Temperature distribution inversion method based on the principle of gradient compactly supported region radius optimization

Abstract

This invention provides a temperature distribution inversion method based on the principle of gradient compactly supported domain radius optimization, comprising: Step 1, dividing the structure under test into unit nodes and obtaining a temperature function correlation model between the unit node temperature value and any point within the structure under test; Step 2, adaptively adjusting the compactly supported domain radius of the function using the temperature gradient of the unit nodes of the structure under test; Step 3, formulating an optimization scheme for the number and location layout of fiber optic grating sensors, and obtaining the optimal sensor configuration through global optimization search; Step 4, constructing a multivariate regression error functional model with regularization terms, and solving for the unit node temperature values ​​by combining the temperature function correlation model between the unit node temperature value and any point within the structure under test, thereby inverting the temperature distribution of the structure under test. This invention reduces unnecessary measurement point placement by optimizing the number and location of fiber optic grating sensors, thereby reducing usage costs and failure risks with minimal impact on the accuracy of temperature field reconstruction.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring, and in particular relates to a temperature distribution inversion method based on the principle of gradient compactly supported domain radius optimization. Background Technology

[0002] Temperature variations have a significant impact on various components of aerospace equipment, such as engines, structures, and electronic systems. In high-temperature environments (such as high-heat radiation zones outside the atmosphere or during engine operation), equipment may overheat, leading to short circuits, material deformation, or damage. During flight, especially in space missions, low-temperature environments can cause metals and other materials to become brittle, affecting structural stability. They can also lead to fuel freezing or poor system lubrication. Therefore, real-time online monitoring of the temperature field can effectively control the cooling system or provide early warnings to prevent equipment damage. It can help maintain suitable operating temperatures for aerospace vehicles and avoid malfunctions caused by abnormal temperatures.

[0003] Fiber optic sensors possess unique advantages such as high flexibility, small core diameter, resistance to electromagnetic interference, integration of signal sensing and transmission, and ease of constructing space-division / wavelength-division multiplexing monitoring arrays. Therefore, they are widely recognized by researchers as the most suitable sensor type for building distributed monitoring networks in smart structures. Combining quasi-distributed fiber Bragg grating sensors with temperature field inversion algorithms promises to provide valuable assistance in overcoming the challenges of efficient sensing and on-orbit identification of globally distributed characteristics of thermal responses in aerospace structures.

[0004] Kriging requires calculating the variogram and solving a system of linear equations. When there are many temperature measurement points, the computational cost of matrix operations increases significantly, leading to reduced computational efficiency. Secondly, the accuracy of kriging is highly dependent on the choice of variogram model (e.g., spherical, exponential, or Gaussian model). Inappropriate model selection or inaccurate parameter fitting can result in biased interpolation results. Furthermore, kriging smooths extreme values, causing local extrema of the temperature field (e.g., high-temperature centers or low-temperature valleys) to be underestimated, making it difficult to reflect the true temperature gradient.

[0005] Neural networks (especially deep learning models) typically require large amounts of high-quality training data to achieve good generalization performance. In regions with scarce data, the model may overfit, resulting in poor generalization ability, and data noise can reduce model robustness, potentially leading to outliers or spurious fluctuations in the inversion results. As a typical "black box" model, the decision-making process of neural networks is difficult to understand intuitively. Furthermore, the performance of neural networks is highly dependent on the selection and preprocessing of input features; even small perturbations in the input data (such as sensor bias) can cause significant changes in the output temperature field. Summary of the Invention

[0006] Purpose of the invention: The technical problem to be solved by this invention is to address the shortcomings of existing technologies by proposing a temperature distribution inversion method based on the principle of gradient compactly supported domain radius optimization, comprising the following steps:

[0007] Step 1: Divide the structure under test into unit nodes, construct the Wendland-Legendre matrix equation, and use the SVD method (singular value decomposition) to solve the matrix equation, thereby obtaining the correlation model between the unit node temperature value and the temperature function between any point in the structure under test.

[0008] Step 2: The radius of the tightly supported domain of the Wendland function is adaptively adjusted by utilizing the temperature gradient of the nodes of the structural unit under test, which effectively avoids the global calculation of the Wendland-Legendre matrix equation and improves the efficiency and accuracy of temperature distribution inversion of the structure under test.

[0009] Step 3: Develop an optimization scheme for the number and location layout of fiber Bragg grating sensors. Through global optimization search, the optimal sensor configuration is finally obtained.

