A low-temperature heating simulation temperature compensation method based on thermal conductivity coefficient optimization

Abstract

The application relates to a low-temperature heating simulation temperature compensation method based on optimization of a thermal conductivity coefficient, and particularly relates to the field of low-temperature heating simulation. A high-fidelity digital twin model is constructed by intelligently optimizing a key equivalent thermal conductivity coefficient. The core lies in that a single reference experiment data is used to automatically determine a group of compensation parameters with clear physical meanings, so that the simulation model can accurately reflect the actual complex heat transfer mechanism. The model obtained in this way can accurately predict the temperature field of equipment under a wide range of low-temperature and heating power working conditions, and can change the traditional heating design depending on experience into accurate design based on reliable digital prediction, thereby significantly improving the efficiency, reliability and safety of a thermal control system design.

Description

Technical Field

[0001] This invention relates to the field of low-temperature heating simulation, and more specifically, to a low-temperature heating simulation temperature compensation method based on thermal conductivity optimization. Background Technology

[0002] In industries such as power, chemical, and energy storage, many critical pieces of equipment, such as tanks in gas-insulated metal-enclosed switchgear, transformer bushings, and various process storage tanks, need to operate in harsh low-temperature environments. To prevent the internal medium from liquefying or solidifying and to ensure normal start-up and safe operation of the equipment, external electric heating systems are typically installed. The core design of this system lies in accurately predicting the temperature distribution of the equipment under specific low-temperature environments and heating power, especially the steady-state and transient temperatures of critical components, in order to determine the optimal heating power, layout scheme, and insulation design. Currently, this prediction work relies heavily on computer-aided engineering simulation. Technology; however, high-precision simulation faces severe challenges due to the complexity of actual products. Heated equipment typically has a multi-layered heterogeneous structure, including an internal metal shell, an external insulating and heat-preserving material layer, and a possible internal fluid domain, such as sulfur hexafluoride gas. In actual working conditions, complex contact thermal resistance, material anisotropy, and non-uniform heat flow caused by localized strip heaters are also involved. These factors together lead to a significant deviation between the prediction results of simulation models based on standard material property parameters from material handbooks and physical experimental measurements, making it difficult to directly guide accurate engineering design and safety assessment.

[0003] The fundamental challenge causing these deviations lies in the efficient and accurate calibration of the equivalent thermal properties of key materials in the simulation model. Current technical practices mainly rely on engineers' experience, employing manual trial and error to repeatedly adjust parameters such as the thermal conductivity of individual materials in the simulation software in order to make the simulation results approximate a specific set of experimental data. This method of single-variable sequential adjustment is not only inefficient but also heavily reliant on personal experience, making it difficult to coordinate the coupling effects between multiple parameters and almost impossible to find the globally optimal parameter combination. More importantly, the parameter set obtained by manual calibration is usually only valid for specific experimental conditions and lacks clear physical meaning support. Therefore, it cannot be reliably extended to other unverified operating conditions such as ambient temperatures and different heating powers, resulting in a significant reduction in the predictive ability and practical value of the simulation. Due to the lack of a systematic, automated, and physically consistent multi-parameter reverse calibration method, the construction of high-fidelity digital simulation models for low-temperature electric heating processes of complex equipment has become a long-standing technical bottleneck that has not been effectively resolved. This forces engineering designs to rely on costly and time-consuming physical prototypes for repeated testing, and may even lead to safety hazards such as local overheating damage or overall insufficient heating of equipment due to inaccurate predictions. Summary of the Invention

[0004] This invention addresses the technical problems existing in the prior art by providing a low-temperature heating simulation temperature compensation method based on thermal conductivity optimization, thereby solving the problems mentioned in the background art.

[0005] The technical solution of this invention to solve the above-mentioned technical problems is as follows: specifically, it includes the following steps: Step S1: Based on the three-dimensional geometric structure of the target device, establish a parametric simulation model, wherein the thermal conductivity of the insulation layer located between the heating tape and the metal shell of the target device is set as the first adjustable parameter, and the thermal conductivity of the metal shell of the target device is set as the second adjustable parameter; construct an automated interface program and input the values ​​of the first and second adjustable parameters, calculate the parametric simulation model through the simulation solver of the automated interface program, and output the simulation temperature data of multiple preset monitoring points on the target device; Step S2: Obtain experimental temperature data of the target device under a single benchmark condition; define a composite loss function, which includes a data fitting term characterizing the difference between the simulated temperature data and the experimental temperature data, and a penalty term constraining the first and second adjustable parameters; with the goal of minimizing the composite loss function, automatically iteratively adjust the values ​​of the first and second adjustable parameters using an optimization algorithm, and perform cyclic simulation calculations through an automated interface program until the optimization termination condition is met, thus obtaining the optimal values ​​of the first and second adjustable parameters; Step S3: Use the optimal first and second adjustable parameter values ​​as fixed parameters and assign them to the parameterized simulation model to obtain the calibrated simulation model; In the calibrated simulation model, input the boundary conditions of a verification condition that are different from the benchmark condition, perform simulation calculations, and obtain the predicted temperature data of multiple monitoring points under the verification condition. Step S4: Encapsulate the calibrated simulation model into a digital twin model that can be used for engineering design; by inputting arbitrary ambient temperature and heating power conditions into the digital twin model, obtain the temperature field distribution of the target device under the corresponding conditions.

[0006] In a preferred embodiment, the specific process of establishing the parametric simulation model in step S1 is as follows: First, based on the three-dimensional geometric model of the target equipment in the computer-aided design, a parametric simulation model for thermal simulation is constructed. The parametric simulation model must fully include the geometric structure and initial material properties of the heating cable, the insulation layer located between the heating cable and the metal shell of the equipment, the metal shell of the target equipment, and the external insulation layer. Secondly, in the definition of the parametric simulation model, the thermal conductivity of the insulating layer is identified separately and set as a variable that can be accessed and modified by an external program. The variable that can be accessed and modified by an external program is defined as the first adjustable parameter. At the same time, the thermal conductivity of the material properties of the metal casing of the target device is also identified separately and set as another variable that can be accessed and modified by an external program. This other variable that can be accessed and modified by an external program is defined as the second adjustable parameter. The above settings allow the numerical solution results of the parametric simulation model to change as the specific values ​​of the first and second adjustable parameters change.

[0007] In a preferred embodiment, the process of calculating the parameterized simulation model through the simulation solver of the automated interface program and outputting the simulation temperature data of multiple preset monitoring points on the target device is as follows: The automation interface program is configured to receive a specific set of input values ​​for the first adjustable parameter and the second adjustable parameter; Subsequently, the automated interface program automatically writes the received set of specific input values ​​for the first and second adjustable parameters into the corresponding material property definition files of the parametric simulation model. Next, the automated interface program automatically calls and drives the integrated thermal simulation solver, loads the parameterized simulation model with updated parameters, and performs a complete steady-state heat conduction simulation calculation under pre-set boundary conditions. The thermal simulation solver performs numerical solutions based on the updated material properties, geometry, and boundary conditions, generating a simulation result file containing complete temperature field data. After the simulation calculation is completed, the automated interface program automatically parses the simulation result file generated by the thermal simulation solver and accurately extracts the temperature values ​​at multiple predefined monitoring points on the target device based on the preset spatial coordinate position information. Following the preset monitoring point index order, the temperature values ​​are bound to the corresponding spatial coordinate location information and organized into a sequence format. The final output is a structured simulation temperature dataset containing temperature data from all monitoring points.

