Deep learning based multi-objective optimization method for complex manufacturing process parameters

Abstract

The application discloses a complex manufacturing process parameter multi-objective optimization method based on deep learning, which comprises the following steps: step 1, manufacturing process forward modeling based on a TCN-Transformer hybrid neural network model; step 2, constructing a manufacturing process parameter multi-objective optimization model; step 3, based on the multi-objective optimization model constructed in step 2, a myxomycete optimization algorithm is used for solving, a Pareto optimal solution set is obtained, and an entropy weight TOPSIS method is used to decide a comprehensive optimal manufacturing process parameter combination from the Pareto optimal solution set. The method solves the problems that in the prior art, due to the complex nonlinear and time sequence relationship between the manufacturing process parameters and the product quality indexes, it is difficult to map, and the quality of a traditional multi-objective optimization algorithm is poor.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing and industrial process optimization technology, specifically involving a multi-objective optimization method for complex manufacturing process parameters based on deep learning. Background Technology

[0002] With the deepening of intelligent manufacturing and Industry 4.0, industrial IoT, big data optimization, and deep learning technologies have been widely applied in production sites, enabling real-time perception and massive time-series data collection of all elements of the manufacturing process (such as equipment status, process parameters, and environmental information). This data contains key information reflecting the final quality indicators and production performance of the product. Manufacturing systems are gradually achieving high-frequency collection and aggregation of full-process, multi-dimensional time-series data, laying a solid foundation for building optimal parameter models for the manufacturing process. Therefore, establishing accurate optimization models using manufacturing process data is crucial for stabilizing product quality, reducing production costs, and improving production efficiency. However, in practical applications, product quality is not affected by a single process parameter, but rather by the combined effect of multiple manufacturing process parameters. The relationship between manufacturing process parameters and product quality indicators typically exhibits complex nonlinearity, strong coupling, and dynamic time-series correlation, resulting in inaccurate mapping relationships between them. Traditional simplified models based on physical mechanisms rely on ideal assumptions and are difficult to adapt to the dynamic disturbances and nonlinear couplings in actual production. While regression methods based on shallow machine learning have a certain fitting ability, they still struggle to accurately characterize the inherent mapping relationship. Therefore, constructing a mapping model that can accurately describe the complex temporal relationships in the manufacturing process, and on this basis, achieving efficient and robust multi-objective parameter optimization, is of great value for improving production efficiency. Existing research on manufacturing process parameter optimization, although incorporating various machine learning methods for modeling, suffers from limitations due to the sheer volume of data. This prevents a systematic consideration of both local temporal patterns and global dependencies, resulting in an inaccurate characterization of the complex nonlinear and temporal mapping relationships between manufacturing process parameters and product quality indicators. Furthermore, the quality of multi-objective optimization algorithms remains poor. Therefore, constructing an integrated technical solution that can accurately characterize the temporal characteristics of the manufacturing process and achieve efficient and robust multi-objective optimization is crucial for improving the intelligent decision-making level of the manufacturing process. Summary of the Invention

[0003] The purpose of this invention is to provide a multi-objective optimization method for complex manufacturing process parameters based on deep learning, which solves the problems of difficulty in mapping the complex nonlinear and temporal relationships between manufacturing process parameters and product quality indicators, as well as the poor quality of traditional multi-objective optimization algorithms in the prior art.

[0004] The technical solution adopted in this invention is a multi-objective optimization method for complex manufacturing process parameters based on deep learning, comprising the following steps: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 2: Construct a multi-objective optimization model for manufacturing process parameters; Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

[0005] The invention is further characterized in that: Step 1 is as follows: Step 1.1: First, determine the manufacturing process parameters and product quality indicators to form the manufacturing process parameter dataset and the product quality indicator dataset. Manufacturing process parameters refer to key parameter variables that are controllable during the manufacturing process and have a significant impact on product quality, while product quality indicators are target values ​​that measure the final performance of the product. Perform data cleaning (removing outliers and filling missing values), normalization (scaling the data to the [0, 1] interval), and serialization preprocessing on the selected manufacturing process parameter dataset and product quality indicator dataset. Then, randomly divide the preprocessed manufacturing process parameter dataset and product quality indicator dataset into training set and test set sets according to a preset ratio (e.g., 8:2). Construct time-series sequence samples for the training set and test set respectively using the sliding window method, and all these samples have a clearly defined time window length L attribute.

[0006] Step 1.2: Configure the specific model parameters for the TCN-Transformer hybrid neural network model; The goal of configuring the TCN model parameters is to enable the receptive field of the multi-layer dilated convolution to cover the entire time window length L. The receptive field of the dilated convolution expands with the increase of the number of layers, the kernel size, and the dilation coefficient. Based on the preprocessed time series samples with a clear time window length L obtained in step 1.1, the TCN model architecture parameters are derived. The architecture parameters include the number of layers, the kernel size, and the dilation coefficient of the TCN model. The TCN model architecture parameters are derived and set according to formula (1): The core operation of TCN model parameter configuration is dilated convolution, and its mathematical definition is shown in formula (1). (1) In the formula, Indicates the position of the output sequence The value; Represents the input sequence; The weight function represents the convolution kernel; This indicates the time node number of the output sequence, specifying the number of the output sequence to be calculated. One value; The length of the convolution kernel is defined, which determines the number of consecutive time steps covered by each convolution operation; Indicates the depth of network layers; Refers to the first The input sequence values ​​of the layer.

[0007] Step 1.3: Based on the time series samples of the training set and the time series samples of the test set prepared in Step 1.1, and the TCN-Transformer hybrid neural network model with parameters configured in Step 1.2, this step trains and verifies the performance of the TCN-Transformer hybrid neural network model and uses it for forward prediction.

[0008] In step 1.2, the TCN-Transformer hybrid neural network model consists of a TCN (Temporal Convolutional Network) model and a Transformer model.

[0009] Step 1.3 specifically involves: First, the time-series samples of the training set divided in step 1.1 are input into the TCN-Transformer hybrid neural network model for processing, which will eventually generate predicted values ​​of the product quality index for the training set. Then, the weight parameters inside the TCN-Transformer hybrid neural network model are adjusted using the backpropagation algorithm, and multiple iterations are repeated until the error between the predicted values ​​of the product quality index for the training set and the actual values ​​of the product quality index for the training set is reduced to close to 0 and shows a convergence trend. At this point, the TCN-Transformer hybrid neural network model is preliminarily trained, and the training is completed. The final evaluation index values ​​on the time-series samples of the training set are recorded. Subsequently, the time-series samples of the test set reserved in step 1.1 are input into the trained TCN-Transformer hybrid neural network model to obtain the corresponding predicted values ​​of the product quality indicators for the test set. The predicted values ​​of the product quality indicators for the test set and the actual values ​​of the product quality indicators for the test set are recorded. The selected evaluation indicators include mean squared error (MSE), mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R). If the mean squared error (MSE), mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of the test set are all greater than the corresponding values ​​on the training set, or the correlation coefficient (R) is less than the corresponding values ​​on the training set, then return to step 1.2 to reconfigure the model architecture parameters. The multi-objective optimization model for manufacturing process parameters established in step 2 is as follows: (2) In the formula: For identifiers, introduce The function is the listed objective function to be optimized; in a multi-objective optimization model for manufacturing process parameters, This indicates the first quality indicator; This indicates the second quality indicator; Indicates the first One quality indicator; It is a set of manufacturing process parameters, which serve as decision variables in the multi-objective optimization model of manufacturing process parameters; It is the first One manufacturing process parameter; and Indicates the first The lower and upper limits of the process allowed by each parameter.

