Structural temperature field inversion method based on tomography and regularization constraint principle

Abstract

The application discloses a structure temperature field inversion method based on a chromatography thought and a regularization constraint principle, and comprises the following steps: arranging temperature measuring points on all unit grid nodes of the peripheral boundary of a wall plate, and constructing a temperature perception observation array; reconstructing a temperature gradient to-be-reconstructed matrix of each unit grid center along X and Y directions by using temperature projection rays, and obtaining a wing wall plate temperature field inversion cloud picture; combining a chromatography principle to construct a temperature gradient unit correlation function matrix, constructing a minimum loss function, and introducing a regularization constraint solution space; substituting temperature values of measuring points extracted from sensor actual measurement or finite element numerical simulation results into the chromatography model, calculating actual temperature gradients corresponding to each unit center position of the structure to be measured, and obtaining theoretical temperature gradient values. The method is helpful to simplify the modeling process, breaks through the limitation that sensors need to be arranged in a structure monitoring blind area in a conventional inversion method, and improves the applicability of a temperature distribution reconstruction process.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring, and specifically relates to a structural temperature field inversion method based on the tomographic concept and the regularization constraint principle. Background Technology

[0002] As components directly exposed to aerodynamic heating and drastic changes in the external environment, aircraft wings experience significant thermal stress and deformation due to uneven temperature distribution on their surface and in critical internal components. This effect alters the wing's aerodynamic shape, affects material properties and structural fatigue life, and ultimately poses a challenge to flight safety. Conducting research on real-time in-service monitoring of wing temperature fields provides crucial support for optimizing aircraft thermal management strategies, identifying high-precision thermal deformation, and implementing thermal control. This research is of critical scientific and engineering value for predicting the lifespan of hot-end engine components, improving the efficiency of thermal protection systems, ensuring structural integrity under complex thermal environments, and optimizing the performance of aircraft thermal management systems.

[0003] Conventional temperature distribution inversion methods, such as spline interpolation and inverse distance weighting, require the deployment of sensors within the monitoring area. This absolute dependence on the measurement points within the monitoring area not only complicates the monitoring system but may also lead to problems such as changes in local heat capacity and heat flow disturbances, making it impossible to reconstruct the edge and discontinuous features of the temperature field.

[0004] Therefore, how to develop a temperature distribution inversion method that only requires placing sensors around the periphery of the monitoring area while ensuring the accuracy of temperature distribution inversion has become a key scientific problem that urgently needs to be solved. Summary of the Invention

[0005] This invention provides a structural temperature field inversion method based on tomography and regularization constraints. By constructing a temperature sensing array arranged around the monitoring area, it overcomes the absolute dependence of conventional temperature field inversion methods on the internal measurement points of the monitoring area. It uses the "projection information" generated by temperature in a specific physical process to solve the inverse problem, and solves the problem that conventional temperature field inversion methods cannot restore the edge and discontinuous features of the temperature field when inverting steep temperature gradients or local anomalies. By constructing a minimum loss function and introducing a regularization constraint solution space, it solves the problem of accumulated inversion error of temperature distribution at non-monitoring points of the measured structure.

[0006] This invention adopts the following technical solution: a structural temperature field inversion method based on tomography and regularization constraint principle, comprising the following steps:

[0007] Step 1: Arrange temperature measurement points on all unit grid nodes on the outer boundary of the wing panel to construct a temperature sensing observation array based on the tomography concept;

[0008] Step 2: Construct a tomographic model and reconstruct the temperature gradient matrix along the X and Y directions at the center of each cell grid using temperature projection rays. , The solution is then performed to obtain the inversion cloud map of the temperature field of the wing panel;

[0009] Step 3: Based on the temperature gradient matrix obtained in Step 2, construct the temperature gradient correlation function matrix. By constructing the correlation minimum loss function and introducing regularization constraint solution space, eliminate the accumulation of temperature distribution inversion error at non-monitoring points of the measured structure.

[0010] Step 4: Substitute the temperature values ​​at the measuring points obtained from sensor measurements or finite element numerical simulations into the tomography model to calculate the actual temperature gradient corresponding to the center position of the e-th element mesh of the measured structure. , And obtain the theoretical temperature gradient value of the structure under test.