[0008] In a preferred embodiment, step S2 involves acquiring experimental temperature data of the target device under a single reference operating condition. The specific process is as follows: A representative single reference condition is determined, which is defined by a specific low ambient temperature value and a specific electric heating power value; the steady thermal state of the single reference condition is reproduced on the experimental platform of the target equipment. Temperature sensors are used to measure the temperature at multiple pre-defined geometric locations on the surface of the target device. The spatial coordinates of these multiple geometric locations correspond one-to-one with the spatial coordinates of multiple pre-defined monitoring points in the parametric simulation model. Record the steady-state temperature readings when all preset geometric locations reach thermal equilibrium under a single benchmark condition, and arrange and store these temperature readings in the order of their corresponding monitoring point numbers to form a structured benchmark experimental temperature dataset.

[0009] In a preferred embodiment, the specific process of defining the composite loss function is as follows: The composite loss function is obtained by weighted summation of the data fitting term and the physical constraint penalty term; The data fitting term is used to quantify the overall deviation between the simulated temperature dataset and the benchmark experimental temperature dataset. The calculation method is as follows: First, calculate the absolute value of the difference between the simulated temperature value in the simulated temperature dataset and the corresponding experimental temperature value in the benchmark experimental temperature dataset at each monitoring point; then, divide the absolute value difference of each monitoring point by a common temperature normalization reference value, which is set as the average temperature value of the benchmark experimental temperature dataset, to obtain the relative error of that monitoring point. Next, the relative error of each monitoring point is raised to a specified power, and the result is multiplied by a weighting coefficient pre-assigned to that monitoring point. Finally, the weighted results of all monitoring points are summed to obtain the total value of the data fitting term. The physical constraint penalty term is used to guide the optimization direction of the first adjustable parameter and the second adjustable parameter. The physical constraint penalty term includes a first penalty factor for the first adjustable parameter and a second penalty factor for the second adjustable parameter. The function of the first penalty factor is to generate a penalty amount proportional to the degree of excess when the value of the first adjustable parameter is greater than the initial thermal conductivity attribute value set for the insulation layer in step S1; otherwise, the penalty amount is zero. The function of the second penalty factor is to generate a penalty amount proportional to the degree of deficiency when the value of the second adjustable parameter is less than the initial thermal conductivity attribute value set for the metal casing of the device in step S1; otherwise, the penalty amount is zero.

[0010] In a preferred embodiment, the specific process of automatically iteratively adjusting the values ​​of the first and second adjustable parameters using an optimization algorithm and performing cyclic simulation calculations through an automated interface program is as follows: First, a global optimization algorithm is selected, and the initial search range of the first and second adjustable parameters, the control parameters of the global optimization algorithm itself, and the optimization termination condition are set. The global optimization algorithm is started, and in its first iteration, the global optimization algorithm generates a set of candidate parameter value combinations consisting of a specific value of the first and second adjustable parameters within the search range. Then, the global optimization algorithm passes the candidate parameter value combinations to the automation interface program; based on the received candidate parameter value combinations, the automation interface program drives the thermal simulation solver to perform a complete steady-state heat conduction simulation calculation on the parameterized simulation model and returns the corresponding simulation temperature dataset. Subsequently, based on the returned simulation temperature dataset, the obtained benchmark experimental temperature dataset, and the current candidate parameter value combination, the composite loss function value under the current candidate parameter value combination is calculated; The global optimization algorithm receives the composite loss function value as feedback and generates the next set of candidate parameter value combinations in the search space according to its internal strategy. Then it repeats the complete steps from passing the candidate parameter value combination to the automated interface program to calculating the composite loss function value under the new candidate parameter value combination. This loop continues until the preset optimization termination condition is reached. When the loop terminates, the values ​​of the first and second adjustable parameters that minimize the composite loss function value in all iterations are recorded as the final optimal values ​​of the first and second adjustable parameters.

[0011] In a preferred embodiment, the specific process of using the optimal first adjustable parameter value and the second adjustable parameter value as fixed parameters in step S3 to obtain the calibrated simulation model is as follows: First, obtain the optimal first adjustable parameter value and the optimal second adjustable parameter value from the output of step S2; Secondly, in the computer, open the model definition file of the established parametric simulation model, find the parameter definition position in the model definition file that represents the thermal conductivity of the insulation layer located between the heat tracing cable and the metal shell of the equipment, and replace the original variable placeholder at the parameter definition position with the optimal first adjustable parameter value, so that the thermal conductivity property of the insulation layer changes from an adjustable state to a fixed value state. At the same time, in the same model definition file, find the parameter definition location representing the thermal conductivity of the target device's metal casing, and replace the original variable placeholder at the parameter definition location with the optimal second adjustable parameter value, so that the thermal conductivity property of the device's metal casing changes from an adjustable state to a fixed value state. After the replacement operation is completed, the modified model definition file is saved. At this point, all material properties in the parametric simulation model, including the thermal conductivity of the insulation layer and the thermal conductivity of the metal shell of the equipment, have become fixed constants that cannot be changed, thus generating a calibrated simulation model with completely determined internal parameters.

[0012] In a preferred embodiment, the specific process of obtaining the predicted temperature data of multiple monitoring points under the verification condition is as follows: First, prepare a list of verification conditions in advance. The list of verification conditions contains at least one verification condition. Each verification condition is defined by a combination of a specified set of ambient temperature values ​​and electric heating power values. At least one of the ambient temperature values ​​and electric heating power values ​​of these verification conditions is different from the corresponding value of the single benchmark condition in step S2. Secondly, for each verification condition in the verification condition list, the following automated calculation process is executed: read the ambient temperature value and electric heating power value of the current verification condition from the verification condition list, use these two values ​​as boundary conditions, and input them into the boundary condition setting module of the calibrated simulation model; Next, the thermal simulation solver associated with the calibrated simulation model is invoked, and the thermal simulation solver is driven to load the calibrated simulation model with the boundary conditions of the current verification working condition set, and a complete steady-state heat conduction simulation calculation is performed. After the simulation calculation is completed, the temperature values ​​at multiple preset monitoring points on the target equipment are extracted. These temperature values ​​are the prediction results of the calibrated simulation model for the temperature distribution of the equipment under the current verification working condition. For each verification condition in the verification condition list, the complete process of reading the ambient temperature value and electric heating power value of the current verification condition as boundary conditions and obtaining the prediction result is repeated until all verification conditions in the verification condition list have been calculated. Finally, the predicted temperature values ​​of all monitoring points obtained under each verification condition are organized in the order of the monitoring point numbers and associated with their corresponding verification condition identification information to form a structured verification predicted temperature dataset. Based on the final structured verification and predicted temperature dataset, a generalization ability qualification judgment is performed. The generalization ability qualification judgment is completed by comparing and analyzing the verification and predicted temperature dataset with the experimental verification temperature data under the corresponding verification conditions obtained in advance through experiments. The comparison and analysis includes calculating the error statistics between the predicted temperature and the experimental verification temperature. If the error statistics meet the preset accuracy acceptance criteria, the calibrated simulation model is judged to have passed the generalization ability qualification judgment.