[0010] Step 3 specifically involves: Step 3.1, Parameter Initialization: Define the objective function and manufacturing process parameters to be optimized, set the number of slime mold individuals and the maximum number of iterations, and define the set of decision variables. China's various decisions Policy variables The range of values ​​for which is defined, i.e., the constraint conditions defined in step 2. This range defines the upper and lower boundaries of the values ​​that each decision variable is allowed to take in actual production; based on the actual process constraints, the initial population, external file elements, and maximum number of iterations for the slime mold optimization algorithm are set. The objective function to be optimized is the optimization objective defined in step 2. Manufacturing process parameters are the set of decision variables. Each decision variable ; Step 3.2: Generate the initial population: Within the range of decision variables, randomly generate slime mold individuals to form the initial population; Step 3.3, Calculate the fitness value: The position vector from step 3.2... Substitute the values ​​into the multi-objective optimization model constructed in step 2, and calculate the objective function value; the calculation result for each slime mold individual is the fitness vector of that individual, denoted as . ; Step 3.4, Pareto Front Calculation: Based on the fitness vector of each slime mold individual calculated in Step 3.3 Pareto dominance relation is used to determine the non-dominated solutions in the current population; the identified non-dominated solutions will be used as a reference for updating individual positions in step 3.5. Step 3.5, Individual Position Update: According to the position iteration criterion of the slime mold optimization algorithm, update the position of each slime mold individual in the population, and check whether the updated position of the individual exceeds the value range of each decision variable set in Step 3.1. If it exceeds the range, make corresponding adjustments. The specific adjustment method is as follows: if the updated position of an individual is less than its lower limit value... Then adjust it to If the updated position of an individual is greater than its upper limit value Then set it to If the updated individual's position is within the interval Inside, it remains unchanged; The formula for updating individual locations is as follows: (3) In the formula: and These represent the number of times the slime mold was present. generation and first The position of the generation; Represents a random number within the range [0,1]; UB and LB represent the upper and lower bounds of the optimization interval, respectively; Indicates the probability of mutation; Indicates the number of iterations; Indicates the first The optimal location for slime mold to adapt to its generation; Indicates the range of values ​​within The random number within, where It decreases as the number of iterations increases, and the expression it satisfies is shown in equation (4); Indicates the weighted parameters reflecting slime mold behavior; and Indicates the first Two randomized locations of slime mold; Decrease exponentially from 1 to 0 generation by generation; The parameter that regulates the behavior of slime molds is expressed in equation (5). in, The expression that satisfies this condition is as follows: (4) In the formula: The output parameter for oscillation amplitude is the result of the formula calculation; arctanh is the hyperbolic arctangent function; its domain is (-1, 1), and its range is all real numbers. In this formula, it is used to map the result of the internal linear combination to a suitable decay curve to ensure... It decays smoothly and non-linearly from a positive value to near 0; This is the current iteration number, i.e., the input variable; This indicates the maximum number of iterations. In equation (3), The parameter representing the regulatory role of slime mold behavior is expressed as: (5) In the formula: Indicates the first The fitness value of each slime mold individual; SF is the global optimal fitness index.

[0011] After obtaining the latest position of each slime mold individual according to the above position update formula (5), check whether the updated position vectors exceed the constraint range defined in step 3.1. If the component exceeds the upper limit, it is updated to the upper limit value, and the component below the lower limit is updated to the lower limit value. The upper limit value and the lower limit value are the maximum and minimum values ​​of each decision variable set in step 3, respectively. Step 3.6, Evaluation and Update: For the population obtained after updating in Step 3.5, the calculation method is the same as in Step 3.3. Specifically, the position vector of each individual is... Substitute the multi-objective optimization model constructed in step 2 and calculate its objective function value: identify the non-dominated solutions in the current population to form a new Pareto front; merge the new Pareto front with the previously saved Pareto front, and use the Pareto dominance relation again to filter out the non-dominated solutions to obtain the updated Pareto front; calculate the fitness value of each slime mold individual in the updated population. Step 3.7, Termination Condition Judgment: Check if the termination condition is met. If it is met, output the final Pareto front as the optimal solution to the multi-objective optimization problem; otherwise, return to step 3.5 to continue the iteration.

[0012] Step 3.2 specifically involves: Within the range of values ​​for the decision variables defined in step 3.1, slime mold individuals are randomly generated to form the initial population; the position vector of each slime mold individual is set as follows: , representing a set of random combinations of manufacturing process parameters, where These are the i decision variables (manufacturing process parameters) defined in step 2; each component of this position vector lies within its corresponding feasible range. The parameters are generated randomly within the system, representing a set of possible combinations of manufacturing process parameters.

[0013] In step 3.7, the termination condition is specifically: if the current iteration number is... If the iteration terminates, the solution is the desired Pareto optimal solution, which is output as the final result of the multi-objective optimization problem; if Then let Then return to step 3.5 to continue updating the individual position and subsequent iterations.

[0014] The beneficial effects of this invention include: (1) Accurate mapping of complex relationships: Due to the complex nonlinear and temporal relationships between manufacturing process parameters and product quality indicators, traditional mechanistic models and shallow machine learning methods are difficult to establish accurate mappings. In view of the complex nonlinear and temporal relationships between manufacturing process parameters and product quality indicators, this invention accurately constructs a deep temporal forward prediction model through a TCN-Transformer hybrid neural network, thereby improving the prediction accuracy of the model.

[0015] (2) Highly Efficient Multi-Objective Optimization: Addressing the issue of poor quality in existing multi-objective optimization algorithms, this invention introduces a slime mold optimization algorithm. By simulating the adaptive search mechanism of slime mold foraging behavior, it yields a better Pareto front distribution quality when solving multi-objective optimization problems of manufacturing process parameters. Comparative examples demonstrate that the method of this invention outperforms traditional optimization algorithms in multi-objective optimization, significantly improving the efficiency and effectiveness of multi-objective optimization.

[0016] (3) Automated Decision-Making Mechanism: Optimization results often require subjective judgment to make choices, lacking an objective and automated decision-making mechanism. Addressing the current lack of efficient and high-quality integrated multi-objective optimization technology solutions, this invention uses the entropy-weighted TOPSIS method to make decisions on the Pareto optimal solution set, automatically outputting the comprehensive optimal combination of manufacturing process parameters. Implementation examples verify that the optimized combination of manufacturing process parameters significantly reduces production costs and energy consumption, providing a complete solution for improving the intelligent decision-making level of the manufacturing process.

