A Deep Learning-Based Method and System for Optimizing Casting Shrinkage Cavity Process Parameters

Abstract

This application discloses a deep learning-based method and system for optimizing process parameters of shrinkage cavity in castings, belonging to the field of parameter optimization technology. The method includes: training a surrogate model to output predicted values ​​and uncertainties of product quality indicators; constructing an uncertainty fusion engine to fuse the uncertainty predicted by the surrogate model, the uncertainty of process parameter fluctuations, and the uncertainty of material parameter ranges; defining and calculating a robustness evaluation index based on the predicted values ​​of product quality indicators and the comprehensive uncertainty envelope; searching for a robust Pareto front solution set with the dual objectives of optimizing both product quality indicators and the robustness evaluation index; and recommending the final process parameter scheme based on the robust Pareto front solution set. This solves the technical problems of existing casting shrinkage cavity process parameter optimization methods that rely on experience and trial and error, resulting in low efficiency and poor accuracy and reliability.

Description

Technical Field

[0001] This application relates to the field of parameter optimization technology, specifically to a method and system for optimizing casting shrinkage process parameters based on deep learning. Background Technology

[0002] With the rapid development of the manufacturing industry, castings have been widely used in many fields. However, the occurrence of shrinkage cavities in castings not only reduces the mechanical properties and service life of castings, but may also lead to product scrap and increase production costs. Traditional methods for optimizing process parameters for shrinkage cavities in castings mainly rely on experience and trial and error, which is not only inefficient, but also makes it difficult to guarantee the accuracy and reliability of the optimization results, thus failing to effectively solve the problem of shrinkage cavities in castings. Summary of the Invention

[0003] This application provides a method and system for optimizing casting shrinkage process parameters based on deep learning, which solves the technical problems of existing methods for optimizing casting shrinkage process parameters that rely on experience and trial and error, resulting in low efficiency and poor accuracy and reliability of results.

[0004] The technical solution to the above-mentioned technical problems in this application is as follows:

[0005] In a first aspect, this application provides a method for optimizing casting shrinkage process parameters based on deep learning, the method comprising:

[0006] Train a proxy model that takes a combination of casting process parameters as input and outputs the predicted values ​​and uncertainties of product quality indicators.

[0007] An uncertainty fusion engine is constructed to fuse the uncertainty of surrogate model prediction, the uncertainty of process parameter fluctuations, and the uncertainty of material parameter ranges, and output a comprehensive uncertainty envelope;

[0008] Based on the predicted values ​​of the product quality indicators and the comprehensive uncertainty envelope, a robustness evaluation index is defined and calculated.

[0009] With the dual objectives of optimizing product quality indicators and robustness evaluation indicators, a multi-objective optimization algorithm is run to search for and obtain a robust Pareto front solution set;

[0010] Based on the robust Pareto front solution set, a final process parameter scheme is recommended.

[0011] Secondly, this application provides a deep learning-based system for optimizing casting shrinkage process parameters, including:

[0012] The model training module is used to train a proxy model, which takes a combination of casting process parameters as input and outputs the predicted value and uncertainty of product quality indicators.

[0013] The parameter fusion module is used to build an uncertainty fusion engine, which fuses the uncertainty of surrogate model prediction, the uncertainty of process parameter fluctuations, and the uncertainty of material parameter ranges, and outputs a comprehensive uncertainty envelope.

[0014] The indicator calculation module is used to define and calculate robustness evaluation indicators based on the predicted values ​​of the product quality indicators and the comprehensive uncertainty envelope.

[0015] The indicator optimization module is used to run a multi-objective optimization algorithm with the dual objectives of optimizing product quality indicators and robustness evaluation indicators, and to search for and obtain a robust Pareto front solution set.

[0016] The scheme recommendation module is used to recommend the final process parameter scheme based on the robust Pareto front solution set.

[0017] This application provides one or more technical solutions, which have at least the following technical effects or advantages:

[0018] This application provides a method and system for optimizing casting shrinkage process parameters based on deep learning. First, a surrogate model is trained using deep learning to output predicted values ​​and uncertainties of product quality indicators, improving prediction accuracy. Second, an uncertainty fusion engine is constructed to integrate multiple uncertainties, considering the impact of process parameter fluctuations and material parameter ranges in actual production, making subsequent analysis and decision-making more consistent with reality. Third, robustness evaluation indicators are defined and calculated based on the predicted values ​​of product quality indicators and the comprehensive uncertainty envelope, evaluating process parameter schemes from multiple dimensions and providing a more comprehensive basis for optimization. Then, a robust Pareto front solution set is obtained by searching with the dual objectives of optimizing product quality indicators and robustness evaluation indicators, improving the robustness of the scheme while ensuring product quality and avoiding production problems caused by various uncertainties. Finally, a final process parameter scheme is recommended based on the robust Pareto front solution set. The solution set is visualized through a human-machine collaborative decision-making interface, and user interaction instructions are received to determine the final scheme, ensuring both the scientific nature of the decision-making and consideration of the user's actual needs and preferences.

[0019] Through the above technical solution, this application effectively solves the shortcomings of existing methods for optimizing casting shrinkage process parameters, improves optimization efficiency, enhances the accuracy and reliability of results, helps reduce the probability of shrinkage problems in castings, reduces production costs, improves the quality and market competitiveness of casting products, and provides technical support for the development of the manufacturing industry. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the deep learning-based method for optimizing casting shrinkage process parameters provided in an embodiment of this application.

[0022] Figure 2 This is a schematic diagram of the structure of the casting shrinkage process parameter optimization system based on deep learning provided in the embodiments of this application.

[0023] The components represented by each number in the attached diagram are explained below:

[0024] Model training module 11, parameter fusion module 12, index calculation module 13, index optimization module 14, and scheme recommendation module 15. Detailed Implementation

[0025] This application provides a method and system for optimizing casting shrinkage process parameters based on deep learning, which addresses the technical problem that existing methods for optimizing casting shrinkage process parameters rely on experience and trial and error, resulting in low efficiency and poor accuracy and reliability.

[0026] 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.

[0027] 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.

[0028] 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 this application. 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 this application can be made without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid unnecessarily obscuring the description of this application. Therefore, this application 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.

[0029] Example 1, as Figure 1 As shown in the embodiments of this application, a method for optimizing casting shrinkage process parameters based on deep learning is provided, including:

[0030] S10: Train a proxy model, which takes the combination of casting process parameters as input and outputs the predicted value and uncertainty of product quality indicators;

[0031] In this embodiment, the surrogate model is first trained. During training, data on casting process parameter combinations and their corresponding product quality indicators are collected. This product quality indicator data is obtained through historical production records, experimental tests, etc. By analyzing and processing the data, the deep learning model structure, such as a neural network, is determined.

[0032] When training the surrogate model, a loss function is used to measure the difference between the model's predicted values ​​and the actual values. The model's parameters are continuously adjusted so that the model can accurately take the combination of casting process parameters as input and output the predicted values ​​and uncertainties of product quality indicators.