[0013] In a preferred embodiment, the specific process of encapsulating the calibrated simulation model into a digital twin model that can be used for engineering design in step S4 is as follows: For the calibrated simulation model that has passed the generalization ability qualification, the model asset encapsulation operation is performed. The model asset encapsulation operation includes two sub-processes: model packaging and interface standardization. The model packaging sub-process is as follows: the calibrated simulation model and all model definition files and computing resources on which it depends for running are integrated and packaged together with the thermal simulation solver executable program and its dependent library files necessary for running the calibrated simulation model to form an independent and portable digital twin model application software package. The interface standardization sub-process is as follows: Define a clear and unified external call interface specification for the digital twin model application software package. This interface specification stipulates that users only need to provide two input parameters to the digital twin model: the ambient temperature value representing the external cold source conditions for the target device to operate, and the heating power value representing the total heat output of the electric heat tracing system. At the same time, the interface specification also stipulates that the standard output of the digital twin model is structured full-scene temperature field data. This full-scene temperature field data includes the temperature values ​​and spatial coordinate information of all spatial nodes in the computational domain, as well as a formatted field data file that can be used to generate a temperature distribution cloud map. After the model asset encapsulation operation is completed, a fully encapsulated digital twin model with standardized input and output interfaces is generated.

[0014] In a preferred embodiment, the specific process of obtaining the temperature field distribution of the target device under corresponding conditions by inputting arbitrary ambient temperature and heating power conditions into the digital twin model is as follows: First, a working condition mapping engine is built and deployed. The working condition mapping engine is a control program used to schedule simulation calculations and process input and output. It is pre-configured to be able to call and drive the encapsulated digital twin model. Secondly, when engineering designers need to make predictions using digital twin models, they submit a working condition query request containing a specified ambient temperature value and a specified heating power value to the working condition mapping engine. After receiving the query request, the working condition mapping engine starts its internal automated solution pipeline, which performs the following operations in sequence: First, it parses the working condition query request and extracts the specified ambient temperature value and heating power value. Second, the extracted ambient temperature and heating power values ​​are automatically injected into the boundary condition configuration inside the digital twin model through the standardized input interface of the digital twin model to set the specific working conditions of the current simulation calculation. Third, the thermal simulation solver integrated within the digital twin model is automatically started, driving the solver to load the digital twin model with the current working condition boundary conditions set through the injection operation, and to perform a complete heat conduction simulation calculation. After the simulation calculation is completed, the working condition field mapping engine automatically extracts the complete temperature field data from the original result file generated by the thermal simulation solver and converts it into the structured full-scene temperature field data format defined by the interface specification. Finally, the operating condition mapping engine returns the formatted temperature field distribution data as a response to the operating condition query request to the engineering designers.

[0015] The beneficial effects of this invention are as follows: by intelligently optimizing the key equivalent thermal conductivity, a high-fidelity digital twin model is constructed; its core lies in using a single benchmark experimental data to automatically determine a set of compensation parameters with clear physical meaning, so that the simulation model can accurately reflect the actual complex heat transfer mechanism; the model obtained thereby can predict the temperature field of the equipment under a wide range of low temperature and heating power conditions with high precision, transforming the traditional experience-based heating design into a precise design based on reliable digital prediction, significantly improving the efficiency, reliability and safety of thermal control system design. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0018] In the description of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0019] In the description of this application, the term "for example" is used to mean "used as an example, illustration, or description." Any embodiment described as "for example" in this application is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is provided to enable any person skilled in the art to make and use the invention. Details are set forth in the following description for purposes of explanation. It should be understood that those skilled in the art will recognize that the invention can be made without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid obscuring the description of the invention with unnecessary detail. Therefore, the invention is not intended to be limited to the embodiments shown, but is consistent with the broadest scope of the principles and features disclosed in this application.

[0020] Example 1 This embodiment provides, for example Figure 1 The method for temperature compensation in low-temperature heating simulation based on thermal conductivity optimization is shown, and specifically includes the following steps: Step S1: Based on the three-dimensional geometric structure of the target device, establish a parametric simulation model, wherein the thermal conductivity of the insulation layer located between the heating tape and the metal shell of the target device is set as the first adjustable parameter, and the thermal conductivity of the metal shell of the target device is set as the second adjustable parameter; construct an automated interface program and input the values ​​of the first and second adjustable parameters, calculate the parametric simulation model through the simulation solver of the automated interface program, and output the simulation temperature data of multiple preset monitoring points on the target device; Step S2: Obtain experimental temperature data of the target device under a single benchmark condition; define a composite loss function, which includes a data fitting term characterizing the difference between the simulated temperature data and the experimental temperature data, and a penalty term constraining the first and second adjustable parameters; with the goal of minimizing the composite loss function, automatically iteratively adjust the values ​​of the first and second adjustable parameters using an optimization algorithm, and perform cyclic simulation calculations through an automated interface program until the optimization termination condition is met, thus obtaining the optimal values ​​of the first and second adjustable parameters; Step S3: Use the optimal first adjustable parameter value and the second adjustable parameter value as fixed parameters and assign them to the parameterized simulation model to obtain the calibrated simulation model; In the calibrated simulation model, input the boundary conditions of at least one verification condition that is different from the benchmark condition, perform simulation calculations, and obtain the predicted temperature data of multiple monitoring points under the verification condition. Step S4: Encapsulate the calibrated simulation model into a digital twin model that can be used for engineering design; by inputting arbitrary ambient temperature and heating power conditions into the digital twin model, obtain the temperature field distribution of the target device under the corresponding conditions.

