Thermophysical parameter identification method based on prior distribution regularization

Abstract

The application discloses a method for identifying thermophysical parameters based on prior distribution regularization, which comprises the following steps: for a heat calibration test of heatproof material, based on the temperature observation data and the identified thermophysical parameters, a covariance matrix of the identified thermophysical parameters is calculated through an information matrix, then the optimal estimation and the covariance matrix of the identified thermophysical parameters are combined to obtain a thermophysical parameter distribution of the heat calibration test, and the thermophysical parameter distribution is taken as a prior distribution; a new batch of heatproof material is tested to obtain a new group of temperature observation data, the prior distribution is combined with the new test data to form a new objective function; the new test data comprises the temperature observation data; and according to the new objective function, the optimal estimation value of the to-be-identified thermophysical parameters is obtained. The application improves the identification precision and accuracy of the thermophysical parameters.

Description

Technical Field

[0001] This application relates to the interdisciplinary field of thermal physics engineering and aerospace engineering, and in particular to a method for identifying thermal property parameters based on prior distribution regularization. Background Technology

[0002] Aircraft encounter complex aerodynamic heating phenomena during high-speed flight. Aerodynamic thermal parameter identification is a technique that uses temperature measurements on the aircraft surface or inside the heat shield to invert and identify aerodynamic thermal parameters such as surface heat flux and thermal property parameters of heat shield materials. It has wide applications in the aerospace field. Thermal property parameters are core physical quantities of thermal protection systems, and their accurate identification is crucial for ensuring the reliability of thermal protection system design. For complex heat transfer situations considering physicochemical coupling such as pyrolysis and radiation, the identification problem needs to be transformed into an optimization problem. This requires establishing corresponding optimization algorithms based on complex heat transfer models and conducting relevant ground tests.

[0003] Given the thermal boundary conditions of a material being loaded, identifying the thermal property parameters in the equations using the temperature information from the measurement points is called the thermal property parameter identification problem, which suffers from ill-posedness. In engineering, experience is often used to select a function (quadratic function, power function) to establish a surrogate model of how thermal property parameters change with temperature. Identifying parameters for this surrogate model can reduce the number of parameters to be identified and improve stability, but it may also introduce bias. Piecewise functions with many parameters may still have high uncertainty due to limitations in measurement accuracy. To handle ill-posedness, regularization methods can be used (parametric function models can also be considered a form of regularization). Regularization methods impose constraints on the problem to ensure the stability of the solution, but they also introduce bias. Tikhonov regularization achieves this by adding a penalty term to the objective function.

[0004] Existing Tikhonov regularization methods for identifying thermal property parameters incorporate Tikhonov regularization into traditional gradient algorithms when solving the inverse problem of heat conduction based on specimen surface temperature. This reduces the impact of temperature measurement errors on the identification results of material thermal property parameters, and regularization parameters are determined using the L-curve criterion. However, this method has the following inherent limitations: it requires multiple iterations to obtain multiple regularization parameters to construct the L-curve, lacking rigorous theoretical guidance; the results are biased estimates, and it is difficult to effectively quantify the uncertainty of the identification results.

[0005] Using a proposed functional relationship between thermal conductivity and temperature as a regularization method, this approach addresses the numerous temperature points at which TACOT's thermophysical parameters change (13 in the initial state and 13 in the carbonized state, totaling 26 thermal conductivity parameters to be identified). By employing this regularization method, identifying multiple unknown parameters is effectively reduced to identifying only a small number. Quadratic functions kv and kc are selected to describe the temperature variation of the initial and carbonized materials, respectively. The core problem with this method is that it sacrifices the realism and complexity of the physical processes with overly simplified mathematics. While reducing the problem's dimensionality and simplifying calculations, it comes at the cost of model distortion, loss of detail, and poor adaptability. This is a serious limitation for materials like TACOT with complex thermophysical behaviors.

[0006] Existing technologies require multiple iterations to obtain several regularization parameters to construct the L-curve, which lacks rigorous theoretical guidance; the results are biased estimates, and it is difficult to effectively quantify the uncertainty of the identification results. Summary of the Invention

[0007] In view of this, this application provides a method for identifying thermal property parameters based on prior distribution regularization, which improves the identification accuracy and precision of thermal property parameters.