[0011] As a preferred embodiment, step 1 includes:

[0012] Based on a scaled-down model of the wing panel, the center of the panel is set as the origin, and X-axis and Y-axis are established along the horizontal and vertical directions, respectively. The panel is then uniformly divided into sections along the X-axis and Y-axis, respectively. Segment, generation Individual grid cells.

[0013] Temperature measurement points are set up on all unit grid nodes along the outer boundary of the wall panel to construct a temperature sensing observation array based on the tomographic concept; the measurement point at the lower left corner of the wall panel is set as the first measurement point, and the measurement points are numbered in a counterclockwise direction. The temperature sensed at the i-th measurement point is... , .

[0014] Define the temperature gradients of the wing panel temperature field along the X and Y directions respectively. , :

[0015] ;

[0016] In the formula, For the sensed temperature, , These are the coordinates corresponding to the X and Y directions.

[0017] Choose a temperature gradient along the X and Y directions. , To be reconstructed, set the temperature gradient along the X and Y directions at the center of all cell meshes. , The values ​​are constants, and the temperature gradient matrices to be reconstructed along the X and Y directions of the center of each cell grid are constructed respectively. , The expression is as follows:

[0018] ;

[0019] In the formula, to , to These represent the temperature gradients along the X and Y directions at the center of each cell grid.

[0020] As a preferred embodiment, step 2 includes:

[0021] A tomographic model is constructed, and a method for solving the temperature gradient reconstruction matrix is ​​proposed to solve the temperature gradient matrix to be reconstructed.

[0022] For any i-th and j-th measuring points in the temperature sensing observation array, if they are not on the same horizontal or vertical line, then the line containing the i-th and j-th measuring points is defined as a straight line. Total A straight line, It is a straight line Angle with the X-axis, straight line The temperature difference between the two measuring points is .

[0023] Number the temperature projection rays and assign straight lines Defined sequentially as rays For any projected ray , and The intersection lengths of the cell grids are as follows: Form an n×n intersection length matrix; where, Indicates the first The projected ray and the first The length of the intersection line of each cell grid.

[0024] For the first projection ray To the A single projected ray can be used to construct a set of equations relating the temperature gradient matrix along the X and Y directions at the center of each cell grid:

[0025] ;

[0026] ;

[0027] The above equation can be further rewritten in the form of a system of matrix equations, as follows:

[0028] ;

[0029] In the formula, This is the intermediate matrix.

[0030] Construct the least-squares error function corresponding to the system of equations involving the temperature gradient matrix along the X and Y directions at the center of each cell grid:

[0031] ;

[0032] When the error function , There exists a unique local minimum point, and the unique local minimum point... , satisfy:

[0033] ;

[0034] This allows for the reconstruction of the temperature gradient matrix along the X and Y directions at the center of each cell grid. , .

[0035] As a preferred embodiment, step 3 includes:

[0036] Based on the divided cell grid, each cell grid has 4 nodes, and each node has one temperature component, for a total of 4 temperature components. Together they form the temperature component vector:

[0037] ;

[0038] Two-dimensional temperature field within a four-node element mesh It can be represented by the temperature combination of all nodes in the grid as:

[0039] ;

[0040] In the formula, For the first Temperature characteristic function of each node Indicates the first in the grid Temperature values ​​of each node.

[0041] Establish reference coordinate systems respectively and physical coordinate system The reference coordinate system A reference mesh used to describe geometrically regular shapes; physical coordinate system Used to describe irregular meshes with irregular geometry.

[0042] The expressions for the temperature values ​​of each node are as follows:

[0043] ;

[0044] In the formula, the coordinate position of the center point of the unit grid in the reference coordinate system is... , , , , These are the temperature characteristic functions of the four nodes.

[0045] By constructing the temperature gradient correlation function matrix This causes the temperature gradient G in the X and Y directions at the center point of the cell grid to be... x G y This can be represented by the nodal temperature vector as follows:

[0046] ;

[0047] In the formula, , This is the gradient correlation function matrix of the center point of the four-node cell grid in the X and Y directions.