[0021] In this embodiment, the specific process of establishing the parameterized simulation model in step S1 is as follows: First, based on the three-dimensional geometric model of the target equipment in the computer-aided design, a parametric simulation model for thermal simulation is constructed. The parametric simulation model must fully include the geometric structure and initial material properties of the heating cable, the insulation layer located between the heating cable and the equipment's metal shell, the target equipment's metal shell, and the external insulation layer. The specific process of constructing the parametric simulation model is as follows: In the computer-aided engineering software, the three-dimensional geometric model of the target equipment is imported, and physical materials are assigned to the corresponding geometries of the heating cable, insulation layer, equipment's metal shell, and external insulation layer, respectively, and a computational mesh for finite element or finite volume calculations is generated. Among them, the insulation layer is given the initial thermal conductivity properties of silicone-based materials, and the equipment's metal shell is given the initial thermal conductivity properties of aluminum alloy or steel. Secondly, in the definition of the parametric simulation model, the thermal conductivity of the insulation layer's material properties is separately identified and set as a variable that can be accessed and modified by an external program. This variable is defined as the first adjustable parameter. The specific process of separately identifying and setting a variable that can be accessed and modified by an external program is as follows: in the material property database or model input file of the simulation software, the numerical field representing the thermal conductivity of the insulation layer is replaced with a variable placeholder marked by a specific string, such as setting it to "{k_insulation}", and it is ensured that the software provides an application programming interface or scripting function that allows an external program to dynamically modify this value by specifying the variable name "k_insulation". Meanwhile, the thermal conductivity of the material properties of the target device's metal casing is also separately identified and set as another variable that can be accessed and modified by an external program. This other variable that can be accessed and modified by an external program is defined as the second adjustable parameter. The setting process is similar to that of the first adjustable parameter, except that the numerical field representing the thermal conductivity of the device's metal casing is replaced with another variable placeholder marked by a specific string, such as "{k_shell}". Through the above settings, the numerical solution results of the parameterized simulation model can change with the specific values ​​of the first and second adjustable parameters. The parameterized simulation model is calculated using the simulation solver of the automated interface program, and the simulated temperature data of multiple preset monitoring points on the target device is output. The specific process is as follows: The automation interface program is configured to receive a specific set of input values ​​for a first adjustable parameter and a second adjustable parameter; the automation interface program is typically written in Python, MATLAB or C# and contains modules for receiving parameters, driving simulation and parsing data; Subsequently, the automated interface program automatically writes the received set of specific input values ​​for the first and second adjustable parameters into the corresponding material property definition files of the parametric simulation model. The writing process is as follows: the automated interface program opens the input file of the parametric simulation model or connects to the simulation process through the software API, finds the variable placeholders "{k_insulation}" and "{k_shell}", and replaces them with the two specific values ​​in the received set of specific input values. Next, the automated interface program automatically calls and drives the integrated thermal simulation solver, loads the parameterized simulation model with updated parameters, and performs a complete steady-state heat conduction simulation calculation under pre-set boundary conditions. The thermal simulation solver performs numerical solutions based on the updated material properties, geometry, and boundary conditions, generating a simulation result file containing complete temperature field data. The specific numerical solution process logic for a complete steady-state heat conduction simulation calculation is as follows: First, the thermal simulation solver reads the model file containing the updated first and second adjustable parameters. Then, based on Fourier's law and the law of conservation of energy, the thermal simulation solver constructs and solves the three-dimensional steady-state heat conduction control equation describing the temperature distribution within the computational domain. The form of this control equation is: the divergence of the heat flux density vector at any point in the computational domain is equal to the intensity of the internal volume heat source generated by the electric heating tape at that point. Here, the heat flux density vector is obtained by multiplying the temperature gradient at that point by the negative value of the material thermal conductivity. The material thermal conductivity is the current first adjustable parameter value in the insulation layer region and the current second adjustable parameter value in the metal shell region of the equipment. The specific process of steady-state heat conduction simulation calculation is as follows: After the thermal simulation solver, such as the steady-state thermal analysis module of ANSYS Mechanical or the "Heat Conduction" physics interface of COMSOL, is invoked, its thermal simulation solver reads the updated model file. The process of the thermal simulation solver numerically discretizing the governing equations is as follows: using the finite element method, the overall computational domain, including the heating tape, insulation layer, equipment metal shell, and insulation layer, is discretized into a large number of elements with specific geometric shapes. Within each element, it is assumed that the temperature distribution can be determined by the nodal temperature values ​​and a set of selected shape functions. A linear combination is used to approximate the equation. This approximate expression is then substituted into the three-dimensional steady-state heat conduction control equation, and the weighted residual method is applied to transform the continuous partial differential equation into a large, sparse system of linear algebraic equations with respect to all nodal temperature unknowns. The coefficient matrix of this system is affected by the material properties of the elements, where the coefficients corresponding to the insulating layer elements are related to the first adjustable parameter value, and the coefficients corresponding to the metal shell elements of the equipment are related to the second adjustable parameter value. The right-hand side of the system is determined by the applied boundary conditions, including the convective heat transfer conditions corresponding to the low-temperature environment and the heat generation rate conditions corresponding to the electric heating tape. Then, an iterative solver, such as the conjugate gradient method or the algebraic multigrid method, is invoked to perform the solution calculation. Taking the conjugate gradient method as an example, the specific calculation process of the iterative solver is as follows: using a set of initially estimated nodal temperature values ​​as the starting point of the iteration, the algorithm searches along the new conjugate direction determined by the current residual vector and the previous search direction in each iteration, calculates an optimal step size, thereby updating the nodal temperature value vector and calculating a new residual vector; this process is repeated until the convergence criterion is met. The condition for convergence is that the L2 norm of the residuals of the equation system is less than a preset convergence threshold, which is usually set to 1.0e-6. The basis for setting the convergence threshold of 1.0e-6 is to balance engineering accuracy and computational efficiency, to ensure that the relative error of the temperature solution is small enough, and to avoid unnecessary iterations. After the calculation is completed, the iterative solver writes the temperature values ​​and heat flux density data of all nodes in the entire computational domain into the result file. The simulation result file format is a standard format such as ".rst", ".odb" or ".vtk". The process of writing the result file is as follows: the iterative solver encodes and stores the temperature values ​​of all nodes obtained after the final iteration convergence, in the order of node number, along with the spatial coordinate information of the nodes and the connection relationship of the elements, according to the selected standard format, to form the simulation result file. After the simulation calculation is completed, the automated interface program automatically parses the simulation result file generated by the thermal simulation solver. Based on the preset spatial coordinate location information, it accurately extracts the temperature values ​​at multiple predefined monitoring points on the target device. The parsing and extraction process is as follows: the automated interface program calls a parsing library that matches the simulation result file format and reads the node coordinates and temperature data arrays from the simulation result file. Then, the program matches the spatial coordinates of the preset multiple monitoring points, such as (0,0,600), (0,0,300), etc., with the node coordinates in the simulation result file. The matching algorithm calculates the Euclidean distance between the preset coordinates and all node coordinates in the simulation result file, selects the node with the smallest distance as the corresponding monitoring point, and extracts the temperature value of that node. The maximum allowable tolerance distance threshold for matching is set to 1.0e-3 meters. Following a preset monitoring point index order, temperature values ​​are bound to their corresponding spatial coordinates and organized into a sequence format. The final output is a structured simulation temperature dataset containing temperature data from all monitoring points. The sequence format is as follows: the extracted temperature values ​​are arranged into a one-dimensional array or list according to the monitoring point index from 1 to N; simultaneously, another list of the same length is generated, storing the corresponding spatial coordinate information in the same order. These two lists together constitute a structured dataset, with the data format being list pairs or dictionaries, so that it can be directly read by subsequent optimization algorithms.

