Thermophysical parameter identification method, device, medium and system based on sensitivity analysis adaptive temperature interval division

Abstract

The application discloses a thermal physical parameter identification method and device based on sensitivity analysis adaptive temperature interval division, a medium and a system, and belongs to the field of thermal physical parameter identification.The method comprises the following steps: step a, initial setting, defining an initial temperature zone according to the temperature range of experimental data, uniformly dividing the entire temperature zone into a plurality of small intervals, and determining a to-be-identified parameter vector K; step b, calculating a temperature field under a given condition based on the to-be-identified parameter vector; step c, calculating a sensitivity index, and aggregating the sensitivity index according to the temperature interval; step d, optimizing and adjusting interval division according to the sensitivity index, and determining an optimal interval division scheme; step e, after a new interval division scheme is generated, verifying the new interval division scheme by using experimental data, and calculating a covariance matrix of parameter estimation to quantify the uncertainty of each identification parameter; if a termination condition is met, the method ends; otherwise, the method returns to step c.The application improves identification accuracy, reliability, robustness and calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of thermophysical parameter identification, and more specifically, to a method, device, medium, and system for thermophysical parameter identification based on sensitivity analysis and adaptive temperature range division. Background Technology

[0002] Effective prediction of the thermal environment inside high-speed aircraft cabins and the heat-bearing capacity of aero-engines and rocket engine combustion chambers depends on two factors: accurate simulation of heat flow on the aircraft surface and combustion chamber walls, and accurate determination of the thermal properties of heat-insulating materials. Currently, most engineering methods for determining the thermal conductivity of materials assume that the thermal conductivity is constant or a known function of temperature variation, employing methods such as steady-state methods, laser methods, and sensitivity methods for parameter identification.

[0003] When the variation of thermal conductivity with temperature is unknown, the thermal conductivity value of the material is usually discretized into temperature intervals, and the value of thermal conductivity in each temperature interval is identified using methods such as the fractional-half method, complex variable differentiation, and genetic algorithms based on the measurement results of the internal or boundary temperature fields of the material. However, in practical engineering applications, it has been found that, because the identification problem is ill-posed, large numerical oscillations may occur in the identification results when the measurement error is large or when there is a certain difference between the calculation model and the actual physical model.

[0004] The drawback of existing techniques is that they divide the entire temperature range uniformly or empirically into several segments and assign a thermal conductivity value to be identified for each segment. This division method does not consider the identifiability between parameters. If the experimental data of adjacent temperature segments show very similar sensitivity patterns to these two parameters (i.e., strong correlation), the inverse problem itself is ill-conditioned. Furthermore, the penalty function method is a passive constraint handling approach. When constraints are violated, it penalizes the solution by reducing its fitness, but it does not actively guide the search towards a healthier parameter space. Sometimes, a solution that satisfies all constraints but has unreasonable parameter values ​​may be selected because of a slightly smaller fitting error, thus masking the ill-conditioned nature of the inverse problem itself. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, device, medium and system for identifying thermophysical parameters based on sensitivity analysis and adaptive temperature range division, which improves accuracy, reliability, robustness and computational efficiency.

[0006] The objective of this invention is achieved through the following solution: A method for identifying thermophysical parameters based on sensitivity analysis and adaptive temperature range division includes the following steps: Step a, initial setup: Define the initial temperature zone based on the temperature range of the experimental data. Divide the entire temperature range into m smaller intervals, and assume that the thermal conductivity of each interval is constant. Then the parameter vector to be identified is ,in It is the transpose symbol; Step b, based on the parameter vector to be identified Calculate the given The temperature field T(x,t) under the given conditions; Step c, calculate the sensitivity index based on the polymerization sensitivity index within the temperature range; Step d: Based on the sensitivity index, optimize and adjust the interval division to determine the optimal interval division scheme; Step e: After generating the new interval partitioning scheme, verify it using experimental data. And calculate the covariance matrix of the parameter estimates to quantize each identification parameter. The uncertainty is calculated; if the termination condition is met, the process ends; otherwise, proceed to step c.