[0048] According to the chain rule:

[0049] ;

[0050] In the formula, This represents the two-dimensional temperature field within a four-node element mesh. It is the inverse of the Jacobian matrix.

[0051] Jacobian matrix The specific expression is:

[0052] ;

[0053] Will , Represented as:

[0054] ;

[0055] Rewritten in matrix form:

[0056] ;

[0057] In the formula, is the derivative matrix of the correlation function in the reference coordinate system.

[0058] Find the partial derivatives of the correlation function of each node in the four-node element mesh in the reference coordinate system:

[0059] ;

[0060] Reference coordinates of the center point of the cell grid Substitute into the above formula:

[0061] ;

[0062] The baseline derivative matrix of the correlation function can be calculated. The value of the element at the reference coordinate (0,0) :

[0063] ;

[0064] Will , Substituting into the Jacobian matrix expression, we get:

[0065]

[0066] The Jacobian matrix is ​​calculated based on the partial derivatives of the association functions of each node. The value of the element at the reference coordinate (0,0) :

[0067] ;

[0068] In the formula, Let be the coordinates of the i-th node in the physical coordinate system.

[0069] Similarly, the inverse of the Jacobian matrix can be obtained. The value of the element at the reference coordinate (0,0) :

[0070] ;

[0071] In the formula, The determinant of the Jacobian matrix, , , , These are the values ​​of the four elements corresponding to the J matrix.

[0072] According to the chain rule, we get:

[0073] .

[0074] As a preferred embodiment, step 4 includes:

[0075] Substituting the temperature value at the measuring point obtained from the sensor's actual measurement or finite element numerical simulation results into the tomography model described in step 2, the actual temperature gradient at the center of the e-th element mesh of the structure is calculated as follows: , .

[0076] After calculating the theoretical temperature gradient value of the structure, an error function Φ between the theoretical and actual values ​​can be constructed, and a regularization constraint space can be introduced. :

[0077] ;

[0078] In the formula, Let be the least squares loss function with respect to the nodal temperature values. Let the gradient correlation function matrix in the x and y directions of the e-th element of the structure be denoted as . This represents the temperature value of the e-th element node; The regularization coefficient is . For loss weight parameters, The data scaling factor is used to scale the error function onto the node temperature vector. Find the partial derivative and make it equal to 0.

[0079] By solving the differential equation, the minimum value of the error function can be obtained:

[0080] ;

[0081] In the formula, The temperature coefficient matrix representing the structure, The temperature amplitude matrix represents the structure.

[0082] The temperature matrix equation can be obtained through calculation:

[0083] ;

[0084] In the formula, , It can be calculated using the following formula:

[0085] ;

[0086] ;

[0087] In the formula, , Let be the gradient correlation function matrix of the e-th unit of the structure in the x and y directions.

[0088] Furthermore, the nodal temperature vector of the four-node element can be obtained. :

[0089] ;

[0090] Based on the node temperature vector of the e-th four-node unit Then Substitute back to the two-dimensional temperature field By using the formula, we can obtain the temperature value at any point within the e-th four-node element.

[0091] By further assembling the units according to their positions and interpolating the temperatures between adjacent nodes, the temperature distribution information of the entire structure can be obtained.

[0092] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0093] 1. This invention utilizes the "projected information" generated by the temperature field during a specific physical process, overcoming the absolute dependence of interpolation methods on measurement points within the monitoring area through inverse problem solving. When retrieving temperature distributions with steep temperature gradients or local anomalies, it can effectively restore the edges and discontinuities of the temperature field. Furthermore, this invention not only solves the problem of temperature distribution retrieval caused by monitoring blind zones where sensors cannot be deployed, but also overcomes the limitations of conventional methods that require sensor deployment within the monitoring area, leading to localized changes in heat capacity and heat flow disturbances.

