Oil and gas cylinder cold heading parameter optimization method based on multi-fidelity data and physical constraint

Abstract

The invention discloses a multi-fidelity data fusion and physical constraint-based cold heading process parameter staged optimization method, which comprises the following steps of: 1) performing calculation through Deform finite element simulation and an empirical formula, constructing a multi-fidelity initial data set, and improving data consistency through normalization and deviation calibration; 2) constructing a multi-fidelity physical information neural network (PINN) model, and establishing a mapping relation between process parameters and forming quality indexes by adopting a staged training strategy and an adaptive weight adjustment mechanism; and 3) verifying the generalization ability of the model by dividing a training set and a test set, ensuring that a prediction result accords with a volume conservation criterion and a material forming limit, and realizing optimization of cold heading process parameters. According to the method, through multi-fidelity data fusion and physical information embedding, on the basis of enhancing a physical mechanism and multi-data collaboration, the data acquisition cost is reduced, and the generalization of the model is improved; and through dynamic weight distribution and a staged training strategy, the prediction precision and reliability are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of metal plastic forming process optimization, and in particular to a method for optimizing cold heading parameters of oil and gas cylinders based on multi-fidelity data and physical constraints. Background Art

[0002] As one of the core processes of metal plastic forming, cold heading plays an important role in the manufacture of key components such as automotive fasteners, aerospace precision parts, and oil and gas cylinders. It achieves cold plastic deformation of metal blanks through high-speed stamping, and has the advantages of high material utilization, high processing efficiency, and excellent product mechanical properties. However, the setting of process parameters (such as reduction ratio, punch speed, and friction coefficient) directly affects the forming quality (such as surface integrity and dimensional accuracy) and production cost. The traditional trial and error method relies on experience to adjust parameters, which is inefficient and costly. Therefore, it is of great significance to construct a high-precision and high-efficiency prediction model for the cold heading process parameters of oil and gas cylinders, and can provide an important reference for the optimization of cold heading process parameters for similar thin-walled pipes.

[0003] The following limitations exist in establishing a cold heading process parameter prediction model:

[0004] 1) Data-driven and separated from physical laws: Traditional deep learning models (such as Artificial Neutral Network and Radial Basis Function) rely on historical data and do not embed physical constraints such as volume conservation and material damage threshold, resulting in the prediction results possibly violating the forming limit.

[0005] 2) High data acquisition cost: High-fidelity simulation data (such as DEFORM) is time-consuming to collect, while low-fidelity empirical formulas cover a wide range but lack accuracy. A single data source cannot achieve both efficiency and accuracy.

[0006] 3) Insufficient model generalization ability: Shallow models (such as orthogonal experiments and Gaussian process regression) find it difficult to capture high-order coupling effects between parameters, resulting in significant prediction deviations in nonlinear scenarios.

[0007] The existing methods for establishing process parameter prediction models are divided into two categories. The first method is to use classical models to deal with the nonlinearity and multi-physical field coupling of the process. For example, in 2022, Mo Jie et al. from Hunan University, in the article "Optimization method of hexagonal punch wear based on orthogonal experiment" (included in "Forging Technology", 2022, 47(9):1-6), designed L 16 Orthogonal testing combined with DEFORM finite element simulation analyzed the impact of factors such as the punch cone angle and hardness on wear. Range analysis and the variance method were used to determine the optimal parameter combination. This method improved optimization efficiency by reducing the number of experiments, but orthogonal testing cannot fully cover all possible parameter combinations.

[0008] In response to the above problems, in 2023, Zha Liangyu of Zhejiang University proposed a multi-objective 3D printing process parameter optimization method (authorization announcement number: CN 115358159 B). This patent combines Gaussian process regression and genetic algorithm to construct a nonlinear proxy model to predict printing quality parameters, and balances the objectives with a multi-objective mixed sampling function to improve the model fitting accuracy and realize automatic optimization of process parameter combinations. However, this method has made many simplifications. If the physical constraints of material plastic deformation are embedded, some optimization solutions may violate physical laws, and practical applications need further verification.

[0009] In summary, the classical model relies on simplified assumptions and is effective in low-dimensional, weakly coupled scenarios. However, when faced with the high strain rate and strong nonlinear coupling characteristics of the cold heading process, its generalization ability decreases significantly, and the data acquisition cost is high.

[0010] The second method is to use deep learning to deal with the nonlinearity of the process and the coupling of multiple physical fields. For example, in 2021, Satoshi Kitayama et al. from the Wrocław University of Technology in Poland, in the article "Multi-objective optimization of process parameters in cold forging minimizing risk of crack and forging energy" (included in the journal "Archives of Civil and Mechanical Engineering", 2021, 21:132-134), addressed the problem that cold forging process parameters are usually adjusted by trial and error, with poor results. Based on the data set obtained by numerical simulation using Deform, the sequential approximate optimization (SAO) method based on the radial basis function network (RBF network) was used for multi-objective design optimization, which reduced the risk of material damage and improved product processing quality. However, the parameter selection of the RBF network is sensitive, which can easily lead to overfitting or underfitting, and the locality of the basis function makes it difficult for the model to explain the relationship between input and output as a whole.