[0033] Furthermore, when training the surrogate model, the quality and diversity of the data also need to be considered. The data may contain noise, outliers, etc., requiring preprocessing such as data cleaning and normalization to improve the model's training effectiveness. Simultaneously, to ensure the model has better generalization ability, the training data should cover various combinations of casting process parameters.

[0034] After training, the surrogate model is evaluated. For example, methods such as cross-validation are used to divide the dataset into training and test sets, and the model's performance is evaluated on the test set. Evaluation metrics may include mean squared error and mean absolute error to ensure the model's predictive accuracy and reliability. Only when the surrogate model reaches a certain performance standard can it be used for subsequent uncertainty fusion and optimization steps.

[0035] Training a proxy model includes:

[0036] Obtain historical production datasets and material specification ranges;

[0037] Based on the historical production dataset, training data is obtained to train a physical information fusion proxy model. The proxy model is built on a Bayesian neural network, and its loss function includes a data fitting term and a physical information penalty term.

[0038] The proxy model outputs the predicted mean and variance of product quality indicators, as well as the model confidence level calculated based on the variance and calibration error.

[0039] In this embodiment, the historical production dataset and material specification range are first obtained. The historical production dataset can be collected from past casting production records, covering product quality index data corresponding to different combinations of casting process parameters. The material specification range defines the range of various parameters of the materials used in the casting process, providing physical information constraints for the model.

[0040] Secondly, when acquiring training data based on historical production datasets, the raw data undergoes screening and processing. Invalid data, outliers, and other noise are removed. The dataset is then divided into training, validation, and test sets in a 7:1.5:1.5 ratio. The training set is used for model training, the validation set is used to adjust the model's hyperparameters during training, and the test set is used for final performance evaluation.

[0041] Furthermore, a physical information fusion surrogate model is trained, which is built upon a Bayesian neural network. The Bayesian neural network handles uncertainty by outputting the predicted mean and variance of product quality indicators, as well as a model confidence score calculated based on the variance and calibration error. The loss function includes a data fitting term and a physical information penalty term. The data fitting term measures the difference between the model's predicted values ​​and the actual values, prompting the model to accurately fit the training data. The physical information penalty term uses physical information such as material specification ranges to constrain the model's output, making the model's predictions more consistent with actual physical laws.

[0042] Specifically, during training, the model parameters are continuously adjusted to minimize the loss function. Optimization algorithms such as stochastic gradient descent can be used to update the model parameters based on the gradient information of the loss function. Simultaneously, to prevent overfitting, regularization methods, such as L1 and L2 regularization, are employed to limit the model's complexity.

[0043] For example, the steps for constructing and training an agent model based on a Bayesian neural network are as follows:

[0044] First, data preparation involves acquiring training data, which is collected based on historical production datasets.

[0045] Secondly, in model construction, the number of nodes in the input layer is equal to the dimension of the input features. For example, if there are 4 features in the combination of casting process parameters, the input layer contains 4 nodes. Set 1-3 hidden layers, and adjust the number of nodes in each layer through experiments, such as 64, 32, etc. The activation function is ReLU. The output layer generally does not use an activation function. For example, if the output takes 2 nodes, directly output continuous values.

[0046] Next, during model training, the predicted values ​​and uncertainties of product quality indicators are used as outputs. The Adam optimizer and mean squared error loss function are used to construct the training framework. The loss function includes a data fitting term and a physical information penalty term. The batch size is set to 32, the total number of training epochs is 50, and an early stopping mechanism with a patience of 5 is introduced. When the validation set loss does not decrease for 5 consecutive epochs, the training process is automatically terminated, resulting in a trained surrogate model. This effectively avoids overfitting while ensuring the model reaches convergence.

[0047] After training, the surrogate model undergoes a comprehensive evaluation. Besides using metrics such as mean squared error and mean absolute error to assess the model's predictive accuracy, it's also necessary to evaluate the reliability of the uncertainty in the model's output. For example, the accuracy of the model's confidence level can be verified by comparing the confidence intervals predicted by the model with the distribution of actual data. Only when the surrogate model meets certain standards in both predictive accuracy and uncertainty assessment can it be applied to subsequent uncertainty fusion and optimization steps to support the optimization of casting shrinkage process parameters.

[0048] Furthermore, the loss function includes a data fitting term and a physical information penalty term, including:

[0049] Based on automatic differentiation technology, the partial derivatives of the physical field predictions output by the proxy model with respect to the spatiotemporal coordinates are calculated.

[0050] Substitute the predicted physical field values ​​and their partial derivatives with respect to the spatiotemporal coordinates into the preset physical control equations, and calculate the difference between the left and right sides of the equations as the physical residuals.

[0051] The mean square error of the physical residual is calculated as a physical information penalty term;

[0052] The mean squared error between the predicted value of the surrogate model and the label value in the training data is calculated as a data fitting term; the training data includes experimental data and high-fidelity simulation data.

[0053] A total loss function is constructed based on a physical information penalty term and a data fitting term;

[0054] An adaptive weight scheduling strategy is adopted, which assigns higher weights to the physical information penalty term in the early stage of training and increases the weights of the data fitting term in the later stage of training.

[0055] In this embodiment, firstly, based on automatic differentiation technology, the partial derivatives of the physical field predictions output by the surrogate model with respect to spatiotemporal coordinates are calculated. Automatic differentiation technology is a method for calculating derivatives; by obtaining the rate of change of the physical field predictions in spatiotemporal coordinates, it provides a basis for subsequent physical residual calculations. This technology allows for the rapid acquisition of the required partial derivative results without manually deriving complex derivative formulas, improving computational efficiency and accuracy.

[0056] Secondly, the predicted physical field values ​​and their partial derivatives with respect to spatiotemporal coordinates are substituted into the preset physical control equations, and the difference between the left and right sides of the equations is calculated as the physical residual. The preset physical control equations are established based on the physical laws of the casting process and describe the evolution of the physical field in space and time. By calculating the physical residual, the degree of deviation between the output of the surrogate model and the actual physical laws can be measured. The smaller the physical residual, the more the model's output conforms to the actual physical situation.

[0057] For example, the physical law is that the equation for heat conduction is: That is, the rate of change of temperature over time minus the effect of heat dissipation and diffusion results in zero. In this application, the entire temperature field T predicted by the neural network is first substituted into the equation, and the rate of change is calculated using automatic differentiation. and heat dissipation items .

[0058] Then, through the formula To perform the calculations, according to the law of conservation of energy, the equations require... The value must be equal to 0. Therefore, the physical residual = The simplified physical residual is .