[0094] 2. The present invention provides a structural temperature field inversion method. It eliminates the need for prior knowledge of material properties and thermal load characteristics, simplifying the modeling process and overcoming the limitation of conventional inverse finite element methods requiring sensor placement in the blind zone of structural monitoring. By employing tomography to construct a temperature gradient element correlation function matrix and introducing a regularized constraint solution space through the construction of a minimum loss function, the method solves the problem of accumulated inversion errors in the blind zone of sensor monitoring during tomography, thereby improving the accuracy of temperature distribution reconstruction and its engineering applicability. Attached Figure Description

[0095] Figure 1 This is a flowchart of the structural temperature field inversion method of the present invention;

[0096] Figure 2 This is a diagram of the temperature sensing array for the wing panel, as shown in the example.

[0097] Figure 3 This is a temperature gradient matrix diagram of the center of the unit grid in the example embodiment;

[0098] Figure 4 This is a projection ray distribution diagram of the wall panel in an embodiment.

[0099] Figure 5 This is a diagram showing the lengths of the intersections between the projected rays and the grid in an embodiment.

[0100] Figure 6 This is a schematic diagram of the node cell mesh in Example 4;

[0101] Figure 7 The thermal response surface temperature inversion cloud map of the honeycomb sandwich panel is shown in the example. Detailed Implementation

[0102] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in this invention. All non-innovative embodiments based on these embodiments by other researchers in the art are within the protection scope of this invention. Furthermore, the step numbers in the embodiments of this invention are only set for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0103] In one embodiment of the present invention, a structural temperature field inversion method based on tomography and regularization constraint principles is provided, such as... Figure 1 As shown, it includes the following steps:

[0104] Step 1: Taking the scaled-down model of the wing panel as an example, set the center of the panel as the origin, and establish the X-axis and Y-axis along the horizontal and vertical directions respectively.

[0105] Divide the wall panel evenly along the X-axis and Y-axis directions respectively. Segment, generation Each element is a grid. Temperature measurement points are placed on all grid nodes on the outer boundary of the wall panel to construct a temperature sensing array based on the tomographic concept.

[0106] The measuring point at the lower left corner of the wall panel is set as the first measuring point. The measuring points are numbered counter-clockwise. The temperature sensed at the i-th measuring point is... , ,like Figure 2 As shown.

[0107] Define the temperature gradients of the wing panel temperature field along the X and Y directions respectively. , :

[0108] (1)

[0109] Choose a temperature gradient along the X and Y directions. , To be reconstructed, set the temperature gradient along the X and Y directions at the center of all cell meshes. , The values ​​are constants, and these are used to construct the temperature gradient matrix to be reconstructed along the X and Y directions at the center of each cell grid. , ,like Figure 3 As shown, its expression is as follows:

[0110] (2)

[0111] Step 2: Propose a method for solving the temperature gradient reconstruction matrix.

[0112] For any i-th and j-th measuring points in the temperature sensing array, if they are not on the same horizontal or vertical line, then the line containing the i-th and j-th measuring points is defined as a straight line. Total A straight line, θ is a straight line Angle with the X-axis, straight line The temperature difference between the two measuring points is ,like Figure 4 As shown.

[0113] Each temperature projection ray is numbered and ray L is defined. 1n+2 For ray 1, ray L 1n+3 For ray 2, ... and so on.

[0114] For any projection ray The lengths of their intersection lines with the n×n cell grid are respectively: They can be composed of Intersection length matrix ,like Figure 5 As shown. Among them, Indicates the first The projected ray and the first The length of the intersection line of each cell grid.

[0115] Intersection matrix The expression is as follows:

[0116] (3)

[0117] For the first projection ray To the A projected ray can be used to construct a set of equations for the temperature gradient matrix along the X and Y directions at the center of each cell grid:

[0118] (4)

[0119] (5)

[0120] Equations (4) and (5) can be further rewritten as a system of matrix equations, and their expressions are as follows:

[0121] (6)

[0122] In equation (6), the intermediate matrix The expression is shown in equation (7):

[0123] (7)

[0124] Based on equation (7), construct the least squares error function corresponding to the set of temperature gradient matrix equations along the X and Y directions at the center of each cell grid:

[0125] (8)

[0126] When the error function , There exists a unique local minimum point, and the unique local minimum point... , satisfy:

[0127] (9)

[0128] This allows for the reconstruction of the temperature gradient matrix along the X and Y directions at the center of each cell grid. , .