[0017] (4) The method of the present invention uses a TCN-Transformer hybrid neural network model and a slime mold optimization algorithm to accurately establish the mapping relationship between manufacturing process parameters and product quality indicators, optimize the configuration of multi-objective manufacturing parameters, and thus improve the stability of product quality indicators. It solves the problems in the prior art, such as the difficulty in mapping the complex nonlinear and temporal relationship between manufacturing process parameters and product quality indicators, and the poor quality of traditional multi-objective optimization algorithms. Attached Figure Description

[0018] Figure 1 This is a flowchart of step 1 in the method of the present invention; Figure 2 This is a network structure diagram of the TCN-Transformer hybrid neural network model in the method of this invention; Figure 3 This is a comparison chart of the forward modeling prediction and the actual value of the CNC milling pin ratio energy consumption based on the TCN-Transformer hybrid neural network model in the method of this invention; Figure 4This is a comparison chart of the forward modeling prediction and the actual value of the CNC milling and pin machining cost based on TCN-Transformer in the method of this invention; Figure 5 This is a graph of the root mean square error function of the predicted milling ratio energy consumption of the CNC milling pin training set in the TCN-Transformer hybrid neural network model of the present invention. Figure 6 This is a loss function curve of the CNC milling pin training set machining ratio energy consumption prediction value of the TCN-Transformer hybrid neural network model in the method of this invention; Figure 7 This is a graph of the root mean square error function of the CNC milling cost prediction value of the TCN-Transformer hybrid neural network model in the method of this invention. Figure 8 This is a loss function curve of the CNC milling pin training set machining cost prediction value of the TCN-Transformer hybrid neural network model in the method of this invention; Figure 9 This is a diagram showing the results of multi-objective optimization of CNC milling pin parameters based on NSGA II; Figure 10 This is a diagram showing the results of multi-objective optimization of CNC milling pin parameters based on MOSMA. Detailed Implementation

[0019] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0020] This invention provides a multi-objective optimization method for complex manufacturing process parameters based on deep learning, as detailed below: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 1 is implemented in the following steps: Step 1.1: First, determine the manufacturing process parameters and product quality indicators to form the manufacturing process parameter dataset and the product quality indicator dataset. Manufacturing process parameters refer to key parameter variables that are controllable during the manufacturing process and have a significant impact on product quality, while product quality indicators are target values ​​that measure the final performance of the product. Perform data cleaning (removing outliers and filling missing values), normalization (scaling the data to the [0, 1] interval), and serialization preprocessing on the selected manufacturing process parameter dataset and product quality indicator dataset. Then, randomly divide the preprocessed manufacturing process parameter dataset and product quality indicator dataset into training set and test set sets according to a preset ratio (e.g., 8:2). Construct time-series sequence samples for the training set and test set respectively using the sliding window method, and all these samples have a clearly defined time window length L attribute.

[0021] Step 1.2: Configure the specific model parameters for the TCN-Transformer hybrid neural network model; The TCN-Transformer hybrid neural network model consists of a TCN (Temporal Convolutional Network) model and a Transformer model. The goal of configuring the TCN model parameters is to enable the receptive field of the multi-layer dilated convolution to cover the entire time window length L. The receptive field of the dilated convolution expands with the increase of the number of layers, the kernel size, and the dilation coefficient. Based on the preprocessed time series samples with a clear time window length L obtained in step 1.1, the TCN model architecture parameters are derived. The architecture parameters include the number of layers, the kernel size, and the dilation coefficient of the TCN model. The TCN model architecture parameters are derived and set according to formula (1): The core operation of TCN model parameter configuration is dilated convolution, and its mathematical definition is shown in formula (1). (1) In the formula, Indicates the position of the output sequence The value; Represents the input sequence; The weight function represents the convolution kernel; This indicates the time node number of the output sequence, specifying the number of the output sequence to be calculated. One value; The length of the convolution kernel is defined, which determines the number of consecutive time steps covered by each convolution operation; Indicates the depth of network layers; Refers to the first The input sequence values ​​of the layer.

[0022] Step 1.3: This step is based on the time series samples of the training set and the time series samples of the test set prepared in Step 1.1, as well as the TCN-Transformer hybrid neural network model with parameters configured in Step 1.2. The TCN-Transformer hybrid neural network model is trained and its performance is verified, and then used for forward prediction. Step 1.3 is implemented as follows: First, the time-series samples of the training set divided in Step 1.1 are input into the TCN-Transformer hybrid neural network model for processing, which will eventually generate predicted values ​​of the product quality indicators for the training set. Then, the weight parameters inside the TCN-Transformer hybrid neural network model are adjusted using the backpropagation algorithm, and multiple iterations are repeated until the error between the predicted values ​​of the product quality indicators for the training set and the true values ​​of the product quality indicators for the training set decreases to close to 0 and shows a convergence trend. At this point, the preliminarily trained TCN-Transformer hybrid neural network model is obtained, and the training is completed. The final evaluation index values ​​on the time-series samples of the training set are recorded. Subsequently, the time-series samples of the test set reserved in step 1.1 are input into the trained TCN-Transformer hybrid neural network model to obtain the corresponding predicted values ​​of the test set product quality indicators. The predicted values ​​of the test set product quality indicators and the actual values ​​of the test set product quality indicators are recorded, and the following evaluation indicators are calculated according to the evaluation indicator formula table in Table 1-1: The selected evaluation indicators include mean squared error (MSE), mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R). If the mean squared error (MSE), mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of the test set are all greater than the corresponding values ​​on the training set, or the correlation coefficient (R) is less than the corresponding values ​​on the training set, then return to step 1.2 to reconfigure the model architecture parameters. Table 1-1 Evaluation Indicator Formula Table

[0023] Note: It is the first in the test set The true value of each sample; It is the first in the test set Predicted values ​​for each sample data; It means The mean of the quality indicators of each test sample; , This represents the number of samples in the test set. Among them, the smaller the MSE, MAE, and RMSE, the smaller the prediction error, and the larger the correlation coefficient (R), the better the prediction effect.

[0024] The TCN-Transformer hybrid neural network model trained above can be used for actual forward modeling predictions of the manufacturing process. See the implementation framework diagram for Step 1. Figure 1 The process includes step 1.1 Preprocessing of manufacturing process parameters, step 1.2 Inputting the TCN-Transformer hybrid neural network model, and step 1.3 Evaluation metrics.

[0025] Step 2: Construct a multi-objective optimization model for manufacturing process parameters; This step aims to utilize the TCN-Transformer hybrid neural network model trained in step 1 to explore the impact of process parameters on product quality, predict the functional relationships of various product quality indicators, and set these functional relationships as follows: Function; defines the product quality index as the optimization objective, expressed as: Each product quality indicator is defined as a set of multiple optimization objectives. Meanwhile, there are a total of i manufacturing process parameters, and the i-th manufacturing process parameter is defined as follows: The set of i manufacturing process parameters is used as decision variables. By establishing the feasible range of values ​​for these manufacturing process parameters in actual production, constrained by factors such as equipment capacity, material properties, and process standards, as the constraints, a multi-objective optimization model for manufacturing process parameters is established as follows: (2) In the formula: For identifiers, introduce The function is the listed objective function to be optimized; in a multi-objective optimization model for manufacturing process parameters, This indicates the first quality indicator; This indicates the second quality indicator; Indicates the first One quality indicator; It is a set of manufacturing process parameters, which serve as decision variables in the multi-objective optimization model of manufacturing process parameters; It is the first One manufacturing process parameter; and Indicates the first The lower and upper limits of the process allowed by each parameter.