[0011] In 2023, Mo Ningning et al. from Guizhou University proposed an optimization method combining BP neural network and genetic algorithm in the article "Research on Optimization of Punching and Bonding Process Parameters for A286 High-temperature Alloy Thin-walled Pipe Fittings" (included in "Forging Technology", 2023, 48(9):64-70). The method optimizes the punch structural parameters with the goal of minimizing the punching and bonding force. This method has certain advantages in modeling multi-parameter nonlinear relationships, but the model relies only on historical data training and does not embed key physical equations such as the law of volume conservation. The prediction results may generate parameter combinations that violate the material forming limit.

[0012] In 2023, Praveenkumar M. Petkar et al. from KLE University of Science and Technology, in the article "A Comparative Study in Forming Behavior of Different Grades of Steel in Cold Forging Backward Extrusion by Integrating Artificial Neural Network (ANN) with Differential Evolution (DE) Algorithm" (included in the journal "Applied Sciences", 2023, 13(3): 1276-1292), addressed the problem of easy damage to the punch during cold forging. They used artificial neural network (ANN) and differential evolution (DE) optimization algorithm to establish a prediction model and optimize the blank size, reduction ratio, punch angle and land height, thereby improving the service life of the punch. However, the ANN model is too dependent on parameters, and the full-factor experimental design and large-scale simulation consume resources, making it difficult to directly apply to industrial real-time optimization.

[0013] In 2024, Wenxia Xu et al. from Wuhan University, in the article "Intelligent optimization of cold radial forging process for 20CrMnTiH alloy based on GA-BP and performance analysis" (included in the journal "International Journal of Advanced Manufacturing Technology", 2024, 135:4281-4307), used defrom to obtain data to construct a double hidden layer BP neural network model based on genetic algorithm optimization for the cold radial forging process of 20CrMnTiH alloy, and combined the NSGA-II algorithm and TOPSIS algorithm to obtain the optimal parameter combination, which significantly improved the workpiece forming quality. However, the initial weight and bias settings of the neural network have a significant impact on the results, and the static weight distribution mechanism cannot adapt to the dynamic evolution of the multi-objective competition relationship in the cold forging process, and is prone to fall into local optimal solutions.

[0014] In summary, deep learning methods (such as Inception-ResNet, Artificial Neutral Network, and Back Propagation) can partially solve nonlinear coupling through automatic feature extraction. However, they generally lack the embedding of physical laws, resulting in insufficient reliability of the optimization solutions and the potential generation of infeasible solutions. Furthermore, they rely on large-scale simulations, which results in high data acquisition costs. Summary of the Invention

[0015] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for optimizing the cold heading parameters of oil and gas cylinders based on multi-fidelity data and physical constraints. The method adopts a multi-fidelity residual learning framework, obtains the initial data set through high-precision simulation based on Deform and fast approximate calculation based on empirical formulas, combines the PINN physical information neural network, integrates the volume invariance criterion and the material's own properties, and establishes a PINN neural network model that integrates physical knowledge through a staged training strategy to achieve efficient and accurate optimization of process parameters.

[0016] The object of the present invention is achieved as follows: a method for optimizing cold heading parameters of oil and gas cylinders based on multi-fidelity data and physical constraints, comprising the following steps:

[0017] Step 1) Calculate the multi-fidelity initial data set through Deform finite element simulation and empirical formula, and improve data consistency through normalization and deviation calibration;

[0018] Step 2) Constructing a multi-fidelity physical information neural network (PINN) model. The model constructs a comprehensive loss function by fusing data-driven loss, physical constraint loss, and multi-fidelity residual loss. It also uses a phased training strategy and an adaptive weight adjustment mechanism to establish a mapping relationship between process parameters and forming quality indicators.

[0019] Step 3) Verify the generalization ability of the model by dividing the training set and the test set to ensure that the prediction results comply with the volume conservation criterion and the material forming limit, and achieve the optimization of the cold heading process parameters.

[0020] Furthermore, the step 1) of constructing the multi-fidelity initial dataset includes the following steps:

[0021] 1-1) High-fidelity data generation: Relying on finite element simulation, the data obtained should have an error within 5% of the actual physical quantities in the cold heading process. The cold heading process was simulated using Deform-3D finite element simulation. Process parameters included the reduction ratio ε, which ranged from 0.5 to 0.9; the punch pressing speed v, which ranged from 10 to 30 mm / s; and the friction coefficient μ, which ranged from 0.05 to 0.15. Forming load and damage value distribution data were obtained, covering at least 50 key parameter combinations.