[0129] Step 3: Based on the unit mesh form defined in Step 1, each mesh has 4 nodes, and each node has one temperature component, for a total of 4 temperature components, such as... Figure 6 As shown, Figure 6 In this embodiment, (a) represents the four-node element mesh. Figure 6 (b) in this embodiment is the four-node unit reference coordinate system.

[0130] The four temperature components together form a temperature component vector:

[0131] (10)

[0132] Two-dimensional temperature field within a four-node element mesh It can be represented by the temperature combination of all nodes in the grid as:

[0133] (11)

[0134] In equation (11), Let i be the temperature characteristic function of the i-th node. This represents the temperature value of the i-th node in the grid.

[0135] Establish reference coordinate systems respectively and physical coordinate system Among them, the reference coordinate system A reference mesh used to describe geometrically regular shapes; physical coordinate system Used to describe irregular meshes with irregular geometry.

[0136] In equation (11), The expression is as follows:

[0137] (12)

[0138] In equation (12), the coordinate position of the unit center point in the reference coordinate system is... .

[0139] By constructing the temperature gradient correlation function matrix This results in temperature gradients in the X and Y directions at the center point of the unit cell. , This can be represented by the nodal temperature vector as follows:

[0140] (13)

[0141] In equation (13), , This is the gradient correlation function matrix of the center point of the four-node unit in the X and Y directions.

[0142] According to the chain rule:

[0143] (14)

[0144] In equation (14), It is a Jacobian matrix. It is the inverse of the Jacobian matrix.

[0145] The specific expression for the Jacobian matrix is ​​as follows:

[0146] (15)

[0147] Combining equation (15), equation (14) can be... , Rewritten as:

[0148] (16)

[0149] Rewrite equation (16) in matrix form:

[0150] (17)

[0151] In equation (17), is the derivative matrix of the correlation function in the reference coordinate system.

[0152] Combining equation (13), we obtain the partial derivatives of the correlation functions of each node in the four-node element mesh in the reference coordinate system in equation (17):

[0153] (18)

[0154] The center point of the unit, i.e., the reference coordinates Substitution formula (18):

[0155] (19)

[0156] According to equation (19), the reference derivative matrix of the correlation function can be calculated. The value of the element at the reference coordinate (0,0):

[0157] (20)

[0158] Will , Substituting into equation (15), we get:

[0159] (twenty one)

[0160] According to equation (18), the values ​​of the elements in the Jacobian matrix J at the reference coordinates (0,0) can be calculated:

[0161] (twenty two)

[0162] Similarly, the inverse of the Jacobian matrix can be obtained. The value of the element at the reference coordinate (0,0):

[0163] (twenty three)

[0164] In equation (23), It is the determinant of the Jacobian matrix.

[0165] According to equation (14), and combining equations (21) and (23), we can obtain:

[0166] (twenty four)

[0167] Step 4: Substitute the temperature value at the measuring point obtained from the sensor measurement or finite element numerical simulation results into the tomography method described in Step 2 to calculate the actual temperature gradient at the center of the e-th unit of the structure. , .

[0168] After calculating the theoretical temperature gradient value of the structure, an error function Φ between the theoretical and actual values ​​can be constructed, and a regularization constraint space can be introduced. :

[0169] (25)

[0170] In equation (25), Let be the least squares loss function with respect to the nodal temperature values. , Let the gradient correlation function matrix in the x and y directions of the e-th element of the structure be denoted as . Let e ​​be the node temperature value of the e-th four-node element. The regularization coefficient is . For loss weight parameters, This is the data scaling factor.