[0022] In this embodiment, it is particularly important to explain step S2, which involves obtaining experimental temperature data of the target device under a single reference operating condition. The specific process is as follows: A representative single reference condition is determined, defined by a specific low ambient temperature and a specific electric heating power. The single reference condition is preferably the most demanding low-temperature heating condition in the intended application, such as an ambient temperature of -40 degrees Celsius and a heating power of 880 watts, to obtain significant temperature gradient and thermal balance data, providing a highly sensitive reference for parameter calibration. The stable thermal state of the single reference condition is reproduced on the physical prototype or experimental platform of the target device. The reproduction process is carried out in a temperature-controlled environmental test chamber to ensure uniform and constant ambient temperature. The criterion for determining a stable thermal state is that the temperature readings at all preset geometric locations change by less than 0.1 degrees Celsius over a continuous period. Temperature sensors are used to measure the temperature at multiple pre-defined geometric locations on the surface of the target device. The spatial coordinates of these multiple geometric locations correspond one-to-one with the spatial coordinates of multiple pre-defined monitoring points in the parametric simulation model. The temperature sensors are thermocouples or resistance temperature detectors (RTDs), and their placement must be ensured by a high-precision positioning device to guarantee that the coordinate deviation from the monitoring points in the simulation model is less than 1 mm, in order to ensure data comparability. Record the steady-state temperature readings when all preset geometric locations reach thermal equilibrium under a single benchmark condition, and arrange and store these temperature readings in the order of their corresponding monitoring point numbers to form a structured benchmark experimental temperature dataset for subsequent optimization calculations. The optimization goal is to find a set of values ​​for the first and second adjustable parameters such that when these values ​​are input into the automated interface program built in step S1, the weighted absolute relative error between the calculated simulation temperature dataset and the benchmark experimental temperature dataset is minimized. At the same time, it ensures that the first adjustable parameter is shifted towards the direction of the initial thermal conductivity property of the material below the insulation layer, and the second adjustable parameter is shifted towards the direction of the initial thermal conductivity property of the material above the metal shell of the device, so as to build high thermal resistance and compensate for thermal imbalance in the parametric simulation model. The specific process of defining the composite loss function is as follows: The composite loss function is obtained by weighted summation of the data fitting term and the physical constraint penalty term; The data fitting term is used to quantify the overall deviation between the simulated temperature dataset and the benchmark experimental temperature dataset. The calculation method is as follows: First, calculate the absolute value of the difference between the simulated temperature value in the simulated temperature dataset and the corresponding experimental temperature value in the benchmark experimental temperature dataset at each monitoring point. Then, divide the absolute difference at each monitoring point by a common temperature normalization reference value, which is set as the average temperature value of the benchmark experimental temperature dataset, to obtain the relative error at that monitoring point. The process of calculating the relative error aims to eliminate the influence of the absolute temperature dimension, making the optimization process focus more on the relative accuracy of the temperature distribution pattern rather than the absolute numerical value. Next, the relative error of each monitoring point is raised to a specified power, and the result is multiplied by a weighting coefficient pre-assigned to that monitoring point. The power in the specified power operation is typically between 1 and 2, for example, 1.5. When the power is 1, the optimization is linearly sensitive to the error; when the power is 2, the optimization punishes larger errors more severely. This design allows for a balance between smoothing errors and highlighting critical errors. The weighting coefficients are assigned based on the engineering importance of the monitoring points. Higher weighting coefficients, such as 0.2, can be assigned to areas prone to overheating or critical temperature measurement points, while lower weights, such as 0.05, are assigned to less important areas. The sum of all weighting coefficients is 1. Finally, the weighted results of all monitoring points are summed to obtain the total value of the data fitting term. The physical constraint penalty term is used to guide the optimization direction of the first adjustable parameter and the second adjustable parameter. The physical constraint penalty term includes a first penalty factor for the first adjustable parameter and a second penalty factor for the second adjustable parameter. The function of the first penalty factor is to generate a penalty amount proportional to the degree of excess when the value of the first adjustable parameter is greater than the initial thermal conductivity attribute value set for the insulation layer in step S1; otherwise, the penalty amount is zero. The penalty amount proportional to the degree of excess is specifically calculated as follows: subtract the initial thermal conductivity attribute value of the insulation layer from the value of the first adjustable parameter, divide the difference by the initial thermal conductivity attribute value to obtain the relative excess amount, and then multiply it by a preset first penalty factor. The second penalty factor functions as follows: when the value of the second adjustable parameter is less than the initial thermal conductivity attribute value set for the metal casing of the equipment in step S1, a penalty amount proportional to the degree of deficiency is generated; otherwise, the penalty amount is zero. The penalty amount proportional to the degree of deficiency is calculated as follows: subtract the value of the second adjustable parameter from the initial thermal conductivity attribute value of the metal casing of the equipment, divide the difference by the initial thermal conductivity attribute value to obtain the relative deficiency amount, and then multiply it by a preset second penalty factor. The first penalty factor and the second penalty factor are used to adjust the strength of the physical constraints, with typical values ​​between 0.1 and 10. They are determined through trial and error or prior knowledge to ensure that the physical constraints can effectively guide the direction during the optimization process without completely suppressing the role of the data fitting term. The specific process of automatically iteratively adjusting the values ​​of the first and second adjustable parameters using an optimization algorithm, and performing cyclic simulation calculations through an automated interface program, is as follows: First, a global optimization algorithm is selected, and the initial search ranges of the first and second adjustable parameters, the control parameters of the global optimization algorithm itself, and the optimization termination condition are set. The global optimization algorithm is preferably a Bayesian optimization algorithm or a genetic algorithm. The Bayesian optimization algorithm is suitable for simulation scenarios with high computational costs. It guides parameter search by constructing a surrogate model and can efficiently find the global optimum. The initial search range of the first adjustable parameter is set to be between 0.1 and 1.5 times the initial thermal conductivity attribute value of the material. The initial search range of the second adjustable parameter is between 1 and 50 times the initial thermal conductivity attribute value of the material. The threshold set in the optimization termination condition, that is, the threshold for the improvement of the composite loss function value, is usually set to a very small positive number, such as 0.001. The global optimization algorithm is started. In its first iteration, the global optimization algorithm generates a set of candidate parameter value combinations within the search range, consisting of a specific value of the first adjustable parameter and a specific value of the second adjustable parameter. Then, the global optimization algorithm passes the candidate parameter value combinations to the automation interface program; based on the received candidate parameter value combinations, the automation interface program drives the thermal simulation solver to perform a complete steady-state heat conduction simulation calculation on the parameterized simulation model and returns the corresponding simulation temperature dataset. Subsequently, based on the returned simulation temperature dataset, the obtained benchmark experimental temperature dataset, and the current candidate parameter value combination, the composite loss function value under the current candidate parameter value combination is calculated; The global optimization algorithm receives the composite loss function value as feedback and, according to its internal strategy, generates the next set of candidate parameter value combinations in the search space. It then repeats the entire process from passing the candidate parameter value combinations to the automated interface program to calculating the composite loss function value under the new candidate parameter value combinations. Taking the Bayesian optimization algorithm as an example, its internal strategy is as follows: based on all evaluated candidate parameter value combinations and their corresponding composite loss function values, a probabilistic surrogate model (usually a Gaussian process model) is constructed regarding the relationship between parameters and the loss function. Then, the algorithm optimizes a sampling function (such as the desired improvement function) and selects the next most promising candidate parameter value combination for evaluation in the search space to reduce the loss function; this process is repeated cyclically. This cycle continues until the preset optimization termination condition is reached. The optimization termination condition includes reaching the maximum number of iterations or the improvement of the composite loss function value in multiple consecutive iterations being less than a set threshold. When the loop terminates, the values ​​of the first and second adjustable parameters that minimize the composite loss function value throughout all iterations are recorded as the final optimal values ​​of the first and second adjustable parameters. The final optimal parameter values ​​have clear physical meanings: the optimal first adjustable parameter value is usually significantly lower than the initial material property value of the insulation layer, reflecting the increase in equivalent thermal resistance caused by factors such as contact thermal resistance in actual assembly; the optimal second adjustable parameter value is usually significantly higher than the initial material property value of the equipment's metal shell, effectively compensating for the thermal conductivity, internal convection, and thermal short-circuit effects of the metal shell itself that were not accurately simulated in the parametric simulation model, thus enabling the calibrated parametric simulation model to more accurately predict the temperature field under a wide range of operating conditions.

