Aluminum alloy heat treatment process parameter optimization method and system based on simulation optimization
By establishing a finite element simulation model and a neural network model for graded heat treatment of aluminum alloys, and combining the evaluation index of strong plasticity synergy and the gradient ascent method, the problems of long R&D cycle, high cost and difficulty in balancing performance contradictions in existing aluminum alloy heat treatment process parameter optimization methods are solved, and rapid, economical and reliable process parameter optimization is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUIZHOU GUICAI INNOVATION TECH (GRP) CO LTD
- Filing Date
- 2026-05-13
- Publication Date
- 2026-06-09
AI Technical Summary
Existing methods for optimizing aluminum alloy heat treatment process parameters suffer from long development cycles, high costs, difficulty in quickly identifying the optimal combination, and difficulty in balancing the contradiction between tensile strength and elongation after fracture. Existing finite element simulations are time-consuming and the surrogate model prediction accuracy is insufficient.
A simulation-based optimization method was adopted to establish a finite element simulation model for graded heat treatment of aluminum alloys. A fully connected neural network surrogate model and a one-dimensional convolutional neural network were constructed. The process parameters were optimized by the strong plasticity synergistic feature evaluation index and the gradient ascent method. Combined with finite element simulation verification, rapid global optimization was achieved.
It achieves efficient and accurate optimization of process parameters, reduces calculation time and cost, balances strength and plasticity, adapts to different application scenarios, and ensures the reliability and engineering feasibility of prediction results.
Smart Images
Figure CN122174587A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of heat treatment process optimization and machine learning technology, specifically to a method and system for optimizing aluminum alloy heat treatment process parameters based on simulation optimization. Background Technology
[0002] 7075 aluminum alloy belongs to the Al-Zn-Mg-Cu series of ultra-high strength aluminum alloys. Due to its excellent specific strength, it is widely used in fields with stringent mechanical performance requirements, such as load-bearing structures in industrial plants, equipment supports, and precision equipment bases. Staged heat treatment is the core process for controlling the microstructure and mechanical properties of 7075 aluminum alloy. Its process parameters include eight continuous parameters: first-stage solution treatment temperature, first-stage solution treatment holding time, second-stage solution treatment temperature, second-stage solution treatment holding time, first-stage aging temperature, first-stage aging holding time, second-stage aging temperature, and second-stage aging holding time.
[0003] Existing process parameter optimization methods have the following shortcomings: Traditional trial-and-error methods rely on experience accumulation, resulting in long development cycles and high costs, making it difficult to quickly locate the optimal combination in a high-dimensional space composed of eight parameters; there is an inherent contradiction between the tensile strength and elongation after fracture of 7075 aluminum alloy, and improving strength often comes at the cost of sacrificing plasticity. Existing methods lack effective evaluation indicators to quantify the degree of synergy between the two, and the optimization results often lose sight of one aspect while focusing on the other; although finite element simulation can accurately predict mechanical properties, a single simulation takes a long time, and its direct application to global optimization is too costly; existing optimization methods based on surrogate models mostly use genetic algorithms, which have slow convergence speeds and are prone to getting trapped in local optima, and the prediction accuracy of surrogate models in the extrapolation region is difficult to guarantee.
[0004] Therefore, there is an urgent need for a process parameter optimization method that can efficiently utilize finite element simulation data, accurately balance strength and plasticity, and has the ability to quickly find global optimization. Summary of the Invention
[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a method and system for optimizing aluminum alloy heat treatment process parameters based on simulation.
[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0007] The simulation-based optimization method for aluminum alloy heat treatment process parameters includes the following steps:
[0008] Step S1: Establish a finite element simulation model for graded heat treatment of aluminum alloy. The input of the finite element simulation model consists of eight process parameters, including the first-stage solution temperature, the first-stage solution holding time, the second-stage solution temperature, the second-stage solution holding time, the first-stage aging temperature, the first-stage aging holding time, the second-stage aging temperature, and the second-stage aging holding time. The output is tensile strength and elongation after fracture.
[0009] Step S2: Generate sample data based on the finite element simulation model, construct and train a fully connected neural network proxy model, wherein the fully connected neural network takes the eight process parameters as input and outputs tensile strength and elongation after fracture.
[0010] Step S3: Define the strong-plasticity synergistic characteristic as a comprehensive index for evaluating process parameter schemes. The strong-plasticity synergistic characteristic is calculated by normalized tensile strength and normalized elongation after fracture.
[0011] Step S4: Expand the training sample set using the fully connected neural network proxy model, construct and train a one-dimensional convolutional neural network as a strong plasticity collaborative feature prediction model, fix the network weights after training, and obtain the optimal combination of process parameters by back-solving using the gradient ascent method.
[0012] Step S5: Input the obtained optimal process parameter combination into the finite element simulation model for verification. If the relative error between the simulation result and the predicted value of the fully connected neural network surrogate model is less than the preset threshold, then proceed to step S6; otherwise, add the simulation result as a new sample point to the training dataset, retrain the fully connected neural network surrogate model, and return to step S2.
