load.

[0005] In one possible implementation of the first aspect, S1, defining a structural monitoring area on a planar structural plate and arranging strain sensors within the monitoring area to acquire the position coordinates of multiple strain measurement points, specifically includes:

[0006] S101. Taking a 1200mm×1200mm planar structural plate with four fixed sides as the object, construct a square planar monitoring area in the middle of the planar structural plate. The size of the monitoring area is 600mm×600mm, and the thickness within the monitoring area is evenly distributed at 5mm.

[0007] S102. Divide the monitoring area into 36 rectangular strain measurement point grids with a size of 100mm×100mm. Select the center position of the 36 strain measurement point grids as strain measurement points and label them sequentially as #1~#36.

[0008] S103. Set a strain sensing path within the monitoring area so that the path passes through strain measurement points #1 to #36 in sequence, and arrange strain sensors on the path to ensure that the strain and position coordinates at the 36 strain measurement points are acquired by the strain sensors.

[0009] Optionally, in another possible implementation of the first aspect, S2, applying a concentrated load within the monitoring area and acquiring and recording strain data at each strain measurement point using strain sensors, specifically includes:

[0010] S201. In the top-down view, construct a plane rectangular coordinate system with the lower left corner of the monitoring area as the origin. The direction from the origin to the lower right corner of the monitoring area is the positive X-axis, and the direction from the origin to the upper left corner of the monitoring area is the positive Y-axis.

[0011] S202. Set the concentrated load to two application conditions: the first application condition is to apply a 1000N concentrated load at coordinates (200mm, 200mm) in the plane rectangular coordinate system; the second application condition is to apply a 2000N concentrated load at coordinates (400mm, 400mm) in the plane rectangular coordinate system.

[0012] S203. Record the strain values ​​at strain measurement points #1 to #36 under the two applied conditions, and denot the strain value at each strain measurement point as S. i，j , where i=1,2 represents the application condition sequence number; j=1,2,3,...,36 represents the strain measurement point number.

[0013] Optionally, in another possible implementation of the first aspect, S3 above, based on the location coordinates of the strain measurement points, the strain data of the strain measurement points, and the radial basis function, constructs a strain field inversion function to describe the strain distribution in the monitoring area, and establishes an error optimization function that includes a fitting error term and a strain field smoothing constraint, specifically including:

[0014] S301. Construct the strain field inversion function f(x,y), which is expressed as:

[0015]

[0016] Where m is the number of strain measurement points, m=36, W i Radial basis coefficient, For undetermined coefficients, are basis functions, and r i For the strain inversion point (x,y) and the i-th strain measurement point (x... i, y i Euclidean distance between them: ;

[0017] S302. Construct an error optimization function E0 that includes a fitting error term and a strain field smoothing constraint, where the fitting error term E1 is expressed as:

[0018]

[0019] The strain field smooth constraint E2 is expressed as:

[0020]

[0021] Where χ is the smoothness constraint weight, used to balance the relative roles of E1 and E2 in the error optimization function. , and For f(x,y) at the strain measurement point (x k ,y k The second derivative value of h x h is the width of the strain measurement grid in the x-direction. y The width of the grid in the y-direction is the value of the strain measurement point.

[0022] Optionally, in another possible implementation of the first aspect, the introduction of principal stress constraints based on the principal stress direction and gradient projection smoothing constraints into the error optimization function in S4 above specifically includes:

[0023] S401. Introduce the principal stress constraint E3 into the error optimization function E0:

[0024] The principal stress unit is defined as the projection l(x,y) of the gradient onto the direction field v, and the gradient onto the direction field v is expressed as follows:

[0025]

[0026]

[0027] in, Let v be the direction vector of the direction field. Let f be the magnitude of the vector in that direction, and ▽f be the gradient of f(x,y); l(x,y) represents the rate of change of the strain field inversion function f(x,y) along the direction v.

[0028] Multiply the length of l(x,y) by the direction field v to obtain the projection vector; take the difference between the gradient ▽f and the projection vector as the vertical component, and minimize the vertical component to obtain the principal stress constraint E3:

[0029]

[0030] Where λ is the principal stress constraint weight;

[0031] Suppose there are m discrete strain measurement points {(x)} within the monitoring area. k ,y k )}, k=1,2,…,m, the direction field v and gradient ▽f take the following values ​​at the kth strain measurement point:

[0032]

[0033] Among them, v x,k v represents the principal stress field in the x-direction at the k-th strain measurement point. y,k f represents the principal stress field in the unit y-direction at the k-th strain measurement point. x,k f represents the gradient value in the x-direction at the k-th strain measurement point. y,k This represents the gradient value in the y-direction at the k-th strain measurement point; the vertical component at the k-th strain measurement point is:

[0034]

[0035] Where I is a 2×2 identity matrix;

[0036] The principal stress constraint E3 is transformed into the following expression:

[0037]

[0038] Where, λ k The integral weight for the k-th strain measurement point is... After expansion, we get:

[0039]

[0040] For gradient ▽f k Discretize:

[0041]

[0042] in, It is the value of the gradient of the radial basis function at the k-th strain measurement point, r. i,k The Euclidean distance between the strain inversion point and the strain measurement point; the discretized gradient ▽f k Represented as matrix multiplication:

[0043]

[0044] Among them, G k It is a 2×m radial basis function gradient matrix, W=(W1, W2,…, W…). m ) T It is the radial basis coefficient vector. It is the linear polynomial part;