[0010] Step 4: Construct a multivariate regression error functional model with regularization term, combine it with the temperature function correlation model between unit node temperature value and any point in the measured structure, solve for unit node temperature value, and then inversely obtain the temperature distribution of the measured structure.

[0011] Step 1 includes: the temperature value at any location within the structure being measured, represented by the temperatures of all element nodes within the structure. The temperature value T(x,y) at any point is represented as:

[0012] (1),

[0013] Where (x,y) represents the coordinates of any point within the region, T(x,y) represents the temperature value at coordinates (x,y) of the measured structure, and A i and B j Here, n represents the number of elements in the grid, m represents the number of Legendre function terms, W(x,y) is the Wendland function, and L(x,y) is the Legendre function.

[0014] (2),

[0015] Unit node temperature within the region is represented by a vector. It means that T n H represents the temperature value of the nth unit node, and H represents the matrix transpose.

[0016] In step 1, the Wendland-Legendre matrix equation is constructed using equation (1):

[0017] (3),

[0018] In equation (3), the matrices W and L, and the coefficient vectors A and B are respectively:

[0019] (4),

[0020] (5),

[0021] (6),

[0022] (7),

[0023] Where (x) k , y k ) represents the coordinates of an element node, k=1, 2...n represents the coordinate positions of all element nodes, A n and B n Let W be the vector of undetermined coefficients. n (x n , y n () represents the Wendland function value at the nth cell node;

[0024] Solve the matrix equation by recombining the coefficient vectors A and B into column vector X, and matrix W and matrix L into matrix Y. The expression is:

[0025] (8),

[0026] Equation (7) can be written as:

[0027] (9),

[0028] The generalized inverse matrix Y of column vectors X and Y is obtained by solving the generalized inverse matrix. + Solving equation (9), we obtain the solution:

[0029] (10)

[0030] The SVD singular value decomposition of matrix Y is performed using the following formula:

[0031] (11),

[0032] in, , U represents the s-th non-zero singular value of matrix Y, where s is the rank of matrix Y, and U and V are the orthogonal matrices AA and NA, respectively. T eigenvectors and orthogonal matrix A T The eigenvectors of A, Σ is the singular value matrix of matrix Y;

[0033] Obtain the generalized inverse matrix Y of matrix Y. + for:

[0034] (12)

[0035] Combining equation (9), the vector X is calculated as follows:

[0036] (13)

[0037] any point within the region Temperature is expressed as:

[0038] (14)

[0039] Will A matrix is ​​denoted as a matrix Then the temperature value at any point within the structure to be inverted is expressed as:

[0040] (15).

[0041] Step 2 includes:

[0042] Calculate the temperature gradient at all element mesh nodes, and define the node temperature gradient that minimizes the internal temperature gradient of the measured structure as . Its corresponding node compact support radius is ;

[0043] The radius of the compacted domain of the i-th cell grid node for:

[0044] (16)

[0045] in, This is the scaling factor.

[0046] Step 3 includes:

[0047] The RMSE fitness function is used as the fitness function f in the fiber optic sensor placement optimization algorithm:

[0048] (17)

[0049] in For the first The actual temperature value at each verification point. For the first Temperature inversion values ​​at each verification point;

[0050] First, each fiber Bragg grating sensor is treated as an independent intelligent entity. The number of all possible placement points of the sensor is set to D, the total number of possible placement node positions of the sensor is set to N, and the maximum number of iterations of the optimization algorithm is set to T. max ;

[0051] The number d and position n of sensors are randomly initialized and arranged using a balance factor B. f Control the switching between exploration and focus behaviors, and choose to enter the exploration or development phase:

[0052] (18)

[0053] Where B0 is a random number ∈ (0,1), t is the current iteration number, and T is the random number. max For the maximum number of iterations, when B f When B > 0.5, it is the exploration phase. f ≤0.5 indicates the focusing stage;

[0054] Using different trigonometric functions for updating, the position update formula for the exploration phase is:

[0055] (19)

[0056] in Let be the updated position of the i-th sensor in the j-th dimension after t+1 iterations. Let be the updated position of the i-th sensor in the j-th dimension after t iterations. Let r1 and r2 be the updated position of the r-th sensor in the j-th dimension after t+1 iterations, where r1 and r2 are random numbers, r1∈(0,1) and r2∈(0,1).