[0026] The multi-objective optimization model is shown in Equation (2). This optimization model is based on the TCN-Transformer hybrid neural network model. Its core objective is to identify the production parameter configuration that can achieve the optimal quality index through the solution and optimization process. This process aims to select the optimal set from many possible combinations of manufacturing process parameters so that it can be applied to the actual manufacturing process, thereby achieving parameter optimization of the manufacturing process.

[0027] Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

[0028] Step 3 specifically involves: Step 3.1, Parameter Initialization: Define the objective function and manufacturing process parameters to be optimized, set the number of slime mold individuals and the maximum number of iterations, and define the set of decision variables. China's various decisions Policy variables The range of values ​​for which is defined, i.e., the constraint conditions defined in step 2. This range defines the upper and lower boundaries of the values ​​that each decision variable is allowed to take in actual production; based on the actual process constraints, the initial population, external file elements, and maximum number of iterations for the slime mold optimization algorithm are set. The objective function to be optimized is the optimization objective defined in step 2. Manufacturing process parameters are the set of decision variables. Each decision variable ; Step 3.2: Generate the initial population: Within the range of decision variables, randomly generate slime mold individuals to form the initial population; Specifically: within the range of values ​​for the decision variables defined in step 3.1, slime mold individuals are randomly generated to form the initial population; the position vector of each slime mold individual is set as... , representing a set of random combinations of manufacturing process parameters, where These are the i decision variables (manufacturing process parameters) defined in step 2; each component of this position vector lies within its corresponding feasible range. Internally randomly generated, representing a set of possible combinations of manufacturing process parameters; Step 3.3, Calculate the fitness value: The position vector from step 3.2... Substitute the values ​​into the multi-objective optimization model constructed in step 2, and calculate the objective function value; the calculation result for each slime mold individual is the fitness vector of that individual, denoted as . .

[0029] Step 3.4, Pareto Front Calculation: Based on the fitness vector of each slime mold individual calculated in Step 3.3 Pareto dominance relation is used to determine the non-dominated solutions in the current population; the identified non-dominated solutions will be used as a reference for updating individual positions in step 3.5. Step 3.5, Individual Position Update: According to the position iteration criterion of the slime mold optimization algorithm, update the position of each slime mold individual in the population, and check whether the updated position of the individual exceeds the value range of each decision variable set in Step 3.1. If it exceeds the range, make corresponding adjustments. The specific adjustment method is as follows: if the updated position of an individual is less than its lower limit value... Then adjust it to If the updated position of an individual is greater than its upper limit value Then set it to If the updated individual's position is within the interval Inside, it remains unchanged; The formula for updating individual locations is as follows: (3) In the formula: and These represent the number of times the slime mold was present. generation and first The position of the generation; Represents a random number within the range [0,1]; UB and LB represent the upper and lower bounds of the optimization interval, respectively; Indicates the probability of mutation; Indicates the number of iterations; Indicates the first The optimal location for slime mold to adapt to its generation; Indicates the range of values ​​within The random number within, where It decreases as the number of iterations increases, and the expression it satisfies is shown in equation (4); Indicates the weighted parameters reflecting slime mold behavior; and Indicates the first Two randomized locations of slime mold; Decrease exponentially from 1 to 0 generation by generation; The parameter that regulates the behavior of slime molds is expressed in equation (5). in, The expression that satisfies this condition is as follows: (4) In the formula: The output parameter for oscillation amplitude is the result of the formula calculation; arctanh is the hyperbolic arctangent function; its domain is (-1, 1), and its range is all real numbers. In this formula, it is used to map the result of the internal linear combination to a suitable decay curve to ensure... It decays smoothly and non-linearly from a positive value to near 0; This is the current iteration number, i.e., the input variable; This indicates the maximum number of iterations. In equation (3), The parameter representing the regulatory role of slime mold behavior is expressed as: (5) In the formula: Indicates the first The fitness value of each slime mold individual; SF is the global optimal fitness index.

[0030] After obtaining the latest position of each slime mold individual according to the above position update formula (5), check whether the updated position vectors exceed the constraint range defined in step 3.1. If the component exceeds the upper limit, it is updated to the upper limit value, and the component below the lower limit is updated to the lower limit value. Among them, the upper limit value and the lower limit value are the maximum and minimum values ​​of each decision variable set in step 3, respectively.

[0031] Step 3.6, Evaluation and Update: For the population obtained after updating in Step 3.5, the calculation method is the same as in Step 3.3. Specifically, the position vector of each individual is... Substitute the multi-objective optimization model constructed in step 2 and calculate its objective function value: identify the non-dominated solutions in the current population to form a new Pareto front; merge the new Pareto front with the previously saved Pareto front, and use the Pareto dominance relation again to filter out the non-dominated solutions to obtain the updated Pareto front; calculate the fitness value of each slime mold individual in the updated population. Step 3.7, Termination Condition Judgment: Check if the termination condition is met. If it is met, output the final Pareto front as the optimal solution to the multi-objective optimization problem; otherwise, return to step 3.5 to continue the iteration. The termination condition is specifically: if the current iteration number is... If the iteration terminates, the solution is the desired Pareto optimal solution, which is output as the final result of the multi-objective optimization problem; if Then let Then return to step 3.5 to continue updating the individual position and subsequent iterations.

[0032] Example 1 1) Screening and pretreatment of key parameters in the manufacturing process To verify the effectiveness of the proposed multi-objective optimization of manufacturing process parameters based on the slime mold optimization algorithm, a CNC milling and pinning dataset of the manufacturing process was selected as the manufacturing process parameters, which includes the spindle speed. Feed per tooth Cutting width Depth of cut Four CNC milling process parameters, consisting of [parameters 1, 2, and 3], are used, with milling specific energy consumption (SEC) and machining cost as product quality indicators. A TCN-Transformer hybrid neural network model is employed to construct the mapping relationship between the manufacturing process parameters and product quality indicators, performing forward modeling.

[0033] The selected manufacturing process parameter dataset and product quality index dataset are preprocessed by data cleaning, normalization and serialization. Then, the preprocessed manufacturing process parameter dataset and product quality index dataset are randomly divided into training set and test set according to a preset ratio of 8:2. The time series sequence samples of training set and test set are constructed on the training set and test set respectively using the sliding window method, and these samples all have a clear time window length L attribute.

[0034] 1.2) TCN-Transformer hybrid neural network model parameter configuration; The network structure of the TCN-Transformer hybrid neural network model is as follows: Figure 2 As shown, TCN - The Transformer network structure starts with a sequence input, followed by a one-dimensional convolutional layer (conv1_1), padded with "ccasual", then a layer normalization layer with 32 channels (layernorm_1), and dropout_1. This loop repeats through the previous one-dimensional convolutional layer and layer normalization layer, followed by a ReLU activation function layer with dropout_2. Then, another one-dimensional convolutional layer is introduced, using 32 and 64 convolutional kernels to extract features from the input data. The two inputs are then element-wise added (add_2). Next, the Transformer model's positional encoding layer, with 32 channels and a maximum position of 128, is introduced. The system then enters a multi-head self-attention layer with 32 output channels, 4 heads, 64 key and query channels, 64 value channels, and self-attention. Following this, a one-dimensional indexing layer is applied. The data is then passed to a fully connected layer (fc), which further combines and transforms the extracted features to extract better data features. Finally, the regression output layer outputs the final result. The parameter settings for the TCN-Transformer hybrid neural network model are shown in Table 1.