[0007] Furthermore, in step c, the sensitivity index is specifically calculated using the following function formula:

[0008] T represents temperature, x represents location coordinates, t represents time, and sensitivity s characterizes the cumulative response of the temperature field gradient across the entire domain.

[0009] Further, in step d, the interval division is optimized and adjusted according to the sensitivity index to determine the optimal interval division scheme, which specifically includes the following sub-steps: For intervals where the sensitivity index is 10% below the average level, merge them with adjacent high-sensitivity intervals and do not identify them separately; or, if the interval is physically important, check whether the experimental data are sufficient in that temperature range and increase the excitation.

[0010] Furthermore, the termination condition is specifically an improvement in uncertainty or reaching the maximum number of iterations.

[0011] A thermal property parameter identification device based on sensitivity analysis and adaptive temperature range division includes: a processor and a memory, wherein the memory stores a computer program, and when the computer program is loaded by the processor, it executes the thermal property parameter identification method based on sensitivity analysis and adaptive temperature range division as described above.

[0012] A computer-readable storage medium storing a computer program that, when loaded by a processor, executes the thermophysical parameter identification method based on sensitivity analysis and adaptive temperature range division as described in any of the preceding claims.

[0013] A thermal property parameter identification system based on sensitivity analysis and adaptive temperature range division includes the thermal property parameter identification device based on sensitivity analysis and adaptive temperature range division as described above.

[0014] The beneficial effects of this invention include: (1) The present invention improves the identification accuracy and reliability: by decoupling the parameters, results with clearer physical meaning and less uncertainty are obtained.

[0015] (2) This invention enhances the robustness of the inversion process by reducing the sensitivity of the results to measurement noise. Specifically, by analyzing the uncertainty of the parameter sensitivity vector under different partitioning schemes and iteratively optimizing the intervals, the strong correlation of parameters is eliminated, making the parameters in each interval independent and distinguishable. The influence of data noise is limited to the local area and will not be amplified or propagated.

[0016] (3) This invention improves computational efficiency by avoiding ineffective searches in ill-conditioned problems and guiding the optimization algorithm to converge quickly. Specifically, a more reasonable temperature range is obtained through the adaptive temperature range division method, avoiding the strong correlation of parameter sensitivity between adjacent temperature ranges, and the corresponding thermophysical parameters are more identifiable. Therefore, the identification computation efficiency is improved, and ineffective searches are avoided. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram illustrating the identification of thermal conductivity coefficients according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the calculation process of an embodiment of the present invention; Figure 3 This is a temperature map of the measuring points with added white noise in an embodiment of the present invention. Detailed Implementation

[0019] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.

[0020] The schematic diagram for determining the thermal conductivity of a material is shown below. Figure 1As shown, the heat transfer problem can be simplified to a one-dimensional heat transfer problem. The heat flow or temperature value at the left and right boundary points are used as boundary conditions, and the heat transfer coefficient is identified by using the temperature history of the boundary points or internal measuring points.

[0021] Without loss of generality, assume that thermal flux boundary conditions are given at the left and right boundaries of the material. x i (i=1, P) represents the location of the temperature measurement point, and P represents the number of measurement points. Then:

[0022] Boundary conditions: x =0: ; x = L : ; Initial conditions: t =0: ; Observation equation: , i=1, P ; in, ρ For material density, C p For the specific heat of the material, This is a temperature measurement value. v ( t () represents the noise level, and T represents the temperature. k ( T () represents the thermal conductivity value. x For position coordinates, Let Q be the initial temperature at the left boundary and Q be the boundary heat flux. Let L be the heat flux at the left boundary at time t, and L be the thickness of the material. Let be the heat flow at the right boundary at time t.