[0008] This application discloses a method for identifying thermal property parameters based on prior distribution regularization, which includes:

[0009] Step 1: For the thermal calibration test of the heat-resistant material, based on its temperature observation data and the identified thermal property parameters, the covariance matrix of the identified thermal property parameters is calculated through the information matrix. Then, the optimal estimate of the identified thermal property parameters and the covariance matrix are combined to obtain the distribution of thermal property parameters of the thermal calibration test and use it as the prior distribution.

[0010] Step 2: Conduct tests on the new batch of heat-resistant materials to obtain a new set of temperature observation data. Combine the prior distribution obtained in Step 1 with the new experimental data to form a new objective function; the new experimental data includes temperature observation data.

[0011] Step 3: Based on the new objective function, obtain the optimal estimate of the thermophysical parameters to be identified.

[0012] Further, step 1 includes:

[0013] The covariance matrix of the identified thermal property parameters asymptotically approaches the inverse of the information matrix M, and the expression for M is:

[0014] (1)

[0015] (2)

[0016] in, For the expectation operator, For temperature observation data, Possible values ​​for the identified thermophysical properties. Given temperature observation data hour The posterior probability density function; The standard deviation of the temperature distribution. The dimension of the temperature data. It is a natural exponential function. for The prior distribution, For a given The theoretical value of temperature at that time The symbol for approximation;

[0017] make ,matrix The covariance matrix of the identified thermal property parameters, This is the inverse of the information matrix;

[0018] The final distribution of thermal property parameters is obtained: the optimal estimate of the identified thermal property parameters. Covariance Matrix .

[0019] Further, step 2 includes:

[0020] The heat transfer control equation used in testing the new batch of heat-resistant materials is:

[0021] (3)

[0022] in, ρ For material density, C p For the specific heat of the material, This is the actual temperature value. For time, For spatial coordinates, The thermal conductivity varies with the actual temperature.

[0023] When testing a new batch of heat-resistant materials, the boundary conditions on both sides of the heat-resistant materials, including the first boundary condition and the second boundary condition, are as follows:

[0024] First boundary condition: When hour, ;

[0025] Second boundary condition: when hour, ;

[0026] in, The temperature at the first boundary or location. For material thickness, The temperature at the second boundary or location;

[0027] The initial conditions used for testing the new batch of heat-resistant materials were:

[0028] when hour, ;

[0029] in, The initial temperature;

[0030] The observation equation used for testing the new batch of heat-resistant materials is:

[0031] (4)

[0032] in, In time Location of temperature measuring point Temperature observation data at the location, In time Location of temperature measuring point The theoretical temperature value at that location, v ( t (time) The measurement noise at that time has a mean of 0 and a standard deviation of . Gaussian distribution The value range is 1 to , This represents the number of measurement points;

[0033] Equation (4) is transformed into a least-squares optimization problem that minimizes the objective function shown in the following formula:

[0034] (5)

[0035] in, Let be the objective function. Possible values ​​for the thermal properties to be identified; the thermal properties to be identified include thermal conductivity and specific heat capacity; For a given The theoretical value of the temperature at that time;

[0036] Using the Tikhonov regularization method, the least squares optimization problem is transformed into an optimization problem that minimizes the objective function represented by the following formula:

[0037] (6)

[0038] in, Let be the objective function. These are the Tikhonov regularization parameters; For modulo operation;

[0039] The optimization problem of minimizing the objective function of formula (6) is equivalent to the maximum a posteriori probability estimation of the thermophysical parameters to be identified:

[0040] (7)

[0041] (8)

[0042] in, For the thermophysical parameters to be identified The maximum posterior probability estimate, To maximize the number of operators, Given temperature observation data Thermophysical parameters to be identified The posterior probability density function, It is a natural exponential function. The standard deviation of the temperature distribution. The standard deviation of the prior distribution of the thermal property parameter to be identified, For the prior expected values ​​of the thermophysical parameters to be identified, To provide the thermophysical property parameters to be identified The theoretical value of temperature at that time The symbol for approximation;

[0043] The optimal estimate in step 1 is... Covariance is D1 Substituting into formula (8), we get formula (9):

[0044] (9)

[0045] in, Given temperature observation data hour The posterior probability density function;

[0046] The maximum a posteriori probability estimate of the thermophysical property parameter to be identified is obtained according to formula (7):

[0047] (10)

[0048] Equation (10) is equivalent to the optimization problem of minimizing the objective function represented by Equation (11):

[0049] (11)

[0050] in, To add the objective function for the distribution of thermal property parameters.