[0013] Step S6: Output the final optimal combination of process parameters and the corresponding tensile strength and elongation after fracture.
[0014] Furthermore, step S2 specifically includes the following steps:
[0015] Step S2.1: In the feasible domain of the eight process parameters, Latin hypercube sampling is used to generate initial sample points, and the finite element simulation model is run to obtain the tensile strength and elongation after fracture corresponding to each sample point, forming a training dataset.
[0016] Step S2.2: Construct a fully connected feedforward neural network containing an input layer, three hidden layers, and an output layer. The input layer has eight nodes, and the output layer has two nodes.
[0017] Step S2.3: Using mean squared error as the loss function, train the fully connected feedforward neural network using the gradient descent optimization algorithm until the loss function converges.
[0018] Furthermore, step S3 specifically includes the following steps:
[0019] Step S3.1: Use the fully connected neural network surrogate model to obtain the predicted tensile strength and elongation after fracture corresponding to the given process parameter vector;
[0020] Step S3.2: Divide the predicted tensile strength value by the tensile strength reference value to obtain the normalized tensile strength, and divide the predicted elongation after fracture by the elongation after fracture reference value to obtain the normalized elongation after fracture.
[0021] Step S3.3: Calculate the generalized geometric mean term, specifically by calculating the product of the normalized tensile strength strength evaluation index raised to the power of the normalized elongation at fracture plasticity evaluation index raised to the power of ...
[0022] Step S3.4: Calculate the exponential decay penalty term, specifically by using the natural constant e as the base and multiplying the negative scene adaptation factor by the absolute value of the difference between the normalized tensile strength and the normalized elongation after fracture, which is the power of the exponent.
[0023] Step S3.5: Multiply the generalized geometric mean term by the exponential decay penalty term to obtain the strong plasticity cooperative eigenvalue.
[0024] Furthermore, both the strength evaluation index and the plasticity evaluation index are positive real numbers greater than zero, and the scene adaptation factor is a non-negative real number.
[0025] Furthermore, in step S4, constructing and training a one-dimensional convolutional neural network specifically includes the following steps:
[0026] The fully connected neural network proxy model is used to generate virtual sample points within the feasible domain of the eight process parameters, and the strong plasticity collaborative feature value corresponding to each virtual sample point is calculated to form an expanded training dataset.
[0027] A one-dimensional convolutional neural network is constructed, which includes an input layer, two one-dimensional convolutional layers, a global average pooling layer, two fully connected layers, and an output layer. The input layer receives the eight process parameters, and the output layer outputs the predicted value of strong plasticity collaborative features.
[0028] A composite loss function is constructed, which includes a mean squared error loss term and a physical monotonic constraint loss term. The physical monotonic constraint loss term is used to penalize the behavior of the network output's partial derivative with respect to the second-level time-effect temperature that violates the preset physical law.
[0029] A strong plasticity collaborative feature prediction model is obtained by training the one-dimensional convolutional neural network by minimizing the composite loss function.
[0030] Furthermore, the specific penalty rule for the physical monotonic constraint loss term is as follows: when the second-level aging temperature is lower than the preset peak temperature, the penalty network outputs a negative partial derivative with respect to that temperature; when the second-level aging temperature is higher than the preset peak temperature, the penalty network outputs a positive partial derivative with respect to that temperature.
[0031] Furthermore, in step S4, obtaining the optimal combination of process parameters through the gradient ascent method specifically includes the following steps:
[0032] Several initial search points are randomly generated within the feasible region of the eight process parameters;
[0033] Fix all weight parameters of the one-dimensional convolutional neural network after training;
[0034] Using the output of the one-dimensional convolutional neural network as the optimization objective and the input process parameter vector as the optimization variable, the gradient of the network output with respect to the input is calculated.
[0035] The process parameter vector is iteratively updated along the gradient direction. If the updated vector exceeds the feasible region boundary, it is projected to the boundary until the convergence condition is met.
[0036] Compare the feature prediction values corresponding to the local optimal solutions converged at each initial search point, and select the process parameter vector corresponding to the maximum value as the optimal solution.
[0037] A simulation-based optimization system for aluminum alloy heat treatment process parameters is provided to implement any of the simulation-based optimization methods for aluminum alloy heat treatment process parameters, including:
[0038] The finite element simulation module is used to build a finite element simulation model of graded heat treatment of aluminum alloys and perform simulation calculations.
[0039] The fully connected neural network surrogate model module is used to build and train a fully connected neural network surrogate model based on simulation sample data, with eight process parameters as inputs and tensile strength and elongation after fracture as outputs.
[0040] A strong plasticity collaborative feature calculation module is used to calculate strong plasticity collaborative features based on the mechanical property prediction values output by the fully connected neural network surrogate model;
[0041] A one-dimensional convolutional neural network module is used to construct and train a feature prediction network with the eight process parameters as input and strong plasticity collaborative features as output. During training, a composite loss function with embedded physical monotonic constraints is used.