[0059] Then, the mean squared error of the physical residuals is calculated as a physical information penalty term. Mean squared error is a commonly used error metric that comprehensively considers the error across all sample points. Using the mean squared error of the physical residuals as a penalty term can encourage the model's output to better conform to physical laws during training. When the physical residuals are large, the value of the physical information penalty term will also increase accordingly, thus occupying a larger proportion in the loss function and guiding the model to adjust its parameters to reduce the physical residuals.

[0060] Simultaneously, the mean squared error between the predicted values ​​of the surrogate model and the label values ​​in the training data is calculated as a data fitting term. The training data includes experimental data and high-fidelity simulation data. The experimental data is obtained through actual casting production experiments and has high realism; the high-fidelity simulation data is obtained through numerical simulation methods and can simulate complex casting processes. Combining these two types of data provides the model with richer information. The data fitting term measures how well the model fits the training data; the smaller the value, the better the model fits the training data.

[0061] Next, a total loss function is constructed based on the physical information penalty term and the data fitting term. The total loss function is the objective function for model training, comprehensively considering the model's ability to fit the data and its adherence to physical laws. By minimizing the total loss function, an optimal set of model parameters can be found, enabling the model to fit the data while also conforming to actual physical laws.

[0062] Finally, an adaptive weight scheduling strategy is adopted, assigning higher weights to the physical information penalty term in the early stages of training and increasing the weights to the data fitting term in the later stages. In the early stages of training, the model has limited understanding of physical laws; assigning higher weights to the physical information penalty term guides the model to quickly learn these laws and avoids it getting trapped in local optima that do not conform to physical reality. As training progresses and the model gradually grasps certain physical laws, increasing the weights to the data fitting term allows the model to better fit the training data, improving its prediction accuracy. Through this adaptive weight scheduling strategy, we can fully leverage the advantages of both physical and data information to improve the performance of the surrogate model.

[0063] Specifically, the adaptive weight scheduling strategy includes:

[0064] The initial value and target final value of the weight coefficient of the physical information penalty item are preset, where the initial value is greater than the target final value;

[0065] During the training of the surrogate model, the weight coefficient value of the physical information penalty term used in the current training round is dynamically calculated according to the proportion of the current training round to the total training rounds. The dynamic calculation follows a preset mathematical decay relationship, so that the weight coefficient value of the physical information penalty term decreases monotonically from the initial value to the target final value as the training rounds increase.

[0066] In each training round, the physical information penalty term is weighted according to the weight coefficient value of the physical information penalty term dynamically calculated in the current round, and the weighted physical information penalty term is added to the data fitting term to form the total loss function of the training round, which is used for surrogate model optimization.

[0067] In this embodiment, firstly, an initial value and a target final value for the weight coefficient of the physical information penalty term are preset, wherein the initial value is greater than the target final value. For example, the initial value is set to 0.8 and the target final value is set to 0.2.

[0068] Secondly, during the training of the surrogate model, the weight coefficient of the physical information penalty term used in the current training round is dynamically calculated according to the proportion of the current training round to the total training rounds. The dynamic calculation follows a preset mathematical decay relationship, so that the weight coefficient of the physical information penalty term decreases monotonically from the initial value to the target final value as the training rounds increase.

[0069] For example, assuming a total of 1000 training rounds, when training reaches round 200, the current training round accounts for 0.2% of the total training rounds. Using a linear decay relationship, the weight coefficient of the physical information penalty term in the current round can be calculated using the formula: Current weight coefficient = Initial value - (Initial value - Target final value) × Current round proportion, i.e., 0.8 - (0.8 - 0.2) × 0.2 = 0.68.

[0070] Furthermore, in each training round, the physical information penalty term is weighted based on the dynamically calculated weight coefficient value of the physical information penalty term for the current round. The weighted physical information penalty term is then added to the data fitting term to form the total loss function for that training round, which is used for surrogate model optimization. For example, in the 200th round, the physical information penalty term is multiplied by 0.68 and then added to the data fitting term to obtain the total loss function for this round.

[0071] Then, optimization algorithms such as stochastic gradient descent are used to update the model parameters based on the gradient information of the total loss function, so that the value of the total loss function continuously decreases.

[0072] As the training rounds increase, the weight coefficient of the physical information penalty term gradually decreases, while the weight of the data fitting term relatively increases. Near the end of training, the weight coefficient of the physical information penalty term approaches the target final value of 0.2. At this point, the model, while adhering to physical laws, focuses more on fitting the training data, thereby improving the model's prediction accuracy. Through an adaptive weight scheduling strategy, the surrogate model can fully utilize physical and data information, continuously optimizing during training and providing more reliable support for optimizing casting shrinkage process parameters.

[0073] S20: Construct an uncertainty fusion engine to fuse the uncertainty of surrogate model prediction, the uncertainty of process parameter fluctuations, and the uncertainty of material parameter ranges, and output a comprehensive uncertainty envelope;

[0074] In this embodiment, an uncertainty fusion engine is constructed. First, the uncertainty in the surrogate model prediction stems from the limitations of the model itself and the incompleteness of the training data. The uncertainty in process parameter fluctuations arises because, in actual casting, process parameters such as temperature, pressure, and pouring speed fluctuate within a certain range. The uncertainty in material parameter ranges arises because the properties of the materials used in casting are not fixed values ​​but vary within a certain range.

[0075] A probability distribution is employed, integrating the uncertainties of surrogate model predictions, process parameter fluctuations, and material parameter ranges. For the surrogate model prediction uncertainty, a corresponding probability distribution is constructed using information such as the variance and confidence level of the output product quality indicators. For the uncertainties of process parameter fluctuations and material parameter ranges, their respective probability distributions are determined based on parameter measurements and statistical analysis in actual production.

[0076] Then, using the Monte Carlo simulation method, random sampling is performed from the probability distributions of various uncertain factors. Each sampling yields a specific set of parameter values, which are then input into the surrogate model to obtain a predicted value for a product quality indicator. This process of sampling and prediction is repeated extensively to obtain a series of predicted product quality indicator values.

[0077] Statistical analysis is performed on the predicted values, such as calculating their mean and variance, to construct a comprehensive uncertainty envelope. This comprehensive uncertainty envelope reflects the possible range of values ​​for the product quality indicators after considering various uncertainty factors.

[0078] The construction of an uncertainty fusion engine includes:

[0079] Analyze historical production data to determine the statistical distribution of key process parameters as a measure of parameter random uncertainty;

[0080] Based on the material specification range, the range uncertainty of key material parameters is defined;

[0081] Monte Carlo sampling is used to fuse and propagate the random uncertainty of the parameters, the interval uncertainty, and the cognitive uncertainty of the proxy model.

[0082] Output the comprehensive uncertainty envelope of product quality indicators under a given combination of process parameters, and calculate the overall reliability of the corresponding combination of process parameters.

