A method for identifying temperature-dependent thermal conductivity coefficient based on experimental data and optimization inversion

Abstract

The application discloses a temperature-dependent thermal conductivity coefficient identification method based on test data and optimization inversion, adopts wavelet transform to carry out noise reduction pretreatment on a temperature sequence containing noise, and obtains smooth temperature data; sets an initial guess value of a thermal conductivity coefficient and a convergence criterion; solves a heat conduction equation based on a current thermal conductivity coefficient to obtain a calculated temperature field; calculates a target function according to the calculated temperature field and the smooth temperature data and judges the convergence; if the convergence is not reached, a conjugate gradient method is used to determine a search direction and an optimal step length according to gradient information, the thermal conductivity coefficient is updated, and iteration is continuously carried out until the convergence condition is met, and then an identification result is output. The method disclosed by the application effectively suppresses noise interference, stably converges in iteration, avoids negative thermal conductivity coefficients, the result has physical rationality, and is suitable for the identification of thermal physical properties under complex heating conditions of various materials.

Description

Technical Field

[0001] This application belongs to the field of engineering thermophysics and computational inversion technology, specifically involving a method for identifying temperature-dependent thermal conductivity coefficients based on experimental data and optimized inversion. Background Technology

[0002] In cutting-edge industrial fields such as aerospace and materials design and application, accurately obtaining the thermal conductivity coefficient of materials as a function of temperature is a crucial prerequisite for conducting thermal structure design, safety assessment, and process optimization. For high-temperature or complex service conditions, especially for advanced resin-based composite materials, direct steady-state measurement methods are difficult to implement reliably. Therefore, inverse problem identification methods based on transient temperature response data have become an important technical approach. These methods measure the temperature evolution of an object during heating and then use numerical simulation models to solve for the material's thermal properties.

[0003] However, solving this type of inverse problem faces two prominent challenges. First, the temperature time series collected in experiments inevitably contains multiple noise components, which are amplified dramatically during the gradient calculation process of the inversion iteration. This leads to the identification results deviating significantly from the true characteristics, and may even cause instability and divergence in the solution process. Second, traditional optimization algorithms, such as the Levenberg-Marquardt method, are prone to getting trapped in local optima due to the combined effects of noise and nonlinearity when calculating the sensitivity coefficient matrix. Furthermore, iterative updates often produce non-physical results such as negative thermal conductivity coefficients, which contradict the physical nature of material thermal diffusion and directly lead to identification failure.

[0004] In summary, existing inversion methods based on temperature test data are insufficient in suppressing data noise and lack effective constraints to maintain the physical rationality of the solution, making it difficult to obtain high-precision thermal conductivity coefficient identification results with clear physical meaning under strong noise background. Summary of the Invention

[0005] To overcome the dual shortcomings of existing inversion methods, such as low identification accuracy under strong noise background and easy generation of non-physical results like negative thermal conductivity coefficients, this application provides a parameter identification method that can stably obtain thermal conductivity coefficients that change with temperature and whose identification results have clear physical meaning.

[0006] To achieve the above technical objectives, this application specifically employs the following technical solution: In one aspect of this application, a method for identifying the temperature-dependent thermal conductivity coefficient based on experimental data and optimized inversion is provided, comprising the following steps: Step S1: Perform wavelet denoising preprocessing on the noisy temperature time series data collected in the experiment to obtain smooth temperature data after denoising; Step S2: Set the initial guess value of the thermal conductivity coefficient as it changes with temperature, the maximum allowable error of the convergence criterion, and the initial value of the number of iteration steps; Step S3: Based on the heat conduction coefficient of the current iteration step, solve the heat conduction control equation to obtain the corresponding calculated temperature field; Step S4: Based on the calculated temperature field and the smoothed temperature data after noise reduction, calculate the objective function value and determine whether the objective function value is less than the maximum allowable error. If yes, determine convergence and output the current thermal conductivity coefficient as the final identification result; otherwise, continue to step S5. Step S5: Based on the conjugate gradient method, determine the search direction and optimal step size of the current iteration step according to the gradient information of the objective function with respect to the thermal conductivity coefficient; Step S6: Update the thermal conductivity coefficient according to the search direction and the optimal step size, and increase the iteration step number by 1, then return to step S3.