[0022] 1-2) Low-fidelity data construction: The data is calculated based on empirical formulas, and the deviation between the obtained data and the actual physical quantities in the actual cold heading process is controlled within 10% to 20%. Based on the principal stress method, the maximum forming load and the maximum damage value of the process parameter power are calculated using empirical formulas to generate 100 to 500 sets of data, covering the extended parameter range of the reduction ratio ε, which ranges from 0.3 to 1.0; the punch speed v, which ranges from 5 to 50 mm / s; and the friction coefficient μ, which ranges from 0.01 to 0.2. The specific formula is as follows:

[0023] The calculation formula for the maximum forming load is shown in formula (1.1):

[0024]

[0025] Where: F max is the maximum forming load of the cold heading and reducing station, K is the comprehensive correction coefficient, Y is the material yield strength, t is the wall thickness of the blank before reducing, D1 is the outer diameter of the blank before reducing, D2 is the outer diameter of the blank after reducing, μ is the friction coefficient, and α is the die entry angle;

[0026] The calculation formula for the maximum damage value is shown in formula (1.2):

[0027]

[0028] Where: A0 is the cross-sectional area of ​​the blank before reduction, F max is the maximum forming load of the cold heading and reducing station, v is the punch pressing speed, v0 is the reference speed of the punch pressing, k1 is the correction coefficient, a is the influence of the reaction forming load on the damage value, b is the amplification effect of the reaction friction coefficient on the damage value, and c is the strain rate sensitivity of the reaction punch speed to the damage value;

[0029] 1-3) Data normalization and alignment: Normalize high-fidelity and low-fidelity data, and calibrate deviations through global mean correction and local segment compensation algorithms to improve dataset consistency.

[0030] Furthermore, the step 2) specifically includes:

[0031] 2-1) Constructing the PINN network architecture: Input layer: four nodes, corresponding to process parameters including wall thickness t, reduction ratio ε, punch pressing speed v, and friction coefficient μ; Hidden layer: three fully connected layers, each with sixteen nodes, using Swish as the activation function; Output layer: two nodes, respectively predicting damage value and forming load, using the linear Purelin activation function; Physical constraint embedding: The volume remains unchanged before and after deformation, and a custom layer is added after the hidden layer to generate the constraint loss term; Material damage value less than the critical damage value meets the material forming limit;

[0032] 2-2) The comprehensive loss function is defined as shown in formula (1.3):

[0033] L total =λ1L data +λ2L volume +λ3L damage +λ4L residual (7.3)

[0034] Where: L total Refers to the comprehensive loss function, L data refers to the data-driven loss, L volume Refers to the volume conservation loss, L damage Refers to the damage constraint loss, L residual refers to the multi-fidelity residual loss, λ1, λ2, λ3, and λ4 are adaptive weight coefficients that balance data fitting with physical constraints;

[0035] Among them, the data-driven loss L is used data To measure the difference between the neural network prediction results and the real high-fidelity data, by minimizing L data , so that the model learns the mapping relationship between process parameters and physical responses as shown in formula (1.4):

[0036]

[0037] Where: is the predicted value of the neural network for the i-th sample, is the real high-fidelity data of the i-th sample, N is the number of high-fidelity training samples; the high-fidelity training samples are data sets with an absolute error between the simulated data and the actual physical quantity of ≤5% and a numerical noise threshold of ≤±2%;

[0038] Using volume conservation loss L volume To ensure that the volume predicted by the model remains unchanged after deformation, as shown in formula (1.5):

[0039]

[0040] Where: is the initial wall thickness and diameter of the i-th sample, t (i) 、D (i) It refers to the predicted deformed wall thickness and diameter of the i-th sample, and N is the number of high-fidelity training samples;

[0041] Using damage constraint loss L damageTo penalize samples whose damage values ​​predicted by the neural network exceed the critical damage threshold of the material, by minimizing the damage constraint loss term, the optimized parameter combination is forced to meet the material forming limit, avoiding cracks or failures caused by damage accumulation, as shown in formula 1.6:

[0042]

[0043] Where: D (i) is the damage value of the i-th sample predicted by the neural network, reflecting the failure risk of the material in plastic deformation, D max is the critical damage threshold of the material, max(0,D (i) -D max ) represents the penalty imposed on the over-limit damage value of the i-th sample, and the loss is zero when it does not exceed the limit. N is the number of high-fidelity training samples;

[0044] Adopting multi-fidelity residual loss L residual To fuse high-fidelity data with low-fidelity data, while covering a wide range of parameter spaces, correcting prediction errors in key areas, reducing dependence on high-cost data, and achieving prediction results close to the 5% accuracy level of high-fidelity data, thereby enhancing the model's generalization ability, as shown in formula (1.7):