[0042] The gradient inverse algorithm module is used to fix the weights of the trained one-dimensional convolutional neural network and search for the optimal combination of process parameters that maximizes the network output in the input space using the gradient ascent method.
[0043] The closed-loop iterative control module is used to compare the error between the simulation verification results and the predicted values of the fully connected neural network surrogate model, and to decide whether to update and re-optimize the model.
[0044] The results output module is used to output the optimal combination of process parameters and the corresponding tensile strength and elongation after fracture.
[0045] Furthermore, the fully connected neural network proxy model module includes:
[0046] The sample generation unit is used to generate initial sample points within the feasible domain of the eight process parameters using Latin hypercube sampling, and to call the finite element simulation module to obtain the corresponding tensile strength and elongation after fracture.
[0047] A network construction unit is used to construct a fully connected feedforward neural network containing an input layer, three hidden layers, and an output layer, wherein the input layer has eight nodes and the output layer has two nodes;
[0048] The loss calculation unit is used to calculate the mean square error between the predicted tensile strength and elongation after fracture output by the network and the true simulation value.
[0049] The parameter update unit is used to update the network weights using gradient descent with the Adam optimizer until the loss function converges.
[0050] Furthermore, the gradient inverse solving module includes:
[0051] An initial point generation unit is used to randomly generate several initial search points within the feasible domain of the eight process parameters.
[0052] The gradient calculation unit is used to fix all the weight parameters of the trained one-dimensional convolutional neural network and calculate the gradient of the network output with respect to the input process parameter vector through the backpropagation algorithm.
[0053] The iterative update unit is used to perform gradient ascent iteration for each initial search point along the gradient direction. If the updated value exceeds the feasible region boundary, it is projected to the boundary.
[0054] The optimal solution selection unit is used to compare the feature prediction values corresponding to the local optimal solutions converged at each initial search point, and select the process parameter vector corresponding to the maximum value as the global optimal solution output.
[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0056] 1. This invention replaces expensive finite element simulation with a fully connected neural network surrogate model. Only a small number of simulation samples are needed to establish a high-precision mapping relationship. Subsequent optimization is based entirely on the surrogate model, which reduces computation time and economic costs.
[0057] 2. The strong plasticity synergistic feature constructed in this invention suppresses bias towards a certain index through a composite structure of a generalized geometric mean term and an exponential decay penalty term. At the same time, it can flexibly adjust the balance weight of strength and plasticity through a scenario adaptation factor, so as to meet the needs of different application scenarios such as heavy load-bearing structures and precision equipment bases.
[0058] 3. This invention embeds a physical monotonic constraint term into the loss function of a one-dimensional convolutional neural network, so that the network prediction surface conforms to the metallurgical law that the performance changes unimodally with aging temperature, and maintains a reliable prediction trend in the extrapolation region, avoiding gradient ascent from converging to a false extremum.
[0059] 4. This invention utilizes a trained differentiable neural network to directly solve for the optimal process parameters in the input space using the gradient ascent method, transforming discrete black-box optimization into continuous gradient optimization, thus improving the convergence speed compared to traditional genetic algorithms.
[0060] 5. This invention uses a closed-loop iterative mechanism of finite element simulation verification and proxy model update to ensure that the final output of the optimal combination of process parameters also has excellent performance in real physical scenarios, and has strong engineering feasibility. Attached Figure Description
[0061] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:
[0062] Figure 1 This is a flowchart illustrating an embodiment of the present invention;
[0063] Figure 2 This is a system schematic diagram according to an embodiment of the present invention;
[0064] Figure 3 This is a flowchart of the gradient ascent backward solution in an embodiment of the present invention. Detailed Implementation
[0065] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
[0066] like Figure 1 As shown, the simulation-based optimization method for aluminum alloy heat treatment process parameters includes the following steps:
[0067] Step S1: Establish a finite element simulation model for graded heat treatment of aluminum alloy. The input of the finite element simulation model consists of eight process parameters, including the first-stage solution temperature, the first-stage solution holding time, the second-stage solution temperature, the second-stage solution holding time, the first-stage aging temperature, the first-stage aging holding time, the second-stage aging temperature, and the second-stage aging holding time. The output is tensile strength and elongation after fracture.
[0068] Step S2: Generate sample data based on the finite element simulation model, construct and train a fully connected neural network proxy model, wherein the fully connected neural network takes the eight process parameters as input and outputs tensile strength and elongation after fracture.
[0069] Step S3: Define the strong-plasticity synergistic characteristic as a comprehensive index for evaluating process parameter schemes. The strong-plasticity synergistic characteristic is calculated by normalized tensile strength and normalized elongation after fracture.
[0070] Step S4: Expand the training sample set using the fully connected neural network proxy model, construct and train a one-dimensional convolutional neural network as a strong plasticity collaborative feature prediction model, fix the network weights after training, and obtain the optimal combination of process parameters by back-solving using the gradient ascent method.
