A method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface

Abstract

This invention provides a method for inversely calculating the heat transfer coefficient at the interface between a pressure casting mold and the casting, relating to the field of metal forming technology. A standardized multi-source aligned dataset is constructed by fusing experimental and simulated data. This not only supplements training samples, significantly reducing the cost of pure experimental data acquisition, but also ensures data consistency through standardization, providing high-quality support for model training. A casting physics-constrained data-driven inverse calculation model is adopted to ensure that the inverse calculation results strictly conform to the physical laws of heat transfer in casting, avoiding the result deviations caused by the "black box" nature of traditional data-driven models. An effective interface heat transfer coefficient correction step is added, correcting the core defect of existing methods that ignore interface contact thermal resistance, improving the engineering practicality of the inverse calculation results. By feeding the corrected heat transfer coefficient back into the dataset and iteratively optimizing the model, adaptive improvement of inverse calculation accuracy is achieved, enhancing the model's adaptability to different casting scenarios and contributing to improved casting forming quality and production stability.

Description

Technical Field

[0001] This invention relates to the field of metal forming technology, and in particular to a method for inversely calculating the heat transfer coefficient at the interface between a pressure casting mold and a casting. Background Technology

[0002] In the metal casting process, the effective heat transfer coefficient at the interface between the mold and the casting is a core parameter that determines the temperature field distribution, solidification rate, and final forming quality of the casting. It directly affects the accuracy of casting numerical simulation and, consequently, the prediction and control of defects such as shrinkage cavities, porosity, and cracks in the casting. The effective heat transfer coefficient at the interface is influenced by multiple factors, including the casting material, mold material, pouring temperature, mold preheating temperature, and interface contact state (gap, oxide layer), exhibiting strong nonlinear and time-varying characteristics. It cannot be directly measured experimentally and can only be obtained indirectly through inverse methods.

[0003] Existing methods for inverse calculation of interfacial heat transfer coefficients are mainly divided into two categories: traditional numerical inverse algorithms and preliminary data-driven methods. Among them, traditional numerical inverse algorithms establish an inverse calculation model based on the heat transfer equation, and then use iterative optimization to make the simulated temperature and experimental temperature measurement data tend to be consistent, thereby solving for the heat transfer coefficient. However, this type of method has problems such as large computational load, slow iteration convergence speed, and sensitivity to initial values. It is difficult to adapt to the inverse calculation of time-varying heat transfer coefficients under multiple coupled process parameters, and it does not consider the accurate correction of interfacial contact thermal resistance, thus limiting its applicability in complex casting scenarios. While preliminary data-driven methods (such as single neural network models) can achieve rapid prediction of heat transfer coefficients through data fitting, they have significant shortcomings: First, they are highly dependent on data samples, requiring the collection of a large amount of experimental data under different process conditions to train the model, resulting in high experimental costs; second, the models have weak generalization ability, making it difficult to transfer to casting scenarios with different materials and mold structures; third, they lack dedicated physical constraint designs for casting heat transfer characteristics, simply embedding general heat transfer equations, leading to significant deviations between the inverse calculation results and the actual physical process, failing to meet the production requirements of high-precision numerical simulation; and fourth, the lack of standardization and alignment of multi-source data (experimental + simulation) results in poor consistency of training samples, further affecting the accuracy of inverse calculations.

[0004] Therefore, it is necessary to propose a method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface to solve or at least alleviate the above-mentioned defects. Summary of the Invention

[0005] The main objective of this invention is to provide a method for inversely calculating the heat transfer coefficient at the interface between the pressure casting mold and the casting, in order to solve the problems of low calculation efficiency, poor accuracy and generalization ability of the inverse calculation of the heat transfer coefficient between the casting and the mold in the prior art.

[0006] To achieve the above objectives, the present invention provides a method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface, comprising the following steps: S1 integrates and processes experimental and simulation data to construct a standardized multi-source aligned dataset; S2, Construct a reverse model driven by casting-specific physical constraint data; S3, the inverse model is trained based on the standardized multi-source aligned dataset, and iterative verification is performed until the preset constraints are met, so as to output a qualified inverse model. S4. Collect actual casting data and add it to the standardized multi-source aligned dataset. Perform preprocessing and feature extraction on the added standardized multi-source aligned dataset to obtain the input feature set to be reversed. Input the input feature set to be reversed into the trained reversed model to reversed calculate the effective heat transfer coefficient of the interface. S5, correct the effective heat transfer coefficient of the interface, update the corrected effective heat transfer coefficient of the interface to the standardized multi-source aligned dataset, so as to output the updated standardized multi-source aligned dataset, and substitute the updated standardized multi-source aligned dataset into the inverse model; S6. Repeat steps S3 to S5 for iterative optimization to achieve adaptive optimization of the model accuracy.