[0045]

[0046] Where: is the predicted value of the jth sample of the low-fidelity model. The low-fidelity model refers to a cold heading process parameter prediction model constructed based on an empirical formula. The absolute error between the low-fidelity model prediction value and the actual physical quantity of the cold heading process is controlled within 10% to 20%; is the true value of the high-fidelity data for the j-th sample, is the residual correction term of the neural network prediction for the jth sample, and M is the number of low- and high-fidelity aligned samples; the low- and high-fidelity aligned samples refer to parameter combinations that have both low-fidelity predicted values ​​and high-fidelity true values, and meet the following conditions: parameter overlap: the process parameters of the samples must fall within the intersection of the high-fidelity data range and the low-fidelity extended range, ensuring that the two types of data are compared at the same parameter points; the high-fidelity sample error is ≤5%, the low-fidelity sample error is ≤20%, and the relative deviation is ≤15%;

[0047] 2-3) Phased training strategies include:

[0048] Pre-training stage: mainly training with low-fidelity data, initializing network weights, and prioritizing fitting low-fidelity data;

[0049] Fine training phase: High-fidelity data and multi-fidelity residual loss are introduced, and dynamic weight adjustment is used to balance data-driven and physical constraints.

[0050] A dynamic weight adjustment mechanism is adopted to update the weight coefficient based on the loss ratio, as shown in formula (1.8):

[0051]

[0052] Where: λ′ i is the temporary weight after adjustment of the i-th loss term at the t-th iteration, is the weight value corresponding to the i-th item at the t-th iteration. When i = 1, 2, 3, 4, They refer to the data-driven loss weight value, volume conservation weight value, damage constraint weight value, and residual loss weight value at the tth iteration respectively. Refers to the value of the i-th loss in the t-th iteration training, and mean() refers to the average of all loss items;

[0053] Weight normalization is performed as shown in formula (1.9):

[0054]

[0055] Where: is the final weight of the i-th loss term at iteration t+1, λ′ i is the temporary weight after adjustment of the i-th loss term at the t-th iteration calculated by formula (1.8), ∑λ′ j is the sum of the temporary weights of all loss terms j = 1, 2, 3, 4, and 3.0 is the set value of the total weight after normalization;

[0056] 2-4) Multi-fidelity residual correction: through the residual term L residual Fusion of high-fidelity data and low-fidelity data, as shown in formula (1.10):

[0057]

[0058] Where: is the predicted value of the jth sample of the low-fidelity model, is the true value of the high-fidelity data for the j-th sample, is the residual correction term of the neural network prediction for the jth sample, and M is the number of low- and high-fidelity alignment samples.

[0059] The present invention adopts the above technical solution, and compared with the existing technology, the beneficial effects are as follows: First, the PINN model is built based on multi-fidelity data fusion and physical constraint embedding: by fusing high-fidelity simulation data with low-fidelity empirical formula data, and embedding the physical laws of the cold heading process, high-fidelity data is used to cover key parameter combinations and low-fidelity data is used to expand the parameter range. At the same time, data consistency is improved through normalization and deviation calibration, reducing dependence on high-cost simulation data and improving data utilization efficiency. At the same time, physical constraints are introduced to prevent traditional data-driven models from generating infeasible solutions due to ignoring physical laws, thereby improving the credibility of prediction results.

[0060] Second, an innovative approach based on dynamic weight adjustment and a phased training strategy: Through phased training (low-fidelity pre-training + high-fidelity fine-tuning) and an adaptive weight allocation mechanism, the optimization objectives of data-driven, physical constraints, and multi-fidelity residual loss are balanced. The pre-training phase initially establishes a parameter-response mapping relationship, while the fine-tuning phase introduces high-fidelity data and physical constraints, dynamically adjusting weights to prioritize key optimization objectives. Simultaneously, a residual correction framework is used to fuse multi-fidelity data and fine-tune prediction errors, effectively enhancing the model's generalization capabilities and avoiding overfitting or local optimality. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a schematic diagram of the overall process of the present invention.

[0062] Figure 2 Schematic diagram of the training process of the PINN model of the present invention. DETAILED DESCRIPTION

[0063] like Figure 1 The method for optimizing cold forging parameters of oil and gas cylinders based on multi-fidelity data and physical constraints includes the following steps:

[0064] Step 1) Constructing a multi-fidelity initial dataset: Calculate the multi-fidelity initial dataset using Deform finite element simulation and empirical formulas, and improve data consistency through normalization and deviation calibration.

