Temperature distribution inversion method based on gradient tightly-supported domain radius optimization principle

Abstract

The invention provides a gradient tightly-supported domain radius optimization principle-based temperature distribution inversion method, which comprises the following steps of: 1, performing unit node division on a measured structure to obtain a unit node temperature value and a temperature function correlation model between any point in the measured structure; step 2, adaptively adjusting a function tight supporting domain radius by using a temperature gradient of a node of a measured structure unit; 3, formulating an optimization scheme of the number and position layout of the fiber grating sensors, and obtaining an optimal configuration form of the sensors through global optimization search; and 4, constructing a multivariable regression error functional model added with a regularization term, solving the unit node temperature value by combining the unit node temperature value with a temperature function correlation model between any points in the measured structure, and performing inversion to obtain the temperature distribution of the measured structure. According to the method, the number and the positions of the fiber grating sensors are optimized, unnecessary measuring point arrangement is reduced, and the use cost and the failure risk are reduced on the premise that the influence on the reconstruction precision of the temperature field is small.

Description

Technical Field

[0001] The present invention belongs to the field of structural health monitoring, and in particular relates to a temperature distribution inversion method based on the gradient compact support region radius optimization principle. Background Art

[0002] Temperature fluctuations have a significant impact on various parts of aerospace equipment, such as engines, structures, and electronic systems. In high-temperature environments (such as those in high-heat radiation zones outside the atmosphere or during engine operation), equipment can overheat, leading to circuit shorts, material deformation, or damage. During flight, especially in space missions, low temperatures can cause embrittlement of metals and other materials, compromising structural stability. They can also lead to fuel freezing or poor lubrication. Therefore, real-time online temperature monitoring can effectively control cooling systems and provide early warnings to prevent equipment damage. This helps maintain appropriate operating temperatures in aerospace equipment and avoid failures caused by temperature anomalies.

[0003] Fiber optic sensors offer unique advantages such as flexibility, thin core diameter, resistance to electromagnetic interference, integrated signal sensing and transmission, and ease of configuration into space-division / wavelength-division multiplexing monitoring arrays. Consequently, they are widely recognized by researchers as the most suitable sensor type for building distributed monitoring networks within smart structures. By combining quasi-distributed fiber Bragg grating (FBG) sensors with temperature field inversion algorithms, they are expected to provide valuable insights into the efficient sensing of thermal responses in aerospace structures and the on-orbit identification of global distribution characteristics.

[0004] Kriging requires calculating the variogram and solving a system of linear equations. When there are many temperature measurement points, the matrix operations required significantly increase, resulting in reduced computational efficiency. Furthermore, the accuracy of kriging is highly dependent on the choice of variogram model (such as spherical, exponential, or Gaussian). Improper model selection or inaccurate parameter fitting can lead to biased interpolation results. Furthermore, kriging smoothes extreme values, which can lead to underestimation of local extremes in the temperature field (such as high-temperature centers or low-temperature valleys), 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 data-scarce areas, the model may overfit, resulting in poor generalization. Data noise can also reduce model robustness, and inversion results may contain outliers or spurious fluctuations. As a typical "black box" model, the decision-making process of neural networks is difficult to intuitively understand. 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 lead to significant changes in the output temperature field. Summary of the Invention

[0006] Purpose of the invention: The technical problem to be solved by the present invention is to address the deficiencies of the prior art and propose a temperature distribution inversion method based on the principle of gradient compact support radius optimization, comprising the following steps: 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 to 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 Wendland function's compact support domain using the temperature gradient of the measured structural unit node, effectively avoiding the global operation of the Wendland-Legendre matrix equation and improving the efficiency and accuracy of the temperature distribution inversion of the measured structure; Step 3: Develop an optimization plan for the number and position layout of fiber Bragg grating sensors, and ultimately obtain the optimal sensor configuration through global optimization search; Step 4: Construct a multivariate regression error functional model with a regularization term, combine the unit node temperature value with the temperature function correlation model of any point in the measured structure, solve the unit node temperature value, and then invert to obtain the temperature distribution of the measured structure.