[0051] Furthermore, the heat transfer control equation is the physical constraint for identifying thermophysical parameters, determining how temperature evolves with material properties and boundary conditions; the observation equation is used to link experimental observations with numerical simulation outputs, forming the basis of the objective function for parameter identification.

[0052] Furthermore, in formula (8), Thermophysical property parameters to be identified The prior distribution when =0、 When the optimal solution of formula (6) is consistent with that of formula (8), the optimal solution is consistent.

[0053] Further, step 3 includes:

[0054] Make the objective function Regarding the thermophysical parameters to be identified The derivative is 0, in order to solve for the thermophysical parameters to be identified. The optimal estimate :

[0055] (12).

[0056] Furthermore, step 3 specifically includes:

[0057] The optimal estimate of the thermophysical property parameter to be identified is obtained by minimizing the new objective function using the sensitivity method.

[0058] Further, step 3 includes:

[0059] Step 31: Provide initial guesses for the thermophysical properties to be identified: , The initial value is ;

[0060] Step 32: Set the iteration termination condition: Parameter change convergence: , For the first The correction amount of the thermal property parameters to be identified in the next iteration It is the Euclidean norm. The number of iterations is a constant. ;

[0061] Step 33: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Substitute into formula (3) and calculate. , For the first The thermal property parameters to be identified in the next iteration For the first The given thermophysical property parameters to be identified in the next iteration The theoretical value of the temperature at that time;

[0062] Step 34: Calculate the temperature error vector ;

[0063] Step 35: Calculate the current objective function using formula (11). ;

[0064] Step 36: Calculate the difference step size The sensitivity matrix is ​​calculated using the finite difference method. ;

[0065] (13)

[0066] Step 37: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the and Substituting into the normal equation of formula (14), we get :

[0067] (14)

[0068] in, It is a sensitivity matrix Transpose of; Sensitivity matrix The Line number Column elements ,in It is the first During the nth iteration, the measurement point is... The temperature value at that moment. It is the first During the nth iteration One thermophysical parameter to be identified ;

[0069] Step 38: Update parameters: ; For the first The thermal property parameters to be identified in the next iteration;

[0070] Step 39: If the termination condition is met, stop the iteration and let... If the termination condition is not met, let Return to step 33 until you get... until.

[0071] Furthermore, after step 3, the method further includes:

[0072] Based on the optimal estimates of the thermal property parameters to be identified, the covariance matrix of the thermal property parameters to be identified is calculated, and the prior distribution of the thermal calibration test of the next heat protection material is obtained.

[0073] Further, obtaining the prior distribution of the next thermal calibration test of the heat-resistant material includes:

[0074] The information matrix used in the new batch of heat-resistant materials is obtained using the following formula. :

[0075] (15)

[0076] (16)

[0077] in, Given temperature observation data Thermophysical parameters to be identified The posterior probability density function, For the thermophysical parameters to be identified The covariance matrix;

[0078] The thermophysical parameters to be identified The optimal estimate Covariance Matrix Together they constitute the prior distribution for the next thermal calibration test of the heat-resistant material.

[0079] Due to the adoption of the above technical solution, this application has the following advantages:

[0080] 1. Significantly improves the physical rationality and stability of the identification results. Existing regularization methods (such as Tikhonov regularization) mostly rely on mathematical smoothness constraints and lack physical guidance. This application introduces a prior distribution based on the statistical characteristics of historical experiments, transforming physical experience into regularization constraints, effectively avoiding deviations of the inversion results from physical reality, and significantly enhancing the stability and reliability of the solution.