[0007] In one implementation, step S1 specifically includes: The Coiflet wavelet function is used as the basis function to perform multi-scale decomposition on the noisy temperature time series data to obtain wavelet coefficients. The wavelet coefficients are processed to retain low-frequency approximation coefficients and suppress or filter out high-frequency detail coefficients. The noise-reduced, smooth temperature data is obtained through wavelet reconstruction.

[0008] In one implementation, the wavelet coefficients are processed using a Bayesian method with the median as the threshold rule.

[0009] In one implementation, in step S2, the initial guess value of the thermal conductivity coefficient is set as the measured value of the thermal conductivity coefficient at room temperature.

[0010] In one implementation, in step S3, the heat conduction control equation is:

[0011] in, For temperature, For material density, For the specific heat capacity of the material, The thermal conductivity coefficient of the current iteration step. The coordinates are in the Cartesian coordinate system. For time.

[0012] In one implementation, in step S4, the objective function is:

[0013] in, To measure the amount of temperature data, , The number of inversion parameters, For the first One inversion parameter, For the first A calculated temperature value, For the first The smooth temperature value after noise reduction.

[0014] In one implementation, the search direction is determined in step S5 as follows: Calculate the conjugate coefficient :

[0015] when hour, ; Determine the search direction :

[0016] when hour, ; in, Let be the gradient vector of the objective function with respect to the thermal conductivity coefficient.

[0017] In one implementation, the gradient vector The components are:

[0018] in, The first derivative of the objective function with respect to the thermal conductivity coefficient; For the first One inversion parameter; For the first One calculated temperature value; For the first The smooth temperature value after noise reduction.

[0019] In one implementation, in step S5, the optimal step size Determined by the following formula:

[0020] in, This is the vector of sensitivity coefficients of the temperature field to the thermal conductivity coefficient; For the first One calculated temperature value; For the first The smooth temperature value after noise reduction; Indicates the search direction.

[0021] In one implementation, in step S6, the thermal conductivity coefficient is updated as follows:

[0022] in, To achieve the optimal step size, For the search direction, This represents the thermal conductivity coefficient for the current iteration step.

[0023] The beneficial effects of this application are as follows: 1. The design method proposed in this application has strong noise resistance and high identification accuracy. It innovatively applies discrete wavelet transform to experimental data preprocessing, which can efficiently extract real temperature change signals from strong noise background, providing "clean" input for solving the inverse problem, significantly reducing the inversion error caused by noise, and improving the final identification accuracy of the thermal conductivity coefficient.

[0024] 2. The inversion process of this application is stable and avoids non-physical solutions. The conjugate gradient method is used as the core optimizer for the inverse problem. This method not only converges quickly, but more importantly, its optimization path is more reliable, effectively escaping local optima and completely avoiding non-physical results such as negative thermal conductivity coefficients during iteration, thus ensuring the robustness of the solution process and the physical meaning of the solution.

[0025] 3. The method described in this application is highly practical and widely applicable. By combining advanced data processing technology with a physics-guided optimization algorithm, a complete and automated identification process is formed. This method has relatively relaxed requirements on the quality of experimental data, is suitable for identifying the thermophysical parameters of various complex heating conditions and multiple materials, and has broad engineering application prospects. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating one implementation of the temperature-dependent thermal conductivity coefficient identification method based on experimental data and optimized inversion in this application. Figure 2 This is a comparative diagram of experimental data before and after wavelet denoising in an embodiment of this application; Figure 3 This is a graph showing the inversion and iteration results of the thermal conductivity coefficient in an embodiment of this application; Figure 4 This is a comparison chart of the inversion and prediction results based on the thermal conductivity coefficient identification value in this application embodiment. Detailed Implementation