[0057] The sensor position update formula for the focusing phase is:

[0058] (20)

[0059] in, This is the current optimal solution after t iterations. Let be the updated position of the i-th sensor after t+1 iterations. Let be the updated position of the i-th sensor after t iterations. Let r be the updated position of the r-th sensor after t iterations, where r3 and r4 are random numbers, r3∈(0,1) and r4∈(0,1), and Tmax is the maximum number of iterations. After updating the position, evaluate the new function fitness.

[0060] To enhance global optimum exploration capabilities, a sensor failure phase is defined. The update formula corresponding to the sensor failure phase location is as follows:

[0061] (twenty one),

[0062] Where r5, r6, and r7 are random numbers ∈ (0,1), r5∈(0,1), r6∈(0,1), and r7∈(0,1), and ub and lb are the upper and lower bounds of the search space, respectively; the iteration stops and the optimal solution is output after the maximum number of iterations is reached.

[0063] Step 4 includes:

[0064] The relationship between the temperature values ​​at measurement points and the temperature values ​​at unit nodes in the measured structure is constructed by using a multivariate regression error functional model with regularization added:

[0065] (twenty two),

[0066] Among them, T q These are the discrete point temperature values ​​measured by the fiber Bragg grating sensor. It is noise.

[0067] Step 4 also includes:

[0068] The error function RSS after adding the regularization term is:

[0069] (twenty three),

[0070] Unit node temperature Represented as:

[0071] (twenty four),

[0072] The optimal solution for the element nodal temperature is obtained by differentiating the error function:

[0073] (25),

[0074] (26)

[0075] in, This is the coefficient for the penalty term.

[0076] In step 4, after obtaining the temperature values ​​of all unit nodes in the structure under test, the coordinates of the required solution points are substituted into equation (15) to invert the temperature distribution of the structure under test.

[0077] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0078] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0079] Beneficial effects: The method of this invention constructs a multivariate regression error functional model with regularization terms. This model does not require prior knowledge of relevant material properties, thermal load characteristics, etc., which significantly simplifies the modeling process and improves the applicability of the temperature distribution inversion process. By adaptively adjusting the radius of the compactly supported domain of the Wendland function using the temperature gradient of the nodes of the measured structural unit, the global calculation of the Wendland-Legendre matrix equation is effectively avoided, improving the efficiency and accuracy of the temperature field inversion of the measured structure. An optimized layout algorithm for fiber Bragg grating sensors is proposed, which reduces the number of redundant sensors, thereby reducing the cost of temperature distribution inversion. Attached Figure Description

[0080] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0081] Figure 1 This is a flowchart of the present invention.

[0082] Figure 2 This is a schematic diagram of a thermal load application condition.

[0083] Figure 3 A schematic diagram showing the node division of a solar panel structure unit.

[0084] Figure 4 This is a graph showing the relationship between the objective function value and the number of iterations.

[0085] Figure 5 This is a schematic diagram of the optimal layout and temperature verification path for the fiber optic sensor after the algorithm has been optimized.

[0086] Figure 6 This is a cloud map showing the temperature inversion of the thermal response surface of a solar panel.

[0087] Figure 7 A schematic diagram comparing the inverted point temperature value with the measured value. Detailed Implementation

[0088] This invention provides a temperature distribution inversion method based on the principle of gradient compactly supported domain radius optimization, such as... Figure 1 As shown, it includes the following steps:

[0089] Step 1: Divide the solar panel structure into unit nodes, construct the Wendland-Legendre matrix equation, and use the SVD method to solve the matrix equation to obtain the temperature function correlation model between the unit node temperature value and any point on the outer surface of the solar panel structure.

[0090] A thermal load is applied to the solar panel structure, and its element nodes are divided, such as... Figure 2 , Figure 3 As shown, the temperature value at any location within the solar panel structure can be represented by the temperatures of all unit nodes within the structure. The temperature value T(x,y) at any point is expressed as:

[0091] ,

[0092] Where (x,y) represents the coordinates of any point within the region, T(x,y) represents the temperature value at coordinates (x,y) of the solar panel structure, and A i and B j Here, n represents the number of element nodes, and m represents the number of Legendre function terms. In this case, the solar panel structure has 25 element nodes and 6 Legendre function terms. The Wendland function W... i (x,y) and Legendre function L j The expression for the (x,y) function is:

[0093] ,

[0094] ,

[0095] Where, r i R is the Euclidean distance from the i-th element node to any point within the measured structure. i The radius of the compact support region of the Wendland function at the cell node. Indicates the first [unit] within the structure under test Coordinates of each unit node;

[0096] ,

[0097] Unit node temperature within the region is represented by a vector. It means, T n H represents the temperature value of the nth unit node, and H represents the matrix transpose.