[0081] 2. Achieving Adaptive Regularization, Overcoming the Limitations of Manual Parameter Selection: Traditional regularization parameters rely on manual trial and error or empirical methods such as L-curves, which suffer from high subjectivity and computational costs. This application automatically determines the regularization strength through the prior covariance matrix, achieving adaptive parameter adjustment, thus ensuring theoretical rigor while significantly improving computational efficiency. Attached Figure Description

[0082] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0083] Figure 1 This is a flowchart illustrating a method for identifying thermal property parameters based on prior distribution regularization according to an embodiment of this application.

[0084] Figure 2 This is a schematic diagram illustrating the identification of thermal conductivity coefficients in an embodiment of this application;

[0085] Figure 3 This is a schematic diagram showing the temperature at both ends of the material and the measuring point in an embodiment of this application;

[0086] Figure 4 This is a schematic diagram of the temperature measurement point with added white noise in an embodiment of this application. Detailed Implementation

[0087] The present application will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only some, not all, of the embodiments of the present application. All other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of the present application.

[0088] See Figure 1 This application provides an embodiment of a thermal property parameter identification method based on prior distribution regularization, which includes:

[0089] Step 1: For the thermal calibration test of the heat-resistant material, based on its temperature observation data and the identified thermal property parameters, the covariance matrix of the identified thermal property parameters is calculated through the information matrix. Then, the optimal estimate of the identified thermal property parameters and the covariance matrix are combined to obtain the distribution of thermal property parameters of the thermal calibration test and use it as the prior distribution.

[0090] Step 2: Conduct tests on the new batch of heat-resistant materials to obtain a new set of temperature observation data. Combine the prior distribution obtained in Step 1 with the new experimental data to form a new objective function; the new experimental data includes temperature observation data.

[0091] Step 3: Based on the new objective function, obtain the optimal estimate of the thermophysical parameters to be identified.

[0092] Optionally, step 1 includes:

[0093] When estimating unknown parameters using limited experimental data, the obtained identification results are approximations of the true values. System identification theory proves that maximum likelihood estimation is asymptotically consistent and asymptotically efficient. The covariance matrix of the identified thermal property parameters asymptotically approaches the inverse of the information matrix M, which is expressed as:

[0094] (1)

[0095] (2)

[0096] in, For the expectation operator, For temperature observation data, Possible values ​​for the identified thermophysical properties. Given temperature observation data hour The posterior probability density function; The standard deviation of the temperature distribution. The dimension of the temperature data. It is a natural exponential function. for The prior distribution, For a given The theoretical value of temperature at that time The symbol for approximation;

[0097] make ,matrix The covariance matrix of the identified thermal property parameters, This is the inverse of the information matrix;

[0098] The final distribution of thermal property parameters is obtained: the optimal estimate of the identified thermal property parameters. Covariance Matrix .

[0099] The Cramer-Rhodes bound not only provides a lower bound on the estimated variance, but also, when there is a sufficient amount of experimental data, the Cramer-Rhodes bound approximates the variance of the maximum likelihood estimate. Therefore, the Cramer-Rhodes bound provides a theoretical measure of the accuracy of parameter estimation.

[0100] Optionally, step 2 includes:

[0101] The schematic diagram for determining the thermal conductivity of a material is shown below. Figure 2 As shown, the heat transfer problem can be simplified to a one-dimensional heat transfer problem. The heat flux or temperature values ​​at the left and right boundary points are used as boundary conditions, respectively. The thermal conductivity coefficient is then identified using the temperature history at the boundary points or internal measuring points. Assume that the left and right boundaries of the material are given heat flux boundary conditions. Location of temperature measuring point This represents the number of measurement points.

[0102] The heat transfer control equation used in testing the new batch of heat-resistant materials is:

[0103] (3)

[0104] in, ρ For material density, C p For the specific heat of the material, This is the actual temperature value. For time, For spatial coordinates, The thermal conductivity varies with the actual temperature.