[0065] Since the cold heading process parameter prediction model needs to take into account both high accuracy and a wide range of input parameters, this paper proposes a cold heading parameter optimization method for oil and gas cylinders based on multi-fidelity data and physical constraints, which specifically includes the following steps:

[0066] 1-1) High-fidelity data generation: Relying on finite element simulation, the data obtained deviates within 5% from the actual physical quantities in the cold heading process. The cold heading process is simulated through Deform-3D finite element simulation. Process parameters include the reduction ratio ε (range 0.5-0.9), the punch pressing speed v (range 10-30 mm / s), and the friction coefficient μ (range 0.05-0.15). Forming load and damage value distribution data are obtained, covering at least 50 groups of key parameter combinations to ensure that the data set is representative of the actual process parameter range.

[0067] 1-2) Low-fidelity data construction: The data is calculated based on empirical formulas. The deviation between the obtained data and the actual physical quantities in the actual cold heading process is controlled at 10% to 20%. Based on the empirical formulas of the maximum forming load and the maximum damage value of the process parameter power of the principal stress method, 100 to 500 sets of data are calculated to cover the extended parameter ranges of the reduction ratio ε (range 0.3 to 1.0), the punch speed v (range 5 to 50 mm / s), and the friction coefficient μ (range 0.01 to 0.2). The specific formula is as follows:

[0068] The calculation formula for the maximum forming load is based on the formula derived from the principal stress method, as shown in formula (1.1):

[0069]

[0070] Where: F max is the maximum forming load of the cold heading and reducing station, K is the comprehensive correction coefficient, which is 1.2-1.5; Y is the material yield strength, t is the wall thickness of the blank before reducing, D1 is the outer diameter of the blank before reducing, D2 is the outer diameter of the blank after reducing, μ is the friction coefficient, and α is the die entry angle;

[0071] The calculation formula of the maximum damage value is constructed by combining the process parameters in a power-order manner, as shown in formula (1.2):

[0072]

[0073] Where: A0 is the cross-sectional area of ​​the blank before reduction, F max is the maximum forming load of the cold heading and reducing station, v is the punch pressing speed, v0 is the reference speed of the punch pressing, generally taken as (10mm / s), k1 is the correction coefficient, a is the influence of the forming load on the damage value, b is the amplification effect of the friction coefficient on the damage value, and c is the strain rate sensitivity of the punch speed to the damage value;

[0074] 1-3) Data normalization and alignment: Normalize high-fidelity and low-fidelity data to eliminate dimensional differences; calibrate the deviation between low-fidelity and high-fidelity data through global mean correction and local segment compensation algorithms to improve data set consistency.

[0075] Step 2) Construct a multi-fidelity physical information neural network (PINN) model. The training process is as follows: Figure 2 As shown in the figure, the model constructs a comprehensive loss function by integrating data-driven loss, physical constraint loss and multi-fidelity residual loss, and adopts a staged training strategy and adaptive weight adjustment mechanism to establish the mapping relationship between process parameters and forming quality indicators;

[0076] 2-1) Building the PINN network architecture:

[0077] Input layer: four nodes, corresponding to process parameters including wall thickness t, reduction ratio ε, punch pressing speed v and friction coefficient μ;

[0078] Hidden layer: three fully connected layers, each with 16 nodes. The activation function uses the Swish function to enhance nonlinear expression capabilities.

[0079] Output layer: two nodes, respectively predicting the maximum forming load F max , maximum damage value D max , the activation function is a linear function (Purelin);

[0080] Physical Constraint Embedding: Add a custom layer after the hidden layer to calculate the volume conservation loss (L volume ) and damage constraint loss (L damage ) to ensure that the prediction results conform to physical laws; the volume remains unchanged before and after deformation, and a custom layer is added after the hidden layer to generate a constraint loss term; the material damage value is less than the critical damage value to meet the material forming limit;

[0081] 2-2) Construction of comprehensive loss function:

[0082] The comprehensive loss function is composed of data-driven loss (L data ), physical constraint loss (L volume , L damage ) and multi-fidelity residual loss (L residual ) weighted composition; as shown in formula (1.3):

[0083] L total =λ1L data +λ2L volume +λ3L damage +λ4L residual (7.3)

[0084] Where: L totalRefers to the comprehensive loss function, L data refers to the data-driven loss, L volume Refers to the volume conservation loss, L damage Refers to the damage constraint loss, L residual refers to the multi-fidelity residual loss, λ1, λ2, λ3, and λ4 are adaptive weight coefficients that balance data fitting with physical constraints;

[0085] Among them, the data-driven loss L is used data To measure the difference between the neural network prediction results and the real high-fidelity data, by minimizing L data , so that the model learns the mapping relationship between process parameters and physical responses as shown in formula (1.4):

[0086]

[0087] Where: is the predicted value of the neural network for the i-th sample, is the real high-fidelity data of the i-th sample, N is the number of high-fidelity training samples; the high-fidelity training samples are datasets with an absolute error between the simulated data and the actual physical quantity of ≤5%; and a numerical noise threshold of ≤±2%;