[0007] Preferably, step S1 specifically includes the following steps: S11, design experimental castings and matching molds, and arrange multiple thermocouples at different depths at the interface between the mold and the casting to collect temperature time series data of the entire casting cycle; S12, by changing the process parameters, multiple sets of thermal cycle datasets containing process parameters, temperature sequence of measuring points, and solid fraction of the casting are obtained; wherein, the process parameters include casting material, pouring temperature, mold preheating temperature, and interface lubrication conditions.

[0008] Preferably, step S12 is followed by the step: S13. Based on the casting heat transfer theory, a one-dimensional heat transfer numerical model of mold-casting is established and solved by the finite volume method. By traversing the effective heat transfer coefficient and thermal property parameters of the interface, a simulated temperature time series dataset aligned with the aforementioned thermal cycle dataset is generated. S14, establish alignment rules between the thermal cycle dataset and the simulated temperature time series dataset, perform outlier cleaning and normalization on the data after alignment, extract the processed process parameters and thermophysical parameters as input features, and construct a standardized multi-source aligned dataset with the effective heat transfer coefficient of the parameterized interface as the label; wherein, the standardized multi-source aligned dataset includes a training dataset and a test dataset.

[0009] Preferably, step S2 specifically includes the following steps: S21, Construct a PhysX-SHAP-Net model, embedding the one-dimensional heat transfer differential equation between the mold and the casting as the core constraint in the model; wherein, the one-dimensional heat transfer differential equation is: in, It is the material density, It is specific heat capacity, Thermal conductivity, For temperature, Time is defined as the coordinate system with the interface between the casting and the mold as the origin, and the direction perpendicular to the interface, pointing from the casting towards the interior of the mold, as... Establish a rectangular coordinate system along the positive axis. As an internal heat source; S22, embed non-negative constraints, bounded constraints, Lipschitz smoothing constraints, and stage transition constraints of the effective heat transfer coefficient of the interface into the model; wherein, the stage transition constraint is triggered by a solid fraction threshold to achieve adaptive switching of the heat transfer coefficient at different stages.

[0010] Preferably, step S22 is followed by the following step: S23, Construct the composite loss function of the model and configure the dynamic weight update rules for each component, the expression of which is: in, It is the total loss function. For data fitting terms, For the residual terms of the heat transfer equation, Boundary condition constraint terms, This is the temperature measurement error term. , , , The dynamic weights of each item; S24. Based on the one-dimensional heat transfer differential equation, various constraints, and the composite loss function, construct a casting-specific physical constraint data-driven inverse model.

[0011] Preferably, step S3 specifically includes the following steps: S31, Input the training dataset into the inverse model and use the gradient iteration method to let the model learn; S32, verify whether the output of the model in each iteration satisfies the physical constraints of heat transfer and the specific physical constraints of the interface heat transfer coefficient; S33, if not satisfied, adjust the model parameters and loss weights until the iteration error is satisfied, and output the successfully trained inverse model; where the satisfied condition is: in, The effective heat transfer coefficient of the interface, This is the convergence threshold, and its value ranges from 10. -4 ~10 -3 .

[0012] Preferably, step S4 specifically includes the following steps: S41: Collect real-time process parameters and temperature time series data of each measuring point during the actual casting production process, and clean, normalize and feature map according to the alignment and preprocessing rules of S11 to S14 to generate the input feature set to be reversed. S42, input the input feature set to be inversely calculated into the trained inverse calculation model to output the parameterized interface effective heat transfer coefficient.

[0013] Preferably, the output of the effective heat transfer coefficient of the parameterized interface is defined as: in, These are the basis function coefficients. These are the preset basis function coefficients.

[0014] Preferably, the correction in step S5 specifically includes the following steps: S51, according to The effective heat transfer coefficient of the interface is corrected; wherein, For the true solid-solid contact heat transfer coefficient between the metal and the mold, For interfacial gap thermal resistance, Thermal resistance of oxide / coating layer; S52, , Using formulas respectively , Calculate; where, For interface thickness, The interfacial thermal conductivity, The thickness of the oxide layer / coating layer, The value represents the thermal conductivity of the oxide / coating layer.