[0045] The principal stress constraint E3 is transformed into the following expression:

[0046] ;

[0047] S402. Introduce the gradient projection smoothing constraint E4 into the error optimization function E0:

[0048] The gradient projection smoothness constraint is defined as the L2 norm of the gradient of l(x,y):

[0049]

[0050] in, Gradient projection smoothing constraint weights;

[0051] The gradient of l(x,y) is approximated using the central difference:

[0052]

[0053] In the formula, Δx represents the difference in the numbers of the continuous strain measurement points in the x-direction, and Δy represents the difference in the numbers of the continuous strain measurement points in the y-direction. Let l(x,y) be the value of the strain measurement point to the right of the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point to the left of the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point above the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point below the k-th strain measurement point;

[0054] Based on the gradient of the approximated l(x,y), E4 is discretized:

[0055]

[0056] Wherein, weight w k Take the proportion of the local grid area;

[0057] Define a vector L = [l1, l2, ..., l m ] T Its relationship with the radial basis coefficient vector W is as follows:

[0058]

[0059] Where V is the direction field projection matrix, each row of the direction field projection matrix acts on the corresponding gradient, and H is the gradient operator matrix, used to map the radial basis coefficient vector W to the gradient of all grid points. V and H are expressed as follows:

[0060]

[0061]

[0062] in, The basis functions represent the strain measurement points m-th;

[0063] Construct the difference matrix D x and D y , so that:

[0064]

[0065] Among them, D x and D y They are respectively:

[0066]

[0067] The gradient projection smoothing constraint E4 is transformed into the following expression:

[0068] Optionally, in another possible implementation of the first aspect, S5 above involves solving the error optimization function after introducing principal stress constraints in the principal stress direction and gradient projection smoothing constraints to obtain the optimal strain field inversion function, and calculating the strain value of each grid node within the monitoring area based on the optimal strain field inversion function to obtain the strain field distribution within the monitoring area, specifically including:

[0069] S501. Apply the following constraint to the radial basis coefficients in f(x,y):

[0070] ;

[0071] S502. Introducing the fitting error term E1, strain field smoothing constraint E2, principal stress constraint E3, and gradient projection smoothing constraint E4, we construct the error optimization function E0 = E1 + E2 + E3 + E4; rewriting the error optimization function E0 in quadratic form E:

[0072]

[0073] in, S is the vector of strain measurement points, ξ and ζ are the weight operators of principal stress constraint E3 and gradient projection smoothness constraint E4, respectively, and K is the radial basis distance matrix, where the element in the i-th row and j-th column is... P is an m×3 matrix:

[0074]

[0075] M2 is the second derivative matrix of the radial basis function, and its elements in the i-th row and j-th column are... M3 and M4 are respectively:

[0076]

[0077]

[0078] S503, Calculate the radial basis coefficients W for each E0. i With undetermined coefficients Taking the partial derivative of W and setting it to zero, we obtain the partial derivative of W. i , The normal equation system:

[0079]

[0080] S504. Solve the system of normal equations to obtain the optimal strain field inversion function:

[0081] ;

[0082] S505. Generate a strain field grid with a resolution of 5 mm within a 600m×600mm monitoring area. Use the optimal strain field inversion function f(x,y) obtained in step S504 to calculate the strain value of each grid node and obtain the strain field distribution in the monitoring area.

[0083] Optionally, in another possible implementation of the first aspect, S6 above, based on the strain field distribution in the monitoring area, calculates the strain gradient vector of each grid node, and iteratively tracks the strain gradient descent trajectory of each grid node using the gradient descent method, forming a set of trajectory endpoints, specifically including:

[0084] S601. For the i-th grid node, N≥i≥1, find the k nearest neighboring grid nodes to the i-th grid node, and calculate the Gaussian weight ω of the j-th neighboring grid node. j , k≥j≥1:

[0085]

[0086] In the formula, d ij σ represents the Euclidean distance between the i-th grid node and its j-th neighboring grid node, and σ represents the Gaussian weighting coefficient.

[0087] S602. Fit a plane to the i-th grid node using its k neighboring grid nodes, and construct a weighted least squares problem. The fitted plane equation and the weighted least squares function are expressed as follows:

[0088]

[0089]

[0090] In the formula, α, β and γ are the coefficients of the fitted plane equation at the i-th grid node, ε0 is the plane fitted strain value, and ε j These are the strain values ​​at the nodes of the strain field grid. The plane fitting strain value of the j-th neighbor point in the plane fitted to the i-th grid node;

[0091] Solving the least squares problem yields the strain gradient vector for the i-th grid node:

[0092] ;

[0093] S603, Let the initial position of the i-th grid node be p0 = (x i , y i The initial step size of the iteration is... After t iterations, the position of the strain gradient descent trajectory is p. t Iterative adaptive step size value As shown in the following formula:

[0094]

[0095] In the formula, Let p be the iteration position of the strain gradient descent trajectory of the i-th grid node. t The strain gradient;

[0096] Based on adaptive step size value Update the gradient descent trajectory position p t+1 :

[0097]

[0098] Each grid node is iteratively updated to obtain the strain gradient descent trajectory corresponding to each grid node, forming a set of trajectory endpoints P:

[0099] .