[0007] Step 1 includes: the temperature value at any position in the measured structure is represented by the temperature of all unit nodes in the structure. The temperature value T(x,y) at any point is expressed as: (1), Where (x, y) is the coordinate of any point in the region, T(x, y) represents the temperature value at the coordinate (x, y) of the structure being measured, and A i and B j is the unknown coefficient, n is the number of unit grid nodes, m is the number of Legendre function terms, W(x,y) is the Wendland function, and L(x,y) is the Legendre function: (2), The temperature of the element nodes in the region is expressed as vector Indicates that T n represents the temperature value of the nth unit node, and H represents the matrix transpose.

[0008] In step 1, the Wendland-Legendre matrix equation is constructed using formula (1): (3), In formula (3), the matrices W and L, and the coefficient vectors A and B are: (4), (5), (6), (7), Where (x k , y k ) represents the coordinates of the unit nodes, k=1, 2...n represents the coordinate positions of all unit nodes, A n and B n is the unknown coefficient vector, W n (x n , y n ) represents the Wendland function value at the nth unit node; Solve the matrix equation, recombine the coefficient vectors A and B into column vector X, and recombine the matrices W and L into matrix Y. The expression is: (8), Formula (7) can be written as: (9), By solving the generalized inverse matrix, we can get the generalized inverse matrix Y of column vectors X and Y. + , solve equation (9) and get the solution: (10), Perform SVD singular value decomposition on matrix Y, the formula is: (11), in, , Represents the sth non-zero singular value of matrix Y, s is the rank of matrix Y, U and V are orthogonal matrices AA respectively T The eigenvectors and orthogonal matrix A T The eigenvectors of A, Σ is the singular value matrix of matrix Y; Get the generalized inverse matrix Y of matrix Y + for: (12), Combining formula (9), we can calculate vector X as: (13), Any point in the area Temperature is expressed as: (14), Will The matrix is denoted as matrix , then the temperature value of any point in the structure to be inverted is expressed as: (15).

[0009] Step 2 includes: Calculate the temperature gradient at all unit grid nodes and set the temperature gradient of the node with the smallest temperature gradient inside the measured structure to be , and the corresponding node tight support radius is ; The radius of the compact support region of the i-th unit grid node for: (16), in, is the scaling factor.

[0010] Step 3 includes: The RMSE fitness function is used as the fitness function f of the fiber optic sensor layout optimization algorithm: (17), in For the The actual temperature value of the verification point, For the Temperature algorithm inversion value of verification points; First, each fiber Bragg grating sensor is equivalent to an independent intelligent individual, the number of all possible sensor layout points is set to D, the total number of all possible sensor layout node positions is set to N, and the maximum number of iterations of the optimization algorithm is set to T. max ; Randomly initialize the number d and position n of the sensors, and use the balance factor B f Control the switch between exploration and focus behavior, and choose to enter the exploration or development phase: (18), Among them, B0∈(0,1) is a random number, t is the current iteration number, T max is the maximum number of iterations, when B f >0.5 is the exploration stage. f ≤0.5 is the focusing stage; Using different trigonometric functions to update, the position update formula in the exploration phase is: (19), in is the updated position of the i-th sensor in the j-th dimension after t+1 iterations, is the updated position of the i-th sensor in the j-th dimension after t iterations, is the updated position of the rth sensor in the jth dimension after t+1 iterations, r1 and r2 are random numbers, r1∈(0,1), r2∈(0,1); The sensor position update formula corresponding to the focusing stage is: (20), in, is the current optimal solution after t rounds of iterations, is the updated position of the i-th sensor after t+1 iterations, is the updated position of the ith sensor after t iterations, is the updated position of the rth sensor after t iterations, r3 and r4 are random numbers, r3∈(0,1), r4∈(0,1), Tmax is the maximum number of iterations, and after the position update, the new function fitness is evaluated; The sensor failure stage is set to enhance the global optimal exploration capability. The update formula corresponding to the position of the sensor failure stage is: (twenty one), Among them, r5, r6, r7 are random numbers ∈(0,1), r5∈(0,1), r6∈(0,1), r7∈(0,1), ub and lb are the upper and lower bounds of the search space respectively; after reaching the maximum number of iterations, the iteration is stopped and the optimal solution is output.