[0027] The technical solution of this application will be clearly and completely described below with reference to specific embodiments. However, those skilled in the art will understand that the embodiments described below are only some embodiments of this application, not all embodiments, and are only used to illustrate this application, and should not be regarded as limiting the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0028] Noise is inevitably mixed into the temperature data obtained from experiments. The problem of inverting the thermal conductivity coefficient is inherently ill-posed, and noise is amplified dramatically during the inversion process, causing the identification results to deviate significantly from the true value or even diverge iteratively. Existing inversion methods have two shortcomings in dealing with the above problems: First, there is a lack of effective experimental data preprocessing methods, and noise directly participates in the inversion calculation; second, the optimization algorithm is inappropriately selected. The Levenberg-Marquardt method is prone to matrix singularity or ill-conditioned problems when solving the sensitivity coefficient matrix, causing the updated thermal conductivity coefficient to have a negative value, which violates the physical nature of heat diffusion. At the same time, this method is prone to getting trapped in local optima.

[0029] This application addresses both input data quality and algorithm stability simultaneously, constructing a complete process for identifying the thermal conductivity coefficient with temperature variations. At the data input end, discrete wavelet transform is used to decompose the noisy temperature signal into multiple scales. Utilizing the difference in amplitude characteristics between noise and the true signal in the wavelet domain, high-frequency noise components are filtered out through thresholding, retaining the low-frequency trend reflecting the true temperature change. Smooth temperature data obtained through wavelet reconstruction is then used as the inversion input. At the inversion optimization end, the conjugate gradient method is introduced to replace the traditional LM method. Leveraging the conjugate gradient method's advantage of conjugate property in determining the search direction, the iterative path can effectively traverse the high-curvature "valley" region of the objective function, reducing the risk of getting trapped in local optima. Simultaneously, the conjugate gradient method determines the optimal step size through linear search, and the update process does not involve matrix inversion, avoiding numerical instability caused by matrix singularities. This ensures that the thermal conductivity coefficient remains positive throughout the iteration process, satisfying physical constraints.

[0030] In one specific implementation, this application provides a method for identifying the temperature-dependent thermal conductivity coefficient based on experimental data and optimized inversion, as shown in the attached figure. Figure 1 As shown, it includes the following steps: Step S1: Wavelet Denoising Preprocessing of Experimental Data. The noisy temperature time series data acquired in the experiment is denoised using discrete wavelet transform. Specifically, the Coiflet wavelet function is used as the basis function to perform multi-scale decomposition of the signal. By setting an appropriate threshold, the wavelet coefficients are processed, retaining low-frequency approximation coefficients that represent the true temperature change trend, while suppressing or filtering out high-frequency detail coefficients dominated by noise. Finally, smoothed temperature data after denoising is obtained through wavelet reconstruction. This step provides high-quality, low-noise input for subsequent inverse problem solving.

[0031] Step S2: Initialization. Given an initial guess of the thermal conductivity coefficient as a function of temperature. (Usually, measurements taken at room temperature are selected), and the maximum permissible error of the convergence criterion is set. And set the number of iterations. .

[0032] Step S3: Solve the forward heat conduction problem. Based on the current iteration step... Corresponding thermal conductivity The two-dimensional heat conduction equation shown in equation (1) is solved using the finite element method, and the corresponding temperature field distribution is calculated. .

[0033] (1) In the formula, For temperature, For material density, For the specific heat capacity of the material, The thermal conductivity coefficient of the current iteration step. The coordinates are in the Cartesian coordinate system. For time.

[0034] Step S4: Convergence assessment. Calculate the objective function using equation (2). And determine whether the objective function is less than the maximum permissible error. If convergence is achieved, the current thermal conductivity coefficient will be output. This serves as the final identification result; otherwise, proceed to step S5. (2) In the formula, To measure the amount of temperature data, , For the amount of inversion data, For the first One inversion parameter, For the first A calculated temperature value, For the first The smooth temperature value after noise reduction.