[0100] Optionally, in another possible implementation of the first aspect, S7 above, performing iterative cluster analysis based on distance statistics on the set of trajectory endpoints, calculating the cluster center coordinates of all trajectory endpoints, and outputting the cluster center coordinates as the application location identification result of the concentrated load, specifically includes:

[0101] S701. Randomly select a trajectory endpoint from the trajectory endpoint set P as the initial cluster center μ0, and calculate the distance from each of the remaining trajectory endpoints in the trajectory endpoint set to the initial cluster center:

[0102]

[0103] S702, Select the option that satisfies d j Less than or equal to 2σ d The endpoints of all trajectories form the point set P. inlier , where σ d Defined as distance from standard deviation:

[0104]

[0105] in, For point set Pinlier The average distance from each point in the cluster to the current cluster center;

[0106] S703, Based on point set P inlier Update the current cluster center coordinates μ as follows:

[0107]

[0108] Among them, (x p ,y p () is a point set P inlier Coordinates of each point in the middle.

[0109] S704. Repeat steps S701-S703 for iterative calculation, continuously updating the point set P. inlier The distance between the current cluster center coordinates and the previous cluster center coordinates is less than 10. -6 The current cluster center coordinates μ are output as the result of the concentrated load application location identification.

[0110] Secondly, embodiments of this application provide a terminal device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the traffic signal control method based on the federated learning framework as described above.

[0111] Thirdly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the concentrated load positioning method based on principal stress constraints and strain gradient trajectory identification as described above.

[0112] Beneficial effects: This application breaks through the limitations of traditional methods that only consider geometric smoothness. By introducing principal stress direction constraints and gradient projection smoothness constraints, it embeds the essential characteristics of structural mechanics into the strain field inversion process, making the reconstructed strain field more consistent with the real physical deformation law. This significantly improves the accuracy and reliability of strain field reconstruction under sparse measurement point conditions. Secondly, it uses Gaussian weighting coefficients to calculate the gradient vector of the strain field grid nodes and iteratively tracks the strain gradient descent trajectory through adaptive step size, transforming the load location problem into a gradient field geometric analysis problem. This does not require a large number of training samples and prior knowledge, and has good generalization performance and real-time monitoring potential. This application establishes an iterative update model based on distance statistics. By analyzing the spatial distribution characteristics of the endpoints of a large number of strain gradient descent trajectories, it extracts the cluster center as the load location identification result, effectively suppressing measurement noise interference, improving the robustness and accuracy of the location results, and realizing an intuitive and effective mapping from distributed strain data to concentrated load application points. Attached Figure Description

[0113] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0114] Figure 1 This is a flowchart illustrating a concentrated load location method based on principal stress constraints and strain gradient trajectory identification provided in an embodiment of this application.

[0115] Figure 2 This is a schematic diagram of the concentrated load loading location identification in the monitoring area provided in an embodiment of this application;

[0116] Figure 3 This is a schematic diagram of the structure of the terminal device provided in the embodiments of this application. Detailed Implementation

[0117] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0118] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0119] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0120] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0121] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0122] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0123] The following description, with reference to the accompanying drawings, details a concentrated load positioning method, terminal device, and storage medium based on principal stress constraints and strain gradient trajectory identification provided in this application.

[0124] Figure 1 The diagram shows a flowchart of a concentrated load location method based on principal stress constraints and strain gradient trajectory identification provided in an embodiment of this application.

[0125] like Figure 1 As shown, the concentrated load localization method based on principal stress constraints and strain gradient trajectory identification includes the following steps:

[0126] S1. Determine the structural monitoring area on the planar structural plate, and arrange strain sensors within the monitoring area to obtain the position coordinates of multiple strain measurement points;

[0127] Furthermore, in this embodiment of the application, step S1 includes:

[0128] S101. Taking a 1200mm×1200mm planar structural plate with four fixed sides as the object, construct a square planar monitoring area in the middle of the planar structural plate. The size of the monitoring area is 600mm×600mm, and the thickness within the monitoring area is evenly distributed at 5mm.

[0129] S102. Divide the monitoring area into 36 rectangular strain measurement point grids with a size of 100mm×100mm. Select the center position of the 36 strain measurement point grids as strain measurement points and label them sequentially as #1~#36.

[0130] S103. Set a strain sensing path within the monitoring area so that the path passes through strain measurement points #1 to #36 in sequence, and arrange strain sensors on the path to ensure that the strain and position coordinates at the 36 strain measurement points are acquired by the strain sensors.

[0131] S2. Apply a concentrated load within the monitoring area and collect and record strain data at each strain measurement point using strain sensors;

[0132] Furthermore, in the embodiments of this application, step S2 above is as follows: Figure 2 As shown, it specifically includes:

[0133] S201. In the top-down view, construct a plane rectangular coordinate system with the lower left corner of the monitoring area as the origin. The direction from the origin to the lower right corner of the monitoring area is the positive X-axis, and the direction from the origin to the upper left corner of the monitoring area is the positive Y-axis.

[0134] S202. Set the concentrated load to two application conditions: The first application condition is to apply a 1000N concentrated load at coordinates (200mm, 200mm) in the Cartesian coordinate system. Figure 2 As shown in (a); the second application condition is to apply a concentrated load of 2000N at coordinates (400mm, 400mm) in a plane rectangular coordinate system, as follows. Figure 2 As shown in (b);

[0135] S203. Record the strain values ​​at strain measurement points #1 to #36 under the two applied conditions, and denot the strain value at each strain measurement point as S. i，j , where i=1,2 represents the application condition sequence number; j=1,2,3,...,36 represents the strain measurement point number.