[0011] Step 4 includes: The relationship between the temperature value of the measuring point and the temperature value of the unit node in the measured structure is constructed by constructing a multivariate regression error functional model with the addition of regularization terms: (twenty two), Among them, T q is the discrete point temperature value measured by the fiber Bragg grating sensor, For noise.

[0012] Step 4 also includes: The error function RSS after adding the regularization term is: (twenty three), Element node temperature Expressed as: (twenty four), The optimal solution of the unit node temperature obtained by derivation of the error function is: (25), (26), in, is the penalty coefficient.

[0013] In step 4, after obtaining the temperature values of all unit nodes in the measured structure, the coordinates of the required solution points are substituted into equation (15) to invert the temperature distribution of the measured structure.

[0014] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the method.

[0015] The present invention also provides a storage medium storing a computer program or instruction, which executes the steps of the method when the computer program or instruction is run on a computer.

[0016] Beneficial effects: The method of the present invention constructs a multivariate regression error functional model with the addition of a regularization term. The model does not require prior knowledge such as relevant material properties and thermal load characteristics, significantly simplifies the modeling process, and improves the applicability of the temperature distribution inversion process. The temperature gradient of the node of the measured structural unit is used to adaptively adjust the radius of the compact support domain of the Wendland function, effectively avoiding the global operation of the Wendland-Legendre matrix equation, and 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 to reduce the number of redundant sensors, thereby reducing the cost of temperature distribution inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more apparent.

[0018] Figure 1 It is a flow chart of the present invention.

[0019] Figure 2 Schematic diagram of thermal load loading condition.

[0020] Figure 3 Schematic diagram of the node division of solar panel structural unit.

[0021] Figure 4 This is a graph showing the relationship between the objective function value and the number of iterations.

[0022] Figure 5 Schematic diagram of the optimal layout and temperature verification path of the optical fiber sensor after the optimization algorithm.

[0023] Figure 6 This is the temperature inversion cloud map of the thermal response surface of the solar panel.

[0024] Figure 7 Schematic diagram of the comparison between the inverted value and the measured value of the temperature at the verification point. DETAILED DESCRIPTION

[0025] The embodiment of the present invention provides a temperature distribution inversion method based on the gradient compact support radius optimization principle, such as Figure 1 As shown, the following steps are included:

[0026] 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 a temperature function correlation model between the unit node temperature value and any point on the outer surface of the solar panel structure; Apply thermal load to the solar panel structure and divide it into unit nodes, such as Figure 2 、 Figure 3 As shown in the figure, the temperature value at any position in the solar panel structure can be represented by the temperature of all unit nodes in the structure. The temperature value T(x,y) at any point can be expressed as: , Among them, (x, y) is the coordinate of any point in the region, T(x, y) represents the temperature value at the coordinate (x, y) of the solar panel structure, and A i and B j is the unknown coefficient, n is the number of unit nodes, m represents the number of Legendre function terms. In this case, the number of unit nodes of the solar panel structure is 25, the number of Legendre function terms is 6, and the Wendland function W i (x,y) and Legendre function L j The (x,y) function expression is: , , Among them, r i is the Euclidean distance between the ith unit node and any point in the measured structure, R i is the radius of the compact support region of the Wendland function at the unit node, Indicates the first Unit node coordinates; , The temperature of the element nodes in the region is expressed as vector Indicates that T n represents the temperature value of the nth unit node, and H represents the matrix transpose; Construct the Wendland-Legendre matrix equation: , In this case, the matrices W and L, and the coefficient vectors A and B are: , , , , Where (x k , y k ) represents the coordinates of the unit nodes, k=1, 2...n represents the coordinate positions of all unit nodes, A n and B n is the unknown coefficient vector, W n (x n , y n ) represents the Wendland function value at the nth unit node; Solve the matrix equation, recombine the coefficient vectors A and B into column vector X, and recombine the matrices W and L into matrix Y. The expression is: , get: , By solving the generalized inverse matrix, we can get the generalized inverse matrix Y of column vectors X and Y. + , and we get the solution: , Perform SVD decomposition on matrix Y, the formula is: , in, , Represents the sth non-zero singular value of matrix Y, s is the rank of matrix Y, U and V are orthogonal matrices AA respectively T The eigenvectors and orthogonal matrix A T The eigenvectors of A, Σ is the singular value matrix of matrix Y; Get the generalized inverse matrix Y of matrix Y + for: , The vector X is calculated as: , In this case, any point in the region Temperature is expressed as: , Will The matrix is recorded as Matrix, the temperature value of any point in the solar panel structure can be expressed as: ; Step 2: Adaptively adjust the radius of the Wendland function's compact support domain using the temperature gradient of the solar panel structure unit node, effectively avoiding the global operation of the Wendland-Legendre matrix equation and improving the efficiency and accuracy of the solar panel structure temperature distribution inversion; The temperature gradient value at the node of the solar panel structure unit is obtained by finite element simulation, and the temperature gradient of the node with the smallest temperature gradient inside the solar panel structure is set to , and the corresponding node tight support radius is ; No. The radius of the compact support region of each unit grid node for: , in, is the scaling factor.

[0027] Step 3: Develop an optimization plan for the number and position layout of fiber Bragg grating sensors, and ultimately obtain the optimal sensor configuration through global optimization search; The RMSE fitness function is used as the fitness function f of the fiber optic sensor layout optimization algorithm: , in is the true value of the temperature at the i-th verification point, is the temperature algorithm inversion value of the i-th verification point; First, each fiber Bragg grating sensor is equivalent to an independent intelligent individual. The number of all possible sensor layout points is set to D, the total scale of all possible sensor layout 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 layout points is 24, the total scale of all possible sensor layout node positions is set to 300, and the maximum number of iterations of the optimization algorithm is set to 100.

[0028] Randomly initialize the number d and position n of the sensors, and use the balance factor B f Control the switch between exploration and focus behavior, and choose to enter the exploration or development phase: , Among them, B0∈(0,1) is a random number. In this case, B0 is 0.5, t is the current iteration number, T max is the maximum number of iterations, when B f >0.5 is the exploration stage. f ≤0.5 is the focusing stage; Using different trigonometric functions to update, the position update formula in the exploration phase is: , in is the updated position of the i-th sensor in the j-th dimension after t+1 iterations, is the updated position of the i-th sensor in the j-th dimension after t iterations, is the updated position of the rth sensor in the jth 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; The sensor position update formula corresponding to the focusing stage is: , in, is the current optimal solution after t rounds of iterations, is the updated position of the i-th sensor after t+1 iterations, is the updated position of the ith sensor after t iterations, is the updated position of the rth sensor after t iterations, r3 and r4 are random numbers ∈(0,1). In this case, r3 and r4 are 0.5 and 0.7. After the position update, the new function fitness is evaluated; The sensor failure stage is set to enhance the global optimal exploration capability. The update formula corresponding to the position of the sensor failure stage is: , Among them, r5, r6, and r7 are random numbers ∈(0,1). In this case, r5, r6, and r7 are 0.8, 0.2, and 0.5, and ub and lb are the upper and lower bounds of the search space respectively. After reaching the maximum number of iterations, the iteration stops and the optimal solution is output. The relationship curve of the objective function value of the optimization algorithm changing with the number of iterations is shown in the figure below. Figure 4 As shown in the figure, the optimal layout of the optical fiber sensor position and the temperature verification point obtained by the optimization algorithm are as follows Figure 5 shown.