[0071] Step S5: Input the obtained optimal process parameter combination into the finite element simulation model for verification. If the relative error between the simulation result and the predicted value of the fully connected neural network surrogate model is less than the preset threshold, then proceed to step S6; otherwise, add the simulation result as a new sample point to the training dataset, retrain the fully connected neural network surrogate model, and return to step S2.
[0072] Step S6: Output the final optimal combination of process parameters and the corresponding tensile strength and elongation after fracture.
[0073] A staged heat treatment simulation model of the aluminum alloy workpiece was established using finite element software such as ABAQUS. The staged heat treatment includes a staged solution treatment stage and a staged aging stage. The staged solution treatment stage consists of a first-stage solution treatment and a second-stage solution treatment: the first-stage solution treatment is performed at a temperature range of 450℃ to 470℃ to allow the low-melting-point eutectic phase to gradually dissolve without burning; the second-stage solution treatment is performed at a temperature range of 470℃ to 490℃ for a short time to promote the complete dissolution of the remaining soluble phase and control the grain size. The staged aging stage consists of a first-stage aging stage and a second-stage aging stage: the first-stage aging stage is performed at a temperature range of 100℃ to 140℃ for a long time; the second-stage aging stage is performed at a temperature range of 150℃ to 180℃ to allow the precipitated phase to grow appropriately to achieve the best balance between strength and plasticity.
[0074] Step S2 specifically includes the following steps:
[0075] Step S2.1: In the feasible domain of the eight process parameters, Latin hypercube sampling is used to generate initial sample points, and the finite element simulation model is run to obtain the tensile strength and elongation after fracture corresponding to each sample point, forming a training dataset.
[0076] Step S2.2: Construct a fully connected feedforward neural network containing an input layer, three hidden layers, and an output layer. The input layer has eight nodes, and the output layer has two nodes.
[0077] Step S2.3: Using mean squared error as the loss function, train the fully connected feedforward neural network using the gradient descent optimization algorithm until the loss function converges.
[0078] The specific structure of the fully connected feedforward neural network includes:
[0079] The input layer consists of 8 neurons, corresponding to 8 process parameters; hidden layer 1 consists of 64 neurons, with ReLU activation function; hidden layer 2 consists of 128 neurons, with ReLU activation function; hidden layer 3 consists of 64 neurons, with ReLU activation function; the output layer consists of 2 neurons, with linear activation function, outputting the predicted tensile strength and predicted elongation after fracture, respectively.
[0080] The Adam optimizer was used for parameter updates, with an initial learning rate of 0.001 and a batch size of 32. Training was iterated until the validation set loss no longer decreased.
[0081] Step S3 specifically includes the following steps:
[0082] Step S3.1: Use the fully connected neural network surrogate model to obtain the predicted tensile strength and elongation after fracture corresponding to the given process parameter vector;
[0083] Step S3.2: Divide the predicted tensile strength value by the tensile strength reference value to obtain the normalized tensile strength, and divide the predicted elongation after fracture by the elongation after fracture reference value to obtain the normalized elongation after fracture.
[0084] The reference value for tensile strength is 600 MPa, which is 1.1 times the target strength of 7075 aluminum alloy heavy load-bearing structure; the reference value for elongation after fracture is 15%, which is 1.5 times the target elongation of the project.
[0085] Step S3.3: Calculate the generalized geometric mean term, specifically by calculating the product of the normalized tensile strength strength evaluation index raised to the power of the normalized elongation at fracture plasticity evaluation index raised to the power of ...
[0086] Step S3.4: Calculate the exponential decay penalty term, specifically by using the natural constant e as the base and multiplying the negative scene adaptation factor by the absolute value of the difference between the normalized tensile strength and the normalized elongation after fracture, which is the power of the exponent.
[0087] Step S3.5: Multiply the generalized geometric mean term by the exponential decay penalty term to obtain the strong plasticity cooperative eigenvalue.
[0088] The specific formula for the generalized geometric mean term is:
[0089]
[0090] in, Represents the generalized geometric mean term. Represents a vector of process parameters. This represents the predicted tensile strength value calculated by the fully connected neural network surrogate model. This represents the reference value for tensile strength. This represents the intensity evaluation index, with a default value of 1.2. This represents the predicted elongation at fracture calculated by the fully connected neural network surrogate model. This indicates the reference value for elongation after fracture. This represents the plasticity evaluation index, which defaults to 1.0 and can be adjusted. and The relative magnitude of the product term can change the nonlinear sensitivity of strength and plasticity in the product term. When either tensile strength or elongation after fracture is too low, the product term will be significantly suppressed, thus inherently promoting the optimization results to tend towards equilibrium.
[0091] The specific formula for the exponential decay penalty term is as follows:
[0092]
[0093] in, This represents the exponential decay penalty term. The scene adaptation factor controls the penalty intensity for the imbalance between strength and plasticity. The larger the value, the stronger the penalty, and the more the optimization result tends to be in balance between strength and plasticity. The smaller the value, the weaker the penalty, and the more the optimization result tends to pursue the improvement of the absolute level of both.