[0098] Construct the Wendland-Legendre matrix equation:

[0099] ,

[0100] In this case, the matrices W and L, and the coefficient vectors A and B are respectively:

[0101] ,

[0102] ,

[0103] ,

[0104] ,

[0105] Where (x) k , y k ) represents the coordinates of an element node, k=1, 2...n represents the coordinate positions of all element nodes, A n and B n Let W be the vector of undetermined coefficients. n (x n , y n () represents the Wendland function value at the nth cell node;

[0106] Solve the matrix equation by recombining the coefficient vectors A and B into column vector X, and matrix W and matrix L into matrix Y. The expression is:

[0107] ,

[0108] get:

[0109] ,

[0110] The generalized inverse matrix Y of column vectors X and Y is obtained by solving the generalized inverse matrix. + The solution is obtained as follows:

[0111] ,

[0112] The SVD decomposition of matrix Y is given by the following formula:

[0113] ,

[0114] in, , U represents the s-th non-zero singular value of matrix Y, where s is the rank of matrix Y, and U and V are the orthogonal matrices AA and NA, respectively. T eigenvectors and orthogonal matrix A T The eigenvectors of A, Σ is the singular value matrix of matrix Y;

[0115] Obtain the generalized inverse matrix Y of matrix Y. + for:

[0116] ,

[0117] The vector X is calculated as follows:

[0118] ,

[0119] In this case, any point within the region Temperature is expressed as:

[0120] ,

[0121] Will The matrix is ​​denoted as Given a matrix, the temperature value at any point within the solar panel structure can be expressed as:

[0122] ;

[0123] Step 2: The radius of the tightly supported domain of the Wendland function is adaptively adjusted by utilizing the temperature gradient of the solar panel structural unit nodes, which effectively avoids the global calculation of the Wendland-Legendre matrix equation and improves the efficiency and accuracy of the temperature distribution inversion of the solar panel structure.

[0124] The temperature gradient values ​​at the nodes of the solar panel structural elements were obtained using finite element simulation. The node temperature gradient with the smallest internal temperature gradient was then defined as... Its corresponding node compact support radius is ;

[0125] No. The radius of the compacted domain of each cell grid node for:

[0126] ,

[0127] in, This is the scaling factor.

[0128] Step 3: Develop an optimization scheme for the number and location layout of fiber Bragg grating sensors. Through global optimization search, the optimal sensor configuration is finally obtained.

[0129] The RMSE fitness function is used as the fitness function f in the fiber optic sensor placement optimization algorithm:

[0130] ,

[0131] in Let i be the actual temperature value at the i-th verification point. The temperature value retrieved from the algorithm at the i-th verification point;

[0132] First, each fiber Bragg grating sensor is treated as an independent intelligent individual. The number of all possible sensor placement points is set to D, the total number of all possible sensor placement node positions is set to N, and the maximum number of iterations of the optimization algorithm is set to Tmax. In this case, the number of all possible sensor placement points is 24, the total number of all possible sensor placement node positions is set to 300, and the maximum number of iterations of the optimization algorithm is set to 100.

[0133] The number d and position n of sensors are randomly initialized and arranged using a balance factor B. f Control the switching between exploration and focus behaviors, and choose to enter the exploration or development phase:

[0134] ,

[0135] Where B0 is a random number ∈ (0,1), in this case B0 is 0.5, t is the current iteration number, and T max For the maximum number of iterations, when B f When B > 0.5, it is the exploration phase. f ≤0.5 indicates the focusing stage;

[0136] Using different trigonometric functions for updating, the position update formula for the exploration phase is:

[0137] ,

[0138] in Let be the updated position of the i-th sensor in the j-th dimension after t+1 iterations. Let be the updated position of the i-th sensor in the j-th dimension after t iterations. Let r1 and r2 be the updated position of the r-th sensor in the j-th dimension after t+1 iterations. r1 and r2 are random numbers ∈ (0,1). In this case, r1 and r2 are 0.6 and 0.4, respectively.