[0015] Preferably, step S52 is followed by the following steps: S53 uses the corrected effective heat transfer coefficient of the interface as a boundary condition and substitutes it into the casting numerical simulation software to predict the temperature field, solidification process and defects of the casting. Based on the prediction results, the casting process parameters are optimized. At the same time, the basis function coefficients and stage characteristic parameters of the corrected effective heat transfer coefficient of the interface are updated into the standardized multi-source aligned dataset, so that the output is the updated standardized multi-source aligned dataset. The updated standardized multi-source aligned dataset is then substituted into the inverse model.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a method for inversely calculating the heat transfer coefficient at the interface between a pressure casting mold and the casting. By fusing experimental and simulated data to construct a standardized multi-source aligned dataset, it not only supplements training samples, significantly reducing the cost of pure experimental data acquisition, but also ensures data consistency through standardization, providing high-quality support for model training. The method employs casting-specific physical constraint data to drive the inverse calculation model, ensuring that the results strictly conform to the physical laws of heat transfer in casting, avoiding the biases caused by the "black box" nature of traditional data-driven models. An additional step for correcting the effective heat transfer coefficient at the interface is added, correcting the core defect of existing methods that ignore interfacial contact thermal resistance, thus improving the engineering practicality of the inverse calculation results. By feeding the corrected heat transfer coefficient back into the dataset and iteratively optimizing the model, adaptive improvement in inverse calculation accuracy is achieved, enhancing the model's adaptability to different casting scenarios, providing high-precision boundary conditions for casting numerical simulation, and contributing to the improvement of casting forming quality and production stability. Attached Figure Description

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

[0018] Figure 1 This is a process flow diagram of the overall reverse engineering method in one embodiment of the present invention.

[0019] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0020] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0023] Furthermore, the technical solutions of the various embodiments can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0024] Please see the appendix Figure 1 The present invention provides a method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface, comprising the following steps: S1 involves fusing and processing experimental and simulated data to construct a standardized multi-source aligned dataset. It's understandable that the interfacial heat transfer coefficient cannot be directly measured experimentally; it can only be indirectly inferred through dynamic changes in the temperature field. Pure experimental data collection is costly and has a limited sample size, making it difficult to cover complex and variable production conditions. Pure simulated data lacks the noise and uncertainty of real physical processes. By fusing experimental and simulated multi-source data, the authenticity of the data can be guaranteed, the sample size can be expanded at low cost, and the heterogeneity of multi-source data can be eliminated through standardization, providing a high-quality foundation for model training.

[0025] S2. Construct a data-driven inverse model based on casting-specific physical constraints. Traditional pure data-driven models are "black box" models, which learn mapping relationships only through data fitting and are prone to producing inverse results that do not conform to the physical laws of heat transfer in casting. This step, however, embeds the core physical laws of heat transfer in casting and the specific characteristics of interfacial heat transfer as constraints into the model, forcing the model output to conform to physical laws. This fundamentally solves the core defects of pure data-driven models, such as weak generalization ability and poor reliability of results.

[0026] S3. Based on the standardized multi-source aligned dataset, the inverse model is trained and iteratively verified until preset constraints are met, outputting a qualified inverse model. Iterative training enables the model to learn the nonlinear mapping relationship between input features and output labels. Simultaneously, real-time verification using physical constraints and convergence condition judgment ensure that the model meets both data fitting accuracy and conforms to the physical laws of casting heat transfer, ultimately outputting a qualified model suitable for engineering applications. This ensures sufficient model training without overfitting, and the output model simultaneously meets physical rationality and engineering accuracy requirements. It replaces traditional manual experience-based inverse calculations and single numerical inverse calculation methods, achieving automation and standardization of interface heat transfer coefficient inverse calculation.

[0027] S4. Collect actual casting data and add it to the standardized multi-source aligned dataset. Preprocess and extract features from the added standardized multi-source aligned dataset to obtain the input feature set to be inverted. Input the input feature set to be inverted into the trained inversion model to invert the effective heat transfer coefficient of the interface. Using the trained model, a fast and automated inversion of the effective heat transfer coefficient of the interface under actual production conditions is achieved. The heat transfer coefficient is output in parameterized form, facilitating subsequent storage, reuse, and numerical simulation. Simultaneously, feature contribution analysis clarifies the influence of each process parameter on the heat transfer coefficient. This achieves second-level fast inversion of the effective heat transfer coefficient of the interface, significantly improving efficiency compared to traditional numerical inversion methods. The parameterized output form is smoother and easier to identify than traditional time-by-time discrete values, facilitating subsequent engineering applications. Interpretability analysis provides a theoretical basis for the precise optimization of casting process parameters.

[0028] S5, the effective heat transfer coefficient of the interface is corrected, and the corrected effective heat transfer coefficient is updated to the standardized multi-source aligned dataset, so that the output is the updated standardized multi-source aligned dataset. The updated standardized multi-source aligned dataset is then substituted into the inverse model. The "effective heat transfer coefficient of the interface" directly obtained by the model is a comprehensive effect of solid-solid contact thermal resistance, interfacial gap thermal resistance, and oxide / coating layer thermal resistance, and is not the true solid-solid contact heat transfer coefficient that can be directly used for numerical simulation. The true heat transfer coefficient is obtained through thermal resistance correction, and the correction data verified by engineering is fed back into the dataset. The model accuracy is continuously improved through iterative optimization. In principle, this corrects the core defect of existing inverse methods that ignore interfacial contact thermal resistance. The corrected heat transfer coefficient can be directly substituted into the casting numerical simulation software as a boundary condition, significantly improving the simulation accuracy.