[0105] When testing a new batch of heat-resistant materials, the boundary conditions on both sides of the heat-resistant materials, including the first boundary condition and the second boundary condition, are as follows:

[0106] First boundary condition: When hour, ;

[0107] Second boundary condition: when hour, ;

[0108] in, The temperature at the first boundary or location. For material thickness, The temperature at the second boundary or location;

[0109] The initial conditions used for testing the new batch of heat-resistant materials were:

[0110] when hour, ;

[0111] in, The initial temperature;

[0112] The observation equation used for testing the new batch of heat-resistant materials is:

[0113] (4)

[0114] in, In time Location of temperature measuring point Temperature observation data at the location, In time Location of temperature measuring point The theoretical temperature value at that location, For time The measurement noise at that time has a mean of 0 and a standard deviation of . Gaussian distribution The value range is 1 to , This represents the number of measurement points;

[0115] Typical calculations of the forward problem of heat conduction are performed given boundary conditions and... The temperature value T in formula (3) under noise-free conditions was calculated using numerical methods. The inverse problem of heat conduction, however, is... In the absence of known information, the temperature T at the measuring point in formula (3) and the observation equation is used to determine the temperature. Because usually If the function form is unknown, the possible range of temperature values ​​needs to be segmented, and the thermal conductivity coefficient value should be a constant or a linear function in each segment.

[0116] To handle ill-posedness, regularization methods can be used (parametric function models can also be viewed as a form of regularization). Regularization methods impose constraints on the problem to ensure the stability of the solution, but also introduce biases. Tikhonov regularization achieves this by adding a penalty term to the objective function.

[0117] The Tikhonov regularization method transforms the original optimization problem (Equation (4)) into a least-squares optimization problem that minimizes the objective function shown in the following equation:

[0118] (5)

[0119] in, Let be the objective function. Possible values ​​for the thermal properties to be identified; the thermal properties to be identified include thermal conductivity and specific heat capacity; For a given The theoretical value of the temperature at that time;

[0120] Using the Tikhonov regularization method, the least squares optimization problem is transformed into an optimization problem that minimizes the objective function represented by the following formula:

[0121] (6)

[0122] in, Let be the objective function. These are the Tikhonov regularization parameters; For modulo operation;

[0123] Considering multiple ground tests, the conditions and structures may differ, but the covariance matrix of the identification results can be regarded as a prior distribution. The optimization problem of minimizing the objective function of equation (6) is equivalent to the maximum a posteriori probability estimation of the thermophysical parameters to be identified:

[0124] (7)

[0125] (8)

[0126] in, For the thermophysical parameters to be identified The maximum posterior probability estimate, To maximize the number of operators, Given temperature observation data Thermophysical parameters to be identified The posterior probability density function, It is a natural exponential function. The standard deviation of the temperature distribution. The standard deviation of the prior distribution of the thermal property parameter to be identified, For the prior expected values ​​of the thermophysical parameters to be identified, To provide the thermophysical property parameters to be identified The theoretical value of temperature at that time The symbol for approximation;

[0127] The optimal estimate in step 1 is... Covariance is D1 Substituting into formula (8), we get formula (9):

[0128] (9)

[0129] in, Given temperature observation data hour The posterior probability density function;

[0130] The maximum a posteriori probability estimate of the thermophysical property parameter to be identified is obtained according to formula (7):

[0131] (10)

[0132] Equation (10) is equivalent to the optimization problem of minimizing the objective function represented by Equation (11):

[0133] (11)

[0134] in, To add the objective function for the distribution of thermal property parameters.

[0135] Optionally, the heat transfer control equation is the physical constraint for identifying thermophysical parameters, determining how the temperature evolves with material properties and boundary conditions; the observation equation is used to link experimental observations with numerical simulation outputs, forming the basis of the objective function for parameter identification.

[0136] Alternatively, in formula (8), Thermophysical property parameters to be identified The prior distribution when =0、 When the optimal solutions of equations (6) and (8) are consistent, the prior distribution of the thermophysical parameters to be identified can be used as a Tikhonov regularization.

[0137] Optionally, step 3 includes:

[0138] Make the objective function Regarding the thermophysical parameters to be identified The derivative is 0, in order to solve for the thermophysical parameters to be identified. The optimal estimate :

[0139] (12).