[0035] Table 1. Parameter settings for the TCN-Transformer hybrid neural network model

[0036] The specific parameters of the TCN-Transformer hybrid neural network model in this embodiment are as follows: the number of channels in the position encoding layer is 32, the maximum position encoding length is 128; the number of output channels in the multi-head self-attention layer is 32, the number of attention heads is 4, the number of key channels is 64, the number of query channels is 64, and the number of value channels is 64; the number of encoder layers is 1.

[0037] 1.3) Model Validation This step, based on the time-series training and test sets prepared in step 1.1, trains and verifies the performance of the TCN-Transformer hybrid neural network model with parameters configured in step 1.2.

[0038] The time series samples of the training set are input into the TCN-Transformer hybrid neural network model to generate predicted values ​​of product quality indicators for the training set. Here, the product quality indicators are the milling specific energy consumption and processing cost of the CNC milling manufacturing process.

[0039] Comparison of forward modeling predictions and actual values ​​of CNC milling cutter energy consumption based on TCN-Transformer hybrid neural network model. Figure 3 As shown, the graph compares the predicted and actual values ​​of the specific energy consumption in the manufacturing process using the TCN-Transformer model. The horizontal axis represents the test set sample number, and the vertical axis represents the specific energy consumption value. The two curves represent the actual measured value and the model's predicted value, respectively. Their high overlap indicates that the model can accurately predict the specific energy consumption in the manufacturing process, verifying the high accuracy of the forward model. The graph also compares the forward model prediction and actual value of CNC milling machining cost based on the TCN-Transformer model. Figure 4 As shown, the comparison between the predicted and actual values ​​of the TCN-Transformer model for the quality indicator of processing cost is also presented. The predicted curve is very close to the actual curve, proving that the model has high accuracy in predicting processing cost and can reliably reflect the mapping relationship between process parameters and cost.

[0040] The TCN-Transformer CNC milling pin quality prediction model was verified to have good prediction accuracy. The obtained forward model can well reflect the mapping relationship between CNC milling pin process parameters and milling pin specific energy consumption and processing cost.

[0041] The root mean square error function curve of the TCN-Transformer hybrid neural network model for predicting milling specific energy consumption on the CNC milling training set in the method of this invention is shown in the figure below. Figure 5 As shown in the figure, the horizontal axis represents the number of training iterations, and the vertical axis represents the root mean square error (RMSE). The curve shows a decreasing trend and gradually converges as the number of iterations increases, indicating that the prediction error of the model for milling specific energy consumption continues to decrease during the training process, and the learning effect is good. Figure 6 This is a graph showing the loss function curve of the TCN-Transformer hybrid neural network model on the CNC milling training set for the predicted milling specific energy consumption. The vertical axis represents the loss function value. The curve also decreases and tends to stabilize as the number of iterations increases, indicating that the model parameter optimization process is effective and the fitting ability is continuously enhanced. Figure 7This is a graph showing the root mean square error (RMSE) function of the TCN-Transformer hybrid neural network model in the method of this invention on the CNC milling training set. The horizontal axis represents the number of iterations, and the vertical axis represents the root mean square error (RMSE). The curve shows a decreasing convergence trend, proving that the model's prediction error for machining costs gradually decreases. Figure 8 This is a graph showing the loss function of the model on the CNC milling training set for predicting machining costs. The loss function value decreases and flattens as the number of iterations increases, further verifying the model's accurate learning of the machining cost mapping relationship during training. The four graphs above collectively demonstrate that the model's predictive performance for different quality indicators steadily improves during the training phase until convergence.

[0042] This phenomenon indicates that the TCN-Transformer hybrid neural network model is gradually improving its data representation ability through parameter optimization, achieving a more accurate distribution of training samples with increasing iterations. Specific prediction and evaluation metrics of the TCN-Transformer hybrid neural network model are shown in Table 2, demonstrating that this method can effectively reflect the mapping relationship between CNC milling manufacturing process parameters and product quality indicators.

[0043] Table 2 Forward Model Results

[0044] 2) Construction of a multi-objective optimization model for CNC milling and pin manufacturing process parameters In CNC milling manufacturing, the specific energy consumption and machining cost of milling are used as objective functions. The specific energy consumption and machining cost of milling are mainly affected by the spindle speed. Feed per tooth Cutting width and depth of cut The influence of spindle speed, therefore Feed per tooth Cutting width and depth of cut These four manufacturing process parameters are used as decision variables. Among them, the milling-to-pin ratio energy consumption function is the forward model between the CNC milling manufacturing process parameters and product quality indicators constructed by the TCN-Transformer hybrid neural network model in the previous section. The processing cost model is shown in the following formula (6): (6) In the formula: This indicates the processing cost (in yuan). This is the unit price for labor costs (yuan / hour); The unit price of cutting fluid consumed per unit time (yuan / hour); The price per unit of time for using the cutting tool (RMB / hour); The price per unit of time for using the machine tool (RMB / hour); Electricity unit price (yuan / ) ), Set the workpiece loading and unloading time to a fixed value (min); For tool sharpening and tool change time (min); The actual cutting time (min) between the tool and the workpiece. Tool life (min); Machine tool life (min). Indicates cutting power (W) Therefore, the multi-objective optimization model for the CNC milling and pin manufacturing process parameters is shown below: (7) In the formula: The first optimization objective, in this embodiment, is the specific energy consumption of milling. The milling specific energy consumption prediction function constructed for the TCN-Transformer hybrid neural network model in step 1; It is the spindle speed. It is the feed per tooth. It is the cutting width. Both cutting depth and cutting depth are used as decision variables; The second optimization objective, in this embodiment, is processing cost; in this embodiment, the constraint condition for each decision variable is: 2800 3600 0.15 mm 0.35 mm 6 mm 10 mm , 0.15mm 0.35 mm .

[0045] 3) Solving the multi-objective optimization model for CNC milling parameters based on slime mold optimization algorithm After determining the milling-to-pin ratio energy consumption and machining cost as objective functions in the CNC milling manufacturing process, and defining the constraints on the CNC milling process parameters, the initial population of the slime mold optimization algorithm is set to 200, the external file elements to 100, and the number of iterations to 100. Global optimization is performed with milling-to-pin ratio energy consumption and machining cost as the objectives. Determining the optimal solution further requires using the entropy-weighted TOPSIS method. TOPSIS, also known as the best-case-best-case distance method, is a ranking technique that aims to determine the order of evaluation by comparing the relative distances between the evaluated object and the ideal optimal solution and the worst solution. Specifically, if an evaluated object is closest to the ideal optimal solution while maintaining the greatest distance from the worst solution, then the object is considered optimal; otherwise, it is considered inferior.

[0046] After analyzing the candidate solution set using the entropy-weighted TOPSIS method, the optimal solution to the CNC milling parameter optimization problem can be obtained. The Pareto optimal process parameter combination is shown in Table 3: Table 3 Comparison of Optimal Process Parameter Combinations

[0047] Comparing the data before and after optimization in Table 3, for the same material cutting situation, the optimized milling parameter configuration saves about 10.94% in cost and about 48.53% in energy consumption compared to the unoptimized configuration.

