A multi-objective optimization design method for auxiliary nozzles with high flow rate and low gas consumption

Abstract

This application relates to a multi-objective optimization design method for auxiliary nozzles with high flow rate and low air consumption, comprising: collecting performance data of auxiliary nozzles of an air-jet loom and preprocessing them; inputting the preprocessed performance data into a trained variational autoencoder to extract latent features; inputting the latent features into a Transformer-based multilayer perceptron to obtain enhanced latent features; passing the enhanced latent features through a trained XGBoost regression model to output optimization objective variables; using the auxiliary nozzle outlet airflow velocity as the first objective value and the air consumption as the second objective value, and using a multi-objective optimization algorithm to optimize the design with maximizing the first objective value as the first objective and minimizing the second objective value as the second objective, to obtain the Pareto front solution between the auxiliary nozzle outlet airflow velocity and the air consumption; and designing a high-speed weft insertion and low-energy-consumption auxiliary nozzle for an air-jet loom based on the Pareto front solution.

Description

Technical Field

[0001] This application relates to the field of multi-objective optimization design technology for auxiliary nozzles, and in particular to a multi-objective optimization design method for auxiliary nozzles with high flow rate and low gas consumption. Background Technology

[0002] Air-jet looms, with their high speed, efficiency, and automation, have become the most promising shuttleless looms. However, their high energy consumption leads to increased production costs for textile companies. Therefore, energy conservation and emission reduction have become important goals for textile enterprises both domestically and internationally. A typical air-jet loom's weft insertion system consists of a main nozzle, auxiliary nozzles, and a reed. There are dozens of auxiliary nozzles, which consume over 80% of the total air and over 70% of the total electrical energy of the entire loom. Furthermore, the airflow velocity of the auxiliary nozzles determines the weft insertion speed and efficiency of the entire loom. Therefore, domestic and international air-jet loom manufacturers are committed to optimizing the structure of the auxiliary nozzles, including increasing the auxiliary jet velocity and reducing nozzle air consumption, thereby improving the overall weft insertion efficiency and reducing the energy consumption of the air-jet loom. Summary of the Invention

[0003] Therefore, it is necessary to provide a multi-objective optimization design method for auxiliary nozzles that achieves high flow rate and low gas consumption. This method includes:

[0004] S1: Collect performance data of the auxiliary nozzles of the air-jet loom and preprocess them; the performance data includes shape parameters and control variables;

[0005] S2: Input the preprocessed performance data into the trained variational autoencoder to extract latent features; input the latent features into a Transformer-based multilayer perceptron to obtain enhanced latent features;

[0006] S3: The enhanced latent features are processed by the trained XGBoost regression model to output the optimized target variables, which include the auxiliary nozzle outlet airflow velocity and air consumption.

[0007] S4: Taking the airflow velocity at the auxiliary nozzle outlet as the first objective value and the gas consumption as the second objective value, and taking maximizing the first objective value as the first objective and minimizing the second objective value as the second objective, a multi-objective optimization algorithm combining whale migration algorithm, fast non-dominated sorting optimization, elite reverse learning strategy, individual adaptive mutation and reverse perturbation strategy is used for optimization design to obtain the Pareto front solution between the airflow velocity at the auxiliary nozzle outlet and the gas consumption.

[0008] S5: Design auxiliary nozzles for air-jet looms based on the Pareto front solution.

[0009] Beneficial effects: This method effectively captures the potential characteristics of auxiliary nozzles and obtains rich Pareto front solutions by combining a multi-objective optimization algorithm with whale migration algorithm, fast non-dominated sorting optimization, elite reverse learning strategy, individual adaptive mutation and reverse perturbation strategy. It successfully achieves efficient optimization of the auxiliary nozzle outlet airflow velocity and air consumption of the auxiliary nozzle of the jet loom, providing a comprehensive optimization scheme and scientific basis for improving the performance of industrial equipment. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a flowchart of the multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles in the embodiments of this application.

[0012] Figure 2 This is a cross-sectional view of the auxiliary nozzle in an embodiment of this application.

[0013] Figure 3 This is a flowchart of the multi-objective optimization algorithm in the embodiments of this application.

[0014] Figure 4 This is a comparison chart of the predicted and actual values ​​of the airflow velocity at the auxiliary nozzle outlet in the embodiments of this application.

[0015] Figure 5 This is a comparison chart of the predicted and actual gas consumption values ​​in the embodiments of this application.