[0083] In this embodiment, firstly, historical production data is analyzed to determine the statistical distribution of key process parameters, which serves as a representation of parameter random uncertainty. Historical production data is a structured record of processes and results accumulated by the enterprise over a long period, reflecting actual production fluctuations. Its core purpose is to quantify the inherent randomness in production. For example, the specific values ​​of temperature in different batches of production can be statistically analyzed, and then statistical methods can be used to determine its distribution characteristics, including parameters such as mean and standard deviation. The statistical distribution can accurately reflect the random fluctuations of process parameters during production, serving as a quantitative representation of parameter random uncertainty.

[0084] For example, suppose the production logs of a foundry for the past 100 batches of similar products show that the pouring temperature required by the process card is 1550°C, but the average value of the actual temperature records is 1552°C, the standard deviation is 8°C, and it roughly conforms to a normal distribution. By analyzing 100 historical data points, the random uncertainty of the key process parameter "pouring temperature" is determined to be: N(1552, 8²).

[0085] Secondly, based on the material specification range, the range uncertainty of key material parameters is defined. The material specification range is a core input parameter, specifically referring to the allowable fluctuation range of the composition or physical properties of key raw materials, such as pig iron, alloys, and inoculants, in casting production. For example, the carbon equivalent in cast iron is 3.9%~4.3%.

[0086] Furthermore, interval uncertainty refers to characterizing the uncertainty of a material's properties by not making probability distribution assumptions about the random fluctuations in its properties, but only by using the upper and lower limits of its allowable fluctuations. In other words, the uncertainty of this parameter is defined as a closed interval, rather than a probability distribution.

[0087] For example, the linear shrinkage rate of a certain cast aluminum alloy is nominally 1.2%, with an allowable fluctuation range of ±0.05%. Its interval uncertainty is then defined as: α∈[1.15%, 1.25%]. By clearly defining the interval uncertainty of key material parameters, the impact of material properties on product quality can be fully considered in subsequent analyses.

[0088] Then, Monte Carlo sampling is used to fuse and propagate the random uncertainties of parameters, interval uncertainties, and cognitive uncertainties of the surrogate model. Monte Carlo sampling is a numerical calculation method based on probability statistics that can randomly draw a large number of samples from the probability distributions of various uncertainties. For random uncertainties of parameters, sampling is performed according to the previously determined statistical distribution; for interval uncertainties, random sampling is performed within the material specification interval; for cognitive uncertainties of the surrogate model, a probability distribution is constructed based on information such as the variance and confidence level of the model output, and sampling is performed. Each sampling yields a set of specific parameter values, which are input into the surrogate model to obtain a predicted value of a product quality indicator. By repeating a large number of sampling and predictions, the possible changes in product quality indicators under the interaction of various uncertainties can be simulated.

[0089] Specifically, the Monte Carlo method works by sampling a large number of random samples from the input distribution. For example, each sampling generates a set of parameters affected by fluctuations, and each set of samples is input into the surrogate model to obtain the corresponding quality prediction distribution, i.e., the mean and variance.

[0090] Finally, the comprehensive uncertainty envelope of the product quality indicators under a given combination of process parameters is output, and the overall reliability of the corresponding process parameter combination is calculated. By statistically analyzing the sampled predicted values ​​of the product quality indicators, the mean, variance, and other statistical measures are calculated to construct the comprehensive uncertainty envelope. The comprehensive uncertainty envelope reflects the possible range of values ​​for the product quality indicators after considering various uncertainty factors. Simultaneously, based on the range and shape of the comprehensive uncertainty envelope, the overall reliability of the corresponding process parameter combination can be calculated. The overall reliability reflects the probability that the product quality will meet the expected standards under the current combination of process parameters.

[0091] The above methods provide a more comprehensive and accurate basis for optimizing the process parameters of shrinkage cavity in castings.

[0092] Furthermore, through Monte Carlo sampling, the random uncertainty of the parameters, the interval uncertainty, and the cognitive uncertainty of the surrogate model are fused and propagated, including:

[0093] For a given combination of process parameters, perform the first layer of Monte Carlo sampling to generate N parameter samples that simulate actual fluctuations based on the statistical distribution of key process parameters.

[0094] For each of the N parameter samples, a second layer of Monte Carlo sampling is performed to uniformly generate M material parameter samples within the allowable range of the key material parameters.

[0095] The generated N multiplied by M comprehensive parameter samples are input into the proxy model to obtain the predicted probability distribution of the corresponding N multiplied by M product quality indicators;

[0096] Aggregate all predicted probability distribution results and calculate the statistical mean and standard deviation of product quality indicators. The statistical mean is used as the predicted mean for the given combination of process parameters, and the standard deviation is used to construct the width of the comprehensive uncertainty envelope.

[0097] Simultaneously, based on the variance information of the N multiplied by M predicted probability distributions, the average variance is calculated as a quantitative value reflecting the model's cognitive uncertainty. This quantitative value is then combined with the standard deviation caused by parameter fluctuations to calculate the overall credibility.

[0098] In this embodiment, firstly, for a given combination of process parameters, a first-level Monte Carlo sampling is performed. Based on the statistical distribution of key process parameters determined by the previous analysis of historical production data, N parameter samples simulating actual fluctuations are generated. For example, for key process parameters such as temperature, pressure, and casting speed, random sampling is performed according to their respective statistical distributions to obtain N different combinations of process parameters, reflecting the random fluctuations of process parameters in actual production.

[0099] Secondly, for each of the N parameter samples, a second layer of Monte Carlo sampling is performed. Within the allowable range of the key material parameters, M material parameter samples are uniformly generated. For example, for key material parameters such as carbon equivalent in cast iron and linear shrinkage rate of cast aluminum alloys, uniform random sampling is performed within their specified ranges, and M different material parameter combinations are matched with each process parameter sample.

[0100] Then, the generated N multiplied by M comprehensive parameter samples are input into the surrogate model. Each comprehensive parameter sample contains a set of process parameters and a set of material parameters, which are sequentially input into the surrogate model to obtain the predicted probability distribution of the corresponding N multiplied by M product quality indicators. The surrogate model will output the possible value range of the product quality indicators and the corresponding probabilities based on the input parameters.

[0101] Next, all predicted probability distribution results are aggregated. Statistical analysis is performed on N multiplied by M predicted probability distributions to calculate the statistical mean and standard deviation of the product quality indicators. The statistical mean is used as the predicted mean for a given combination of process parameters, reflecting the average expected value of the product quality indicators after considering various uncertainties. The standard deviation is used to construct the width of the comprehensive uncertainty envelope; the larger the standard deviation, the greater the fluctuation range of the product quality indicators, and the higher the uncertainty.

[0102] Simultaneously, the average variance is calculated based on the variance information of the N multiplied by M predicted probability distributions. This average variance, as a quantitative value reflecting the model's cognitive uncertainty, embodies the prediction uncertainty caused by the surrogate model's inherent limitations and incomplete training data. This quantitative value is then combined with the standard deviation caused by parameter fluctuations to calculate the overall reliability.