[0048] 4) Results Analysis Next, this chapter will compare the established TCN-Transformer hybrid neural network model with the Non-dominated Sorting Genetic Algorithm-II (NSGAII) and the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to verify the effectiveness of the multi-objective slime mold optimization algorithm. In the NSGAII algorithm, the population size is set to 100, the number of iterations to 100, the mutation factor to 0.5, and the crossover probability to 0.9. The optimization results are as follows: Figure 9 As shown in the figure, the Pareto front obtained by the NSGA-II algorithm is concentrated between RMB 12.935 and RMB 12.96 in terms of cost.

[0049] In the MOPSO algorithm, with a population size of 100, 100 iterations, a mutation factor of 0.5, and a crossover probability of 0.8, the optimization effect is as follows: Figure 10 As shown. Figure 10The optimization results obtained by the MOPSO algorithm are shown, with energy consumption values ​​ranging from 19.674 J to 19.681 J. Combining the two figures, it can be seen that compared to the MOSMA-based multi-objective optimization method for manufacturing process parameters proposed in this chapter, the Pareto front solution set of the multi-objective optimization results based on NSGAⅡ and MOPSO has a higher range. Table 4 shows a comparison of the optimal process parameter combinations selected from the obtained Pareto optimal solutions.

[0050] Table 4 Comparison of Optimal Process Parameter Combinations

[0051] As shown in Table 4, the multi-objective optimization of manufacturing process parameters based on the slime mold optimization algorithm achieves lower processing costs and milling-to-displacement energy consumption. Compared to the NSGA I and PSO algorithms, the multi-objective slime mold optimization algorithm improves the optimization effect on processing costs by approximately 3.28% and 3.18%, respectively, and the optimization effect on milling-to-displacement energy consumption by approximately 44.34% and 44.1%, respectively. Therefore, the multi-objective optimization of manufacturing process parameters based on the slime mold optimization algorithm has a better optimization effect, enabling the acquisition of optimal quality indicators while obtaining the optimal combination of process parameters.

[0052] This invention utilizes a TCN-Transformer hybrid neural network model and a slime mold optimization algorithm to accurately establish the mapping relationship between manufacturing process parameters and product quality indicators, optimizing multi-objective manufacturing parameter configurations and thus improving the stability of product quality indicators. It solves the problems of existing technologies, such as the difficulty in mapping the complex nonlinear and temporal relationships between manufacturing process parameters and product quality indicators, and the poor quality of traditional multi-objective optimization algorithms.

[0053] Example 2 A deep learning-based multi-objective optimization method for parameters in complex manufacturing processes includes the following steps: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 2: Construct a multi-objective optimization model for manufacturing process parameters; Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

[0054] Example 3 A deep learning-based multi-objective optimization method for parameters in complex manufacturing processes includes the following steps: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 1 is as follows: Step 1.1: First, determine the manufacturing process parameters and product quality indicators to form a manufacturing process parameter dataset and a product quality indicator dataset; perform data cleaning, normalization, and serialization preprocessing on the selected manufacturing process parameter dataset and product quality indicator dataset; then, randomly divide the preprocessed manufacturing process parameter dataset and product quality indicator dataset into a training set and a test set according to a preset ratio; construct time series samples for the training set and the test set respectively using the sliding window method on the training set and the test set. Step 1.2: Configure the specific model parameters for the TCN-Transformer hybrid neural network model; Based on the preprocessed time series samples obtained in step 1.1, the TCN model architecture parameters are derived, including the number of layers, convolution kernel size, and dilation coefficient of the TCN model. The TCN model architecture parameters are derived and set according to formula (1): The core operation of TCN model parameter configuration is dilated convolution, and its mathematical definition is shown in formula (1). (1) In the formula, Indicates the position of the output sequence The value; Represents the input sequence; The weight function represents the convolution kernel; This indicates the time node number of the output sequence, specifying the number of the output sequence to be calculated. One value; The length of the convolution kernel is defined, which determines the number of consecutive time steps covered by each convolution operation; Indicates the depth of network layers; Refers to the first The input sequence values ​​of the layer.

[0055] Step 1.3: Train and validate the TCN-Transformer hybrid neural network model, and use it for forward prediction.

[0056] Step 2: Construct a multi-objective optimization model for manufacturing process parameters; Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

[0057] Example 4 A deep learning-based multi-objective optimization method for parameters in complex manufacturing processes includes the following steps: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 1 is as follows: Step 1.1: First, determine the manufacturing process parameters and product quality indicators to form a manufacturing process parameter dataset and a product quality indicator dataset; perform data cleaning, normalization, and serialization preprocessing on the selected manufacturing process parameter dataset and product quality indicator dataset; then, randomly divide the preprocessed manufacturing process parameter dataset and product quality indicator dataset into a training set and a test set according to a preset ratio; construct time series samples for the training set and the test set respectively using the sliding window method on the training set and the test set. Step 1.2: Configure the specific model parameters for the TCN-Transformer hybrid neural network model; Based on the preprocessed time series samples obtained in step 1.1, the TCN model architecture parameters are derived, including the number of layers, convolution kernel size, and dilation coefficient of the TCN model. The TCN model architecture parameters are derived and set according to formula (1): The core operation of TCN model parameter configuration is dilated convolution, and its mathematical definition is shown in formula (1). (1) In the formula, Indicates the position of the output sequence The value; Represents the input sequence; The weight function represents the convolution kernel; This indicates the time node number of the output sequence, specifying the number of the output sequence to be calculated. One value; The length of the convolution kernel is defined, which determines the number of consecutive time steps covered by each convolution operation; Indicates the depth of network layers; Refers to the first The input sequence values ​​of the layer.

[0058] In step 1.2, the TCN-Transformer hybrid neural network model consists of a TCN model and a Transformer model.

[0059] Step 1.3: Train and validate the TCN-Transformer hybrid neural network model, and use it for forward prediction.

[0060] Step 2: Construct a multi-objective optimization model for manufacturing process parameters; Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

[0061] Example 5 A deep learning-based multi-objective optimization method for parameters in complex manufacturing processes includes the following steps: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 1 is as follows: Step 1.1: First, determine the manufacturing process parameters and product quality indicators to form a manufacturing process parameter dataset and a product quality indicator dataset; perform data cleaning, normalization, and serialization preprocessing on the selected manufacturing process parameter dataset and product quality indicator dataset; then, randomly divide the preprocessed manufacturing process parameter dataset and product quality indicator dataset into a training set and a test set according to a preset ratio; construct time series samples for the training set and the test set respectively using the sliding window method on the training set and the test set. Step 1.2: Configure the specific model parameters for the TCN-Transformer hybrid neural network model; Based on the preprocessed time series samples obtained in step 1.1, the TCN model architecture parameters are derived, including the number of layers, convolution kernel size, and dilation coefficient of the TCN model. The TCN model architecture parameters are derived and set according to formula (1): The core operation of TCN model parameter configuration is dilated convolution, and its mathematical definition is shown in formula (1). (1) In the formula, Indicates the position of the output sequence The value; Represents the input sequence; The weight function represents the convolution kernel; This indicates the time node number of the output sequence, specifying the number of the output sequence to be calculated. One value; The length of the convolution kernel is defined, which determines the number of consecutive time steps covered by each convolution operation; Indicates the depth of network layers; Refers to the first The input sequence values ​​of the layer.