[0136] S3. Based on the location coordinates of the strain measurement points, the strain data of the strain measurement points, and the radial basis function, construct a strain field inversion function to describe the strain distribution in the monitoring area, and establish an error optimization function that includes fitting error terms and strain field smoothing constraints.

[0137] Furthermore, in this embodiment of the application, step S3 includes:

[0138] S301. Construct the strain field inversion function f(x,y), which is expressed as:

[0139]

[0140] Where m is the number of strain measurement points, m=36, W i Radial basis coefficient, For undetermined coefficients, are basis functions, and ri For the strain inversion point (x,y) and the i-th strain measurement point (x... i, y i The Euclidean distance between them. ;

[0141] S302. Construct an error optimization function E0 that includes a fitting error term and a strain field smoothing constraint, where the fitting error term E1 is expressed as:

[0142]

[0143] The strain field smooth constraint E2 is expressed as:

[0144]

[0145] Where χ is the smoothness constraint weight, used to balance the relative roles of E1 and E2 in the error optimization function. , and For f(x,y) at the strain measurement point (x k ,y k The second derivative value of h x h is the width of the strain measurement grid in the x-direction. y The width of the grid in the y-direction is the value of the strain measurement point.

[0146] S4. Principal stress constraints based on principal stress directions and gradient projection smoothing constraints are introduced into the error optimization function to correct the strain field inversion function;

[0147] Furthermore, in this embodiment of the application, step S4 includes:

[0148] S401. Introduce the principal stress constraint E3 into the error optimization function E0:

[0149] The principal stress unit is defined as the projection l(x,y) of the gradient onto the direction field v, and the gradient onto the direction field v is expressed as follows:

[0150]

[0151]

[0152] in, Let v be the direction vector of the direction field. Let f be the magnitude of the vector in that direction, and ▽f be the gradient of f(x,y); l(x,y) represents the rate of change of the strain field inversion function f(x,y) along the direction v.

[0153] Multiply the length of l(x,y) by the direction field v to obtain the projection vector; take the difference between the gradient ▽f and the projection vector as the vertical component, and minimize the vertical component to obtain the principal stress constraint E3:

[0154]

[0155] Where λ is the principal stress constraint weight;

[0156] Suppose there are m discrete strain measurement points {(x)} within the monitoring area. k ,y k )}, k=1,2,…,m, the direction field v and gradient ▽f take the following values ​​at the kth strain measurement point:

[0157]

[0158] Among them, v x,k v represents the principal stress field in the x-direction at the k-th strain measurement point. y,k f represents the principal stress field in the unit y-direction at the k-th strain measurement point. x,k f represents the gradient value in the x-direction at the k-th strain measurement point. y,k This represents the gradient value in the y-direction at the k-th strain measurement point; the vertical component at the k-th strain measurement point is:

[0159]

[0160] Where I is a 2×2 identity matrix;

[0161] The principal stress constraint E3 is transformed into the following expression:

[0162]

[0163] Where, λ k The integral weight for the k-th strain measurement point is... After expansion, we get:

[0164]

[0165] For gradient ▽f k Discretize:

[0166]

[0167] in, It is the value of the gradient of the radial basis function at the k-th strain measurement point, r. i,k The Euclidean distance between the strain inversion point and the strain measurement point; the discretized gradient ▽f k Represented as matrix multiplication:

[0168]

[0169] Among them, G k It is a 2×m radial basis function gradient matrix, W=(W1, W2,…, W…). m ) T It is the radial basis coefficient vector. It is the linear polynomial part;

[0170] The principal stress constraint E3 is transformed into the following expression:

[0171] ;

[0172] It should be noted that when solving the system of equations later, the cross terms and constant terms will be eliminated, so they can be ignored.

[0173] S402. Introduce the gradient projection smoothing constraint E4 into the error optimization function E0:

[0174] The gradient projection smoothness constraint is defined as the L2 norm of the gradient of l(x,y):

[0175]

[0176] in, Gradient projection smoothing constraint weights;

[0177] The gradient of l(x,y) is approximated using the central difference:

[0178]

[0179] In the formula, Δx represents the difference in the numbers of the continuous strain measurement points in the x-direction, and Δy represents the difference in the numbers of the continuous strain measurement points in the y-direction. Let l(x,y) be the value of the strain measurement point to the right of the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point to the left of the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point above the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point below the k-th strain measurement point;

[0180] Based on the gradient of the approximated l(x,y), E4 is discretized:

[0181]

[0182] Wherein, weight w k Take the proportion of the local grid area;

[0183] Define a vector L = [l1, l2, ..., l m ] TIts relationship with the radial basis coefficient vector W is as follows:

[0184]

[0185] Where V is the direction field projection matrix, each row of the direction field projection matrix acts on the corresponding gradient, and H is the gradient operator matrix, used to map the radial basis coefficient vector W to the gradient of all grid points. V and H are expressed as follows:

[0186]

[0187]

[0188] in, The basis functions represent the strain measurement points m-th;

[0189] Construct the difference matrix D x and D y , so that:

[0190]

[0191] Among them, D x and D y They are respectively:

[0192]

[0193] The gradient projection smoothing constraint E4 is transformed into the following expression:

[0194] .