[0094] The specific formula for the strong plasticity synergistic eigenvalue is as follows:
[0095]
[0096] in, This represents the synergistic characteristic value of strength and plasticity. It is dimensionless, and the larger the value, the better the overall performance of the corresponding process parameter scheme in terms of strength, plasticity, and the balance between the two.
[0097] Both the strength evaluation index and the plasticity evaluation index are positive real numbers greater than zero, and the scene adaptation factor is a non-negative real number.
[0098] In step S4, constructing and training a one-dimensional convolutional neural network specifically includes the following steps:
[0099] The fully connected neural network proxy model is used to generate virtual sample points within the feasible domain of the eight process parameters, and the strong plasticity collaborative feature value corresponding to each virtual sample point is calculated to form an expanded training dataset.
[0100] A one-dimensional convolutional neural network is constructed, which includes an input layer, two one-dimensional convolutional layers, a global average pooling layer, two fully connected layers, and an output layer. The input layer receives the eight process parameters, and the output layer outputs the predicted value of strong plasticity collaborative features.
[0101] A composite loss function is constructed, which includes a mean squared error loss term and a physical monotonic constraint loss term. The physical monotonic constraint loss term is used to penalize the behavior of the network output's partial derivative with respect to the second-level time-effect temperature that violates the preset physical law.
[0102] A strong plasticity collaborative feature prediction model is obtained by training the one-dimensional convolutional neural network by minimizing the composite loss function.
[0103] The specific penalty rule for the physical monotonic constraint loss term is as follows: when the second-level aging temperature is lower than the preset peak temperature, the penalty network outputs a negative partial derivative with respect to that temperature; when the second-level aging temperature is higher than the preset peak temperature, the penalty network outputs a positive partial derivative with respect to that temperature.
[0104] Virtual sample points are generated within the feasible domain of the eight process parameters using the fully connected neural network proxy model, and the strong plasticity collaborative feature value corresponding to each virtual sample point is calculated to form an expanded training dataset.
[0105] A one-dimensional convolutional neural network is constructed, which includes an input layer, two one-dimensional convolutional layers, a global average pooling layer, two fully connected layers, and an output layer. The input layer receives the eight process parameters, and the output layer outputs the predicted value of strong plasticity collaborative features.
[0106] The specific structure of a one-dimensional convolutional neural network is as follows:
[0107] The input layer is an 8-dimensional vector; the first 1D convolutional layer consists of 32 kernels with a kernel size of 3 and a stride of 1, using ReLU activation; the second 1D convolutional layer consists of 64 kernels with a kernel size of 3 and a stride of 1, using ReLU activation; a global average pooling layer averages the feature map output from the second convolutional layer along the spatial dimension, compressing it into a 64-dimensional vector; the first fully connected layer consists of 64 neurons using ReLU activation; the second fully connected layer consists of 32 neurons using ReLU activation; the output layer consists of 1 neuron using a linear activation function, outputting a strongly plastic collaborative feature prediction value.
[0108] A composite loss function is constructed, which includes a mean squared error loss term and a physical monotonic constraint loss term. The physical monotonic constraint loss term is used to penalize the behavior of the network output's partial derivative with respect to the second-level time-effect temperature that violates the preset physical law.
[0109] The specific formula for the composite loss function is as follows:
[0110]
[0111] in, Represents the composite loss function. Indicates batch size, This represents the strong plasticity collaborative feature value of the b-th sample predicted by the network. This represents the true strong plasticity collaborative feature value of the b-th sample calculated by the fully connected neural network surrogate model. This refers to the second-stage aging temperature in the process parameters. This represents the numerical value of the second-stage aging temperature of the b-th sample. This indicates the preset peak temperature, set to 160℃. Represents a symbolic function. This represents the physical regularization coefficient, with a value ranging from 0.01 to 0.1.
[0112] When the second-stage aging temperature is lower than the preset peak temperature, the penalty network outputs a negative partial derivative with respect to temperature; when the second-stage aging temperature is higher than the preset peak temperature, the penalty network outputs a positive partial derivative with respect to temperature. Below the peak aging temperature, as the aging temperature increases, the number of precipitates increases, and the strength and overall performance should show an upward trend; above the peak temperature, the precipitates coarsen, and the overall performance should show a downward trend. Through physical constraints, a one-dimensional convolutional neural network can be guided to learn a feature mapping relationship that conforms to real physical laws.
[0113] The one-dimensional convolutional neural network is trained by minimizing the composite loss function to obtain a strong plasticity synergistic feature prediction model. The Adam optimizer is used with an initial learning rate of 0.001. The validation set loss is monitored during training, and early stopping is used to prevent overfitting. After training, the one-dimensional convolutional neural network can predict the strong plasticity synergistic feature values corresponding to any combination of process parameters with high accuracy and high physical consistency.
[0114] The optimal combination of process parameters, determined after meeting the verification conditions or reaching the maximum number of iterations, along with their corresponding tensile strength and elongation after fracture, will be output in a readable format to directly guide the production of graded heat treatment of aluminum alloys.