[0062] In step 1.2, the TCN-Transformer hybrid neural network model consists of a TCN model and a Transformer model.

[0063] Step 1.3: Train and validate the TCN-Transformer hybrid neural network model, and use it for forward prediction.

[0064] Step 1.3 specifically involves: First, the time-series samples of the training set divided in step 1.1 are input into the TCN-Transformer hybrid neural network model for processing, which will eventually generate predicted values ​​of the product quality index for the training set. Then, the weight parameters inside the TCN-Transformer hybrid neural network model are adjusted using the backpropagation algorithm, and multiple iterations are repeated until the error between the predicted values ​​of the product quality index for the training set and the actual values ​​of the product quality index for the training set is reduced to close to 0 and shows a convergence trend. At this point, the TCN-Transformer hybrid neural network model is preliminarily trained, and the training is completed. The final evaluation index values ​​on the time-series samples of the training set are recorded. Subsequently, the time-series samples of the test set reserved in step 1.1 are input into the trained TCN-Transformer hybrid neural network model to obtain the corresponding predicted values ​​of the product quality indicators for the test set. The predicted values ​​of the product quality indicators for the test set and the actual values ​​of the product quality indicators for the test set are recorded, and the following evaluation indicators are calculated according to the evaluation indicator formula table in Table 1-1: The selected evaluation indicators include mean squared error, mean absolute error, root mean square error, mean absolute percentage error, and correlation coefficient. If the mean squared error, mean absolute error, root mean square error, and mean absolute percentage error of the test set are all greater than the corresponding values ​​on the training set, or the correlation coefficient is less than the corresponding values ​​on the training set, then return to step 1.2 to reconfigure the model architecture parameters. Step 2: Construct a multi-objective optimization model for manufacturing process parameters; Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

[0065] Example 6 A deep learning-based multi-objective optimization method for parameters in complex manufacturing processes includes the following steps: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 1 is as follows: Step 1.1: First, determine the manufacturing process parameters and product quality indicators to form a manufacturing process parameter dataset and a product quality indicator dataset; perform data cleaning, normalization, and serialization preprocessing on the selected manufacturing process parameter dataset and product quality indicator dataset; then, randomly divide the preprocessed manufacturing process parameter dataset and product quality indicator dataset into a training set and a test set according to a preset ratio; construct time series samples for the training set and the test set respectively using the sliding window method on the training set and the test set. Step 1.2: Configure the specific model parameters for the TCN-Transformer hybrid neural network model; Based on the preprocessed time series samples obtained in step 1.1, the TCN model architecture parameters are derived, including the number of layers, convolution kernel size, and dilation coefficient of the TCN model. The TCN model architecture parameters are derived and set according to formula (1): The core operation of TCN model parameter configuration is dilated convolution, and its mathematical definition is shown in formula (1). (1) In the formula, Indicates the position of the output sequence The value; Represents the input sequence; The weight function represents the convolution kernel; This indicates the time node number of the output sequence, specifying the number of the output sequence to be calculated. One value; The length of the convolution kernel is defined, which determines the number of consecutive time steps covered by each convolution operation; Indicates the depth of network layers; Refers to the first The input sequence values ​​of the layer.

[0066] In step 1.2, the TCN-Transformer hybrid neural network model consists of a TCN model and a Transformer model.

[0067] Step 1.3: Train and validate the TCN-Transformer hybrid neural network model, and use it for forward prediction.

[0068] Step 1.3 specifically involves: First, the time-series samples of the training set divided in step 1.1 are input into the TCN-Transformer hybrid neural network model for processing, which will eventually generate predicted values ​​of the product quality index for the training set. Then, the weight parameters inside the TCN-Transformer hybrid neural network model are adjusted using the backpropagation algorithm, and multiple iterations are repeated until the error between the predicted values ​​of the product quality index for the training set and the actual values ​​of the product quality index for the training set is reduced to close to 0 and shows a convergence trend. At this point, the TCN-Transformer hybrid neural network model is preliminarily trained, and the training is completed. The final evaluation index values ​​on the time-series samples of the training set are recorded. Subsequently, the time-series samples of the test set reserved in step 1.1 are input into the trained TCN-Transformer hybrid neural network model to obtain the corresponding predicted values ​​of the product quality indicators for the test set. The predicted values ​​of the product quality indicators for the test set and the actual values ​​of the product quality indicators for the test set are recorded, and the following evaluation indicators are calculated according to the evaluation indicator formula table in Table 1-1: The selected evaluation indicators include mean squared error, mean absolute error, root mean square error, mean absolute percentage error, and correlation coefficient. If the mean squared error, mean absolute error, root mean square error, and mean absolute percentage error of the test set are all greater than the corresponding values ​​on the training set, or the correlation coefficient is less than the corresponding values ​​on the training set, then return to step 1.2 to reconfigure the model architecture parameters. Step 2: Construct a multi-objective optimization model for manufacturing process parameters; The multi-objective optimization model for manufacturing process parameters established in step 2 is as follows: (2) In the formula: For identifiers, introduce The function is the listed objective function to be optimized; in a multi-objective optimization model for manufacturing process parameters, This indicates the first quality indicator; This indicates the second quality indicator; Indicates the first One quality indicator; It is a set of manufacturing process parameters, which serve as decision variables in the multi-objective optimization model of manufacturing process parameters; It is the first One manufacturing process parameter; and Indicates the first The lower and upper limits of the process allowed by each parameter.

[0069] Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

Claims

1. A multi-objective optimization method for complex manufacturing process parameters based on deep learning, characterized in that, Includes the following steps: Step 1: Forward modeling of the manufacturing process based on the TCN-Transformer hybrid neural network model; Step 2: Construct a multi-objective optimization model for manufacturing process parameters; Step 3: Based on the multi-objective optimization model constructed in Step 2, this step uses the slime mold optimization algorithm to solve the problem, obtains the Pareto optimal solution set, and uses the entropy weight TOPSIS method to determine the comprehensive optimal combination of manufacturing process parameters from the Pareto optimal solution set.

2. The multi-objective optimization method for complex manufacturing process parameters based on deep learning according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: First, determine the manufacturing process parameters and product quality indicators to form a manufacturing process parameter dataset and a product quality indicator dataset; perform data cleaning, normalization and serialization preprocessing on the selected manufacturing process parameter dataset and product quality indicator dataset. Subsequently, the preprocessed manufacturing process parameter dataset and product quality index dataset were randomly divided into training set and test set according to a preset ratio; time series samples of training set and test set were constructed on the training set and test set respectively using the sliding window method. Step 1.2: Configure the specific model parameters for the TCN-Transformer hybrid neural network model; Based on the preprocessed time series samples obtained in step 1.1, the TCN model architecture parameters are derived, including the number of layers, convolution kernel size, and dilation coefficient of the TCN model. The TCN model architecture parameters are derived and set according to formula (1): The core operation of TCN model parameter configuration is dilated convolution, and its mathematical definition is shown in formula (1). （1） In the formula, Indicates the position of the output sequence The value; Represents the input sequence; The weight function represents the convolution kernel; This indicates the time node number of the output sequence, specifying the number of the output sequence to be calculated. One value; The length of the convolution kernel is defined, which determines the number of consecutive time steps covered by each convolution operation; Indicates the depth of network layers; Refers to the first The input sequence values ​​of the layer; Step 1.3: Train and validate the TCN-Transformer hybrid neural network model, and use it for forward prediction.