[0016] Figure 6 This is a schematic diagram of the Pareto front solution obtained in the embodiments of this application. Detailed Implementation

[0017] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0018] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0019] like Figure 1 As shown, this embodiment provides a multi-objective optimization design method for auxiliary nozzles with high flow rate and low gas consumption. The method includes:

[0020] S1: Collect performance data of the auxiliary nozzle of the air-jet loom and preprocess it; the performance data includes shape parameters and control variables.

[0021] In this embodiment, the structure of the auxiliary nozzle is as follows: Figure 2 As shown, the shape parameters include the inlet size D1 of the auxiliary nozzle, the pipe size D2, the outlet orifice diameter d, the number of small orifices n, the diameter G between the centers of the two small orifices, and the outlet taper. α The controlled variables are the airflow velocity at the auxiliary nozzle outlet and the air consumption. The airflow velocity at the auxiliary nozzle outlet determines the weft insertion efficiency of the auxiliary nozzle, and the air consumption determines the energy consumption of the entire air-jet loom. In this embodiment, the number of holes n=[2,3,4,5,6]. In practical applications, this design method can also be applied to the multi-objective optimization design of multi-hole auxiliary nozzles with a larger number of holes.

[0022] In this embodiment, the preprocessing includes:

[0023] The performance data is subjected to outlier detection, and abnormal performance data is removed.

[0024] Standardize normal performance data.

[0025] S2: Input the preprocessed performance data into the trained variational autoencoder to extract latent features; input the latent features into a Transformer-based multilayer perceptron to obtain enhanced latent features.

[0026] Specifically, the variational autoencoder includes a first input layer (a fully connected layer in this embodiment), an encoder, and a decoder. The encoder includes a first fully connected layer and a second fully connected layer. The decoder is used to reconstruct the latent features output by the encoder and output the reconstructed value of the performance data.

[0027] In the trained variational autoencoder, the first input layer maps the performance data to the latent space, the first fully connected layer outputs the mean of the latent space, and the second fully connected layer outputs the log-variance of the latent space; based on the mean and the log-variance of the latent space, reparameterization is performed to obtain the latent features of the performance data.

[0028] Furthermore, the training process of the variational autoencoder is as follows: with the goal of minimizing the reconstruction error and KL divergence, the variational autoencoder is hyperparameter tuned using a Bayesian optimization algorithm to select the optimal first hyperparameter combination of the variational autoencoder. The first hyperparameter includes the dimension of the latent space, the batch size, and the first learning rate.

[0029] Variational autoencoders (VAEs) effectively handle nonlinear relationships in data by introducing the idea of ​​generative models and have good feature learning capabilities, making them particularly suitable for complex and high-dimensional data.

[0030] In this embodiment, the Transformer-based multilayer perceptron includes: a second input layer (a fully connected layer in this embodiment), a Transformer module, and an output layer; the latent features are input to the multilayer perceptron via the second input layer, the Transformer module enhances the input latent features based on a self-attention mechanism, and the output layer maps the output of the Transformer module to the dimensions of each optimization target variable to obtain the enhanced latent features.

[0031] As a deep neural network, the multilayer perceptron can automatically learn complex nonlinear relationships between input features, giving the model stronger expressive power. At the same time, through the self-attention mechanism, the Transformer can help the model capture more important information and complex features hidden in the data, enhance feature learning ability, improve the model's ability to capture long-range dependencies and global features, and enhance the modeling ability of complex data patterns, thereby further improving the model's fitting ability and prediction accuracy.

[0032] S3: The enhanced latent features are processed by the trained XGBoost regression model to output the optimized target variables, which include the auxiliary nozzle outlet airflow velocity and air consumption.

[0033] Specifically, the process of obtaining the target variable for optimization includes:

[0034] The enhanced latent features are then combined with the original target variables to obtain a feature set;

[0035] The feature set is input into the trained XGBoost regression model, and the optimized target variable is output.

[0036] In this embodiment, the training process of the XGBoost regression model includes:

[0037] The feature set is divided into a training set and a test set;

[0038] The XGBoost regression model is trained based on the training set and the predicted value is output. With the goal of minimizing the root mean square error between the predicted value and the true value, the hyperparameters of the XGBoost regression model are tuned using the Bayesian optimization algorithm. The optimal combination of the second hyperparameters of the XGBoost regression model is selected. The second hyperparameters include the tree depth, the second learning rate, and the regularization strength.

[0039] The trained XGBoost regression model is evaluated based on the test set.