[0023] Typical calculations of the forward problem of heat conduction are performed given boundary conditions and... k ( T The temperature value in equation (1) under noise-free conditions was calculated using numerical methods. T The inverse problem of heat conduction is... k ( T In the absence of an unknown value, based on equation (1) and the temperature measurement values ​​in the observation equation... Determine k ( T ). Due to usually k ( T If the function form of the temperature 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. Figure 1 middle, (0, t() represents the boundary temperature data at any time t on the left boundary of z=0. (0, t () represents the boundary heat flux density at any time t on the left boundary at z=0. ( L , t () represents the boundary temperature data at time t on the right boundary of z=L. ( L , t ) represents the boundary heat flux density at time t on the right boundary of z=L, z represents the spatial coordinate (axial direction), z∈[0,L], L represents the thickness of the material, and P represents the different measurement point locations selected.

[0024] Thermophysical parameter identification is an important inverse problem in heat transfer, with the core objective of inferring internal thermal properties (such as thermal conductivity and specific heat capacity) from observed system data (e.g., temperature distribution). Unlike direct problems (finding the response given parameters), identification problems are essentially "cause-and-effect," meaning inferring the cause from the result, which inherently makes the problem complex and challenging. A typical characteristic of this type of problem is "ill-posedness"—the solution is extremely sensitive to small errors in the measurement data, which can lead to results that deviate significantly from the true values. For example, sensor noise or insufficient measurement point distribution can render the parameter inversion results unreliable.

[0025] To address these issues, the engineering community often uses surrogate models to simplify the inversion process. For example, assuming a functional relationship (such as a quadratic or power function) between thermophysical parameters and temperature transforms the continuous parameter distribution into an identification problem with a small number of undetermined coefficients. While this method reduces noise interference, it relies excessively on prior assumptions. If the actual material properties do not conform to the physical laws of the model function, it may introduce systematic biases. For instance, if the thermal conductivity of a material undergoes a sudden change near the phase transition point, and the surrogate model assumes global smoothness, it can lead to non-negligible errors in the inversion results. Furthermore, while piecewise functions or multi-parameter joint inversion can improve local accuracy, the increased number of parameters may exacerbate ill-conditioning, further amplifying the impact of measurement noise.

[0026] In the identification of thermal conductivity of materials, the accuracy of parameter identification varies significantly in different temperature ranges. Furthermore, parameters (such as thermal conductivity) in adjacent temperature ranges are prone to strong correlation due to similar physical mechanisms or strong correlation of measurement data, which leads to unstable inversion results.

[0027] To address this problem, the inventors of this invention propose a method for rationally dividing the temperature range based on sensitivity analysis. The specific method and logic are as follows: This invention specifically defines the following sensitivity function:

[0028] x represents the location coordinates, which characterize the cumulative response of the temperature field gradient (the rate of temperature change in space and time) over the entire domain. A region with high sensitivity implies: (1) High sensitivity: The temperature field is more sensitive to changes in thermal property parameters (such as thermal conductivity k). Small perturbations in parameters can lead to significant changes in the temperature field, making it easier to capture by experimental data.

[0029] (2) High identification potential: Within this range, parameter inversion is more robust to noise and has higher identification accuracy.

[0030] Based on the above definition of the sensitivity function, a further provision is provided for a thermal property parameter identification scheme based on sensitivity analysis and adaptive temperature range division, including corresponding methods, equipment, media, and systems. In a preferred embodiment, a method for thermal property parameter identification based on sensitivity analysis and adaptive temperature range division is specifically provided, such as... Figure 2 As shown, it includes the following steps: Step a, initial setup: Define the initial temperature zone based on the temperature range of the experimental data. Divide the entire temperature range into m smaller intervals, assuming that the thermal conductivity is constant within each interval. Then the parameter vector to be identified is ,in This is the transpose symbol.

[0031] Step b, optimize the parameter vector to be identified Calculate the given The temperature field T(x,t) is given.