[0035] Step S5: Determine the search direction based on the conjugate gradient method. This step is one of the core improvements of this application. Considering that the conjugate gradient method is an efficient optimization algorithm, its search direction has conjugate properties, which can more effectively cross the "valley" of the objective function, thereby greatly reducing the risk of getting trapped in a local optimum. Furthermore, since the conjugate gradient method updates the solution through linear search in the determined search direction, its iterative process is more stable and can effectively avoid the matrix singularity or ill-conditioned problems that may occur in the LM method, thereby avoiding the non-physical situation of the heat conduction coefficient being updated to a negative value. Therefore, this application introduces the conjugate gradient method, and first calculates the conjugate coefficient using the following formula (3). : (3) In the formula, The first derivative of the objective function with respect to the thermal conductivity coefficient is expressed as shown in equation (4): (4) Then, the iterative search direction is determined by calculating the following equation (5). : (5) The optimal step size is obtained by calculating using equation (6). : (6) Among them, the sensitivity coefficient It was obtained by the method of complex variable differentiation.

[0036] Step S6: Update the thermal conductivity coefficient. Based on the search direction determined in step S5. and the optimal step size obtained through linear search The thermal conductivity coefficient is updated according to the following formula: (6) Subsequently, Then return to step S3 for the next iteration, until the convergence condition is met in step S4.

[0037] Example (1) Preprocessing data: The fourth-order Coiflet wavelet function was used as the basis function, and the number of decomposition layers was set to 5 to perform multi-scale decomposition of the signal. Then, the Bayesian method was used, and the median was selected as the threshold rule to process the wavelet coefficients. The low-frequency approximation coefficients that represent the true temperature change trend were retained, while the high-frequency detail coefficients dominated by noise were suppressed or filtered out. Finally, the denoised smooth temperature data was obtained by wavelet reconstruction. The experimental data and the data after noise reduction are compared in the attached figure. Figure 2 As shown.

[0038] (2) Set the initial guess value of thermal conductivity The corresponding temperature range is 300K~1500K, with a temperature point set every 100K, for a total of 13 discrete temperature points. All values ​​are initially set to 0.1W / (m²) based on ambient temperature measurements. K); Set the maximum permissible error for the convergence criterion. Current iteration step And then begin the inversion calculation of the thermal conductivity coefficient.

[0039] (3) Based on the current iteration step Corresponding thermal conductivity For each temperature point, a virtual value is assigned. For small perturbations, perform heat conduction calculations to obtain the corresponding temperature field. .

[0040] (4) Calculate the objective function using formula (2). ,judge The requirement was not met, so we proceeded to step (5) to perform the calculation.

[0041] (5) Using the given formulas (3)-(6) above, calculate the current iteration step. Corresponding search direction and optimal step size .

[0042] (6) Update the iteration step using formula (7). Corresponding thermal conductivity Return to step (3) and continue iterating.

[0043] After 75 iterations, the calculation met the convergence condition, and the change history of the thermal conductivity coefficient was retrieved. As attached Figure 3 As shown, the thermal conductivity curve identified by the method of this application is smooth and has a clear physical meaning. Based on The temperature inversion results obtained from the heat conduction simulation are attached. Figure 4 As shown in the left figure, the inversion results agree very well with the experimental results. Meanwhile, to verify the inverted thermal conductivity coefficient... robustness, based on Heat conduction simulations were performed on another set of experiments, and the comparison between the predicted results and the experimental data is attached. Figure 4 As shown in the right figure, the predicted value and the experimental measurement value are in good agreement.

[0044] Although the embodiments of this application have been described above in conjunction with the accompanying drawings, this application is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of this application, and these are all within the scope of protection of this application.