[0088] Using volume conservation loss L volume To ensure that the volume predicted by the model remains unchanged after deformation, as shown in formula (1.5):

[0089]

[0090] Where: is the initial wall thickness and diameter of the i-th sample, t (i) 、D (i) It refers to the predicted deformed wall thickness and diameter of the i-th sample, and N is the number of high-fidelity training samples;

[0091] Using damage constraint loss L damage To penalize samples whose damage values ​​predicted by the neural network exceed the critical damage threshold of the material, by minimizing the damage constraint loss term, the optimized parameter combination is forced to meet the material forming limit, avoiding cracks or failures caused by damage accumulation, as shown in formula 1.6:

[0092]

[0093] Where: D (i) is the damage value of the i-th sample predicted by the neural network, reflecting the failure risk of the material in plastic deformation, D max is the critical damage threshold of the material, max(0,D (i) -D max) represents the penalty imposed on the over-limit damage value of the i-th sample, and the loss is zero when it does not exceed the limit. N is the number of high-fidelity training samples;

[0094] Adopting multi-fidelity residual loss L residual To fuse high-fidelity data with low-fidelity data, while widely covering the parameter space, correcting the prediction error in key areas, reducing the dependence on high-cost data, and at the same time, the prediction results can be close to the 5% accuracy level of high-fidelity data, enhancing the generalization ability of the model, as shown in formula (1.7):

[0095]

[0096] Where: is the predicted value of the jth sample of the low-fidelity model. The low-fidelity model refers to the cold heading process parameter prediction model constructed based on the empirical formula (principal stress method, power fitting). The absolute error between the low-fidelity model prediction value and the actual physical quantity of the cold heading process is controlled within 10% to 20%; is the true value of the high-fidelity data for the j-th sample, is the residual correction term of the neural network prediction for the jth sample, and M is the number of low- and high-fidelity aligned samples; low- and high-fidelity aligned samples refer to parameter combinations that have both low-fidelity predicted values ​​and high-fidelity true values, and meet the following conditions: 1) Parameter overlap: the process parameters of the samples must fall within the intersection of the high-fidelity data range and the low-fidelity extended range at the same time, ensuring that the two types of data are comparable at the same parameter points; 2) The high-fidelity sample error is ≤5%, the low-fidelity sample error is ≤20%, and the relative deviation is ≤15%

[0097] 2-3) Phased training strategies include:

[0098] Pre-training stage: Based on low-fidelity data, the network weights are initialized, and λ1 = 2.0, λ2 = 1.0, λ3 = 1.0, and λ4 = 0 are set to preliminarily establish the mapping relationship between process parameters and response indicators;

[0099] Fine training phase: High-fidelity data and multi-fidelity residual loss are introduced, and dynamic weight adjustment is used to balance data-driven and physical constraints.

[0100] A dynamic weight adjustment mechanism is adopted to update the weight coefficient based on the loss ratio, as shown in formula (1.8):

[0101]

[0102] Where: λ′ i is the temporary weight after adjustment of the i-th loss term at the t-th iteration, is the weight value corresponding to the i-th item at the t-th iteration. When i = 1, 2, 3, 4, They refer to the data-driven loss weight value, volume conservation weight value, damage constraint weight value, and residual loss weight value at the tth iteration respectively; Refers to the value of the i-th loss in the t-th iteration training, and mean() refers to the average of all loss items;

[0103] To prevent weight oscillation, the updated weights are normalized, as shown in formula (1.9):

[0104]

[0105] Where: is the final weight of the i-th loss term at iteration t+1, λ′ i is the temporary weight after adjustment of the i-th loss term at the t-th iteration calculated by formula (1.8), ∑λ′ j is the sum of the temporary weights of all loss terms j = 1, 2, 3, 4, and 3.0 is the set value of the total weight after normalization;

[0106] 2-4) Multi-fidelity residual correction: through the residual term L residual Fusion of high-fidelity data and low-fidelity data, as shown in formula (1.10):

[0107]

[0108] Where: is the predicted value of the jth sample of the low-fidelity model, is the true value of the high-fidelity data for the j-th sample, is the residual correction term of the neural network prediction for the jth sample, and M is the number of low- and high-fidelity alignment samples.

[0109] Step 3) Model Verification and Optimization: Verify the generalization ability of the model by dividing the training set into a test set and verify whether the prediction results meet the volume invariance criterion and the material's inherent properties, ensuring that the model maintains high accuracy and physical credibility while achieving efficient calculations.

[0110] The dataset is divided into training and test sets at an 8:2 ratio to evaluate the generalization ability of the model. The validation indicators include:

[0111] 3-1) Physical Constraint Compliance: Check Volume Conservation (|V initial -V predicted |) is below a threshold (e.g. 1%).