[0103] For example, assuming N is 100 and M is 50, a total of 5000 comprehensive parameter samples are generated. After calculation using the surrogate model, the predicted probability distributions of 5000 sets of product quality indicators are obtained. Aggregate analysis of these 5000 distributions yields a statistical mean of 80 and a standard deviation of 5 for the product quality indicators. This indicates that under the current combination of process parameters, the average expected value of the product quality indicators is 80, and the range of fluctuation can be represented by the standard deviation of 5, which can be used to construct the width of the comprehensive uncertainty envelope. Simultaneously, based on the variance information of the 5000 predicted probability distributions themselves, the average variance is calculated to be 3. The average variance of 3 is combined with the standard deviation of 5 caused by parameter fluctuations, and through weighted summation, the overall confidence level of this process parameter combination is calculated. Assuming the calculated overall confidence level is 0.8, this indicates that under the current combination of process parameters, the probability of the product quality meeting the expected standard is 80%.

[0104] By comprehensively considering the cognitive uncertainty of the model and the fluctuation uncertainty of the parameters, the likelihood of the product quality reaching the expected standard under the current combination of process parameters is assessed.

[0105] S30: Based on the predicted values ​​of the product quality indicators and the comprehensive uncertainty envelope, define and calculate the robustness evaluation index;

[0106] In this embodiment, to more scientifically evaluate the merits of the casting shrinkage process, a robustness evaluation index is defined and calculated based on the predicted values ​​of product quality indicators and the comprehensive uncertainty envelope. First, the robustness evaluation index measures the stability and reliability of product quality when the process faces various uncertainties. The robustness evaluation index is defined as the probability that the predicted value of the product quality indicator falls within the comprehensive uncertainty envelope. A higher probability indicates a more robust process under uncertain conditions, and a more stable ability to achieve the expected product quality standards.

[0107] Furthermore, when calculating this robustness evaluation index, the predicted probability distribution of the product quality indicators obtained through Monte Carlo sampling and the constructed comprehensive uncertainty envelope are used as the basis. For each predicted probability distribution, the proportion of its portion falling within the comprehensive uncertainty envelope is determined.

[0108] Step S30 in the method includes:

[0109] The robustness evaluation index R is calculated using the formula: R = (μ × f(Cm, Co)) / (σ + ε).

[0110] Where μ is the predicted mean of the product quality index, σ is the standard deviation of the comprehensive uncertainty envelope, Cm is the model confidence level, Co is the overall confidence level, f(Cm,Co) is the confidence-based gain function, and ε is a minimal constant to prevent division by zero.

[0111] In this embodiment, firstly, the predicted mean μ of the product quality indicators is calculated by aggregating the predicted probability distributions of N multiplied by M groups of product quality indicators obtained from previous Monte Carlo sampling. This statistical mean reflects the average expected value of the product quality indicators after considering various uncertainties. The standard deviation σ of the comprehensive uncertainty envelope is used to construct the width of the comprehensive uncertainty envelope. The larger the standard deviation, the greater the fluctuation range of the product quality indicators, and the higher the uncertainty.

[0112] Model confidence Cm reflects the reliability of the surrogate model's own predictions and is related to factors such as the training quality and data completeness of the surrogate model. Overall confidence Co reflects the probability that the product quality will meet the expected standards under the current combination of process parameters. It is calculated by combining the quantified value of the model's cognitive uncertainty with the standard deviation caused by parameter fluctuations.

[0113] The confidence-based gain function f(Cm, Co) adjusts the robustness evaluation index based on model confidence and overall confidence. Its specific form can be designed according to actual conditions, aiming to more reasonably assess the robustness of the process while considering the confidence of the model and process parameters. For example, when both model confidence and overall confidence are high, this function can appropriately increase the value of the robustness evaluation index to reflect the advantages of the process under reliable model and parameter conditions.

[0114] The minimum constant ε is used to prevent division by zero during calculations, ensuring the stability and accuracy of the calculations.

[0115] Furthermore, when calculating the robustness evaluation index R, the values ​​of the above parameters are substituted into the formula R = (μ × f(Cm, Co)) / (σ + ε). For example, assuming the predicted mean μ of the product quality index is 85, the standard deviation σ of the comprehensive uncertainty envelope is 6, the model confidence level Cm is 0.9, the overall confidence level Co is 0.8, the confidence-based gain function f(Cm, Co) is calculated to be 1.1, and the minimum constant ε is set to 0.001. Then, substituting into the formula, we get: R = (85 × 1.1) / (6 + 0.001) = 93.5 / 6.001 ≈ 15.58.

[0116] The robustness evaluation index R, obtained through calculation, can be used to intuitively assess the robustness of the current casting shrinkage process in the face of various uncertainties. The larger the R value, the more robust the process is in uncertain environments, and the more consistently the product quality can meet the expected standards.

[0117] S40: With the dual objectives of optimizing product quality indicators and the robustness evaluation indicators, run a multi-objective optimization algorithm to search for and obtain a robust Pareto front solution set;

[0118] In this embodiment, to simultaneously improve the product quality of the casting shrinkage process and its robustness in dealing with uncertainties, a multi-objective optimization algorithm is run with the dual objectives of optimizing product quality indicators and robustness evaluation indicators to search for a robust Pareto front solution set. The multi-objective optimization algorithm aims to find a set of non-dominated solutions, i.e., a robust Pareto front solution set, in which no single solution can improve a particular objective without compromising other objectives.

[0119] When running a multi-objective optimization algorithm, the algorithm type and parameter settings are first determined. During the search process, new combinations of process parameters are continuously generated, and the product quality index and robustness evaluation index corresponding to each combination are calculated. The process parameter combinations are evaluated and screened, retaining solutions that perform well on both objectives. Through iteration, the algorithm gradually approaches the robust Pareto front solution set.

[0120] Specifically, step S40 in the method includes:

[0121] An improved multi-objective Bayesian optimization algorithm is employed, wherein the acquisition function is guided by the model confidence.

[0122] In the non-dominated ranking of population iterations, individuals with similar robustness evaluation indicators are given priority for selection based on overall reliability.

[0123] The final output is a robust Pareto front solution set that achieves the best overall performance in terms of product quality, robustness, and reliability.

[0124] In this embodiment, an improved multi-objective Bayesian optimization algorithm is first employed to more effectively search for robust Pareto front solutions. The algorithm's acquisition function is guided by model confidence, indicating that during the search process, it tends to explore regions with higher surrogate model confidence. Regions with high model confidence tend to have more reliable predictions, reducing unnecessary searches and improving algorithm efficiency.

[0125] For example, model confidence guidance can be expressed as aEI(x) = EI(x) × g(C_m(x)). Here, EI(x) is the traditional expected improvement value, and g(C_m(x)) is a monotonically increasing function of the model confidence C_m(x). When the EI values ​​of two candidate points are similar, the point with higher model confidence will receive a larger acquisition function value and will be prioritized for the next high-fidelity evaluation. This step allows the optimization algorithm to proactively avoid parameter regions where model cognition is ambiguous and predictions are unreliable, even in Pareto front searches, tending to find robust solutions in spaces where the model has learned more thoroughly.