Claims

1. A method for identifying the temperature-dependent thermal conductivity coefficient based on experimental data and optimized inversion, characterized in that, Includes the following steps: Step S1: Perform wavelet denoising preprocessing on the noisy temperature time series data collected in the experiment to obtain smooth temperature data after denoising; Step S2: Set the initial guess value of the thermal conductivity coefficient as it changes with temperature, the maximum allowable error of the convergence criterion, and the initial value of the number of iteration steps; Step S3: Based on the heat conduction coefficient of the current iteration step, solve the heat conduction control equation to obtain the corresponding calculated temperature field; Step S4: Based on the calculated temperature field and the smoothed temperature data after noise reduction, calculate the objective function value and determine whether the objective function value is less than the maximum allowable error. If yes, determine convergence and output the current thermal conductivity coefficient as the final identification result; otherwise, continue to step S5. Step S5: Based on the conjugate gradient method, determine the search direction and optimal step size of the current iteration step according to the gradient information of the objective function with respect to the thermal conductivity coefficient; Step S6: Update the thermal conductivity coefficient according to the search direction and the optimal step size, and increase the iteration step number by 1, then return to step S3.

2. The method for identifying the thermal conductivity coefficient with temperature based on experimental data and optimized inversion according to claim 1, characterized in that, Step S1 specifically includes: The Coiflet wavelet function is used as the basis function to perform multi-scale decomposition on the noisy temperature time series data to obtain wavelet coefficients. The wavelet coefficients are processed to retain low-frequency approximation coefficients and suppress or filter out high-frequency detail coefficients. The noise-reduced, smooth temperature data is obtained through wavelet reconstruction.

3. The method for identifying the thermal conductivity coefficient with temperature based on experimental data and optimized inversion according to claim 2, characterized in that, When processing the wavelet coefficients, a Bayesian method is used, with the median as the threshold rule.

4. The method for identifying the temperature-dependent thermal conductivity coefficient based on experimental data and optimized inversion according to claim 1, characterized in that, In step S2, the initial guess value of the thermal conductivity coefficient is set as the measured value of the thermal conductivity coefficient at room temperature.

5. The method for identifying the thermal conductivity coefficient with temperature based on experimental data and optimization inversion according to claim 1, characterized in that, In step S3, the heat conduction control equation is: in, For temperature, For material density, For the specific heat capacity of the material, The thermal conductivity coefficient of the current iteration step. The coordinates are in the Cartesian coordinate system. For time.

6. The method for identifying the temperature-dependent thermal conductivity coefficient based on experimental data and optimized inversion according to claim 1, characterized in that, In step S4, the objective function is: in, To measure the amount of temperature data, , The number of inversion parameters, For the first One inversion parameter, For the first A calculated temperature value, For the first The smooth temperature value after noise reduction.

7. The method for identifying the thermal conductivity coefficient with temperature based on experimental data and optimization inversion according to claim 1, characterized in that, In step S5, the search direction is determined as follows: Calculate the conjugate coefficient : when hour, ; Determine the search direction : when hour, ; in, Let be the gradient vector of the objective function with respect to the thermal conductivity coefficient.

8. The method for identifying the thermal conductivity coefficient with temperature based on experimental data and optimization inversion according to claim 7, characterized in that, The gradient vector The components are: in, The first derivative of the objective function with respect to the thermal conductivity coefficient; For the first One inversion parameter; For the first One calculated temperature value; For the first The smooth temperature value after noise reduction.

9. The method for identifying the thermal conductivity coefficient with temperature based on experimental data and optimization inversion according to claim 7, characterized in that, In step S5, the optimal step size Determined by the following formula: in, This is the vector of sensitivity coefficients of the temperature field to the thermal conductivity coefficient; For the first One calculated temperature value; For the first The smooth temperature value after noise reduction; Indicates the search direction.

10. The method for identifying the thermal conductivity coefficient with temperature based on experimental data and optimization inversion according to claim 1, characterized in that, In step S6, the thermal conductivity coefficient is updated as follows: in, To achieve the optimal step size, For the search direction, This represents the thermal conductivity coefficient for the current iteration step.

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