[0140] Optionally, step 3 specifically includes:

[0141] The optimal estimate of the thermophysical property parameter to be identified is obtained by minimizing the new objective function using the sensitivity method.

[0142] Optionally, step 3 includes:

[0143] Step 31: Provide initial guesses for the thermophysical properties to be identified: , The initial value is ;

[0144] Step 32: Set the iteration termination condition: Parameter change convergence: , For the first The correction amount of the thermal property parameters to be identified in the next iteration It is the Euclidean norm. The number of iterations is a constant. ;

[0145] Step 33: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Substitute into formula (3) and calculate. , For the first The thermal property parameters to be identified in the next iteration For the first The given thermophysical property parameters to be identified in the next iteration The theoretical value of the temperature at that time;

[0146] Step 34: Calculate the temperature error vector ;

[0147] Step 35: Calculate the current objective function using formula (11). ;

[0148] Step 36: Calculate the difference step size The sensitivity matrix is ​​calculated using the finite difference method. ;

[0149] (13)

[0150] Step 37: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the and Substituting into the normal equation of formula (14), we get :

[0151] (14)

[0152] in, It is a sensitivity matrix Transpose of; Sensitivity matrix The Line number Column elements ,in It is the first During the nth iteration, the measurement point is... The temperature value at that moment. It is the first During the nth iteration One thermophysical parameter to be identified ;

[0153] Step 38: Update parameters: ; For the first The thermal property parameters to be identified in the next iteration;

[0154] Step 39: If the termination condition is met, stop the iteration and let... If the termination condition is not met, let Return to step 33 until you get... until.

[0155] Optionally, after step 3, the method further includes:

[0156] Based on the optimal estimates of the thermal property parameters to be identified, the covariance matrix of the thermal property parameters to be identified is calculated, and the prior distribution of the thermal calibration test of the next heat protection material is obtained.

[0157] Optionally, obtaining the prior distribution of the next thermal calibration test of the heat-resistant material includes:

[0158] The information matrix used in the new batch of heat-resistant materials is obtained using the following formula. :

[0159] (15)

[0160] (16)

[0161] in, Given temperature observation data Thermophysical parameters to be identified The posterior probability density function, For the thermophysical parameters to be identified The covariance matrix;

[0162] The thermophysical parameters to be identified The optimal estimate Covariance Matrix Together they constitute the prior distribution for the next thermal calibration test of the heat-resistant material.

[0163] This application creatively transforms the "statistical characteristics of historical identification results" into an "adaptive regularization constraint with clear physical meaning," specifically manifested in:

[0164] Quantification and utilization of prior knowledge: Instead of empirically selecting regularization parameters, the parameter covariance matrix identified from historical experimental data is used as quantifiable prior knowledge. This matrix simultaneously includes the uncertainty of the parameters and the correlation between the parameters.

[0165] Adaptability and theoretical rigor: This method is essentially an implementation of Bayesian maximum a posteriori probability estimation. The strength of regularization is determined by the historical data itself, eliminating the need for manual trial and error, thus exhibiting theoretical adaptability. Furthermore, it is directly linked to the Cramer-Rhodes lower bound, guaranteeing the statistical optimality of the estimation.

[0166] This application improves the physical rationality and reliability of parameter identification:

[0167] Existing methods presuppose functional forms (such as quadratic functions or power functions) to describe the parameter variation patterns, which carries the risk of distorted identification results due to model assumption biases. This application aims to overcome the constraints of empirical models by introducing a prior distribution based on the statistical characteristics of historical experiments to construct a regularization constraint mechanism with clear physical meaning, ensuring that the identification results conform to actual physical laws.

[0168] This application optimizes the adaptability and theoretical rigor of regularization constraints:

[0169] In traditional Tikhonov regularization methods, regularization parameters are often selected based on human experience, lacking theoretical guidance and easily leading to overfitting or underfitting. This application proposes using the inverse of the prior covariance matrix as the regularization term, and establishing an intrinsic relationship between the regularization parameter and parameter uncertainty based on Cramer-Rhodes bound theory, thereby achieving adaptive optimization of regularization constraints and enhancing the stability and theoretical consistency of the solution.