[0040] The XGBoost regression model improves the model's generalization ability through ensemble learning, enabling it to handle high-dimensional features and is robust to outliers and noisy data.

[0041] S4: Taking the auxiliary jet outlet airflow velocity as the first objective value and the gas consumption as the second objective value, and taking maximizing the first objective value as the first objective and minimizing the second objective value as the second objective, a multi-objective optimization algorithm combining whale migration algorithm, fast non-dominated sorting optimization, elite reverse learning strategy, individual adaptive mutation and reverse perturbation strategy is used for optimization design to obtain the Pareto front solution between the auxiliary jet outlet airflow velocity and the gas consumption.

[0042] Specifically, such as Figure 3 As shown, the process of optimization design using a multi-objective optimization algorithm includes:

[0043] Step 1: Generate a population using an elite reverse learning strategy. Each individual in the population consists of different enhanced latent features, a first target value, and a second target value. Each individual is assigned a randomly selected index, and the first target and the second target corresponding to each individual are calculated through a proxy model to obtain the solution corresponding to each individual. The solution includes the solution for the first target and the solution for the second target.

[0044] In this embodiment, the position information of each individual in the whale migration algorithm is initialized randomly. Since random initialization increases the range of feasible solutions, prolongs the search time, and fails to obtain the optimal solution position, an elite back-learning strategy is used to generate the population, specifically including:

[0045] A random population is generated, and for each individual in the random population, a reverse individual is generated to form a reverse population. The calculation formula is as follows:

[0046] ;

[0047] in, This represents the i-th reversed individual in a random population; This represents a random number within the range (0,1); L represents the maximum range; U represents the minimum range. This represents the i-th individual in a random population;

[0048] Calculate the fitness value of each individual in the random population, and form an elite group from the top N / 2 individuals with the lowest fitness values. Compare the fitness values ​​of the top elite individual in the elite group with their corresponding reversed individual, and retain the better one as the top elite individual of the new generation. The calculation formula is as follows:

[0049] ;

[0050] in, This represents the e-th new generation's first elite individual; This represents the e-th first elite individual; This represents the reverse individual of the e-th first elite individual;

[0051] By iterating through all the top elite individuals in the elite group, a new elite group is obtained;

[0052] The N / 2 individuals with the lowest fitness values ​​in the reverse population are merged with the N / 2 first elite individuals in the new elite population to obtain population P (with N individuals).

[0053] Step 2: Perform the first non-dominated sorting based on the solutions corresponding to each individual, and assign a level value to each individual, where the level value represents the level of the frontier to which the individual belongs;

[0054] Step 3: For any layer of the frontier, calculate the crowding degree of each individual within it;

[0055] include:

[0056] For the solutions corresponding to all individuals in any frontier layer, sort them according to the first objective value and the second objective value respectively;

[0057] For the first / second objective, the crowding degree of the first and last individuals sorted under that objective is set to infinity;

[0058] For each non-boundary individual in the frontier, its crowding component on the target m is calculated using the following formula:

[0059] ;

[0060] in, This represents the crowding component of the i-th individual on target m; This represents the target value of the i-th individual after sorting, which is the adjacent individual i+1 on the target m. This represents the target value of the i-th individual after sorting, which is the adjacent i-1 individuals on the target m. This represents the maximum target value for all individuals on target m; This represents the minimum target value for all individuals on target m;

[0061] The normalized crowding components calculated for each target are summed to obtain the individual's crowding degree, calculated as follows:

[0062] ;

[0063] in, represents the crowding degree of the i-th individual; M is the number of objectives; in multi-objective optimization, the larger this crowding distance, the greater the sparsity of individuals in the frontier, and the better solutions are preserved to a certain extent;

[0064] Step 4: Select the individual with the highest crowding density at the forefront of the first layer as the leader, and introduce a gradually decreasing random perturbation to the leader's position; guide other individuals to move towards the position of the randomly perturbated leader to update the positions of other individuals, thus obtaining the second population;

[0065] Step 5: Merge the population with the second population to obtain a new population;

[0066] Step 6: Perform a second non-dominated sorting based on the solutions corresponding to each individual in the new population, and assign a second-level value to each individual. The second-level value represents the level of the second frontier to which the individual belongs.