[0112] 3-2) Prediction accuracy: Calculate the mean square error (MSE) and determination coefficient (R) of the forming load and damage value. 2 ).

[0113] The present invention proposes a parameter optimization method for cold forging of oil and gas cylinders based on multi-fidelity data and physical constraints. By integrating the volume invariance principle and the material forming limit, it ensures that the optimized solution strictly conforms to physical laws such as volume conservation, thereby improving the reliability and generalization of the model. At the same time, a multi-fidelity residual learning framework is adopted to integrate data from high-precision simulation and fast approximate calculation (empirical formula), significantly reducing data acquisition and computing costs, and reducing dependence on a single data source. A prediction model with both data-driven efficiency and physical credibility is constructed to achieve efficient and accurate optimization of process parameters.

[0114] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some of the technical features therein according to the disclosed technical content without creative labor, and these substitutions and modifications are all within the protection scope of the present invention.

Claims

1. A method for optimizing cold heading parameters of oil and gas cylinders based on multi-fidelity data and physical constraints, characterized by: The following steps are involved: Step 1) Calculate the multi-fidelity initial data set through Deform finite element simulation and empirical formula, and improve data consistency through normalization and deviation calibration; Step 2) Constructing a multi-fidelity physical information neural network (PINN) model. The model constructs a comprehensive loss function by fusing data-driven loss, physical constraint loss, and multi-fidelity residual loss. It also uses a phased training strategy and an adaptive weight adjustment mechanism to establish a mapping relationship between process parameters and forming quality indicators. Step 3) Verify the generalization ability of the model by dividing the training set and the test set to ensure that the prediction results comply with the volume conservation criterion and the material forming limit, and achieve the optimization of the cold heading process parameters.

2. The method for optimizing cold heading parameters of oil and gas cylinders based on multi-fidelity data and physical constraints according to claim 1, characterized in that: The construction of the multi-fidelity initial dataset in step 1) includes the following steps: 1-1) High-fidelity data generation: Relying on finite element simulation, the data obtained should have an error within 5% of the actual physical quantities in the cold heading process. The cold heading process was simulated using Deform-3D finite element simulation. Process parameters included the reduction ratio ε, which ranged from 0.5 to 0.9; the punch pressing speed v, which ranged from 10 to 30 mm / s; and the friction coefficient μ, which ranged from 0.05 to 0.

15. Forming load and damage value distribution data were obtained, covering at least 50 key parameter combinations. 1-2) Low-fidelity data construction: The data is calculated based on empirical formulas, and the deviation between the obtained data and the actual physical quantities in the actual cold heading process is controlled within 10% to 20%. Based on the principal stress method, the maximum forming load and the maximum damage value of the process parameter power are calculated using empirical formulas to generate 100 to 500 sets of data, covering the extended parameter range of the reduction ratio ε, which ranges from 0.3 to 1.0; the punch speed v, which ranges from 5 to 50 mm / s; and the friction coefficient μ, which ranges from 0.01 to 0.

2. The specific formula is as follows: The calculation formula for the maximum forming load is shown in formula (1.1): Where: F max is the maximum forming load of the cold heading and reducing station, K is the comprehensive correction coefficient, Y is the material yield strength, t is the wall thickness of the blank before reducing, D1 is the outer diameter of the blank before reducing, D2 is the outer diameter of the blank after reducing, μ is the friction coefficient, and α is the die entry angle; The calculation formula for the maximum damage value is shown in formula (1.2): Where: A0 is the cross-sectional area of ​​the blank before reduction, F max is the maximum forming load of the cold heading and reducing station, v is the punch pressing speed, v0 is the reference speed of the punch pressing, k1 is the correction coefficient, a is the influence of the reaction forming load on the damage value, b is the amplification effect of the reaction friction coefficient on the damage value, and c is the strain rate sensitivity of the reaction punch speed to the damage value; 1-3) Data normalization and alignment: Normalize high-fidelity and low-fidelity data, and calibrate deviations through global mean correction and local segment compensation algorithms to improve dataset consistency.