[0032] Step c, calculate the sensitivity index according to formula (2), based on the polymerization sensitivity index within the temperature range. Step d: Determine the optimal interval division scheme. For intervals with very low sensitivity, consider merging them with adjacent high-sensitivity intervals instead of identifying them separately. Alternatively, if the interval is physically important, check whether the experimental data for that temperature range is sufficient and consider increasing the excitation.

[0033] Step e, after generating the new interval partitioning scheme, uses experimental data to verify and identify the... Based on the final sensitivity matrix, the covariance matrix of the parameter estimates is calculated to quantify each identification parameter. The uncertainty is calculated. If the termination condition is met (the uncertainty is significantly improved, or the maximum number of iterations is reached), the process ends; otherwise, it jumps to step c.

[0034] The technical effects of the embodiments of the present invention are verified as follows: Using the method of this invention, a typical heat-resistant material identification example is provided, where the thermal conductivity coefficient changes significantly with temperature. = 1300 kg / m 3 , C p = 110 0J / (kg·K), L = 0.02 m, T K = 278 K, surface emissivity is 0.76. A constant heat flux of 50,000 W / m is given at the left end of the material. 2 The right end is insulated. A measuring point is located inside the material. L =0.01m. The temperature at the measuring point can be calculated using simulation, such as... Figure 3 As shown.

[0035] Using the temperatures at both ends as temperature boundary conditions, the thermal conductivity can be identified using the intermediate measuring point. Initial parameter values ​​were all selected as 1.0. After optimization and iteration, Table 1 presents the identification results, and Table 2 presents the covariance of the identification results.

[0036] Table 1. Comparison of Identification Results with True Values ​​(Considering White Noise)

[0037] Table 2. Covariance Matrix of Identification Results (Unit: W² / (m²·K²))

[0038] Table 3 shows the thermal conductivity and corresponding temperature ranges obtained using the adaptive method, while Table 4 shows the Cramer-Rhodes boundary at this point. It can be seen that the maximum variance at this point is 0.0279, while the maximum variance of the standard method is 0.2007. The accuracy of the adaptive partitioning identification results has been significantly improved.

[0039] Table 3. Covariance Matrix of Identification Results Based on Adaptive Temperature Zoning

[0040] Table 4. Cramé-Rhodes covariance matrix based on adaptive temperature zoning identification parameters (unit: W² / (m²·K²))

[0041] It should be noted that, within the scope of protection defined in the claims of this invention, the following embodiments can be combined and / or extended or replaced in any logical manner from the above specific embodiments, such as the disclosed technical principles, disclosed technical features or implicitly disclosed technical features.

[0042] Example 1 A method for identifying thermophysical parameters based on sensitivity analysis and adaptive temperature range division includes the following steps: Step a, initial setup: Define the initial temperature zone based on the temperature range of the experimental data. Divide the entire temperature range into m smaller intervals, and assume that the thermal conductivity of each interval is constant. Then the parameter vector to be identified is ,in It is the transpose symbol; Step b, based on the parameter vector to be identified Calculate the given The temperature field T(x,t) under the given conditions; Step c, calculate the sensitivity index based on the polymerization sensitivity index within the temperature range; Step d: Based on the sensitivity index, optimize and adjust the interval division to determine the optimal interval division scheme; Step e: After generating the new interval partitioning scheme, verify it using experimental data. And calculate the covariance matrix of the parameter estimates to quantize each identification parameter. The uncertainty is calculated; if the termination condition is met, the process ends; otherwise, proceed to step c.

[0043] Example 2 Based on Example 1, in step c, the sensitivity index is specifically calculated using the following function formula:

[0044] T represents temperature, x represents location coordinates, t represents time, and sensitivity s characterizes the cumulative response of the temperature field gradient across the entire domain.