[0171] Apply the error function to the node temperature vector Find the partial derivative and set it to zero. By solving the differential equation, the minimum value of the error function can be obtained:

[0172] (26)

[0173] In equation (26), The temperature coefficient matrix representing the structure, This represents the temperature amplitude matrix of the structure. The temperature matrix equation can be obtained through calculation:

[0174] (27)

[0175] In equation (27), , It can be calculated using equations (28) and (29):

[0176] (28)

[0177] (29)

[0178] Combining equations (27), (28), and (29), the nodal temperature vector of the four-node element can be further calculated. :

[0179] (30)

[0180] Based on the node temperature vector of the e-th four-node unit Then Substituting back into equation (11), we can obtain the temperature value at any point within the e-th unit.

[0181] By further assembling the components based on their locations and interpolating the temperatures between adjacent nodes, the temperature distribution information of the entire structure can be obtained. Figure 7 This is a cloud map of the thermal response surface temperature distribution of the wall panel obtained by inversion under the single heat source loading condition in this embodiment.

[0182] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A structural temperature field inversion method based on tomography and regularization constraint principles, characterized in that, Includes the following steps: Step 1: Arrange temperature measurement points on all unit grid nodes on the outer boundary of the wing panel to construct a temperature sensing observation array based on the tomography concept; Step 2: Construct a tomographic model and reconstruct the temperature gradient matrix along the X and Y directions at the center of each cell grid using temperature projection rays. , The solution is then performed to obtain the inversion cloud map of the temperature field of the wing panel; Step 3: Based on the temperature gradient matrix obtained in Step 2, construct the temperature gradient correlation function matrix. By constructing the correlation minimum loss function and introducing regularization constraint solution space, eliminate the accumulation of temperature distribution inversion error at non-monitoring points of the measured structure. Step 4: Substitute the temperature values ​​at the measuring points obtained from actual sensor measurements or finite element numerical simulations into the tomography model to calculate the temperature of the measured structure. The actual temperature gradient corresponding to the center position of each cell grid is: , And obtain the theoretical temperature gradient value of the structure under test, including: The theoretical temperature gradient of the structure under test is calculated, the error function Φ between the theoretical and actual values ​​is constructed, and a regularization constraint space is introduced. Eliminate the accumulation of temperature distribution inversion errors at non-monitoring points of the measured structure: ； In the formula, The regularization coefficient is . For loss weight parameters, This is the data scaling factor; The least squares loss function for the node temperature values. Let be the gradient correlation function matrix of the e-th unit in the x-direction of the structure. Let e ​​be the temperature vector of the e-th unit node; Apply the error function to the node temperature vector By taking the partial derivatives and setting them to zero, and then solving the differential equation, we can obtain the minimum value of the error function: ； In the formula, The temperature coefficient matrix representing the structure, The temperature amplitude matrix representing the structure is obtained through calculation, and the temperature matrix equation is as follows: ； , The calculation is as follows: ； ； In the formula, , Let the gradient correlation function matrix in the x and y directions of the e-th element of the structure be denoted as . Obtain the nodal temperature vector of the four-node element. : ； Based on the temperature vector of the e-th unit node ,Will Substitute back to the two-dimensional temperature field The expression is used to obtain the temperature value at any point within the e-th unit; the units are assembled according to their positions, and the temperatures between adjacent nodes are interpolated to obtain the temperature distribution information of the entire measured structure.

2. The structural temperature field inversion method according to claim 1, characterized in that, Step 1 includes: Based on a scaled-down model of the wing panel, the center of the panel is set as the origin. X-axis and Y-axis are established along the horizontal and vertical directions respectively. The panel is then uniformly divided into sections along the X-axis and Y-axis directions respectively. Segment, generation Individual grid cells; Temperature measurement points were set up on all unit grid nodes along the outer boundary of the wall panel to construct a temperature sensing observation array based on the tomographic concept; the temperature measurement point at the lower left corner of the wall panel was set as the first measurement point, and the measurement points were numbered in a counterclockwise direction, the second and third points being numbered in the third direction. The temperature sensed at each measuring point is , ; Define the temperature gradients of the wing panel temperature field along the X and Y directions respectively. , : ； In the formula, For the sensed temperature, , These are the coordinates corresponding to the X and Y directions.