[0029] S6. Repeat steps S3-S5 for iterative optimization to achieve adaptive optimization of the inverse model accuracy. Through data feedback and incremental learning, the model's generalization ability and inverse accuracy are continuously improved, enabling stable adaptation to complex casting scenarios with different alloy materials and process parameters. Thus, with the accumulation of production data, incremental learning allows for fine-tuning of the model, continuously improving its generalization ability and inverse accuracy, adapting to more casting scenarios. Based on the updated incremental dataset, transfer learning is used to fine-tune the trained PhysX-SHAP-Net model, achieving reconvergence in just 30-50 iterations. Repeating steps S3-S5 further improves the model's accuracy. In a preferred embodiment of the present invention, step S1 specifically includes the following steps: S11 involves designing an experimental casting and matching mold, and placing multiple thermocouples at different depths at the interface between the mold and the casting to collect time-series temperature data throughout the casting cycle. It's important to note that temperature is a directly measurable physical quantity in the casting heat transfer process. The time-series temperature data at the interface and different depths in the mold completely record the entire process of heat transfer from the casting to the mold, serving as the core basis for inverse calculation of the interface heat transfer coefficient. This achieves multi-dimensional, high-resolution acquisition of the temperature field at the interface and inside the mold, avoiding local errors caused by single-point temperature measurement and providing accurate raw temperature data for subsequent inverse calculations.

[0030] S12, by changing the process parameters, multiple sets of thermal cycling datasets containing process parameters, measurement point temperature sequence, and casting solid fraction are obtained; wherein, the process parameters include casting material, pouring temperature, mold preheating temperature, and interface lubrication conditions; it is understood that the interface heat transfer coefficient is coupled with multiple factors such as casting material, pouring temperature, mold preheating temperature, and interface lubrication conditions, exhibiting strong nonlinear characteristics. In this way, an experimental dataset covering mainstream production conditions is constructed, which fully captures the variation law of interface heat transfer coefficient under different process conditions, and provides a representative labeled sample basis for model training.

[0031] In a preferred embodiment of the present invention, step S12 is followed by the following step: S13. A one-dimensional heat transfer numerical model of mold-casting is established based on the casting heat transfer theory and solved using the finite volume method. By traversing the effective heat transfer coefficient and thermal property parameters of the interface, a simulated temperature time series dataset aligned with the aforementioned thermal cycle dataset is generated. Numerical simulation has the advantages of low cost, high speed, and batch data generation, which can effectively supplement the deficiency of insufficient experimental data and ensure the spatiotemporal consistency of the data. By traversing the effective heat transfer coefficient, process parameters, and material thermal property parameters of the interface, multiple sets of simulated temperature time series data are generated, and the measurement point positions and time steps of all simulated data are completely consistent with the experimental data, which greatly reduces the time and economic cost of experimental data acquisition, while enriching the diversity of training samples and improving the generalization ability of the model.

[0032] S14, establish alignment rules between the thermal cycling dataset and the simulated temperature time series dataset. After alignment, perform outlier cleaning and normalization on the data, extract the processed process parameters and thermophysical parameters as input features, and use the effective heat transfer coefficient of the parameterized interface as a label to construct a standardized multi-source aligned dataset. The standardized multi-source aligned dataset includes a training dataset and a test dataset. Experimental data and simulated data differ in measurement accuracy, data format, and noise level. Directly mixing them for training can lead to model convergence difficulties and decreased inverse calculation accuracy. Therefore, spatiotemporal alignment rules are established between experimental and simulated data to unify data format and timestamps. After cleaning outliers, all features are normalized using min-max normalization. Process parameters, thermophysical parameters, and temperature time series features are extracted as model input features. Using the effective heat transfer coefficient of the parameterized interface as a label, the training dataset and test dataset are divided, thereby eliminating the heterogeneity of multi-source data, ensuring the consistency and quality of training data, and laying the foundation for stable model convergence and high-precision inverse calculation.

[0033] In a preferred embodiment of the present invention, step S2 specifically includes the following steps: S21, Construct a PhysX-SHAP-Net model, embedding the one-dimensional heat transfer differential equation between the mold and the casting as the core constraint in the model; wherein, the one-dimensional heat transfer differential equation is: in, It is the material density, It is specific heat capacity, Thermal conductivity, For temperature, Time is defined as the coordinate system with the interface between the casting and the mold as the origin, and the direction perpendicular to the interface, pointing from the casting towards the interior of the mold, as... Establish a rectangular coordinate system along the positive axis. As an internal heat source, the heat transfer between the mold and the casting strictly follows the one-dimensional heat transfer differential equation. Embedding this equation as a core constraint into the model forces the model output to conform to the basic heat transfer law, fundamentally avoiding physically unreasonable reverse calculation results. This organically combines prior physical knowledge with data-driven methods, preserving the fitting ability of the data-driven model while ensuring the physical consistency of the reverse calculation results, thus solving the problem of poor generalization ability of pure data-driven models.