[0067] Step 7: For any layer of the second frontier, calculate the second crowding degree of each individual; select the individual with the highest second crowding degree in the first layer of the second frontier as the new leader;

[0068] Step 8: Perform adaptive mutation on individuals in the new population to generate new individuals, thereby enhancing the algorithm's ability to escape local space;

[0069] Specifically, each individual in the population has a certain probability of undergoing mutation:

[0070] ;

[0071] ;

[0072] in, This represents the i-th new individual; This represents the average position of the current NL leaders in the whale pod; Indicates the location of the leader of the whale pod; This represents the adaptive probability variation factor, whose value increases as the number of iterations increases. Indicates the current iteration step; Indicates the maximum number of iterations; It represents the Hadamardi (or Hadama) stack; This means generating a 1-row, D-column matrix where each element is a random number uniformly distributed in the interval [0,1), and D represents the dimension of the population. Represents the i-th individual; This represents the (i-1)th individual.

[0073] The currently iteratively optimal individual guides the position updates of other individuals, and all other whales follow the leader in their position updates. The mutation operation randomly selects the positional features of the whale leader and changes their values; the resulting mutations will generate new positional variations for the leader and follower individuals in the whale population. The adaptive mutation operation randomly selects certain positional features of the whale leader and changes their values; the resulting mutations will generate new solutions for the leader and most followed individuals in the whale population.

[0074] Step 9: Enhance the algorithm's ability to escape local space through the above perturbation strategy. After updating the position through perturbation mutation, introduce a greedy strategy to compare the fitness values ​​of individuals before and after mutation and update the leader; the update formula is:

[0075] ;

[0076] in, Indicates the position of the updated leader; This represents the individual before mutation at the t-th iteration; This represents the individual after mutation in the t-th iteration; Indicates the fitness value;

[0077] Step 10: Before each generation update, the top k individuals with the highest level values ​​are taken as elite individuals. Each elite individual is subjected to a reverse perturbation strategy to output the corresponding solution or perturbation solution, and its solution or perturbation solution is directly passed to the next generation to improve the algorithm accuracy and convergence speed.

[0078] Step 11: Iterate through steps 2-10 until the preset maximum number of iterations is reached, and obtain the Pareto front solution between the auxiliary jet outlet airflow velocity and the air consumption.

[0079] Furthermore, non-dominated sorting includes:

[0080] Determine the dominance relationship between individual A and individual B:

[0081] If the solutions to both objective functions for individual A are better than those for individual B, then individual A dominates individual B.

[0082] Otherwise, individual B dominates individual A;

[0083] Individual A is a non-dominated individual when the solutions to both objective functions for individual A are better than the solutions to both objective functions for all other individuals.

[0084] Multiple fronts are set up. The first front contains all non-dominated individuals, and each subsequent front contains individuals dominated by a different number of individuals.

[0085] Based on the number of individuals dominating each frontier, multiple frontiers are divided into different levels;

[0086] Assign a level to each individual in the frontier as its corresponding level value; the lower the level value of an individual, the higher the quality of its corresponding solution.

[0087] Furthermore, the strategy of applying reverse perturbation to elite individuals includes:

[0088] Step 1: Subtract the solution corresponding to each elite individual from the sum of the upper and lower bounds of the solution dimension to obtain the preliminary reverse solution corresponding to each elite individual;

[0089] Step 2: Calculate and compare the fitness of the preliminary reverse solution with that of the solution. If the fitness of the preliminary reverse solution is less than that of the solution, the solution is still adopted; otherwise, the preliminary reverse solution is adopted as the reverse solution of the corresponding solution.

[0090] Step 3: Calculate the perturbation solution based on the solution and its inverse solution. The calculation formula is:

[0091] ;

[0092] ;

[0093] in, This represents the perturbation solution corresponding to the j-th solution of the i-th elite individual; This represents the j-th solution for the i-th elite individual; Let represent the reverse solution corresponding to the j-th solution of the i-th elite individual; This represents a random disturbance term, which generally follows a normal distribution. Indicates standard deviation; This represents the disturbance intensity factor. The ratio of the solution moving towards the reverse solution is controlled. When the ratio is 1, the solution jumps completely to the reverse solution. When the ratio is 0, the original solution is maintained.

[0094] In this embodiment, it is necessary to ensure that the perturbation solution remains within the upper and lower bounds of the solution, which is expressed as:

[0095] ;

[0096] in, This represents the perturbation solution corresponding to the j-th solution of the i-th elite individual after constraints; Represents the upper bound of the dimension of the solution; Denotes the lower bound of the dimension of the solution;

[0097] Step 4: Determine whether the perturbation solution is better than the corresponding solution. If the perturbation solution is better than the corresponding solution, replace the corresponding solution with the perturbation solution; otherwise, the original solution is still used.