[0029] Step 4: Construct a multivariate regression error functional model with a regularization term, combine the unit node temperature value with the temperature function correlation model between any point in the solar panel structure, solve the unit node temperature value, and then invert to obtain the temperature distribution of the solar panel structure.

[0030] The relationship between the temperature values of the measuring points and the temperature values of the unit nodes in the solar panel structure is constructed by constructing a multivariate regression error functional model with regularization terms: , Among them, T q is the discrete point temperature value measured by the fiber Bragg grating sensor, For noise; The error function RSS after adding the regularization term is: , Element node temperature Expressed as: , The optimal solution of the unit node temperature obtained by derivation of the error function is: , , Where λ is the penalty coefficient. In this case, λ is set to 0.001. H represents the matrix transpose. Calculate the temperature values of all unit nodes in the solar panel structure, and then substitute the coordinates of the required solution points into The temperature distribution of the solar panel structure can be inverted. The temperature inversion cloud diagram of the solar panel thermal response surface obtained in this case is shown as follows: Figure 6 As shown. Figure 7 The figure shows a comparison diagram of the temperature inversion value and the measured value at the verification point.

[0031] The present invention provides a temperature distribution inversion method based on the principle of gradient compact support radius optimization. There are many methods and approaches to implement this technical solution. The above is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention. Any components not specified in this embodiment may be implemented using existing technologies.

Claims

1. A temperature distribution inversion method based on the principle of gradient compact support radius optimization is characterized by: The following steps are involved: Step 1: Divide the structure under test into unit nodes, construct the Wendland-Legendre matrix equation, and solve the matrix equation to obtain the temperature function correlation model between the unit node temperature value and any point in the structure under test; Step 2, using the temperature gradient of the measured structural unit node to adaptively adjust the radius of the Wendland function's compact support domain; Step 3: Develop an optimization plan for the number and position layout of fiber Bragg grating sensors, and ultimately obtain the optimal sensor configuration through global optimization search; Step 4: Construct a multivariate regression error functional model with a regularization term, combine the unit node temperature value with the temperature function correlation model of any point in the measured structure, solve the unit node temperature value, and then invert to obtain the temperature distribution of the measured structure.

2. The method according to claim 1, characterized in that Step 1 includes: the temperature value at any position in the measured structure is represented by the temperature of all unit nodes in the structure. The temperature value T(x,y) at any point is expressed as: （1）， Where (x, y) is the coordinate of any point in the region, T(x, y) represents the temperature value at the coordinate (x, y) of the structure being measured, and A i and B j is the unknown coefficient, n is the number of unit grid nodes, m is the number of Legendre function terms, W(x,y) is the Wendland function, and L(x,y) is the Legendre function: （2）， The temperature of the element nodes in the region is expressed as vector Indicates that T n represents the temperature value of the nth unit node, and H represents the matrix transpose.