3. The structural temperature field inversion method according to claim 2, characterized in that, With the temperature gradient , To be reconstructed, construct the temperature gradient matrix to be reconstructed along the X and Y directions from the center of each cell grid. , : ； In the formula, to , to These represent the temperature gradients along the X and Y directions at the center of each cell grid.

4. The structural temperature field inversion method according to claim 3, characterized in that, Step 2 includes: To solve for the temperature gradient matrix to be reconstructed, for any i-th and j-th measuring points in the temperature sensing observation array, if they are not on the same horizontal or vertical line, the line containing the i-th and j-th measuring points is defined as... common A straight line, It is a straight line Angle with the X-axis, straight line The temperature difference between the two measuring points is ; Number the temperature projection rays and assign straight lines Defined sequentially as rays For any projected ray , and The intersection lengths of the cell grids are as follows: ,composition The intersection length matrix is ​​represented as: ； in, Indicates the first The projected ray and the first The length of the intersection line of each cell grid; For the first projection ray To the Using projected rays, construct a set of equations for the temperature gradient matrix along the X and Y directions at the center of each cell grid: ； ； in, to Ray 1 to Ray The temperature difference between the two ends of each ray; to Show Article 1 to Article 2 The projected ray and the first The length of the intersection line of each cell grid; The temperature gradient matrix equations can be rewritten in matrix equation form as follows: ； In the formula, The intermediate matrix is ​​expressed as follows: ； Construct the least squares error function corresponding to the system of equations involving the temperature gradient matrix along the X and Y directions at the center of each cell grid. , : ； When the error function , When a unique local minimum exists, the unique local minimum is... , satisfy: ； In the formula, the superscript T indicates transpose; the temperature gradient matrix along the X and Y directions involving the center of each cell grid is reconstructed. , .

5. The structural temperature field inversion method according to claim 3, characterized in that, Step 3 includes: Construct a temperature gradient correlation function matrix. Each cell grid has 4 nodes, and each node has a temperature component, which together form a temperature component vector: ； In the formula, These are the temperature components for each node. This represents the temperature value of the i-th node in the grid; Two-dimensional temperature field within a four-node element mesh Represented by the combination of temperatures of all nodes in the mesh: ； In the formula, Let i be the temperature characteristic function of the i-th node; Construct the temperature gradient correlation function matrix This causes the temperature gradient in the X and Y directions at the center point of the cell grid to... , The node temperature vector is represented as follows: ； In the formula, , This is the gradient correlation function matrix of the center point of the four-node cell grid in the X and Y directions.

6. The structural temperature field inversion method according to claim 5, characterized in that, Establish reference coordinate systems respectively and physical coordinate system The reference coordinate system A reference mesh describing a regular geometry, the physical coordinate system The expression for the nodal temperature characteristic function of a geometrically irregular mesh is as follows: ； In the formula, This represents the coordinate position of the center point of the unit grid in the reference coordinate system. , , , These are the temperature characteristic functions of the four nodes.

7. The structural temperature field inversion method according to claim 6, characterized in that, Step 3 also includes: For the temperature gradient correlation function matrix To solve this problem, we can use the chain rule for differentiation: ； In the formula, This represents the two-dimensional temperature field within a four-node element mesh. It is the inverse of the Jacobian matrix; The Jacobian matrix J is expressed as: ； , The expression is: ； Rewritten in matrix form: ； In the formula, The derivative matrix of the correlation function in the reference coordinate system; Find the partial derivatives of the correlation function of each node in the four-node element mesh in the reference coordinate system: ； Substitute the reference coordinates of the cell grid center point ,get: ； Calculate the baseline derivative matrix of the correlation function The value of the element at the reference coordinate (0,0) : ； Will , Substitute into the Jacobian matrix The expression yields: ； In the formula, Let be the coordinate position of the i-th node in the physical coordinate system; The Jacobian matrix is ​​calculated. The value of the element at the reference coordinate (0,0) : ； Similarly, we obtain the inverse of the Jacobian matrix. The value of the element at the reference coordinate (0,0) : ； Combining the chain rule, we get: ； In the formula, det(J) is the determinant of the Jacobian matrix. , , , These are the values ​​of the four elements corresponding to the J matrix.

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