[0126] Secondly, in the non-dominated ranking stage of population iteration, for individuals with similar robustness evaluation indicators, individuals with higher overall reliability are prioritized. Overall reliability reflects the probability that the product quality will meet the expected standards under the current combination of process parameters. Prioritizing individuals with higher overall reliability ensures that the final solution is more advantageous in terms of achieving the expected product quality standards.

[0127] Throughout the search process, the algorithm continuously generates new combinations of process parameters. For each new combination, the algorithm uses the previously implemented Monte Carlo sampling method to fuse and propagate the random uncertainty, interval uncertainty, and cognitive uncertainty of the surrogate model, resulting in the corresponding product quality index and robustness evaluation index. Then, the process parameter combinations are evaluated and screened, eliminating combinations that perform poorly in both product quality and robustness evaluation indices, retaining only the better-performing solutions.

[0128] As the iterations continue, the algorithm gradually approaches the robust Pareto front solution set. The final output robust Pareto front solution set is the optimal solution in terms of product quality, robustness, and reliability. It represents the best combination of process parameters that, under the current algorithm and conditions, can simultaneously ensure product quality in the casting shrinkage process and robustness in dealing with uncertainties.

[0129] S50: Based on the robust Pareto front solution set, recommend the final process parameter scheme.

[0130] In this embodiment, the final process parameter scheme is recommended based on the obtained robust Pareto front solution set and by considering multiple factors. First, the actual production cost needs to be considered. Different combinations of process parameters may correspond to different costs such as raw material consumption, energy consumption, and equipment depreciation.

[0131] Secondly, certain combinations of process parameters may lead to excessively long production cycles, affecting overall production efficiency. In actual production, it is necessary to quickly bring products to market to generate profits, so priority should be given to selecting process parameter combinations that can both ensure product quality and robustness and improve production efficiency.

[0132] The recommended final process parameter scheme includes:

[0133] The robust Pareto front solution set is visualized through a human-machine collaborative decision-making interface. Each solution in the robust Pareto front solution set is labeled with its corresponding model confidence and overall credibility. The visualization is achieved by plotting the robustness-performance Pareto front in a two-dimensional chart. Each point in the two-dimensional chart represents a candidate solution. The horizontal axis is the predicted value of the product quality index, the vertical axis is the robustness evaluation index, and the color of the point maps the overall credibility.

[0134] Receive user interaction instructions, determine the final solution, and generate a complete report that includes process parameters, performance predictions, uncertainty assessments, and credibility ratings.

[0135] In this embodiment, the robust Pareto front solution set is first visualized through a human-machine collaborative decision-making interface. A robustness-performance Pareto front is plotted in a two-dimensional chart, with each point representing a candidate solution. The horizontal axis represents the predicted value of the product quality indicator, and the vertical axis represents the robustness evaluation indicator. The color of the point maps to the overall credibility. This visualization method makes the differences between different solutions in terms of product quality, robustness, and credibility more apparent. For example, darker-colored points represent solutions with higher overall credibility, allowing decision-makers to quickly identify solutions with a higher probability of achieving the expected product quality standards.

[0136] Meanwhile, each solution in the robust Pareto front solution set is labeled with its corresponding model confidence and overall credibility. The model confidence reflects the reliability of the surrogate model for its own predictions, while the overall credibility reflects the likelihood that the product quality will meet the expected standards under the current combination of process parameters.

[0137] Secondly, it receives user interaction commands. Decision-makers can operate on the visual interface, such as clicking and dragging, to select a solution that meets their needs. During the process, users can comprehensively consider various factors based on information such as model confidence, overall credibility, product quality indicators, and robustness evaluation indicators to determine the final solution.

[0138] Furthermore, after the final solution is determined, a complete report will be generated, including process parameters, performance predictions, uncertainty assessments, and credibility ratings. The process parameters section lists the various process parameters corresponding to this solution, providing clear guidance for actual production.

[0139] In summary, compared to existing technologies, this application optimizes the shrinkage cavity process in castings by considering various factors such as model cognitive uncertainty and parameter fluctuation uncertainty. When determining the final process parameter scheme, a robust Pareto front solution set is obtained through a search, and the solution set is visualized through a human-machine collaborative decision-making interface, allowing decision-makers to intuitively select based on information such as model confidence, overall credibility, product quality indicators, and robustness evaluation indicators.

[0140] In summary, the embodiments of this application have at least the following technical effects:

[0141] This application provides a deep learning-based method for optimizing casting shrinkage process parameters. First, a surrogate model is trained using deep learning to output predicted values ​​and uncertainties of product quality indicators, improving prediction accuracy. Second, an uncertainty fusion engine is constructed to integrate multiple uncertainties, considering the impact of process parameter fluctuations and material parameter ranges in actual production, making subsequent analysis and decision-making more consistent with reality. Third, robustness evaluation indices are defined and calculated based on the predicted values ​​of product quality indicators and the comprehensive uncertainty envelope, evaluating process parameter schemes from multiple dimensions and providing a more comprehensive basis for optimization. Then, a robust Pareto front solution set is obtained by searching with the dual objectives of optimizing product quality indicators and robustness evaluation indices, improving the robustness of the scheme while ensuring product quality and avoiding production problems caused by various uncertainties. Finally, a final process parameter scheme is recommended based on the robust Pareto front solution set. The solution set is visualized through a human-machine collaborative decision-making interface, and user interaction instructions are received to determine the final scheme, ensuring both the scientific nature of the decision-making and consideration of the user's actual needs and preferences. Through the above technical solution, this application effectively solves the shortcomings of existing methods for optimizing casting shrinkage process parameters, improves optimization efficiency, enhances the accuracy and reliability of results, helps reduce the probability of shrinkage problems in castings, reduces production costs, improves the quality and market competitiveness of casting products, and provides technical support for the development of the manufacturing industry.

[0142] Example 2, as Figure 2 As shown, based on the same inventive concept as the deep learning-based method for optimizing casting shrinkage process parameters provided in Embodiment 1, this application also provides a deep learning-based system for optimizing casting shrinkage process parameters, including:

[0143] Model training module 11 is used to train a proxy model, which takes a combination of casting process parameters as input and outputs the predicted value and uncertainty of product quality indicators.

[0144] The parameter fusion module 12 is used to build an uncertainty fusion engine, which fuses the uncertainty of the surrogate model prediction, the uncertainty of process parameter fluctuations, and the uncertainty of material parameter ranges, and outputs a comprehensive uncertainty envelope.

[0145] The indicator calculation module 13 is used to define and calculate the robustness evaluation index based on the predicted value of the product quality index and the comprehensive uncertainty envelope.