[0023] In this embodiment, it is specifically necessary to explain the process in step S3, where the optimal first and second adjustable parameter values ​​are used as fixed parameters and assigned to the parameterized simulation model to obtain the calibrated simulation model. First, obtain the optimal first adjustable parameter value and the optimal second adjustable parameter value from the output of step S2; Secondly, in the computer, open the model definition file of the established parametric simulation model. Locate the parameter definition position in the model definition file that represents the thermal conductivity of the insulation layer located between the heating cable and the metal shell of the equipment. Replace the original variable placeholder at this parameter definition position with the optimal first adjustable parameter value, so that the thermal conductivity property of the insulation layer changes from an adjustable state to a fixed value state. The model definition file is usually a text-formatted input file, such as ANSYS APDL script file, ABAQUS INP file, or COMSOL MPH file. The operation of finding the parameter definition position and replacing it is implemented by writing a script program. This script program reads the optimal first adjustable parameter value, searches for a specific keyword or variable name (such as "{k_insulation}") representing the thermal conductivity of the insulation layer in the model definition file, and replaces the entire matched field with the specific numeric string of the optimal parameter value. Simultaneously, within the same model definition file, the parameter definition location representing the thermal conductivity of the target device's metal casing is located. The original variable placeholder at this parameter definition location is replaced with the optimal second adjustable parameter value, thus changing the thermal conductivity property of the device's metal casing from an adjustable state to a fixed value state. This operation is similar to the process of replacing insulation layer parameters, and is executed by the same script program. It searches for another specific keyword or variable name (such as "{k_shell}") representing the thermal conductivity of the metal casing and performs a value replacement. After the replacement operation is completed, save the modified model definition file. At this point, all material properties in the parametric simulation model, including the thermal conductivity of the insulation layer and the thermal conductivity of the equipment's metal casing, have become unchangeable fixed constants. This generates a new simulation model with completely determined internal parameters, which is the calibrated simulation model. After generating the calibrated simulation model, a unique version identifier can be assigned to it, and the updated model definition file can be archived to distinguish it from the original parametric simulation model and the numerous intermediate versions generated during the optimization process. The specific process for obtaining predicted temperature data from multiple monitoring points under verification conditions is as follows: First, prepare a list of verification conditions in advance. The list of verification conditions contains at least one verification condition. Each verification condition is defined by a combination of a specified set of ambient temperature values ​​and electric heating power values. At least one of the ambient temperature values ​​and electric heating power values ​​of these verification conditions is different from the corresponding value of the single benchmark condition in step S2. The list of verification conditions is usually stored in the computer as a table or array data structure. Each row or each element records the ambient temperature and heating power value of a certain condition. Secondly, for each verification condition in the verification condition list, the following automated calculation process is executed: read the ambient temperature value and electric heating power value of the current verification condition from the verification condition list, use these two values ​​as boundary conditions, and input them into the boundary condition setting module of the calibrated simulation model; Next, the thermal simulation solver associated with the calibrated simulation model is invoked, driving the thermal simulation solver to load the calibrated simulation model with the boundary conditions of the current verification condition set, and to perform a complete steady-state heat conduction simulation calculation. The specific process of the steady-state heat conduction simulation calculation, including the establishment of the governing equations, numerical discretization, and solution logic, is the same as the calculation process for the parameterized simulation model. The difference is that the material parameters (the first adjustable parameter and the second adjustable parameter) of the model used in this calculation are fixed at their optimal values, and the boundary conditions are the values ​​of the current verification condition. After the simulation calculation is completed, the temperature values ​​at multiple preset monitoring points on the target device are extracted by calling the result file parsing program. The extraction process is the same as the process of extracting simulation temperature data from the simulation result file, including parsing the result file, matching nodes according to preset coordinates, and reading temperature values. These temperature values ​​are the prediction results of the calibrated simulation model for the temperature distribution of the device under the current verification condition. For each verification condition in the verification condition list, the complete process of reading the ambient temperature value and electric heating power value of the current verification condition as boundary conditions and obtaining the prediction result is repeated until all verification conditions in the verification condition list have been calculated. Finally, the predicted temperature values ​​of all monitoring points obtained under each verification condition are organized in the order of the monitoring point numbers and associated with their corresponding verification condition identification information to form a structured verification predicted temperature dataset. Based on the final structured verification and predicted temperature dataset, a generalization ability qualification judgment is performed. The generalization ability qualification judgment is completed by comparing and analyzing the verification and predicted temperature dataset with the experimental verification temperature data under the corresponding verification conditions obtained in advance through experiments. The comparison and analysis includes calculating the error statistics between the predicted temperature and the experimental verification temperature. If the error statistics meet the preset accuracy acceptance criteria, the calibrated simulation model is judged to have passed the generalization ability qualification judgment.

[0024] In this embodiment, the specific process of encapsulating the calibrated simulation model into a digital twin model that can be used for engineering design in step S4 is as follows: For calibrated simulation models that pass the generalization ability assessment, a model asset encapsulation operation is performed. This operation includes two sub-processes: model packaging and interface standardization. The model packaging sub-process involves integrating and packaging the calibrated simulation model and all model definition files and computational resources it depends on, along with the executable program for the thermal simulation solver and its dependent library files necessary for running the calibrated simulation model, into an independent and portable digital twin model application software package. This packaging sub-process can be implemented using software containerization technology, such as packaging the calibrated simulation model, the thermal simulation solver, and its runtime environment into a Docker container image. The digital twin model application software package contains everything needed to run the simulation, ensuring consistent execution capabilities across different computing environments. The interface standardization sub-process is as follows: Define a clear and unified external call interface specification for the digital twin model application software package. This interface specification stipulates that external programs or users only need to provide two input parameters to the digital twin model: the ambient temperature value representing the external cold source conditions for the target device to operate, and the heating power value representing the total heat output of the electric heat tracing system. The interface specification is usually provided in the form of an application programming interface, such as defining a set of functions or service endpoints that receive the ambient temperature value and heating power value as input parameters and return structured data. At the same time, the interface specification also stipulates that the standard output of the digital twin model is structured full-scene temperature field data. This full-scene temperature field data includes the temperature values ​​and spatial coordinate information of all spatial nodes in the computational domain, as well as a formatted field data file that can be used to generate a temperature distribution cloud map. The structured full-scene temperature field data can be organized into a data structure in JavaScript object representation format, or a specific binary format file containing node temperature arrays, coordinate arrays, and metadata, to facilitate subsequent processing and visualization. After the model asset encapsulation operation is completed, a fully encapsulated digital twin model with standardized input and output interfaces is generated. As a software asset that can be deployed and executed independently, the optimal first and second adjustable parameter values ​​encapsulated in the digital twin model, as well as the verified physical model structure, are all fixed and can no longer be modified, ensuring the consistency and reliability of the digital twin model's predictive behavior. The specific process of obtaining the temperature field distribution of the target device under corresponding conditions by inputting arbitrary ambient temperature and heating power conditions into the digital twin model is as follows: First, build and deploy a working condition mapping engine. The working condition mapping engine is a control program used to schedule simulation calculations and process input and output. It is pre-configured to be able to call and drive the encapsulated digital twin model. The working condition mapping engine can be deployed on a local server or cloud computing platform. It is usually implemented as a resident microservice or background process that listens for and processes working condition query requests from the outside. Secondly, when engineering designers need to make predictions using digital twin models, they submit a condition query request to the condition mapping engine, which includes a specified ambient temperature value and a specified heating power value. The condition query request can be submitted through a graphical user interface form, command-line parameters, or a web application programming interface call, and it explicitly includes the specific ambient temperature value and heating power value that the user wants to simulate. After receiving the query request, the condition mapping engine starts its internal automated solution pipeline, which performs the following operations in sequence: First, it parses the condition query request and extracts the specified ambient temperature value and heating power value. The parsing process includes verifying the format and range of the input data to ensure that it is within a reasonable engineering value range. Second, the extracted ambient temperature and heating power values ​​are automatically injected into the boundary condition configuration inside the digital twin model through the standardized input interface of the digital twin model to set the specific working conditions of the current simulation calculation. The injection operation is completed by calling the standardized application programming interface provided by the digital twin model, or by modifying the configuration file template in the digital twin model application software package. Third, the integrated thermal simulation solver within the digital twin model is automatically launched, driving the solver to load the digital twin model with the current operating condition boundary conditions set through the injection operation, and execute a complete heat conduction simulation calculation. The specific process of a complete heat conduction simulation calculation is as follows: the integrated thermal simulation solver within the digital twin model is launched, and the model configuration with the updated current operating condition boundary conditions is read; since the material parameters of the digital twin model (the optimal first adjustable parameter value and the second adjustable parameter value) have been fixed during encapsulation, this simulation calculation will solve the three-dimensional steady-state heat conduction control equation based on these fixed optimal material parameters and the currently input operating condition boundary conditions; its solution logic is consistent with the core process of calculation for the parameterized simulation model and the calibrated simulation model, both involving the discretization of the control equation, the construction and iterative solution of the linear equation system, but the object of calculation here is the encapsulated, parameter-unchangeable digital twin model, and the boundary conditions are dynamically determined by the user's real-time query; the convergence threshold and the iterative solver settings use the preset values ​​when the model was encapsulated; After the simulation calculation is completed, the working condition field mapping engine automatically extracts the complete temperature field data from the original result file generated by the thermal simulation solver and converts it into a structured full-scene temperature field data format defined by the interface specification. The extraction and conversion process is completed by the result parser embedded in the working condition field mapping engine. This result parser can recognize the specific file format output by the thermal simulation solver, read the node temperature and coordinates, and reorganize the data according to the predefined JavaScript object representation or other structured formats. Finally, the operating condition mapping engine returns the formatted temperature field distribution data as a response to the operating condition query request to the engineering designers. The returned temperature field distribution data enables the engineering designers to immediately obtain the detailed thermal state of the target equipment under the specified operating conditions, including the specific temperature values ​​of each monitoring point and the temperature cloud maps of the overall and local areas. This provides an immediate and highly accurate digital basis for heating power decisions, thermal design verification, or operational safety assessments. The entire process, from submitting the query to obtaining the result, is fully automated and requires no manual intervention in the simulation software.