[0115] like Figure 3 As shown, step S4, obtaining the optimal combination of process parameters through the gradient ascent method specifically includes the following steps:
[0116] Several initial search points are randomly generated within the feasible region of the eight process parameters;
[0117] Fix all weight parameters of the one-dimensional convolutional neural network after training;
[0118] Using the output of the one-dimensional convolutional neural network as the optimization objective and the input process parameter vector as the optimization variable, the gradient of the network output with respect to the input is calculated.
[0119] The process parameter vector is iteratively updated along the gradient direction. If the updated vector exceeds the feasible region boundary, it is projected to the boundary until the convergence condition is met.
[0120] Compare the feature prediction values corresponding to the local optimal solutions converged at each initial search point, and select the process parameter vector corresponding to the maximum value as the optimal solution.
[0121] K initial process parameter vectors are randomly generated within the feasible region. K is generally 20 to 30 to cover different regions and reduce the risk of getting trapped in local optima.
[0122] Freeze all weights and bias parameters of the one-dimensional convolutional neural network trained in stage one, making it a deterministic differentiable function from input to output;
[0123] Using the output of the one-dimensional convolutional neural network as the optimization objective and the input process parameter vector as the optimization variable, the gradient of the network output with respect to the input is calculated.
[0124] For the process parameter vector of the current iteration step t, the partial derivatives of the predicted value of strong plasticity synergistic features with respect to each component of the input vector are calculated using the backpropagation algorithm, i.e., the gradient vector.
[0125] The process parameter vector is iteratively updated along the gradient direction. If the updated vector exceeds the feasible region boundary, it is projected to the boundary until the convergence condition is met.
[0126] The update formula for gradient ascent is:
[0127]
[0128] in, and This represents the vector of process parameters for iteration step t+1 and iteration step t. This represents the learning rate, typically ranging from 0.01 to 0.05. This represents the partial derivatives of the predicted value of the strong plasticity synergistic feature with respect to each component of the input vector, i.e., the gradient vector. If any updated component exceeds the feasible region boundary of the process parameter, it is truncated to the boundary value. The iteration terminates when the improvement of the strong plasticity synergistic feature over several consecutive iterations is less than a preset threshold of 10. -4 Or reach the maximum number of iterations of 500;
[0129] Compare the feature prediction values corresponding to the local optimal solutions converged at each initial search point, and select the process parameter vector corresponding to the maximum value as the optimal solution;
[0130] After performing the gradient ascent iteration for each initial search point, K convergent local optimal process parameter vectors are obtained. Each vector is input into a one-dimensional convolutional neural network to calculate the corresponding strong plasticity synergistic feature prediction value. The vector that maximizes the strong plasticity synergistic feature prediction value is selected as the output of the global optimal process parameter combination.
[0131] The inverse solution method transforms the discrete black-box optimization problem into a continuous gradient optimization problem for the input of a differentiable neural network. It leverages the efficiency of the automatic differentiation framework, and its convergence speed is significantly better than traditional methods such as genetic algorithms. At the same time, since the one-dimensional convolutional neural network embeds physical monotonic constraints during training, the predicted surface is smooth and the location of the extreme point conforms to the real physical laws, effectively avoiding the gradient ascent from converging to false extremes.
[0132] Input the optimal combination of process parameters obtained in step S4 into the finite element simulation model established in step S1, run a high-precision simulation to obtain the actual tensile strength and elongation after fracture, calculate the relative error, and set the preset threshold to 5%. If the relative error is less than 5%, the accuracy of the surrogate model is considered to meet the requirements, and step S6 is executed to output the results; otherwise, the new sample points are added to the training dataset, the fully connected neural network surrogate model is retrained, only the weight parameters are updated, and then the process returns to step S2 to continue execution. The closed-loop iteration process is executed at most three times. If the convergence condition is still not met after three iterations, the combination of process parameters with the highest actual strength-plasticity synergistic feature value in each verification is output as the final result.
[0133] like Figure 2 As shown, a simulation-based optimization system for aluminum alloy heat treatment process parameters is used to implement any of the simulation-based optimization methods for aluminum alloy heat treatment process parameters, including:
[0134] The finite element simulation module is used to build a finite element simulation model of graded heat treatment of aluminum alloys and perform simulation calculations.
[0135] The fully connected neural network surrogate model module is used to build and train a fully connected neural network surrogate model based on simulation sample data, with eight process parameters as inputs and tensile strength and elongation after fracture as outputs.
[0136] A strong plasticity collaborative feature calculation module is used to calculate strong plasticity collaborative features based on the mechanical property prediction values output by the fully connected neural network surrogate model;
[0137] A one-dimensional convolutional neural network module is used to construct and train a feature prediction network with the eight process parameters as input and strong plasticity collaborative features as output. During training, a composite loss function with embedded physical monotonic constraints is used.
[0138] The gradient inverse algorithm module is used to fix the weights of the trained one-dimensional convolutional neural network and search for the optimal combination of process parameters that maximizes the network output in the input space using the gradient ascent method.