3. The multi-objective optimization method for complex manufacturing process parameters based on deep learning according to claim 2, characterized in that, In step 1.2, the TCN-Transformer hybrid neural network model consists of a TCN model and a Transformer model.

4. The multi-objective optimization method for complex manufacturing process parameters based on deep learning according to claim 2, characterized in that, Step 1.3 specifically involves: First, the time-series samples of the training set divided in step 1.1 are input into the TCN-Transformer hybrid neural network model for processing, which will eventually generate predicted values ​​of the product quality index for the training set. Then, the weight parameters inside the TCN-Transformer hybrid neural network model are adjusted using the backpropagation algorithm, and multiple iterations are repeated until the error between the predicted values ​​of the product quality index for the training set and the actual values ​​of the product quality index for the training set is reduced to close to 0 and shows a convergence trend. At this point, the preliminarily trained TCN-Transformer hybrid neural network model is obtained, and the training is completed. The final evaluation index values ​​on the time-series samples of the training set are recorded. Subsequently, the time-series samples of the test set reserved in step 1.1 are input into the trained TCN-Transformer hybrid neural network model to obtain the corresponding predicted values ​​of the product quality indicators for the test set. The predicted values ​​of the product quality indicators for the test set and the actual values ​​of the product quality indicators for the test set are recorded. The selected evaluation indicators include mean squared error, mean absolute error, root mean square error, mean absolute percentage error, and correlation coefficient. If the mean squared error, mean absolute error, root mean square error, and mean absolute percentage error of the test set are all greater than the corresponding values ​​on the training set or the correlation coefficient is less than the corresponding values ​​on the training set, then return to step 1.2 to reconfigure the model architecture parameters.

5. The multi-objective optimization method for complex manufacturing process parameters based on deep learning according to claim 2, characterized in that, The multi-objective optimization model for manufacturing process parameters established in step 2 is as follows: （2） In the formula: For identifiers, introduce The function is the listed objective function to be optimized; in a multi-objective optimization model for manufacturing process parameters, This indicates the first quality indicator; This indicates the second quality indicator; Indicates the first One quality indicator; It is a set of manufacturing process parameters, which serve as decision variables in the multi-objective optimization model of manufacturing process parameters; It is the first One manufacturing process parameter; and Indicates the first The lower and upper limits of the process allowed by each parameter.

6. The multi-objective optimization method for complex manufacturing process parameters based on deep learning according to claim 2, characterized in that, Step 3 specifically involves: Step 3.1, Parameter Initialization: Define the objective function and manufacturing process parameters to be optimized, set the number of slime mold individuals and the maximum number of iterations, and define the set of decision variables. China's various decisions Policy variables The range of values ​​for which is defined, i.e., the constraint conditions defined in step 2. ; The objective function to be optimized is the optimization objective defined in step 2. Manufacturing process parameters are the set of decision variables. Each decision variable ; Step 3.2: Generate the initial population: Within the range of decision variables, randomly generate slime mold individuals to form the initial population; Step 3.3, Calculate the fitness value: The position vector from step 3.2... Substitute the values ​​into the multi-objective optimization model constructed in step 2, and calculate the objective function value; the calculation result for each slime mold individual is the fitness vector of that individual, denoted as . ; Step 3.4, Pareto Front Calculation: Based on the fitness vector of each slime mold individual calculated in Step 3.3 Pareto dominance relation is used to determine the non-dominated solutions in the current population; the identified non-dominated solutions will be used as a reference for updating individual positions in step 3.

5. Step 3.5, Individual Position Update: According to the position iteration criterion of the slime mold optimization algorithm, update the position of each slime mold individual in the population, and check whether the updated position of the individual exceeds the value range of each decision variable set in Step 3.

1. If it exceeds the range, make corresponding adjustments. The specific adjustment method is as follows: if the updated position of an individual is less than its lower limit value... Then adjust it to If the updated position of an individual is greater than its upper limit value Then set it to If the updated individual's position is within the interval Inside, it remains unchanged; The formula for updating individual locations is as follows: (3) In the formula: and These represent the number of times the slime mold was present. generation and first The position of the generation; Represents a random number within the range [0,1]; UB and LB represent the upper and lower bounds of the optimization interval, respectively; Indicates the probability of mutation; Indicates the number of iterations; Indicates the first The optimal location for slime mold to adapt to its generation; Indicates the range of values ​​within The random number within, where It decreases as the number of iterations increases, and the expression it satisfies is shown in equation (4); Indicates the weighted parameters reflecting slime mold behavior; and Indicates the first Two randomized locations of slime mold; Decrease exponentially from 1 to 0 generation by generation; The parameter that regulates the behavior of slime molds is expressed in equation (5). in, The expression that satisfies this condition is as follows: （4） In the formula: The output parameter is the oscillation amplitude, which is the result of the formula calculation; arctanh is the hyperbolic arctangent function; its domain is (-1, 1), and its range is all real numbers; This is the current iteration number, i.e., the input variable; Indicates the maximum number of iterations; In equation (3), The parameter representing the regulatory role of slime mold behavior is expressed as: (5) In the formula: Indicates the first The fitness value of each slime mold individual; SF is the global optimal fitness index; After obtaining the latest position of each slime mold individual according to the position update formula (5), check whether the updated position vectors exceed the constraint range defined in step 3.

1. If the component exceeds the upper limit, it is updated to the upper limit value, and the component below the lower limit is updated to the lower limit value. The upper limit value and the lower limit value are the maximum and minimum values ​​of each decision variable set in step 3, respectively. Step 3.6, Evaluation and Update: For the population obtained after updating in Step 3.5, the calculation method is the same as in Step 3.

3. Specifically, the position vector of each individual is... Substitute the multi-objective optimization model constructed in step 2 and calculate its objective function value: identify the non-dominated solutions in the current population to form a new Pareto front; merge the new Pareto front with the previously saved Pareto front, and use the Pareto dominance relation again to filter out the non-dominated solutions to obtain the updated Pareto front; calculate the fitness value of each slime mold individual in the updated population. Step 3.7, Termination Condition Judgment: Check if the termination condition is met. If it is met, output the final Pareto front as the optimal solution to the multi-objective optimization problem; otherwise, return to step 3.5 to continue the iteration.

7. The multi-objective optimization method for complex manufacturing process parameters based on deep learning according to claim 2, characterized in that, Step 3.2 specifically involves: Within the range of values ​​for the decision variables defined in step 3.1, slime mold individuals are randomly generated to form the initial population; the position vector of each slime mold individual is set as follows: , representing a set of random combinations of manufacturing process parameters, where These are the i decision variables defined in step 2; each component of the position vector lies within its corresponding feasible range. The parameters are generated randomly within the system, representing a set of possible combinations of manufacturing process parameters.

8. The multi-objective optimization method for complex manufacturing process parameters based on deep learning according to claim 2, characterized in that, In step 3.7, the termination condition is specifically: if the current iteration number is... If the iteration terminates, the solution is the desired Pareto optimal solution, which is output as the final result of the multi-objective optimization problem; if Then let Then return to step 3.5 to continue updating the individual position and subsequent iterations.

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