[0034] S22, embedding non-negative constraints, bounded constraints, Lipschitz smoothing constraints, and stage transition constraints of the effective heat transfer coefficient of the interface into the model; wherein, the stage transition constraint uses the solid fraction threshold as the trigger condition to realize the adaptive switching of the heat transfer coefficient at different stages; the interface heat transfer coefficient has a clear physical boundary and variation law during the casting process. By embedding these prior knowledge into the model through mathematical constraints, the solution space of the model can be effectively reduced, the convergence can be accelerated, and the inverse calculation accuracy can be improved, so as to further limit the output range of the model and avoid the model from producing abrupt changes and inverse calculation results that exceed the physical boundary. At the same time, it accurately captures the stage variation characteristics of the interface heat transfer coefficient during the casting process.

[0035] In a preferred embodiment of the present invention, the step S22 is followed by the following step: S23, Construct the composite loss function of the model and configure the dynamic weight update rules for each component, the expression of which is: in, It is the total loss function. For data fitting terms, For the residual terms of the heat transfer equation, Boundary condition constraint terms, This is the temperature measurement error term. , , , The dynamic weights of each item are used; a single loss function cannot simultaneously take into account the data fitting accuracy, physical constraint satisfaction and measurement error robustness. The multi-item dynamic weight loss function can balance the priority of each optimization objective; improve the model's robustness to measurement noise, and at the same time ensure the model's convergence efficiency and accuracy at different training stages.

[0036] S24. Based on the one-dimensional heat transfer differential equation, various constraints, and the composite loss function, a casting-specific physical constraint data-driven inverse model is constructed. After organically integrating the above modules, an end-to-end interface heat transfer coefficient inverse model is formed, realizing automated mapping from input features to output results. Then, a deep learning model specifically for casting interface heat transfer coefficient inverse calculation is constructed, which can complete the entire process from data input to heat transfer coefficient output without manual intervention, greatly improving the efficiency and accuracy of inverse calculation.

[0037] Furthermore, step S3 specifically includes the following steps: S31, the training dataset is input into the inverse model, and the gradient iteration method is used to allow the model to learn. The gradient iteration method adjusts the model parameters through the backpropagation algorithm, minimizes the loss function, and enables the model to learn the mapping relationship between input features and output labels, so as to learn the variation law of interface heat transfer coefficient under different process conditions and achieve high-precision data fitting.

[0038] S32, verify whether the output of the model in each iteration satisfies the physical constraints of heat transfer and the specific physical constraints of the interface heat transfer coefficient; S33, if not satisfied, adjust the model parameters and loss weights until the iteration error is satisfied, and output the successfully trained inverse model; where the satisfied condition is: in, The effective heat transfer coefficient of the interface, This is the convergence threshold, and its value ranges from 10. -4 ~10 -3 It is understandable that, because the model may get stuck in a local optimum during training, causing the output to violate physical laws, real-time verification can promptly detect and correct such problems, ensuring that the model maintains physical rationality throughout the training process and avoids converging to an unrealistic solution; if this is not satisfied, the model parameters and loss weights are adjusted, and the relative change of the loss function ( The iterative change value and When the ratio of the two components is less than the convergence threshold, the model is considered to have converged, and training can be stopped at this point to avoid overfitting.

[0039] Furthermore, step S4 specifically includes the following steps: S41: Collect real-time process parameters and temperature time series data of each measuring point during the actual casting production process, and clean, normalize and feature map according to the alignment and preprocessing rules of S11 to S14 to generate the input feature set to be reversed. S42, input the input feature set to be inversely calculated into the trained inverse calculation model to output the effective heat transfer coefficient of the parameterized interface; there may be differences between actual production data and experimental data in terms of acquisition equipment and data format. Unified preprocessing can ensure the consistency of model input. Preprocessing can refer to S11 to S14 to eliminate the distribution differences between actual production data and training data and ensure the accuracy of the model inverse calculation results.

[0040] Furthermore, the output of the effective heat transfer coefficient of the parameterized interface is defined as: in, These are the basis function coefficients. These are the preset basis function coefficients.

[0041] Furthermore, the correction in step S5 specifically includes the following steps: S51, according to The effective heat transfer coefficient of the interface is corrected; wherein, For the true solid-solid contact heat transfer coefficient between the metal and the mold, For interfacial gap thermal resistance, The model calculates the effective heat transfer coefficient, not the actual solid-solid contact heat transfer coefficient, by using a correction formula to correct the core defect of the existing inverse calculation method that ignores the interface heat resistance. This allows us to obtain the actual contact heat transfer coefficient that conforms to the actual working conditions.