[0098] Step 5: Iterate through steps 1-4 until the preset maximum number of iterations is reached, at which point the process terminates.

[0099] S5: Design an auxiliary nozzle for high-speed weft insertion and low energy consumption air jet loom based on the Pareto front solution.

[0100] To demonstrate the performance advantages of the multi-objective optimization design method for high flow rate and low gas consumption of the auxiliary nozzle provided in this embodiment, the mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and R are used as the metrics. 2 Using the value as the first evaluation index, a comparative experiment was conducted, and the experimental results are shown in Table 1.

[0101] Table 1 is a comparison table of the results of the first evaluation indicator;

[0102] Model MAE MSE RMSE <![CDATA[R 2 ]]> VAE-XGB 3.1619 21.2751 4.6125 0.8389 VAE-XGB-OPT 0.7281 1.3031 1.1415 0.9791 VAE-MLP-XGB-OPT 0.3901 0.5472 0.7397 0.9932 VAE-Transformer-XGB-OPT 0.3321 0.4504 0.6711 0.9939

[0103] In Table 1, the VAE-XGB model includes a variational autoencoder and an XGBoost regression model; the VAE-XGB-OPT model includes a Bayesian-optimized variational autoencoder and an XGBoost regression model; the VAE-MLP-XGB-OPT model includes a conventional multilayer perceptron, a Bayesian-optimized variational autoencoder, and an XGBoost regression model; and the VAE-Transformer-XGB-OPT model is the model provided in this embodiment, which includes a Transformer-based multilayer perceptron (TR-MLP), a Bayesian-optimized (OPT) variational autoencoder (VAE), and an XGBoost regression model (XGB).

[0104] Table 1 shows a significant optimization trend in the performance of the four models, with MAE, MSE, and RMSE gradually decreasing, and R... 2The values ​​gradually increase, indicating that the improvement from the VAE-XGB model to the model provided in this embodiment has continuously improved the model's predictive ability. Comparison shows that the VAE-Transformer-XGB-OPT model has the lowest error, indicating that the model after multi-layer optimization performs best among the four models, possessing extremely high accuracy. Meanwhile, R... 2 A value of 0.9939 indicates that the model performs exceptionally well in data fitting, explaining 99.39% of the data variability. The combined advantages of VAE, TR-MLP, and XGB enable the model to achieve a good balance in feature learning, nonlinear relationship modeling, and efficient tree model training, thereby improving overall performance.

[0105] VAE can effectively encode input data and extract key features, while TR-MLP and XGB further improve the accuracy of the model through hierarchical learning and ensemble learning, enabling the model to better cope with the complexity and noise of the data, have strong generalization ability, and avoid the risk of overfitting.

[0106] As a tree-based ensemble method, XGB is highly robust to outliers and noise in row data and can maintain high prediction accuracy. This approach, which combines deep learning and ensemble learning, can effectively avoid the shortcomings of a single model and enhance the model's adaptability to different datasets.

[0107] The VAE-Transformer-XGB-OPT model structure is highly flexible, allowing the parameters of VAE, TR-MLP, and XGB to be adjusted according to different data characteristics and task requirements, thereby optimizing model performance. It is particularly suitable for processing various types of data (such as numerical, categorical, and high-dimensional data), enabling it to achieve good performance in various scenarios.

[0108] The VAE-Transformer-XGB-OPT model combines the advantages of VAE, MLP, and XGB, exhibiting excellent performance in accuracy, robustness, and generalization ability. It can handle complex and high-dimensional data, demonstrating strong adaptability, and is particularly suitable for tasks requiring high prediction accuracy. Furthermore, the VAE-Transformer-XGB-OPT model performs best among the four models, exhibiting the lowest prediction error and the highest R² value, making it suitable for tasks with high accuracy requirements. Since industrial machines often require high precision, the model's prediction requirements are also high. A comparison chart of the auxiliary nozzle outlet airflow velocity and gas consumption predicted by the VAE-Transformer-XGB-OPT model with the actual values ​​is shown below. Figure 4 , Figure 5As shown in the figure, the predicted values ​​of the model are close to the actual values. Therefore, the model performs excellently in terms of fitting degree and accuracy, and can be used for prediction in industrial production. It can provide good prediction data for nozzles and save costs.