[0146] The indicator optimization module 14 is used to run a multi-objective optimization algorithm with the dual objectives of optimizing product quality indicators and robustness evaluation indicators, and to search for and obtain a robust Pareto front solution set.

[0147] The scheme recommendation module 15 is used to recommend the final process parameter scheme based on the robust Pareto front solution set.

[0148] Furthermore, in one embodiment of the application, training a proxy model includes:

[0149] Obtain historical production datasets and material specification ranges;

[0150] Based on the historical production dataset, training data is obtained to train a physical information fusion proxy model. The proxy model is built on a Bayesian neural network, and its loss function includes a data fitting term and a physical information penalty term.

[0151] The proxy model outputs the predicted mean and variance of product quality indicators, as well as the model confidence level calculated based on the variance and calibration error.

[0152] Furthermore, in one embodiment, the loss function includes a data fitting term and a physical information penalty term, including:

[0153] Based on automatic differentiation technology, the partial derivatives of the physical field predictions output by the proxy model with respect to the spatiotemporal coordinates are calculated.

[0154] Substitute the predicted physical field values ​​and their partial derivatives with respect to the spatiotemporal coordinates into the preset physical control equations, and calculate the difference between the left and right sides of the equations as the physical residuals.

[0155] The mean square error of the physical residual is calculated as a physical information penalty term;

[0156] The mean squared error between the predicted value of the surrogate model and the label value in the training data is calculated as a data fitting term; the training data includes experimental data and high-fidelity simulation data.

[0157] A total loss function is constructed based on a physical information penalty term and a data fitting term;

[0158] An adaptive weight scheduling strategy is adopted, which assigns higher weights to the physical information penalty term in the early stage of training and increases the weights of the data fitting term in the later stage of training.

[0159] Furthermore, in one embodiment, the adoption of an adaptive weight scheduling strategy includes:

[0160] The initial value and target final value of the weight coefficient of the physical information penalty item are preset, where the initial value is greater than the target final value;

[0161] During the training of the surrogate model, the weight coefficient value of the physical information penalty term used in the current training round is dynamically calculated according to the proportion of the current training round to the total training rounds. The dynamic calculation follows a preset mathematical decay relationship, so that the weight coefficient value of the physical information penalty term decreases monotonically from the initial value to the target final value as the training rounds increase.

[0162] In each training round, the physical information penalty term is weighted according to the weight coefficient value of the physical information penalty term dynamically calculated in the current round, and the weighted physical information penalty term is added to the data fitting term to form the total loss function of the training round, which is used for surrogate model optimization.

[0163] In one embodiment, constructing an uncertainty fusion engine includes:

[0164] Analyze historical production data to determine the statistical distribution of key process parameters as a measure of parameter random uncertainty;

[0165] Based on the material specification range, the range uncertainty of key material parameters is defined;

[0166] Monte Carlo sampling is used to fuse and propagate the random uncertainty of the parameters, the interval uncertainty, and the cognitive uncertainty of the proxy model.

[0167] Output the comprehensive uncertainty envelope of product quality indicators under a given combination of process parameters, and calculate the overall reliability of the corresponding combination of process parameters.

[0168] Furthermore, in one embodiment, Monte Carlo sampling is used to fuse and propagate the random uncertainty of the parameters, the interval uncertainty, and the cognitive uncertainty of the surrogate model, including:

[0169] For a given combination of process parameters, perform the first layer of Monte Carlo sampling to generate N parameter samples that simulate actual fluctuations based on the statistical distribution of key process parameters.

[0170] For each of the N parameter samples, a second layer of Monte Carlo sampling is performed to uniformly generate M material parameter samples within the allowable range of the key material parameters.

[0171] The generated N multiplied by M comprehensive parameter samples are input into the proxy model to obtain the predicted probability distribution of the corresponding N multiplied by M product quality indicators;

[0172] Aggregate all predicted probability distribution results and calculate the statistical mean and standard deviation of product quality indicators. The statistical mean is used as the predicted mean for the given combination of process parameters, and the standard deviation is used to construct the width of the comprehensive uncertainty envelope.

[0173] Simultaneously, based on the variance information of the N multiplied by M predicted probability distributions, the average variance is calculated as a quantitative value reflecting the model's cognitive uncertainty. This quantitative value is then combined with the standard deviation caused by parameter fluctuations to calculate the overall credibility.

[0174] In one embodiment, the indicator calculation module 13 is specifically used for:

[0175] The robustness evaluation index R is calculated using the formula: R = (μ × f(Cm, Co)) / (σ + ε).

[0176] Where μ is the predicted mean of the product quality index, σ is the standard deviation of the comprehensive uncertainty envelope, Cm is the model confidence level, Co is the overall confidence level, f(Cm,Co) is the confidence-based gain function, and ε is a minimal constant to prevent division by zero.

[0177] In one embodiment, the indicator optimization module 14 is specifically used for:

[0178] An improved multi-objective Bayesian optimization algorithm is employed, wherein the acquisition function is guided by the model confidence.

[0179] In the non-dominated ranking of population iterations, individuals with similar robustness evaluation indicators are given priority for selection based on overall reliability.

[0180] The final output is a robust Pareto front solution set that achieves the best overall performance in terms of product quality, robustness, and reliability.

[0181] Furthermore, in one embodiment, a recommended final process parameter scheme includes:

[0182] The robust Pareto front solution set is visualized through a human-machine collaborative decision-making interface. Each solution in the robust Pareto front solution set is labeled with its corresponding model confidence and overall credibility. The visualization is achieved by plotting the robustness-performance Pareto front in a two-dimensional chart. Each point in the two-dimensional chart represents a candidate solution. The horizontal axis is the predicted value of the product quality index, the vertical axis is the robustness evaluation index, and the color of the point maps the overall credibility.

[0183] Receive user interaction instructions, determine the final solution, and generate a complete report that includes process parameters, performance predictions, uncertainty assessments, and credibility ratings.

[0184] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, the above description focuses on specific embodiments of this specification. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some implementations, multitasking and parallel processing are possible or may be advantageous.

[0185] The above description is only a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0186] This specification and accompanying drawings are merely illustrative examples of this application and are intended to cover any and all modifications, variations, combinations, or equivalents within the scope of this application. Clearly, those skilled in the art can make various alterations and modifications to this application without departing from its scope. Therefore, if such modifications and modifications fall within the scope of this application and its equivalents, this application intends to include such modifications and modifications.