[0139] The closed-loop iterative control module is used to compare the error between the simulation verification results and the predicted values of the fully connected neural network surrogate model, and to decide whether to update and re-optimize the model.
[0140] The results output module is used to output the optimal combination of process parameters and the corresponding tensile strength and elongation after fracture.
[0141] The fully connected neural network proxy model module includes:
[0142] The sample generation unit is used to generate initial sample points within the feasible domain of the eight process parameters using Latin hypercube sampling, and to call the finite element simulation module to obtain the corresponding tensile strength and elongation after fracture.
[0143] A network construction unit is used to construct a fully connected feedforward neural network containing an input layer, three hidden layers, and an output layer, wherein the input layer has eight nodes and the output layer has two nodes;
[0144] The loss calculation unit is used to calculate the mean square error between the predicted tensile strength and elongation after fracture output by the network and the true simulation value.
[0145] The parameter update unit is used to update the network weights using gradient descent with the Adam optimizer until the loss function converges.
[0146] The gradient inverse solution module includes:
[0147] An initial point generation unit is used to randomly generate several initial search points within the feasible domain of the eight process parameters.
[0148] The gradient calculation unit is used to fix all the weight parameters of the trained one-dimensional convolutional neural network and calculate the gradient of the network output with respect to the input process parameter vector through the backpropagation algorithm.
[0149] The iterative update unit is used to perform gradient ascent iteration for each initial search point along the gradient direction. If the updated value exceeds the feasible region boundary, it is projected to the boundary.
[0150] The optimal solution selection unit is used to compare the feature prediction values corresponding to the local optimal solutions converged at each initial search point, and select the process parameter vector corresponding to the maximum value as the global optimal solution output.
[0151] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.
[0152] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.
Claims
1. A method for optimizing aluminum alloy heat treatment process parameters based on simulation, characterized in that, Includes the following steps: Step S1: Establish a finite element simulation model for graded heat treatment of aluminum alloy. The input of the finite element simulation model consists of eight process parameters, including the first-stage solution temperature, the first-stage solution holding time, the second-stage solution temperature, the second-stage solution holding time, the first-stage aging temperature, the first-stage aging holding time, the second-stage aging temperature, and the second-stage aging holding time. The output is tensile strength and elongation after fracture. Step S2: Generate sample data based on the finite element simulation model, construct and train a fully connected neural network proxy model, wherein the fully connected neural network takes the eight process parameters as input and outputs tensile strength and elongation after fracture. Step S3: Define the strong-plasticity synergistic characteristic as a comprehensive index for evaluating process parameter schemes. The strong-plasticity synergistic characteristic is calculated by normalized tensile strength and normalized elongation after fracture. Step S4: Expand the training sample set using the fully connected neural network proxy model, construct and train a one-dimensional convolutional neural network as a strong plasticity collaborative feature prediction model, fix the network weights after training, and obtain the optimal combination of process parameters by back-solving using the gradient ascent method. Step S5: Input the obtained optimal process parameter combination into the finite element simulation model for verification. If the relative error between the simulation result and the predicted value of the fully connected neural network surrogate model is less than the preset threshold, then proceed to step S6; otherwise, add the simulation result as a new sample point to the training dataset, retrain the fully connected neural network surrogate model, and return to step S2. Step S6: Output the final optimal combination of process parameters and the corresponding tensile strength and elongation after fracture.
2. The method according to claim 1, characterized in that, Step S2 specifically includes the following steps: Step S2.1: In the feasible domain of the eight process parameters, Latin hypercube sampling is used to generate initial sample points, and the finite element simulation model is run to obtain the tensile strength and elongation after fracture corresponding to each sample point, forming a training dataset. Step S2.2: Construct a fully connected feedforward neural network containing an input layer, three hidden layers, and an output layer. The input layer has eight nodes, and the output layer has two nodes. Step S2.3: Using mean squared error as the loss function, train the fully connected feedforward neural network using the gradient descent optimization algorithm until the loss function converges.
3. The method according to claim 2, characterized in that, Step S3 specifically includes the following steps: Step S3.1: Use the fully connected neural network surrogate model to obtain the predicted tensile strength and elongation after fracture corresponding to the given process parameter vector; Step S3.2: Divide the predicted tensile strength value by the tensile strength reference value to obtain the normalized tensile strength, and divide the predicted elongation after fracture by the elongation after fracture reference value to obtain the normalized elongation after fracture. Step S3.3: Calculate the generalized geometric mean term, specifically by calculating the product of the normalized tensile strength strength evaluation index raised to the power of the normalized elongation at fracture plasticity evaluation index raised to the power of ... Step S3.4: Calculate the exponential decay penalty term, specifically by using the natural constant e as the base and multiplying the negative scene adaptation factor by the absolute value of the difference between the normalized tensile strength and the normalized elongation after fracture, which is the power of the exponent. Step S3.5: Multiply the generalized geometric mean term by the exponential decay penalty term to obtain the strong plasticity cooperative eigenvalue.