[0139] The sensor position update formula for the focusing phase is:

[0140] ,

[0141] in, This is the current optimal solution after t iterations. Let be the updated position of the i-th sensor after t+1 iterations. Let be the updated position of the i-th sensor after t iterations. Let r be the updated position of the r-th sensor after t iterations, where r3 and r4 are random numbers ∈ (0,1). In this case, r3 and r4 are 0.5 and 0.7, respectively. After updating the position, evaluate the new function fitness.

[0142] To enhance global optimum exploration capabilities, a sensor failure phase is defined. The update formula corresponding to the sensor failure phase location is as follows:

[0143] ,

[0144] Where r5, r6, and r7 are random numbers ∈ (0,1), in this case, r5, r6, and r7 are taken as 0.8, 0.2, and 0.5, respectively, and ub and lb are the upper and lower bounds of the search space, respectively. The iteration stops after reaching the maximum number of iterations and the optimal solution is output. The relationship between the objective function value of the optimization algorithm and the number of iterations is shown in the graph below. Figure 4 As shown, the optimal layout of the fiber optic sensor and the temperature verification point obtained through the optimization algorithm are as follows: Figure 5 As shown.

[0145] Step 4: Construct a multivariate regression error functional model with regularization terms, combine it with the correlation model between the unit node temperature value and the temperature function between any point in the solar panel structure, solve for the unit node temperature value, and then inversely obtain the temperature distribution of the solar panel structure.

[0146] The relationship between the temperature values ​​at measuring points and the temperature values ​​at unit nodes in a solar panel structure is constructed by using a multivariate regression error functional model with regularization added:

[0147] ,

[0148] Among them, T q These are the discrete point temperature values ​​measured by the fiber Bragg grating sensor. For noise;

[0149] The error function RSS after adding the regularization term is:

[0150] ,

[0151] Unit node temperature Represented as:

[0152] ,

[0153] The optimal solution for the element nodal temperature is obtained by differentiating the error function:

[0154] ,

[0155] ,

[0156] Where λ is the penalty term coefficient, which is 0.001 in this case, and H represents matrix transpose. The temperature values ​​of all unit nodes within the solar panel structure are calculated, and then the coordinates of the required solution points are substituted into... The temperature distribution of the solar panel structure can be inverted from the data obtained in this case. The temperature inversion cloud map of the solar panel thermal response surface obtained in this case is shown in the figure below. Figure 6 As shown. Figure 7 The figure shown is a schematic diagram comparing the temperature inversion value and the measured value at the verification point.

[0157] This invention provides a temperature distribution inversion method based on the principle of gradient compactly supported domain radius optimization. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A temperature distribution inversion method based on the principle of gradient compactly supported domain radius optimization, characterized in that, Includes the following steps: Step 1: Divide the structure under test into unit nodes, construct the Wendland-Legendre matrix equation, solve the matrix equation, and thus obtain the temperature function correlation model between the unit node temperature value and any point in the structure under test. Step 2: Adaptively adjust the radius of the compactly supported domain of the Wendland function using the temperature gradient of the nodes of the structural unit under test; Step 3: Develop an optimization scheme for the number and location layout of fiber Bragg grating sensors. Through global optimization search, the optimal sensor configuration is finally obtained. Step 4: Construct a multivariate regression error functional model with regularization term, combine it with the temperature function correlation model between unit node temperature value and any point in the measured structure, solve the unit node temperature value, and then invert to obtain the temperature distribution of the measured structure. Step 1 includes: the temperature value at any location within the structure being measured, represented by the temperatures of all element nodes within the structure. The temperature value T(x,y) at any point is represented as: （1）， Where (x,y) represents the coordinates of any point within the region, T(x,y) represents the temperature value at coordinates (x,y) of the measured structure, and A i and B j Here, n represents the number of elements in the grid, m represents the number of Legendre function terms, W(x,y) is the Wendland function, and L(x,y) is the Legendre function. （2）， Unit node temperature within the region is represented by a vector. It means that T n H represents the temperature value of the nth unit node, and H represents the matrix transpose. Construct the Wendland-Legendre matrix equation using equation (1): （3）， In equation (3), the matrices W and L, and the coefficient vectors A and B are respectively: （4）， （5）， （6）， （7）， Where (x) k , y k ) represents the coordinates of an element node, k=1, 2...n represents the coordinate positions of all element nodes, A n and B n Let W be the vector of undetermined coefficients. n (x n , y n () represents the Wendland function value at the nth cell node; Step 2 includes: Calculating the temperature gradient at all element mesh nodes, and setting the node temperature gradient that minimizes the internal temperature gradient of the structure under test as... Its corresponding node compact support radius is ; The radius of the compacted domain of the i-th cell grid node for: （16）， in, This is the scaling factor.