Claims

1. A method for optimizing casting shrinkage process parameters based on deep learning, characterized in that, The method includes: Train a proxy model that takes a combination of casting process parameters as input and outputs the predicted values ​​and uncertainties of product quality indicators. An uncertainty fusion engine is constructed to fuse the uncertainty of surrogate model prediction, the uncertainty of process parameter fluctuations, and the uncertainty of material parameter ranges, and output a comprehensive uncertainty envelope; Based on the predicted values ​​of the product quality indicators and the comprehensive uncertainty envelope, a robustness evaluation index is defined and calculated. With the dual objectives of optimizing product quality indicators and robustness evaluation indicators, a multi-objective optimization algorithm is run to search for and obtain a robust Pareto front solution set; Based on the robust Pareto front solution set, the final process parameter scheme is recommended; Training an agent model includes: Obtain historical production datasets and material specification ranges; Based on the historical production dataset, training data is obtained to train a physical information fusion proxy model. The proxy model is built on a Bayesian neural network, and its loss function includes a data fitting term and a physical information penalty term. The proxy model outputs the predicted mean, variance, and model confidence level of the product quality indicators based on the variance and calibration error. Constructing an uncertainty fusion engine, including: Analyze historical production data to determine the statistical distribution of key process parameters as a measure of parameter random uncertainty; Based on the material specification range, the range uncertainty of key material parameters is defined; Monte Carlo sampling is used to fuse and propagate the random uncertainty of the parameters, the interval uncertainty, and the cognitive uncertainty of the proxy model. Output the comprehensive uncertainty envelope of product quality indicators under a given combination of process parameters, and calculate the overall reliability of the corresponding combination of process parameters; Through Monte Carlo sampling, the random uncertainty of the parameters, the interval uncertainty, and the cognitive uncertainty of the surrogate model are fused and propagated, including: For a given combination of process parameters, perform the first layer of Monte Carlo sampling to generate N parameter samples that simulate actual fluctuations based on the statistical distribution of key process parameters. For each of the N parameter samples, a second layer of Monte Carlo sampling is performed to uniformly generate M material parameter samples within the allowable range of the key material parameters. The generated N multiplied by M comprehensive parameter samples are input into the proxy model to obtain the predicted probability distribution of the corresponding N multiplied by M product quality indicators; Aggregate all predicted probability distribution results and calculate the statistical mean and standard deviation of product quality indicators. The statistical mean is used as the predicted mean for the given combination of process parameters, and the standard deviation is used to construct the width of the comprehensive uncertainty envelope. Simultaneously, based on the variance information of the N multiplied by M predicted probability distributions, the average variance is calculated as a quantitative value reflecting the model's cognitive uncertainty. This quantitative value is then combined with the standard deviation caused by parameter fluctuations to calculate the overall credibility.

2. The method for optimizing casting shrinkage process parameters based on deep learning according to claim 1, characterized in that, The loss function includes a data fitting term and a physical information penalty term, including: Based on automatic differentiation technology, the partial derivatives of the physical field predictions output by the proxy model with respect to the spatiotemporal coordinates are calculated. Substitute the predicted physical field values ​​and their partial derivatives with respect to the spatiotemporal coordinates into the preset physical control equations, and calculate the difference between the left and right sides of the equations as the physical residuals. The mean square error of the physical residual is calculated as a physical information penalty term; The mean squared error between the predicted value of the surrogate model and the label value in the training data is calculated as a data fitting term; the training data includes experimental data and high-fidelity simulation data. A total loss function is constructed based on a physical information penalty term and a data fitting term; An adaptive weight scheduling strategy is adopted, which assigns higher weights to the physical information penalty term in the early stage of training and increases the weights of the data fitting term in the later stage of training.

3. The method for optimizing casting shrinkage process parameters based on deep learning according to claim 2, characterized in that, The adaptive weight scheduling strategy includes: The initial value and target final value of the weight coefficient of the physical information penalty item are preset, where the initial value is greater than the target final value; During the training of the surrogate model, the weight coefficient value of the physical information penalty term used in the current training round is dynamically calculated according to the proportion of the current training round to the total training rounds. The dynamic calculation follows a preset mathematical decay relationship, so that the weight coefficient value of the physical information penalty term decreases monotonically from the initial value to the target final value as the training rounds increase. In each training round, the physical information penalty term is weighted according to the weight coefficient value of the physical information penalty term dynamically calculated in the current round, and the weighted physical information penalty term is added to the data fitting term to form the total loss function of the training round, which is used for surrogate model optimization.

4. The method for optimizing casting shrinkage process parameters based on deep learning according to claim 1, characterized in that, Based on the predicted values ​​of the product quality indicators and the comprehensive uncertainty envelope, robustness evaluation indicators are defined and calculated, including: The robustness evaluation index R is calculated using the formula: R = (μ × f(Cm, Co)) / (σ + ε). Where μ is the predicted mean of the product quality index, σ is the standard deviation of the comprehensive uncertainty envelope, Cm is the model confidence level, Co is the overall confidence level, f(Cm,Co) is the confidence-based gain function, and ε is a minimal constant to prevent division by zero.

5. The method for optimizing casting shrinkage process parameters based on deep learning according to claim 4, characterized in that, With the dual objectives of optimizing product quality indicators and the aforementioned robustness evaluation indicators, a multi-objective optimization algorithm is run to search for and obtain a robust Pareto front solution set, including: An improved multi-objective Bayesian optimization algorithm is employed, wherein the acquisition function is guided by the model confidence. In the non-dominated ranking of population iterations, individuals with similar robustness evaluation indicators are given priority for selection based on overall reliability. The final output is a robust Pareto front solution set that achieves the best overall performance in terms of product quality, robustness, and reliability.

6. The method for optimizing casting shrinkage process parameters based on deep learning according to claim 1, characterized in that, Recommended final process parameter scheme, including: The robust Pareto front solution set is visualized through a human-machine collaborative decision-making interface. Each solution in the robust Pareto front solution set is labeled with its corresponding model confidence and overall credibility. The visualization is achieved by plotting the robustness-performance Pareto front in a two-dimensional chart. Each point in the two-dimensional chart represents a candidate solution. The horizontal axis is the predicted value of the product quality index, the vertical axis is the robustness evaluation index, and the color of the point maps the overall credibility. Receive user interaction instructions, determine the final solution, and generate a complete report that includes process parameters, performance predictions, uncertainty assessments, and credibility ratings.

7. A deep learning-based system for optimizing casting shrinkage process parameters, characterized in that, The method for optimizing casting shrinkage process parameters based on deep learning as described in any one of claims 1-6 includes: The model training module is used to train a proxy model, which takes a combination of casting process parameters as input and outputs the predicted value and uncertainty of product quality indicators. The parameter fusion module is used to build an uncertainty fusion engine, which fuses the uncertainty of surrogate model prediction, the uncertainty of process parameter fluctuations, and the uncertainty of material parameter ranges, and outputs a comprehensive uncertainty envelope. The indicator calculation module is used to define and calculate robustness evaluation indicators based on the predicted values ​​of the product quality indicators and the comprehensive uncertainty envelope. The indicator optimization module is used to run a multi-objective optimization algorithm with the dual objectives of optimizing product quality indicators and robustness evaluation indicators, and to search for and obtain a robust Pareto front solution set. The scheme recommendation module is used to recommend the final process parameter scheme based on the robust Pareto front solution set.

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