[0042] S52, , Using formulas respectively , Calculate; where, For interface thickness, The interfacial thermal conductivity, The thickness of the oxide layer / coating layer, The thermal conductivity of the oxide / coating layer is given. The gap thermal resistance and coating layer thermal resistance can be quantitatively calculated using their thickness and thermal conductivity, enabling accurate correction of the effective heat transfer coefficient. The corrected heat transfer coefficient can be directly used as a boundary condition in casting numerical simulation software.

[0043] Furthermore, the steps following step S52 specifically include: In step S53, the corrected effective interface heat transfer coefficient is used as a boundary condition and substituted into the casting numerical simulation software to predict the casting temperature field, solidification process, and defects. Based on the prediction results, the casting process parameters are optimized. Simultaneously, the basis function coefficients and stage characteristic parameters of the corrected effective interface heat transfer coefficient are updated to the standardized multi-source aligned dataset, with the updated standardized multi-source aligned dataset as the output. This updated standardized multi-source aligned dataset is then substituted into the inverse model. The true heat transfer coefficient obtained through inverse calculation is the core boundary condition for the casting numerical simulation. Meanwhile, the actual production data verified by engineering is the core sample for improving model performance. The corrected true interface heat transfer coefficient is used as a boundary condition and substituted into the ProCAST casting numerical simulation software to predict the casting temperature field, solidification process, and shrinkage cavities and porosity defects. Based on the simulation results, the preheating temperature of the original mold is optimized and adjusted, and the cooling medium flow rate is appropriately increased to improve the solidification uniformity of the casting. At the same time, the basis function coefficients, stage characteristic parameters, and corresponding process parameters and temperature data of the corrected interface heat transfer coefficient are fed back into the standardized multi-source aligned dataset in S1 to update the multi-source dataset.

[0044] To facilitate understanding by those skilled in the art, an example is provided below: Design an A356 aluminum alloy experimental casting and a matching mold. Ten K-type thermocouples are evenly arranged at the interface between the mold and the casting. Four, three, and three K-type thermocouples are arranged at mold depths of 5mm, 10mm, and 15mm, respectively, for a total of 20 temperature measurement points. All thermocouples are connected to a data acquisition instrument to collect the temperature time sequence data of each measurement point during the casting process. The sampling interval is set to 1 second. By changing four core process parameters, multiple rounds of casting cycle experiments were conducted. The specific process parameter adjustment ranges are as follows: casting material (A356 aluminum alloy, A6061 aluminum alloy), pouring temperature (680℃, 700℃, 720℃), mold preheating temperature (100℃, 150℃, 200℃), and interface lubrication conditions (graphite coating, water glass coating, no coating). A total of 3×3×2×3=54 rounds of casting cycle experiments were conducted. In each round of experiments, process parameters, temperature time series data at each measuring point, and corresponding solid fraction data of the casting were collected simultaneously, and finally 54 complete thermal cycle datasets were obtained.

[0045] Based on casting heat transfer theory, a one-dimensional heat transfer model of mold-casting was established. The temperature field was solved using the finite volume method, generating 216 sets of simulated temperature time-series data. The measurement point locations and time steps of the simulated data were completely consistent with the experimental data, which were used to supplement the training samples. A total of 270 sets of supplemented data were produced, reducing the cost of experimental data acquisition. The supplemented dataset was standardized and preprocessed, and labeled as training set, validation set, and test set.

[0046] A casting-specific PhysX-SHAP-Net model was constructed. The model structure includes an input layer, a feature extraction layer, a physical constraint embedding layer, a loss function calculation layer, an output layer, and a SHAP interpretability analysis module. The one-dimensional heat transfer differential equation between the mold and the casting serves as the core constraint. A casting-specific multi-term dynamic weight function was designed, including data fitting terms, heat transfer equation residual terms, boundary condition constraint terms, and temperature measurement error terms. Finally, an artificial swarm optimization algorithm was introduced to jointly optimize the PhysX-SHAP-Net model, optimizing hyperparameters and the weights of each term in the loss function. The optimization objective was to minimize the inverse calculation error on the test dataset. A SHAP analysis module was embedded at the model output to calculate the SHAP value of each input feature, clarifying the contribution of each feature to the inverse calculation result and enabling interpretability analysis of the inverse calculation result.