[0045] Example 3 Based on Example 1, in step d, the interval division is optimized and adjusted according to the sensitivity index to determine the optimal interval division scheme, which specifically includes the following sub-steps: For intervals where the sensitivity index is 10% below the average level, merge them with adjacent high-sensitivity intervals and do not identify them separately; or, if the interval is physically important, check whether the experimental data are sufficient in that temperature range and increase the excitation.

[0046] Example 4 Based on Example 1, the termination condition is specifically the improvement of uncertainty or reaching the maximum number of iterations.

[0047] Example 5 A thermal property parameter identification device based on sensitivity analysis and adaptive temperature range division includes a processor and a memory. The memory stores a computer program. When the computer program is loaded by the processor, it executes the thermal property parameter identification method based on sensitivity analysis and adaptive temperature range division as described in any one of Embodiments 1 to 4.

[0048] Example 6 A computer-readable storage medium storing a computer program, which, when loaded by a processor, executes the thermophysical parameter identification method based on sensitivity analysis and adaptive temperature range division as described in any one of Embodiments 1 to 4.

[0049] Example 7 A thermal property parameter identification system based on sensitivity analysis and adaptive temperature range division includes the thermal property parameter identification device based on sensitivity analysis and adaptive temperature range division as described in Example 5.

[0050] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0051] According to one aspect of the present invention, a computer program product or computer program is provided, the computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and executes the computer instructions, causing the computer device to perform the methods provided in the various optional implementations described above.

[0052] In another aspect, embodiments of the present invention also provide a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods described in the above embodiments.

Claims

1. A method for identifying thermophysical parameters based on sensitivity analysis and adaptive temperature range division, characterized in that, Includes the following steps: Step a, initial setup: Define the initial temperature zone based on the temperature range of the experimental data. Divide the entire temperature range into m smaller intervals, and assume that the thermal conductivity of each interval is constant. Then the parameter vector to be identified is ,in It is the transpose symbol; Step b, based on the parameter vector to be identified Calculate the given The temperature field T(x,t) under the given conditions; Step c, calculate the sensitivity index based on the polymerization sensitivity index within the temperature range; Step d: Based on the sensitivity index, optimize and adjust the interval division to determine the optimal interval division scheme; Step e: After generating the new interval partitioning scheme, verify it using experimental data. And calculate the covariance matrix of the parameter estimates to quantize each identification parameter. The uncertainty is calculated; if the termination condition is met, the process ends; otherwise, proceed to step c. In step c, the sensitivity index is specifically calculated using the following function formula: T represents temperature, x represents location coordinates, t represents time, and sensitivity s characterizes the cumulative response of the temperature field gradient over the entire domain; In step d, the interval division is optimized and adjusted according to the sensitivity index to determine the optimal interval division scheme, which specifically includes the following sub-steps: For intervals where the sensitivity index is 10% below the average level, merge them with adjacent high-sensitivity intervals and do not identify them separately; or, if the interval is physically important, check whether the experimental data are sufficient in that temperature range and increase the excitation.

2. The method for identifying thermophysical parameters based on adaptive temperature range division using sensitivity analysis according to claim 1, characterized in that, The termination condition is specifically the improvement of uncertainty or reaching the maximum number of iterations.

3. A thermophysical parameter identification device based on sensitivity analysis and adaptive temperature range division, characterized in that, include: The processor and memory, wherein the memory stores a computer program that, when loaded by the processor, executes the thermophysical parameter identification method based on sensitivity analysis and adaptive temperature range division as described in any one of claims 1 to 2.

4. A computer-readable storage medium, characterized in that, A computer program is stored in a readable storage medium, which, when loaded by a processor, executes the thermophysical parameter identification method based on sensitivity analysis and adaptive temperature range division as described in any one of claims 1 to 2.

5. A system for identifying thermal property parameters based on sensitivity analysis and adaptive temperature range division, characterized in that, This includes the thermophysical parameter identification device based on sensitivity analysis and adaptive temperature range division as described in claim 3.

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