3. The method according to claim 2, characterized in that In step 1, the Wendland-Legendre matrix equation is constructed using formula (1): （3）， In formula (3), the matrices W and L, and the coefficient vectors A and B are: （4）， （5）， （6）， （7）， Where (x k , y k ) represents the coordinates of the unit nodes, k=1, 2...n represents the coordinate positions of all unit nodes, A n and B n is the unknown coefficient vector, W n (x n , y n ) represents the Wendland function value at the nth unit node; Solve the matrix equation, recombine the coefficient vectors A and B into column vector X, and recombine the matrices W and L into matrix Y. The expression is: （8）， Formula (7) can be written as: （9）， By solving the generalized inverse matrix, we can get the generalized inverse matrix Y of column vectors X and Y. + , solve equation (9) and get the solution: （10）， Perform SVD singular value decomposition on matrix Y, the formula is: （11）， in, , Represents the sth non-zero singular value of matrix Y, s is the rank of matrix Y, U and V are orthogonal matrices AA respectively T The eigenvectors and orthogonal matrix A T The eigenvectors of A, Σ is the singular value matrix of matrix Y; Get the generalized inverse matrix Y of matrix Y + for: （12）， Combining formula (9), we can calculate vector X as: （13）， Any point in the area Temperature is expressed as: （14）， Will The matrix is denoted as matrix , then the temperature value of any point in the structure to be inverted is expressed as: （15）。 4. The method according to claim 3, characterized in that Step 2 includes: Calculate the temperature gradient at all unit grid nodes and set the temperature gradient of the node with the smallest temperature gradient inside the measured structure to be , and the corresponding node tight support radius is ; The radius of the compact support region of the i-th unit grid node for: （16）， in, is the scaling factor.

5. The method according to claim 4, characterized in that Step 3 includes: The RMSE fitness function is used as the fitness function f of the fiber optic sensor layout optimization algorithm: （17）， in is the true value of the temperature at the i-th verification point, is the temperature algorithm inversion value of the i-th verification point; First, each fiber Bragg grating sensor is equivalent to an independent intelligent individual, the number of all possible sensor layout points is set to D, the total number of all possible sensor layout node positions is set to N, and the maximum number of iterations of the optimization algorithm is set to T. max ; Randomly initialize the number d and position n of the sensors, and use the balance factor B f Control the switch between exploration and focus behavior, and choose to enter the exploration or development phase: （18）， Among them, B0∈(0,1) is a random number, t is the current iteration number, T max is the maximum number of iterations, when B f >0.5 is the exploration stage. f ≤0.5 is the focusing stage; Using different trigonometric functions to update, the position update formula in the exploration phase is: （19）， in is the updated position of the i-th sensor in the j-th dimension after t+1 iterations, is the updated position of the i-th sensor in the j-th dimension after t iterations, is the updated position of the rth sensor in the jth dimension after t+1 iterations, r1 and r2 are random numbers, r1∈(0,1), r2∈(0,1); The sensor position update formula corresponding to the focusing stage is: （20）， in, is the current optimal solution after t rounds of iterations, is the updated position of the i-th sensor after t+1 iterations, is the updated position of the ith sensor after t iterations, is the updated position of the rth sensor after t iterations, r3 and r4 are random numbers, r3∈(0,1), r4∈(0,1), Tmax is the maximum number of iterations, and after the position update, the new function fitness is evaluated; The sensor failure stage is set to enhance the global optimal exploration capability. The update formula corresponding to the position of the sensor failure stage is: （21）， Among them, r5, r6, r7 are random numbers ∈(0,1), r5∈(0,1), r6∈(0,1), r7∈(0,1), ub and lb are the upper and lower bounds of the search space respectively; after reaching the maximum number of iterations, the iteration is stopped and the optimal solution is output.

6. The method according to claim 5, characterized in that Step 4 includes: The relationship between the temperature value of the measuring point and the temperature value of the unit node in the measured structure is constructed by constructing a multivariate regression error functional model with the addition of regularization terms: （22）， Among them, T q is the discrete point temperature value measured by the fiber Bragg grating sensor, For noise.

7. The method according to claim 6, characterized in that Step 4 also includes: The error function RSS after adding the regularization term is: （23）， Element node temperature Expressed as: （24）， The optimal solution of the unit node temperature obtained by derivation of the error function is: （25）， （26）， in, is the penalty coefficient.

8. The method according to claim 7, characterized in that In step 4, after obtaining the temperature values of all unit nodes in the measured structure, the coordinates of the required solution points are substituted into equation (15) to invert the temperature distribution of the measured structure.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 8 are executed.

Images