4. The method according to claim 3, characterized in that, Both the strength evaluation index and the plasticity evaluation index are positive real numbers greater than zero, and the scene adaptation factor is a non-negative real number.
5. The method according to claim 4, characterized in that, In step S4, constructing and training a one-dimensional convolutional neural network specifically includes the following steps: The fully connected neural network proxy model is used to generate virtual sample points within the feasible domain of the eight process parameters, and the strong plasticity collaborative feature value corresponding to each virtual sample point is calculated to form an expanded training dataset. A one-dimensional convolutional neural network is constructed, which includes an input layer, two one-dimensional convolutional layers, a global average pooling layer, two fully connected layers, and an output layer. The input layer receives the eight process parameters, and the output layer outputs the predicted value of strong plasticity collaborative features. A composite loss function is constructed, which includes a mean squared error loss term and a physical monotonic constraint loss term. The physical monotonic constraint loss term is used to penalize the behavior of the network output's partial derivative with respect to the second-level time-effect temperature that violates the preset physical law. A strong plasticity collaborative feature prediction model is obtained by training the one-dimensional convolutional neural network by minimizing the composite loss function.
6. The method according to claim 5, characterized in that, The specific penalty rule for the physical monotonic constraint loss term is as follows: when the second-level aging temperature is lower than the preset peak temperature, the penalty network outputs a negative partial derivative with respect to that temperature; when the second-level aging temperature is higher than the preset peak temperature, the penalty network outputs a positive partial derivative with respect to that temperature.
7. The method according to claim 6, characterized in that, In step S4, obtaining the optimal combination of process parameters by inverse solution using the gradient ascent method specifically includes the following steps: Several initial search points are randomly generated within the feasible region of the eight process parameters; Fix all weight parameters of the one-dimensional convolutional neural network after training; Using the output of the one-dimensional convolutional neural network as the optimization objective and the input process parameter vector as the optimization variable, the gradient of the network output with respect to the input is calculated. The process parameter vector is iteratively updated along the gradient direction. If the updated vector exceeds the feasible region boundary, it is projected to the boundary until the convergence condition is met. Compare the feature prediction values corresponding to the local optimal solutions converged at each initial search point, and select the process parameter vector corresponding to the maximum value as the optimal solution.
8. A simulation-based optimization system for aluminum alloy heat treatment process parameters, used to implement the simulation-based optimization method for aluminum alloy heat treatment process parameters as described in any one of claims 1-7, characterized in that, include: The finite element simulation module is used to build a finite element simulation model of graded heat treatment of aluminum alloys and perform simulation calculations. The fully connected neural network surrogate model module is used to build and train a fully connected neural network surrogate model based on simulation sample data, with eight process parameters as inputs and tensile strength and elongation after fracture as outputs. A strong plasticity collaborative feature calculation module is used to calculate strong plasticity collaborative features based on the mechanical property prediction values output by the fully connected neural network surrogate model; A one-dimensional convolutional neural network module is used to construct and train a feature prediction network with the eight process parameters as input and strong plasticity collaborative features as output. During training, a composite loss function with embedded physical monotonic constraints is used. The gradient inverse algorithm module is used to fix the weights of the trained one-dimensional convolutional neural network and search for the optimal combination of process parameters that maximizes the network output in the input space using the gradient ascent method. The closed-loop iterative control module is used to compare the error between the simulation verification results and the predicted values of the fully connected neural network surrogate model, and to decide whether to update and re-optimize the model. The results output module is used to output the optimal combination of process parameters and the corresponding tensile strength and elongation after fracture.
9. The system according to claim 8, characterized in that, The fully connected neural network proxy model module includes: The sample generation unit is used to generate initial sample points within the feasible domain of the eight process parameters using Latin hypercube sampling, and to call the finite element simulation module to obtain the corresponding tensile strength and elongation after fracture. A network construction unit is used to construct a fully connected feedforward neural network containing an input layer, three hidden layers, and an output layer, wherein the input layer has eight nodes and the output layer has two nodes; The loss calculation unit is used to calculate the mean square error between the predicted tensile strength and elongation after fracture output by the network and the true simulation value. The parameter update unit is used to update the network weights using gradient descent with the Adam optimizer until the loss function converges.
10. The system according to claim 9, characterized in that, The gradient inverse solution module includes: An initial point generation unit is used to randomly generate several initial search points within the feasible domain of the eight process parameters. The gradient calculation unit is used to fix all the weight parameters of the trained one-dimensional convolutional neural network and calculate the gradient of the network output with respect to the input process parameter vector through the backpropagation algorithm. The iterative update unit is used to perform gradient ascent iteration for each initial search point along the gradient direction. If the updated value exceeds the feasible region boundary, it is projected to the boundary. The optimal solution selection unit is used to compare the feature prediction values corresponding to the local optimal solutions converged at each initial search point, and select the process parameter vector corresponding to the maximum value as the global optimal solution output.