[0025] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0026] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0027] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0028] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0029] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0030] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0031] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A low-temperature heating simulation temperature compensation method based on thermal conductivity coefficient optimization, characterized in that, Specifically, the steps include the following: Step S1: Based on the three-dimensional geometric structure of the target device, establish a parametric simulation model, wherein the thermal conductivity of the insulation layer located between the heating tape and the metal shell of the target device is set as the first adjustable parameter, and the thermal conductivity of the metal shell of the target device is set as the second adjustable parameter; construct an automated interface program and input the values ​​of the first and second adjustable parameters, calculate the parametric simulation model through the simulation solver of the automated interface program, and output the simulation temperature data of multiple preset monitoring points on the target device to form a simulation temperature dataset; Step S2: Obtain experimental temperature data of the target device under a single benchmark operating condition to form a benchmark experimental temperature dataset; define a composite loss function, which includes a data fitting term characterizing the difference between the simulated temperature data and the experimental temperature data, and a penalty term constraining the first and second adjustable parameters; with the goal of minimizing the composite loss function, use an optimization algorithm to automatically iteratively adjust the values ​​of the first and second adjustable parameters, and perform cyclic simulation calculations through an automated interface program until the optimization termination condition is met, obtaining the optimal values ​​of the first and second adjustable parameters; the specific process of defining the composite loss function is as follows: The composite loss function is obtained by weighted summation of the data fitting term and the physical constraint penalty term; The data fitting term is used to quantify the overall deviation between the simulated temperature dataset and the benchmark experimental temperature dataset. The calculation method is as follows: First, calculate the absolute value of the difference between the simulated temperature value in the simulated temperature dataset and the corresponding experimental temperature value in the benchmark experimental temperature dataset at each monitoring point; then, divide the absolute value difference of each monitoring point by a common temperature normalization reference value, which is set as the average temperature value of the benchmark experimental temperature dataset, to obtain the relative error of that monitoring point. Next, the relative error of each monitoring point is raised to a specified power, and the result is multiplied by a weighting coefficient pre-assigned to that monitoring point. Finally, the weighted results of all monitoring points are summed to obtain the total value of the data fitting term. The physical constraint penalty term is used to guide the optimization direction of the first adjustable parameter and the second adjustable parameter. The physical constraint penalty term includes a first penalty factor for the first adjustable parameter and a second penalty factor for the second adjustable parameter. The function of the first penalty factor is to generate a penalty amount proportional to the degree of excess when the value of the first adjustable parameter is greater than the initial thermal conductivity attribute value set for the insulation layer in step S1; otherwise, the penalty amount is zero. The function of the second penalty factor is to generate a penalty amount proportional to the degree of deficiency when the value of the second adjustable parameter is less than the initial thermal conductivity attribute value set for the metal shell of the device in step S1; otherwise, the penalty amount is zero. Step S3: Use the optimal first and second adjustable parameter values ​​as fixed parameters and assign them to the parameterized simulation model to obtain the calibrated simulation model; In the calibrated simulation model, input the boundary conditions of a verification condition that are different from the benchmark condition, perform simulation calculations, and obtain the predicted temperature data of multiple monitoring points under the verification condition. Step S4: Encapsulate the calibrated simulation model into a digital twin model that can be used for engineering design; by inputting arbitrary ambient temperature and heating power conditions into the digital twin model, obtain the temperature field distribution of the target device under the corresponding conditions.

2. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 1, characterized in that: In step S1, the specific process of establishing the parametric simulation model is as follows: First, based on the three-dimensional geometric model of the target equipment in the computer-aided design, a parametric simulation model for thermal simulation is constructed. The parametric simulation model must fully include the geometric structure and initial material properties of the heating cable, the insulation layer located between the heating cable and the metal shell of the equipment, the metal shell of the target equipment, and the external insulation layer. Secondly, in the definition of the parametric simulation model, the thermal conductivity of the insulating layer is identified separately and set as a variable that can be accessed and modified by an external program. The variable that can be accessed and modified by an external program is defined as the first adjustable parameter. At the same time, the thermal conductivity of the material properties of the metal casing of the target device is also identified separately and set as another variable that can be accessed and modified by an external program. This other variable that can be accessed and modified by an external program is defined as the second adjustable parameter. The above settings allow the numerical solution results of the parametric simulation model to change as the specific values ​​of the first and second adjustable parameters change.

3. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 2, characterized in that: The simulation solver, which uses an automated interface program, calculates the parameterized simulation model and outputs the simulation temperature data for multiple preset monitoring points on the target device. The specific process is as follows: The automation interface program is configured to receive a specific set of input values ​​for the first adjustable parameter and the second adjustable parameter; Subsequently, the automated interface program automatically writes the received set of specific input values ​​for the first and second adjustable parameters into the corresponding material property definition files of the parametric simulation model. Next, the automated interface program automatically calls and drives the integrated thermal simulation solver, loads the parameterized simulation model with updated parameters, and performs a complete steady-state heat conduction simulation calculation under pre-set boundary conditions. The thermal simulation solver performs numerical solutions based on the updated material properties, geometry, and boundary conditions, generating a simulation result file containing complete temperature field data. After the simulation calculation is completed, the automated interface program automatically parses the simulation result file generated by the thermal simulation solver and accurately extracts the temperature values ​​at multiple predefined monitoring points on the target device based on the preset spatial coordinate position information. Following the preset monitoring point index order, the temperature values ​​are bound to the corresponding spatial coordinate location information and organized into a sequence format. The final output is a structured simulation temperature dataset containing temperature data from all monitoring points.

4. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 3, characterized in that: In step S2, the experimental temperature data of the target device under a single reference operating condition is obtained. The specific process is as follows: A single benchmark condition is determined, and the steady thermal state of the single benchmark condition is reproduced on the experimental platform of the target equipment. Temperature sensors are used to measure the temperature at multiple pre-defined geometric locations on the surface of the target device. The spatial coordinates of these multiple geometric locations correspond one-to-one with the spatial coordinates of multiple pre-defined monitoring points in the parametric simulation model. Record the steady-state temperature readings when all preset geometric locations reach thermal equilibrium under a single benchmark condition, and arrange and store these temperature readings in the order of their corresponding monitoring point numbers to form a structured benchmark experimental temperature dataset.

5. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 4, characterized in that: The specific process of automatically iteratively adjusting the values ​​of the first and second adjustable parameters using an optimization algorithm and performing cyclic simulation calculations through an automated interface program is as follows: First, a global optimization algorithm is selected, and the initial search range of the first and second adjustable parameters, the control parameters of the global optimization algorithm itself, and the optimization termination condition are set. The global optimization algorithm is started, and in its first iteration, the global optimization algorithm generates a set of candidate parameter value combinations consisting of a specific value of the first and second adjustable parameters within the search range. Then, the global optimization algorithm passes the candidate parameter value combinations to the automation interface program; based on the received candidate parameter value combinations, the automation interface program drives the thermal simulation solver to perform a complete steady-state heat conduction simulation calculation on the parameterized simulation model and returns the corresponding simulation temperature dataset. Subsequently, based on the returned simulation temperature dataset, the obtained benchmark experimental temperature dataset, and the current candidate parameter value combination, the composite loss function value under the current candidate parameter value combination is calculated; The global optimization algorithm receives the composite loss function value as feedback and generates the next set of candidate parameter value combinations in the search space according to its internal strategy. Then it repeats the complete steps from passing the candidate parameter value combination to the automated interface program to calculating the composite loss function value under the new candidate parameter value combination. This loop continues until the preset optimization termination condition is reached. When the loop terminates, the values ​​of the first and second adjustable parameters that minimize the composite loss function value in all iterations are recorded as the final optimal values ​​of the first and second adjustable parameters.

6. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 5, characterized in that: In step S3, the optimal first and second adjustable parameter values ​​are used as fixed parameters and assigned to the parameterized simulation model to obtain the calibrated simulation model. The specific process is as follows: First, obtain the optimal first adjustable parameter value and the optimal second adjustable parameter value from the output of step S2; Secondly, in the computer, open the model definition file of the established parametric simulation model, find the parameter definition position in the model definition file that represents the thermal conductivity of the insulation layer located between the heat tracing cable and the metal shell of the equipment, and replace the original variable placeholder at the parameter definition position with the optimal first adjustable parameter value, so that the thermal conductivity property of the insulation layer changes from an adjustable state to a fixed value state. At the same time, in the same model definition file, find the parameter definition location representing the thermal conductivity of the target device's metal casing, and replace the original variable placeholder at the parameter definition location with the optimal second adjustable parameter value, so that the thermal conductivity property of the device's metal casing changes from an adjustable state to a fixed value state. After the replacement operation is completed, the modified model definition file is saved. At this point, all material properties in the parametric simulation model, including the thermal conductivity of the insulation layer and the thermal conductivity of the metal shell of the equipment, have become fixed constants that cannot be changed, thus generating a calibrated simulation model with completely determined internal parameters.

7. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 6, characterized in that: The specific process for obtaining the predicted temperature data from multiple monitoring points under the verification condition is as follows: First, prepare a list of verification conditions in advance. The list of verification conditions contains at least one verification condition. Each verification condition is defined by a combination of a specified set of ambient temperature values ​​and electric heating power values. At least one of the ambient temperature values ​​and electric heating power values ​​of these verification conditions is different from the corresponding value of the single benchmark condition in step S2. Secondly, for each verification condition in the verification condition list, the following automated calculation process is executed: read the ambient temperature value and electric heating power value of the current verification condition from the verification condition list, use these two values ​​as boundary conditions, and input them into the boundary condition setting module of the calibrated simulation model; Next, the thermal simulation solver associated with the calibrated simulation model is invoked, and the thermal simulation solver is driven to load the calibrated simulation model with the boundary conditions of the current verification working condition set, and a complete steady-state heat conduction simulation calculation is performed. After the simulation calculation is completed, the temperature values ​​at multiple preset monitoring points on the target equipment are extracted. These temperature values ​​are the prediction results of the calibrated simulation model for the temperature distribution of the equipment under the current verification working condition. For each verification condition in the verification condition list, repeat the complete process from reading boundary conditions to obtaining prediction results until all verification conditions in the verification condition list have been calculated. Finally, the predicted temperature values ​​of all monitoring points obtained under each verification condition are organized in the order of the monitoring point numbers and associated with their corresponding verification condition identification information to form a structured verification predicted temperature dataset. Based on the final structured verification and predicted temperature dataset, a generalization ability qualification judgment is performed. The generalization ability qualification is determined by comparing and analyzing the verification predicted temperature dataset with the experimental verification temperature data under the corresponding verification conditions obtained in advance through experiments. The comparison and analysis includes calculating the error statistics between the predicted temperature and the experimental verification temperature. If the error statistics meet the preset accuracy acceptance criteria, the calibrated simulation model is determined to have passed the generalization ability qualification.

8. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 7, characterized in that: In step S4, the specific process of encapsulating the calibrated simulation model into a digital twin model that can be used for engineering design is as follows: For the calibrated simulation model that has passed the generalization ability qualification test, perform the model asset encapsulation operation, which includes two sub-processes: model packaging and interface standardization. The model packaging process is as follows: the calibrated simulation model and all model definition files and computing resources on which it depends for running, along with the thermal simulation solver executable program and its dependent library files necessary for running the calibrated simulation model, are integrated and packaged together to form an independent, portable digital twin model application software package. The interface standardization sub-process is as follows: Define a clear and unified external call interface specification for the digital twin model application software package. This interface specification stipulates that users only need to provide two input parameters to the digital twin model: the ambient temperature value representing the external cold source conditions for the target device to operate, and the heating power value representing the total heat output of the electric heat tracing system. At the same time, the interface specification also stipulates that the standard output of the digital twin model is structured full-scene temperature field data. This full-scene temperature field data includes the temperature values ​​and spatial coordinate information of all spatial nodes in the computational domain, as well as a formatted field data file that can be used to generate a temperature distribution cloud map. After the model asset encapsulation operation is completed, a fully encapsulated digital twin model with standardized input and output interfaces is generated.

9. The low-temperature heating simulation temperature compensation method based on thermal conductivity optimization according to claim 8, characterized in that: The specific process of obtaining the temperature field distribution of the target device under corresponding conditions by inputting arbitrary ambient temperature and heating power conditions into the digital twin model is as follows: First, a working condition mapping engine is built and deployed. The working condition mapping engine is a control program used to schedule simulation calculations and process input and output. It is pre-configured to be able to call and drive the encapsulated digital twin model. Secondly, when engineering designers need to make predictions using digital twin models, they submit a working condition query request to the working condition mapping engine, which includes a specified ambient temperature value and a specified heating power value. After receiving the query request, the working condition mapping engine starts its internal automated solution pipeline, which performs the following operations in sequence: First, it parses the working condition query request and extracts the specified ambient temperature value and heating power value. Second, the extracted ambient temperature and heating power values ​​are automatically injected into the boundary condition configuration inside the digital twin model through the standardized input interface of the digital twin model to set the specific working conditions of the current simulation calculation. Third, the thermal simulation solver integrated within the digital twin model is automatically started, driving the solver to load the digital twin model with the current working condition boundary conditions set through the injection operation, and to perform a complete heat conduction simulation calculation. After the simulation calculation is completed, the working condition field mapping engine automatically extracts the complete temperature field data from the original result file generated by the thermal simulation solver and converts it into the structured full-scene temperature field data format defined by the interface specification. Finally, the operating condition mapping engine returns the formatted temperature field distribution data as a response to the operating condition query request to the engineering designers.

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