[0195] S5. Solve the error optimization function after introducing principal stress constraints in the principal stress direction and gradient projection smoothing constraints to obtain the optimal strain field inversion function, and calculate the strain value of each grid node in the monitoring area based on the optimal strain field inversion function to obtain the strain field distribution in the monitoring area.

[0196] Furthermore, in this embodiment of the application, step S5 includes:

[0197] S501. Apply the following constraint to the radial basis coefficients in f(x,y):

[0198] ;

[0199] S502. Introducing the fitting error term E1, strain field smoothing constraint E2, principal stress constraint E3, and gradient projection smoothing constraint E4, we construct the error optimization function E0 = E1 + E2 + E3 + E4; rewriting the error optimization function E0 in quadratic form E:

[0200]

[0201] in, S is the vector of strain measurement points, ξ and ζ are the weight operators of principal stress constraint E3 and gradient projection smoothness constraint E4, respectively, and K is the radial basis distance matrix, where the element in the i-th row and j-th column is... P is an m×3 matrix:

[0202]

[0203] M2 is the second derivative matrix of the radial basis function, and its elements in the i-th row and j-th column are... M3 and M4 are respectively:

[0204]

[0205]

[0206] S503, Calculate the radial basis coefficients W for each E0. i With undetermined coefficients Taking the partial derivative of W and setting it to zero, we obtain the partial derivative of W. i , The normal equation system:

[0207]

[0208] Where a = (a0, a1, a2) T S is the vector of strain measurement points; A is an m×m matrix containing contributions from fitting error, smoothing constraint, principal stress constraint, and gradient projection smoothing constraint; P is an m×3 matrix.

[0209]

[0210] S504. Solve the system of normal equations to obtain the optimal strain field inversion function:

[0211] ;

[0212] S505. Generate a strain field grid with a resolution of 5 mm within a 600m×600mm monitoring area. Use the optimal strain field inversion function f(x,y) obtained in step S504 to calculate the strain value of each grid node and obtain the strain field distribution in the monitoring area.

[0213] S6. Based on the strain field distribution in the monitoring area, calculate the strain gradient vector of each grid node, and iteratively track the strain gradient descent trajectory of each grid node using the gradient descent method, and form a set of trajectory endpoints.

[0214] Furthermore, in this embodiment of the application, step S6 includes:

[0215] S601. For the i-th grid node, N≥i≥1, find the k nearest neighboring grid nodes to the i-th grid node, and calculate the Gaussian weight ω of the j-th neighboring grid node. j , k≥j≥1:

[0216]

[0217] In the formula, d ij σ represents the Euclidean distance between the i-th grid node and its j-th neighboring grid node, and σ represents the Gaussian weighting coefficient.

[0218] S602. Fit a plane to the i-th grid node using its k neighboring grid nodes, and construct a weighted least squares problem. The fitted plane equation and the weighted least squares function are expressed as follows:

[0219]

[0220]

[0221] In the formula, α, β and γ are the coefficients of the fitted plane equation at the i-th grid node, ε0 is the plane fitted strain value, and ε j These are the strain values ​​at the nodes of the strain field grid. The plane fitting strain value of the j-th neighbor point in the plane fitted to the i-th grid node;

[0222] Solving the least squares problem yields the strain gradient vector for the i-th grid node:

[0223] ;

[0224] S603, Let the initial position of the i-th grid node be p0 = (x i , y i The initial step size of the iteration is... After t iterations, the position of the strain gradient descent trajectory is p. t Iterative adaptive step size value As shown in the following formula:

[0225]

[0226] In the formula, Let p be the iteration position of the strain gradient descent trajectory of the i-th grid node. t The strain gradient;

[0227] Based on adaptive step size value Update the gradient descent trajectory position p t+1 :

[0228]

[0229] Each grid node is iteratively updated to obtain the strain gradient descent trajectory corresponding to each grid node, forming a set of trajectory endpoints P:

[0230] .

[0231] S7. Perform iterative cluster analysis based on distance statistics on the set of trajectory endpoints, calculate the cluster center coordinates of all trajectory endpoints, and output the cluster center coordinates as the result of the application position identification of the concentrated load.

[0232] Furthermore, in this embodiment of the application, step S7 includes:

[0233] S701. Randomly select a trajectory endpoint from the trajectory endpoint set P as the initial cluster center μ0, and calculate the distance from each of the remaining trajectory endpoints in the trajectory endpoint set to the initial cluster center:

[0234]

[0235] S702, Select the option that satisfies d j Less than or equal to 2σ d The endpoints of all trajectories form the point set P. inlier , where σ d Defined as distance from standard deviation:

[0236]

[0237] in, For point set P inlier The average distance from each point in the cluster to the current cluster center;

[0238] S703, Based on point set P inlier Update the current cluster center coordinates μ as follows:

[0239] ;

[0240] Among them, (x p ,y p () is a point set P inlier Coordinates of each point in the middle;

[0241] S704. Repeat steps S701-S703 for iterative calculation, continuously updating the point set P. inlier The distance between the current cluster center coordinates and the previous cluster center coordinates is less than 10. -6 The current cluster center coordinates μ are output as the result of the concentrated load application location identification.