[0170] Considering the example where the material has temperature boundary conditions on both sides, the material , , The measuring point is located at 0.005m. Temperatures at both ends and at the measuring point, as follows: Figure 2 and Figure 3 Table 2 provides the set values ​​for thermal conductivity.

[0171] Add the standard deviation to the temperature measurement data at each measuring point. Gaussian white noise of 10 Kelvin, such as Figure 3 As shown, the thermal conductivity is identified using the temperatures in the graph. Table 1 presents the covariance of the identification results for Experiment 1 (without regularization, directly using one set of temperature data). Considering using the covariance of the identification results from Experiment 1 (Table 1) as the prior distribution to identify the thermal conductivity of Experiment 2 (using the results of Experiment 1 as the prior), Table 2 also presents the identification results. It can be seen that the overall identification error is smaller in this case. This example allows for preliminary verification of the effectiveness of prior distribution regularization. Figure 4 A schematic diagram of the temperature measurement point with added white noise is given.

[0172] Table 1. Covariance of Identification Results in Experiment 1

[0173]

[0174] In Table 1, , , , , These represent the thermal conductivity of the material at different temperatures.

[0175] Table 2. Comparison of identification results with true values

[0176]

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A method for identifying thermal property parameters based on prior distribution regularization, characterized in that, include: Step 1: For the thermal calibration test of the heat-resistant material, based on its temperature observation data and the identified thermal property parameters, the covariance matrix of the identified thermal property parameters is calculated through the information matrix. Then, the optimal estimate of the identified thermal property parameters and the covariance matrix are combined to obtain the distribution of thermal property parameters of the thermal calibration test and use it as the prior distribution. Step 2: Conduct tests on the new batch of heat-resistant materials to obtain a new set of temperature observation data. Combine the prior distribution obtained in Step 1 with the new experimental data to form a new objective function; the new experimental data includes temperature observation data. Step 3: Based on the new objective function, obtain the optimal estimate of the thermal property parameter to be identified; Step 1 includes: The covariance matrix of the identified thermal property parameters asymptotically approaches the inverse of the information matrix M, and the expression for M is: (1) (2) in, For the expectation operator, For temperature observation data, Possible values ​​for the identified thermophysical properties. Given temperature observation data hour The posterior probability density function; The standard deviation of the temperature distribution. The dimension of the temperature data. It is a natural exponential function. for The prior distribution, For a given The theoretical value of temperature at that time The symbol for approximation; make ,matrix The covariance matrix of the identified thermal property parameters, This is the inverse of the information matrix; The final distribution of thermal property parameters is obtained: the optimal estimate of the identified thermal property parameters. Covariance Matrix ; Step 2 includes: The heat transfer control equation used in testing the new batch of heat-resistant materials is: (3) in, ρ For material density, C p For the specific heat of the material, This is the actual temperature value. For time, For spatial coordinates, The thermal conductivity varies with the actual temperature. When testing a new batch of heat-resistant materials, the boundary conditions on both sides of the heat-resistant materials, including the first boundary condition and the second boundary condition, are as follows: First boundary condition: When hour, ; Second boundary condition: when hour, ; in, The temperature at the first boundary or location. For material thickness, The temperature at the second boundary or location; The initial conditions used for testing the new batch of heat-resistant materials were: when hour, ; in, The initial temperature; The observation equation used for testing the new batch of heat-resistant materials is: (4) in, In time Location of temperature measuring point Temperature observation data at the location, In time Location of temperature measuring point The theoretical temperature value at that location, For time The measurement noise at that time has a mean of 0 and a standard deviation of . Gaussian distribution The value range is 1 to , This represents the number of measurement points; Equation (4) is transformed into a least-squares optimization problem that minimizes the objective function shown in the following formula: (5) in, Let be the objective function. Possible values ​​for the thermal properties to be identified; the thermal properties to be identified include thermal conductivity and specific heat capacity; For a given The theoretical value of the temperature at that time; Using the Tikhonov regularization method, the least squares optimization problem is transformed into an optimization problem that minimizes the objective function represented by the following formula: (6) in, Let be the objective function. These are the Tikhonov regularization parameters; For modulo operation; The optimization problem of minimizing the objective function of formula (6) is equivalent to the maximum a posteriori probability estimation of the thermophysical parameters to be identified: (7) (8) in, For the thermophysical parameters to be identified The maximum posterior probability estimate, To maximize the number of operators, Given temperature observation data Thermophysical parameters to be identified The posterior probability density function, It is a natural exponential function. The standard deviation of the temperature distribution. The standard deviation of the prior distribution of the thermal property parameter to be identified, For the prior expected values ​​of the thermophysical parameters to be identified, To provide the thermophysical property parameters to be identified The theoretical value of temperature at that time The symbol for approximation; The optimal estimate in step 1 is... Covariance is D1 Substituting into formula (8), we get formula (9): (9) in, Given temperature observation data hour The posterior probability density function; The maximum a posteriori probability estimate of the thermophysical property parameter to be identified is obtained according to formula (7): (10) Equation (10) is equivalent to the optimization problem of minimizing the objective function represented by Equation (11): (11) in, To add the objective function for the distribution of thermal property parameters.