3. The method for optimizing cold heading parameters of oil and gas cylinders based on multi-fidelity data and physical constraints according to claim 1, characterized in that: The step 2) specifically includes: 2-1) Constructing the PINN network architecture: Input layer: four nodes, corresponding to process parameters including wall thickness t, reduction ratio ε, punch pressing speed v, and friction coefficient μ; Hidden layer: three fully connected layers, each with sixteen nodes, using Swish as the activation function; Output layer: two nodes, respectively predicting damage value and forming load, using the linear Purelin activation function; Physical constraint embedding: The volume remains unchanged before and after deformation, and a custom layer is added after the hidden layer to generate the constraint loss term; Material damage value less than the critical damage value meets the material forming limit; 2-2) The comprehensive loss function is defined as shown in formula (1.3): L total =λ1L data +λ2L volume +λ3L damage +λ4L residual (0.3) Where: L total Refers to the comprehensive loss function, L data refers to the data-driven loss, L volume Refers to the volume conservation loss, L damage Refers to the damage constraint loss, L residual refers to the multi-fidelity residual loss, λ1, λ2, λ3, and λ4 are adaptive weight coefficients that balance data fitting with physical constraints; Among them, the data-driven loss L is used data To measure the difference between the neural network prediction results and the real high-fidelity data, by minimizing L data , so that the model learns the mapping relationship between process parameters and physical responses as shown in formula (1.4): Where: is the predicted value of the neural network for the i-th sample, is the real high-fidelity data of the i-th sample, N is the number of high-fidelity training samples; the high-fidelity training samples are data sets with an absolute error between the simulated data and the actual physical quantity of ≤5% and a numerical noise threshold of ≤±2%; Using volume conservation loss L volume To ensure that the volume predicted by the model remains unchanged after deformation, as shown in formula (1.5): Where: is the initial wall thickness and diameter of the i-th sample, t (i) 、D (i) It refers to the predicted deformed wall thickness and diameter of the i-th sample, and N is the number of high-fidelity training samples; Using damage constraint loss L damage To penalize samples whose damage values ​​predicted by the neural network exceed the critical damage threshold of the material, by minimizing the damage constraint loss term, the optimized parameter combination is forced to meet the material forming limit, avoiding cracks or failures caused by damage accumulation, as shown in formula 1.6: Where: D (i) is the damage value of the i-th sample predicted by the neural network, reflecting the failure risk of the material in plastic deformation, D max is the critical damage threshold of the material, max(0,D (i) -D max ) represents the penalty imposed on the over-limit damage value of the i-th sample, and the loss is zero when it does not exceed the limit. N is the number of high-fidelity training samples; Adopting multi-fidelity residual loss L residual To fuse high-fidelity data with low-fidelity data, while covering a wide range of parameter spaces, correcting prediction errors in key areas, reducing dependence on high-cost data, and achieving prediction results close to the 5% accuracy level of high-fidelity data, thereby enhancing the model's generalization ability, as shown in formula (1.7): Where: is the predicted value of the jth sample of the low-fidelity model. The low-fidelity model refers to a cold heading process parameter prediction model constructed based on an empirical formula. The absolute error between the low-fidelity model prediction value and the actual physical quantity of the cold heading process is controlled within 10% to 20%; is the true value of the high-fidelity data for the j-th sample, is the residual correction term of the neural network prediction for the jth sample, and M is the number of low- and high-fidelity aligned samples; the low- and high-fidelity aligned samples refer to parameter combinations that have both low-fidelity predicted values ​​and high-fidelity true values, and meet the following conditions: parameter overlap: the process parameters of the samples must fall within the intersection of the high-fidelity data range and the low-fidelity extended range, ensuring that the two types of data are compared at the same parameter points; the high-fidelity sample error is ≤5%, the low-fidelity sample error is ≤20%, and the relative deviation is ≤15%; 2-3) Phased training strategies include: Pre-training stage: mainly training with low-fidelity data, initializing network weights, and prioritizing fitting low-fidelity data; Fine training phase: High-fidelity data and multi-fidelity residual loss are introduced, and dynamic weight adjustment is used to balance data-driven and physical constraints. A dynamic weight adjustment mechanism is adopted to update the weight coefficient based on the loss ratio, as shown in formula (1.8): Where: i ′ is the temporary weight after adjustment of the i-th loss term at the t-th iteration, is the weight value corresponding to the i-th item at the t-th iteration. When i = 1, 2, 3, 4, They refer to the data-driven loss weight value, volume conservation weight value, damage constraint weight value, and residual loss weight value at the tth iteration respectively. Refers to the value of the i-th loss in the t-th iteration training, and mean() refers to the average of all loss items; Weight normalization is performed as shown in formula (1.9): Where: is the final weight of the i-th loss term at iteration t+1, λ i ′ is the temporary weight of the adjusted i-th loss term at the t-th iteration calculated by formula (1.8), ∑λ j ′ is the sum of the temporary weights of all loss terms, j = 1, 2, 3, 4, and 3.0 is the set value of the total weight after normalization; 2-4) Multi-fidelity residual correction: through the residual term L residual Fusion of high-fidelity data and low-fidelity data, as shown in formula (1.10): Where: is the predicted value of the jth sample of the low-fidelity model, is the true value of the high-fidelity data for the j-th sample, is the residual correction term of the neural network prediction for the jth sample, and M is the number of low- and high-fidelity alignment samples.

Images