[0242] This application provides a concentrated load location method based on principal stress constraints and strain gradient trajectory identification. First, strain sensors are deployed within the monitoring area of ​​a planar structural plate to collect strain data at measurement points. A strain field inversion function is constructed based on radial basis functions, and an error optimization function including fitting error terms and smoothing constraints is established. Principal stress direction constraints and gradient projection smoothing constraints are introduced to form a comprehensive error function, which is then solved to obtain the optimal strain field distribution. Next, the strain gradient vector of each grid node is calculated, and the gradient trajectory is traced using the gradient descent method. Finally, iterative clustering analysis based on distance statistics is performed on the trajectory endpoints, and the cluster centers are output as the concentrated load application location identification results. This application can improve the concentrated load location accuracy, enhance noise resistance, and achieve fast, stable load location identification without requiring a large number of training samples.

[0243] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0244] To implement the above embodiments, this application also proposes a terminal device.

[0245] Figure 3 This is a schematic diagram of the structure of a terminal device according to an embodiment of this application.

[0246] like Figure 3 As shown, the terminal device 200 includes:

[0247] The system includes a memory 210 and at least one processor 220, and a bus 230 connecting different components (including the memory 210 and the processor 220). The memory 210 stores a computer program, which, when executed by the processor 220, implements the concentrated load positioning method based on principal stress constraint and strain gradient trajectory identification as described in the embodiments of this application.

[0248] Bus 230 represents one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. For example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0249] Terminal device 200 typically includes various electronically readable media. These media can be any available media that can be accessed by terminal device 200, including volatile and non-volatile media, removable and non-removable media.

[0250] Memory 210 may also include computer system readable media in the form of volatile memory, such as RAM 240 and / or cache 250. Terminal device 200 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 260 may be used to read and write non-removable, non-volatile magnetic media (… Figure 3 Not shown; usually referred to as a "hard drive"). Although Figure 3 As not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk") and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 230 via one or more data media interfaces. Memory 210 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of this application.

[0251] A program / utility 280 having a set (at least one) of program modules 270 may be stored in, for example, memory 210. Such program modules 270 include—but are not limited to—an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 270 typically perform the functions and / or methods described in the embodiments of this application.

[0252] Terminal device 200 can also communicate with one or more external devices 290 (e.g., keyboard, pointing device, display 291, etc.), and with one or more devices that enable a user to interact with terminal device 200, and / or with any device that enables terminal device 200 to communicate with one or more other computing devices (e.g., network card, modem, etc.). This communication can be performed via input / output (I / O) interface 292. Furthermore, terminal device 200 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 293. As shown, network adapter 293 communicates with other modules of terminal device 200 via bus 230. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with terminal device 200, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0253] The processor 220 performs various functional applications and data processing by running programs stored in the memory 210.

[0254] It should be noted that the implementation process and technical principles of the terminal device in this embodiment are explained in the foregoing description of the concentrated load positioning method based on principal stress constraint and strain gradient trajectory identification in this application embodiment, and will not be repeated here.

[0255] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0256] This application provides a computer program product that, when run on a terminal device, enables the terminal device to implement the steps described in the various method embodiments above.

[0257] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to a photographing device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some regions, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0258] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0259] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0260] In the embodiments provided in this application, it should be understood that the disclosed terminal devices and methods can be implemented in other ways. For example, the terminal device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0261] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0262] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A concentrated load location method based on principal stress constraints and strain gradient trajectory identification, characterized in that, Includes the following steps: S1. Determine the structural monitoring area on the planar structural plate, and arrange strain sensors within the monitoring area to obtain the position coordinates of multiple strain measurement points; S2. Apply a concentrated load within the monitoring area and collect and record strain data at each strain measurement point using strain sensors; S3. Based on the location coordinates of the strain measurement points, the strain data of the strain measurement points, and the radial basis function, construct a strain field inversion function to describe the strain distribution in the monitoring area, and establish an error optimization function that includes fitting error terms and strain field smoothing constraints. S301. Construct the strain field inversion function f(x,y), which is expressed as: ； Where m is the number of strain measurement points, m=36, W i Radial basis coefficient, For undetermined coefficients, are basis functions, and r i For the strain inversion point (x,y) and the i-th strain measurement point (x... i, y i Euclidean distance between them: ; S302. Construct an error optimization function E0 that includes a fitting error term and a strain field smoothing constraint, where the fitting error term E1 is expressed as: ； where S i，j is the strain value of each strain measurement point, where i = 1, 2, represents the number of the working condition; j = 1, 2, 3,..., 36, represents the number of the strain measurement point; The strain field smooth constraint E2 is expressed as: ； Where χ is the smoothness constraint weight, used to balance the relative roles of E1 and E2 in the error optimization function. , and For f(x,y) at the strain measurement point (x k ,y k The second derivative value of h x h is the width of the strain measurement grid in the x-direction. y The width of the grid in the y-direction for strain measurement points; S4. Principal stress constraints based on principal stress directions and gradient projection smoothing constraints are introduced into the error optimization function to correct the strain field inversion function; S401. Introduce the principal stress constraint E3 into the error optimization function E0: The principal stress unit is defined as the projection l(x,y) of the gradient onto the direction field v, and the gradient onto the direction field v is expressed as follows: ； ； in, Let v be the direction vector of the direction field. Let f be the magnitude of the vector in that direction, and ▽f be the gradient of f(x,y); l(x,y) represents the rate of change of the strain field inversion function f(x,y) along the direction v. Multiply the length of l(x,y) by the direction field v to obtain the projection vector; take the difference between the gradient ▽f and the projection vector as the vertical component, and minimize the vertical component to obtain the principal stress constraint E3: ； Where λ is the principal stress constraint weight; S402. Introduce the gradient projection smoothing constraint E4 into the error optimization function E0: The gradient projection smoothness constraint is defined as the L2 norm of the gradient of l(x,y): ； in, The gradient projection smoothing constraint weights are used; the error optimization function is E0 = E1 + E2 + E3 + E4. S5. Solve the error optimization function after introducing principal stress constraints in the principal stress direction and gradient projection smoothing constraints to obtain the optimal strain field inversion function, and calculate the strain value of each grid node in the monitoring area based on the optimal strain field inversion function to obtain the strain field distribution in the monitoring area. S6. Based on the strain field distribution in the monitoring area, calculate the strain gradient vector of each grid node, and iteratively track the strain gradient descent trajectory of each grid node using the gradient descent method, and form a set of trajectory endpoints. S7. Perform iterative cluster analysis based on distance statistics on the set of trajectory endpoints, calculate the cluster center coordinates of all trajectory endpoints, and output the cluster center coordinates as the result of the application position identification of the concentrated load.