2. The method according to claim 1, characterized in that, The heat transfer control equation is the physical constraint for identifying thermophysical parameters, determining how temperature evolves with material properties and boundary conditions; the observation equation is used to link experimental observations with numerical simulation outputs, forming the basis of the objective function for parameter identification.

3. The method according to claim 1, characterized in that, In formula (8), Thermophysical property parameters to be identified The prior distribution when =0、 When the optimal solution of formula (6) is consistent with that of formula (8), the optimal solution is consistent.

4. The method according to claim 1, characterized in that, Step 3 includes: Make the objective function Regarding the thermophysical parameters to be identified The derivative is 0, in order to solve for the thermophysical parameters to be identified. The optimal estimate : (12)。 5. The method according to claim 1, characterized in that, Step 3 specifically includes: The optimal estimate of the thermophysical property parameter to be identified is obtained by minimizing the new objective function using the sensitivity method.

6. The method according to claim 5, characterized in that, Step 3 includes: Step 31: Provide initial guesses for the thermophysical properties to be identified: , The initial value is ; Step 32: Set the iteration termination condition: Parameter change convergence: , For the first The correction amount of the thermal property parameters to be identified in the next iteration It is the Euclidean norm. The number of iterations is a constant. ; Step 33: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Substitute into formula (3) and calculate. , For the first The thermal property parameters to be identified in the next iteration For the first The given thermophysical property parameters to be identified in the next iteration The theoretical value of the temperature at that time; Step 34: Calculate the temperature error vector ; Step 35: Calculate the current objective function using formula (11). ; Step 36: Calculate the difference step size The sensitivity matrix is ​​calculated using the finite difference method. ; (13) Step 37: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and Substituting into the normal equation of formula (14), we get : (14) in, It is a sensitivity matrix Transpose of; Sensitivity matrix The Line 1 Column elements ,in It is the first During the nth iteration, the measurement point is... The temperature value at that moment. It is the first During the nth iteration One thermophysical parameter to be identified ; Step 38: Update parameters: ; For the first The thermal property parameters to be identified in the next iteration; Step 39: If the termination condition is met, stop the iteration and let... If the termination condition is not met, let Return to step 33 until you get... until.

7. The method according to claim 1, characterized in that, After step 3, the following is also included: Based on the optimal estimates of the thermal property parameters to be identified, the covariance matrix of the thermal property parameters to be identified is calculated, and the prior distribution of the thermal calibration test of the next heat protection material is obtained.

8. The method according to claim 7, characterized in that, Obtaining the prior distribution of the next thermal calibration test for the heat-resistant material includes: The information matrix used in the new batch of heat-resistant materials is obtained using the following formula. : (15) (16) in, Given temperature observation data Thermophysical parameters to be identified The posterior probability density function, For the thermophysical parameters to be identified The covariance matrix; The thermophysical parameters to be identified The optimal estimate Covariance Matrix Together they constitute the prior distribution for the next thermal calibration test of the heat-resistant material.

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