2. The method according to claim 1, characterized in that, In step 1, the matrix equation is solved, and the coefficient vectors A and B are recombine into column vector X, and matrices W and L are recombine into matrix Y, expressed as: （8）， Equation (7) can be written as: （9）， The generalized inverse matrix Y of column vectors X and Y is obtained by solving the generalized inverse matrix. + Solving equation (9), we obtain the solution: （10）， The SVD singular value decomposition of matrix Y is performed using the following formula: （11）， in, , U represents the s-th non-zero singular value of matrix Y, where s is the rank of matrix Y, and U and V are the orthogonal matrices AA and NA, respectively. T eigenvectors and orthogonal matrix A T The eigenvectors of A, Σ is the singular value matrix of matrix Y; Obtain the generalized inverse matrix Y of matrix Y. + for: （12）， Combining equation (9), the vector X is calculated as follows: （13）， any point within the region Temperature is expressed as: （14）， Will A matrix is ​​denoted as a matrix Then the temperature value at any point within the structure to be inverted is expressed as: （15）。 3. The method according to claim 2, characterized in that, Step 3 includes: The RMSE fitness function is used as the fitness function f in the fiber optic sensor placement optimization algorithm: （17）， in Let i be the actual temperature value at the i-th verification point. The temperature value retrieved from the algorithm at the i-th verification point; First, each fiber Bragg grating sensor is treated as an independent intelligent entity. The number of all possible placement points of the sensor is set to D, the total number of possible placement node positions of the sensor is set to N, and the maximum number of iterations of the optimization algorithm is set to T. max ; The number d and position n of sensors are randomly initialized and arranged using a balance factor B. f Control the switching between exploration and focus behaviors, and choose to enter the exploration or development phase: （18）， Where B0 is a random number ∈ (0,1), t is the current iteration number, and T is the random number. max For the maximum number of iterations, when B f When B > 0.5, it is the exploration phase. f ≤0.5 indicates the focusing stage; Using different trigonometric functions for updating, the position update formula for the exploration phase is: （19）， in Let be the updated position of the i-th sensor in the j-th dimension after t+1 iterations. Let be the updated position of the i-th sensor in the j-th dimension after t iterations. Let r1 and r2 be the updated position of the r-th sensor in the j-th dimension after t+1 iterations, where r1 and r2 are random numbers, r1∈(0,1) and r2∈(0,1). The sensor position update formula for the focusing phase is: （20）， in, This is the current optimal solution after t iterations. Let be the updated position of the i-th sensor after t+1 iterations. Let be the updated position of the i-th sensor after t iterations. Let r be the updated position of the r-th sensor after t iterations, where r3 and r4 are random numbers, r3∈(0,1) and r4∈(0,1), and Tmax is the maximum number of iterations. After updating the position, evaluate the new function fitness. To enhance global optimum exploration capabilities, a sensor failure phase is defined. The update formula corresponding to the sensor failure phase location is as follows: （21）， Where r5, r6, and r7 are random numbers ∈ (0,1), r5∈(0,1), r6∈(0,1), and r7∈(0,1), and ub and lb are the upper and lower bounds of the search space, respectively; the iteration stops and the optimal solution is output after the maximum number of iterations is reached.

4. The method according to claim 3, characterized in that, Step 4 includes: The relationship between the temperature values ​​at measurement points and the temperature values ​​at unit nodes in the measured structure is constructed by using a multivariate regression error functional model with regularization added: （22）， Among them, T q These are the discrete point temperature values ​​measured by the fiber Bragg grating sensor. It is noise.

5. The method according to claim 4, characterized in that, Step 4 also includes: The error function RSS after adding the regularization term is: （23）， Unit node temperature Represented as: （24）， The optimal solution for the element nodal temperature is obtained by differentiating the error function: （25）， （26）， in, This is the coefficient for the penalty term.

6. The method according to claim 5, characterized in that, In step 4, after obtaining the temperature values ​​of all unit nodes in the structure under test, the coordinates of the required solution points are substituted into equation (15) to invert the temperature distribution of the structure under test.

7. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 6.

8. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 6.

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