2. The method as described in claim 1, characterized in that, Step S1 involves determining a structural monitoring area on the planar structural plate and arranging strain sensors within the monitoring area to obtain the position coordinates of multiple strain measurement points. Specifically, this includes: S101. Taking a 1200mm×1200mm planar structural plate with four fixed sides as the object, a square planar monitoring area is constructed in the middle of the planar structural plate. The size of the monitoring area is 600mm×600mm, and the thickness within the monitoring area is evenly distributed at 5mm. S102. The monitoring area is evenly divided into 36 rectangular strain measurement point grids with a size of 100mm×100mm. The center position of the 36 strain measurement point grids is selected as the strain measurement point, and they are numbered sequentially as #1~#36. S103. Set a strain sensing path within the monitoring area, so that the path passes through strain measurement points #1 to #36 in sequence, and arrange strain sensors on the path to ensure that the strain and position coordinates at the 36 strain measurement points are acquired by the strain sensors.

3. The method as described in claim 2, characterized in that, S2, applying a concentrated load within the monitoring area and collecting and recording strain data at each strain measurement point using strain sensors, specifically includes: S201. In a top-down view, construct a plane rectangular coordinate system with the lower left corner of the monitoring area as the origin. The direction from the origin to the lower right corner of the monitoring area is the positive X-axis, and the direction from the origin to the upper left corner of the monitoring area is the positive Y-axis. S202. Set the concentrated load to two application conditions: the first application condition is to apply a 1000N concentrated load at coordinates (200mm, 200mm) in the plane rectangular coordinate system; the second application condition is to apply a 2000N concentrated load at coordinates (400mm, 400mm) in the plane rectangular coordinate system. S203. Record the strain values ​​at strain measurement points #1 to #36 under the two applied conditions, and denot the strain value at each strain measurement point as S. i，j , where i=1,2 represents the application condition sequence number; j=1,2,3,...,36 represents the strain measurement point number.