[0047] The predefined training and validation sets are input into the model for training. The maximum number of training iterations is set to 300, and an early stopping strategy is enabled. Training stops prematurely if the model performance fails to improve after 50 consecutive iterations. Each iteration verifies whether the model output meets the constraints; if not, adjustments are made until the constraints are met. These constraints include: (1) Residual constraints of the heat transfer equation, with the absolute value of the residual less than 1.0 × 10⁻⁶. -3 ℃ / s 2 ; (2) Boundary condition constraints, namely, the continuity error of heat flux density at the mold / casting interface is less than 150W / m. 2 ; (3) Physical rationality constraints of temperature field, that is, the predicted temperature shall not exceed the maximum casting temperature, nor shall it be lower than room temperature (25℃). (4) Inversely calculate the interfacial heat transfer coefficient and maintain it. Reasonable range; In this embodiment, the convergence condition is met after 214 training rounds, at which point all physical constraints are satisfied, and the residual of the heat transfer equation is 0.72 × 10⁻³ °C / s. 2 The interfacial heat flux density error is 122 W / m. 2 The temperature field ranges from 25℃ to 720℃, and the interfacial heat transfer coefficient is... This indicates that the model has converged and training is complete.

[0048] To validate the trained model, an inverse accuracy test can be performed using a test dataset. The validation parameters are the mean absolute error (MAE) and the root mean square error (RMSE). After testing, , The reverse calculation yields excellent accuracy.

[0049] After preprocessing the standardized multi-source aligned dataset with added actual casting data, feature extraction is performed to obtain the input feature set to be inverted. The input feature set to be inverted is then input into a trained PhysX-SHAP-Net model. The model outputs the effective heat transfer coefficient of the parameterized interface. At the same time, the SHAP module outputs the contribution of each input feature, clarifying the influence of key process parameters on the heat transfer coefficient.

[0050] According to the SHAP interpretability analysis, the SHAP value of the casting material is +0.11, which has a weak positive effect on the heat transfer coefficient; the SHAP value of the pouring temperature is +0.16, which has a weak positive contribution; the SHAP value of the mold preheating temperature is -0.19, which has a weak to moderate negative contribution; and the SHAP value of the interface lubrication condition is +0.37, which has a strong positive contribution.

[0051] After correction using a correction formula, this embodiment takes graphite coating + air gap as an example, with the interface gap thickness... =8×10- 6 m; thermal conductivity of air within the gap Graphite coating thickness, =2×10- 5 m; thermal conductivity of graphite Finally, the goal was achieved. , The heat transfer coefficient is obtained by inverse model calculation Finally, the true interfacial heat transfer coefficient is obtained. .

[0052] Finally, the corrected real interface heat transfer coefficient was calculated. The casting finite element simulation software was used to simulate the temperature field and solidification process as the heat transfer boundary condition at the mold-casting interface. The simulation results showed that the local solidification rate of the casting was too slow at the original mold preheating temperature of 200℃, which easily led to shrinkage defects. Based on this, the mold preheating temperature was optimized and adjusted to 150℃, and the flow rate of the cooling medium was appropriately increased, which improved the solidification uniformity of the casting and significantly reduced the internal defect rate, thus improving the casting forming quality.

[0053] In the specific incremental update process, measured temperature curves, corrected interfacial heat transfer coefficients, and process parameters of A356 aluminum alloy under different casting temperatures and lubrication conditions were continuously collected. Subsequently, approximately 30 additional sets of actual working condition data were added, supplementing the original dataset of 270 sets, resulting in an expanded updated dataset of over 300 sets. After standardizing, spatiotemporally aligning, and labeling the new data using the aforementioned method, the already trained PhysX-SHAP-Net model was fine-tuned based on transfer learning. It only required 30-50 iterations to reconverge, significantly shortening the training time compared to training from scratch. After the incremental update, the MAE of the model under the new casting conditions further improved from 310 to [missing value]. Its generalization ability is significantly enhanced, and it can stably adapt to different alloy materials, different coating types and multi-batch continuous production scenarios, allowing the model to achieve a better generalization ability and accuracy, and adapt to more casting scenarios.

[0054] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for inversely calculating the heat transfer coefficient at the interface between a pressure casting mold and a casting, characterized in that, Includes the following steps: S1 integrates and processes experimental and simulation data to construct a standardized multi-source aligned dataset; S2, Construct a reverse model driven by physical constraint data specific to casting; S3, the inverse model is trained based on the standardized multi-source aligned dataset and iteratively verified until the preset constraints are met, so as to output a qualified inverse model. S4. Collect actual casting data and add it to the standardized multi-source aligned dataset. Perform preprocessing and feature extraction on the added standardized multi-source aligned dataset to obtain the input feature set to be reversed. Input the input feature set to be reversed into the trained reversed model to reversed calculate the effective heat transfer coefficient of the interface. S5, correct the effective heat transfer coefficient of the interface, update the corrected effective heat transfer coefficient of the interface to the standardized multi-source aligned dataset, so as to output the updated standardized multi-source aligned dataset, and substitute the updated standardized multi-source aligned dataset into the inverse model; S6. Repeat steps S3 to S5 for iterative optimization to achieve adaptive optimization of the model accuracy.

2. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11, design experimental castings and matching molds, and arrange multiple thermocouples at different depths at the interface between the mold and the casting to collect temperature time series data of the entire casting cycle; S12, by changing the process parameters, multiple sets of thermal cycle datasets containing process parameters, temperature sequence of measuring points, and solid fraction of the casting are obtained; wherein, the process parameters include casting material, pouring temperature, mold preheating temperature, and interface lubrication conditions.

3. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 2, characterized in that, The step S12 is followed by the following step: S13. Based on the casting heat transfer theory, a one-dimensional heat transfer numerical model of mold-casting is established and solved by the finite volume method. By traversing the effective heat transfer coefficient and thermal property parameters of the interface, a simulated temperature time series dataset aligned with the aforementioned thermal cycle dataset is generated. S14, establish alignment rules between the thermal cycle dataset and the simulated temperature time series dataset, perform outlier cleaning and normalization on the data after alignment, extract the processed process parameters and thermophysical parameters as input features, and construct a standardized multi-source aligned dataset with the effective heat transfer coefficient of the parameterized interface as the label; wherein, the standardized multi-source aligned dataset includes a training dataset and a test dataset.

4. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 1, characterized in that, Step S2 specifically includes the following steps: S21, Construct a PhysX-SHAP-Net model, embedding the one-dimensional heat transfer differential equation between the mold and the casting as the core constraint in the model; wherein, the one-dimensional heat transfer differential equation is: in, It is the material density, It is specific heat capacity, Thermal conductivity, For temperature, Time is defined as the coordinate system with the interface between the casting and the mold as the origin, and the direction perpendicular to the interface, pointing from the casting towards the interior of the mold, as... Establish a rectangular coordinate system along the positive axis. As an internal heat source; S22, embed non-negative constraints, bounded constraints, Lipschitz smoothing constraints, and stage transition constraints of the effective heat transfer coefficient of the interface into the model; wherein, the stage transition constraint is triggered by a solid fraction threshold to achieve adaptive switching of the heat transfer coefficient at different stages.

5. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 4, characterized in that, The step S22 is followed by the following step: S23, Construct the composite loss function of the model and configure the dynamic weight update rules for each component, the expression of which is: in, It is the total loss function. For data fitting terms, For the residual terms of the heat transfer equation, Boundary condition constraints, This is the temperature measurement error term. , , , The dynamic weights of each item; S24. Based on the one-dimensional heat transfer differential equation, various constraints, and the composite loss function, construct a casting-specific physical constraint data-driven inverse model.

6. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 3, characterized in that, Step S3 specifically includes the following steps: S31, Input the training dataset into the inverse model and use the gradient iteration method to let the model learn; S32, verify whether the output of the model in each iteration satisfies the physical constraints of heat transfer and the specific physical constraints of the interface heat transfer coefficient; S33, if not satisfied, adjust the model parameters and loss weights until the iteration error is satisfied, and output the successfully trained inverse model; where the satisfied condition is: in, The effective heat transfer coefficient of the interface, This is the convergence threshold, and its value ranges from 10. -4 ~10 -3 .

7. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 3, characterized in that, Step S4 specifically includes the following steps: S41: Collect real-time process parameters and temperature time series data of each measuring point during the actual casting production process, and clean, normalize and feature map according to the alignment and preprocessing rules of S11 to S14 to generate the input feature set to be reversed. S42, input the input feature set to be inversely calculated into the trained inverse calculation model to output the parameterized interface effective heat transfer coefficient.

8. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 7, characterized in that, The output of the effective heat transfer coefficient of the parameterized interface is defined as follows: in, These are the coefficients of the basis functions. These are the preset basis function coefficients.

9. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 7, characterized in that, The correction in step S5 specifically includes the following steps: S51, according to The effective heat transfer coefficient of the interface is corrected; wherein, For the true solid-solid contact heat transfer coefficient between the metal and the mold, For interfacial gap thermal resistance, Thermal resistance of oxide / coating layer; S52, , Using formulas respectively , Calculate; where, For interface thickness, The interfacial thermal conductivity, The thickness of the oxide layer / coating layer, The value represents the thermal conductivity of the oxide / coating layer.

10. The method for inversely calculating the heat transfer coefficient at the pressure casting mold-casting interface according to claim 9, characterized in that, The steps following step S52 specifically include: S53 uses the corrected effective heat transfer coefficient of the interface as a boundary condition and substitutes it into the casting numerical simulation software to predict the temperature field, solidification process and defects of the casting. Based on the prediction results, the casting process parameters are optimized. At the same time, the basis function coefficients and stage characteristic parameters of the corrected effective heat transfer coefficient of the interface are updated into the standardized multi-source aligned dataset, so that the output is the updated standardized multi-source aligned dataset. The updated standardized multi-source aligned dataset is then substituted into the inverse model.

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