4. The method as described in claim 3, characterized in that, The S4 step of introducing principal stress constraints based on principal stress directions and gradient projection smoothing constraints into the error optimization function specifically includes: S401. Introduce the principal stress constraint E3 into the error optimization function E0: The principal stress unit is defined as the projection l(x,y) of the gradient onto the direction field v, and the gradient onto the direction field v is expressed as follows: ； ； in, Let v be the direction vector of the direction field. Let f be the magnitude of the vector in that direction, and ▽f be the gradient of f(x,y); l(x,y) represents the rate of change of the strain field inversion function f(x,y) along the direction v. Multiply the length of l(x,y) by the direction field v to obtain the projection vector; take the difference between the gradient ▽f and the projection vector as the vertical component, and minimize the vertical component to obtain the principal stress constraint E3: ； Where λ is the principal stress constraint weight; Suppose there are m discrete strain measurement points {(x)} within the monitoring area. k ,y k )}, k=1,2,…,m, the direction field v and gradient ▽f take the following values ​​at the kth strain measurement point: ； Among them, v x,k v represents the principal stress field in the x-direction at the k-th strain measurement point. y,k f represents the principal stress field in the unit y-direction at the k-th strain measurement point. x,k f represents the gradient value in the x-direction at the k-th strain measurement point. y,k This represents the gradient value in the y-direction at the k-th strain measurement point; the vertical component at the k-th strain measurement point is: ； Where I is a 2×2 identity matrix; The principal stress constraint E3 is transformed into the following expression: ； Where, λ k The integral weight for the k-th strain measurement point is... After expansion, we get: ； For gradient ▽f k Discretize: ； in, It is the value of the gradient of the radial basis function at the k-th strain measurement point, r. i,k The Euclidean distance between the strain inversion point and the strain measurement point; the discretized gradient ▽f k Represented as matrix multiplication: ； Among them, G k It is a 2×m radial basis function gradient matrix, W=(W1, W2,…, W…). m ) T It is the radial basis coefficient vector. It is the linear polynomial part; The principal stress constraint E3 is transformed into the following expression: ； S402. Introduce the gradient projection smoothing constraint E4 into the error optimization function E0: The gradient projection smoothness constraint is defined as the L2 norm of the gradient of l(x,y): ； in, Gradient projection smoothing constraint weights; The gradient of l(x,y) is approximated using the central difference: ； In the formula, Δx represents the difference in the numbers of the continuous strain measurement points in the x-direction, and Δy represents the difference in the numbers of the continuous strain measurement points in the y-direction. Let l(x,y) be the value of the strain measurement point to the right of the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point to the left of the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point above the k-th strain measurement point. Let l(x,y) be the value of the strain measurement point below the k-th strain measurement point; Based on the gradient of the approximated l(x,y), E4 is discretized: ； Wherein, weight w k Take the proportion of the local grid area; Define a vector L = [l1, l2, ..., l m ] T Its relationship with the radial basis coefficient vector W is as follows: ； Where V is the direction field projection matrix, each row of the direction field projection matrix acts on the corresponding gradient, and H is the gradient operator matrix, used to map the radial basis coefficient vector W to the gradient of all grid points. V and H are expressed as follows: ； ； in, The basis functions represent the strain measurement points m-th; Construct the difference matrix D x and D y , so that: ； Among them, D x and D y They are respectively: ； ； The gradient projection smoothing constraint E4 is transformed into the following expression: 。 5. The method as described in claim 4, characterized in that, S5 involves solving the error optimization function after introducing principal stress constraints in the principal stress direction and gradient projection smoothing constraints to obtain the optimal strain field inversion function. Based on the optimal strain field inversion function, the strain value of each grid node in the monitoring area is calculated to obtain the strain field distribution in the monitoring area. Specifically, this includes: S501. Apply the following constraint to the radial basis coefficients in f(x,y): ； S502. Introducing the fitting error term E1, strain field smoothing constraint E2, principal stress constraint E3, and gradient projection smoothing constraint E4, we construct the error optimization function E0 = E1 + E2 + E3 + E4; rewriting the error optimization function E0 in quadratic form E: ； in, S is the vector of strain measurement points, ξ and ζ are the weight operators of principal stress constraint E3 and gradient projection smoothness constraint E4, respectively, and K is the radial basis distance matrix, where the element in the i-th row and j-th column is... P is an m×3 matrix: ； M2 is the second derivative matrix of the radial basis function, and its elements in the i-th row and j-th column are... M3 and M4 are respectively: ； ； S503, Calculate the radial basis coefficients W for each E0. i With undetermined coefficients Taking the partial derivative of W and setting it to zero, we obtain the partial derivative of W. i , The normal equation system: ； S504. Solve the normal equations to obtain the optimal strain field inversion function: ； S505. Generate a strain field grid with a resolution of 5 mm within a 600m×600mm monitoring area. Use the optimal strain field inversion function f(x,y) obtained in step S504 to calculate the strain value of each grid node and obtain the strain field distribution in the monitoring area.

6. The method as described in claim 5, characterized in that, S6, based on the strain field distribution in the monitoring area, calculates the strain gradient vector for each grid node, and iteratively tracks the strain gradient descent trajectory of each grid node using the gradient descent method, forming a set of trajectory endpoints, specifically including: S601. For the i-th grid node, N≥i≥1, find the k nearest neighboring grid nodes to the i-th grid node, and calculate the Gaussian weight ω of the j-th neighboring grid node. j , k≥j≥1: ； In the formula, d ij σ represents the Euclidean distance between the i-th grid node and its j-th neighboring grid node, and σ represents the Gaussian weighting coefficient. S602. Fit a plane to the i-th grid node using its k neighboring grid nodes, and construct a weighted least squares problem. The fitted plane equation and the weighted least squares function are expressed as follows: ； ； In the formula, α, β and γ are the coefficients of the fitted plane equation at the i-th grid node, ε0 is the plane fitted strain value, and ε j These are the strain values ​​at the nodes of the strain field grid. The plane fitting strain value of the j-th neighbor point in the plane fitted to the i-th grid node; Solving the least squares problem yields the strain gradient vector for the i-th grid node: ； S603, Let the initial position of the i-th grid node be p0 = (x i , y i The initial step size of the iteration is... After t iterations, the position of the strain gradient descent trajectory is p. t Iterative adaptive step size value As shown in the following formula: ； In the formula, Let p be the iteration position of the strain gradient descent trajectory of the i-th grid node. t The strain gradient; Based on adaptive step size value Update the gradient descent trajectory position p t+1 : ； Each grid node is iteratively updated to obtain the strain gradient descent trajectory corresponding to each grid node, forming a set of trajectory endpoints P: 。 7. The method as described in claim 6, characterized in that, S7 involves performing iterative cluster analysis based on distance statistics on the set of trajectory endpoints, calculating the cluster center coordinates of all trajectory endpoints, and outputting these cluster center coordinates as the result of the concentrated load application location identification. Specifically, this includes: S701. Randomly select a trajectory endpoint from the trajectory endpoint set P as the initial cluster center μ0, and calculate the distance from each of the remaining trajectory endpoints in the trajectory endpoint set to the initial cluster center: ； S702, Select the option that satisfies d j Less than or equal to 2σ d The endpoints of all trajectories form the point set P. inlier , where σ d Defined as distance from standard deviation: ； in, For point set P inlier The average distance from each point in the cluster to the current cluster center; S703, According to the point set P inlier Update the current cluster center coordinates μ as follows: ； Among them, (x p ,y p () is a point set P inlier Coordinates of each point in the middle; S704. Repeat steps S701-S703 for iterative calculation, continuously updating the point set P. inlier The distance between the current cluster center coordinates and the previous cluster center coordinates is less than 10. -6 The current cluster center coordinates μ are output as the result of the concentrated load application location identification.

8. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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