[0109] Meanwhile, the multi-objective optimization algorithm combining whale migration algorithm, fast non-dominated sorting optimization, elite reverse learning strategy, individual adaptive mutation and reverse perturbation strategy has the following advantages compared with the simple fast elite multi-objective genetic algorithm (NSGA-II):

[0110] 1. Comparative experiments with other optimization algorithms show that the optimization framework in this embodiment demonstrates significant advantages in predicting and optimizing the performance of nozzles for jet looms, effectively balancing the multi-objective optimization problem of speed and air consumption. Experimental results also indicate that combining a trained surrogate model with the optimization algorithm significantly improves the accuracy of performance prediction and yields more diverse Pareto front solutions, providing reliable technical support for industrial process optimization.

[0111] 2. The multi-objective optimization algorithm consistently finds 16 Pareto front solutions in each run (while the NSGA-II algorithm finds approximately 8). The consistency of the results indicates that the multi-objective optimization algorithm combined with whale migration provided in this embodiment has a more stable search process and is capable of overcoming the effects of random disturbances. To demonstrate the performance advantages of the multi-objective optimization algorithm used in the high-flow-rate and low-gas-consumption optimization design of the auxiliary nozzle provided in this embodiment, Inverse Generational Distance (IGD), Generational Distance (GD), Hypervolume (HV), and Spacing values ​​are used as evaluation indicators. The comparison results between the multi-objective optimization algorithm and the NSGA-II algorithm are shown in Table 2.

[0112] Table 2 is a comparison table of the results of the second evaluation index;

[0113] Evaluation indicators MOWMA NSGA-II IGD(Obtained_Pareto,True_Pareto) 0.0478 0.0482 GD(Obtained_Pareto,True_Pareto) 0.0003 0.0005 HV(Obtained_Pareto,True_Pareto) 0.1831 0.1831 Spacing(Obtained_Pareto) 0.0682 0.0696

[0114] IGD is a metric that measures the distance between the non-dominated solution set generated by an algorithm and the true Pareto front. It calculates the sum of the distances from each point on the true Pareto front to the nearest non-dominated solution and takes the average. A smaller IGD value indicates that the solution set generated by the algorithm is closer to the true Pareto front.

[0115] GD is a variant of IGD that calculates the sum of the distances from each non-dominated solution to the nearest point on the true Pareto front and takes the average. The smaller the GD value, the better the solution set generated by the algorithm is distributed on the Pareto front.

[0116] The Hidden Value (HV) metric measures the size of the region covered by the non-dominated solution set generated by the algorithm. Typically, this region is defined between the minimum and maximum values ​​of the objective function. A larger HV value indicates that the solution set generated by the algorithm covers a wider range within the objective function space.

[0117] Spacing is a metric that measures the average distance between solutions in the non-dominated solution set generated by the algorithm. The smaller the spacing value, the denser the solutions within the solution set and the higher the diversity.

[0118] The results stabilize at a relatively high number of solutions, demonstrating the robustness of multi-objective optimization algorithms in optimization problems.

[0119] 3. In data testing, the Pareto front solution found by the multi-objective optimization algorithm covers a wider range of auxiliary jet outlet airflow velocities and air consumption combinations, and the solution is evenly distributed across different objectives, such as... Figure 6 As shown. This diversity stems from the perturbation introduced by simulated annealing, which allows the algorithm to escape local regions during the optimization process, ensuring that the solution set is not only more numerous but also more evenly distributed.

[0120] 4. The multi-objective optimization algorithm uses a reverse perturbation strategy to escape local optima when the objective function is embedded in a local optimum by using the reverse solution and the perturbation solution. Data experiments show that the multi-objective optimization algorithm can more effectively find a balance between maximizing speed and minimizing gas consumption.

[0121] 5. In multiple runs, although the multi-objective optimization algorithm incorporated a reverse perturbation strategy, slightly increasing computational overhead, its convergence speed still showed a significant advantage. Compared to NSGA-II, the multi-objective optimization algorithm found richer Pareto front solutions in fewer iterations, reducing overall computation time.

[0122] 6. Multi-objective optimization algorithms can more flexibly adjust themselves to explore different solution regions in order to cope with the diversity of data.

[0123] The multi-objective optimization design method for high flow rate and low air consumption auxiliary nozzles provided in this embodiment, through comparative experiments with other optimization algorithms, demonstrates significant advantages in the performance prediction and optimization of nozzles for air-jet looms. It effectively balances the multi-objective optimization problem of speed and air consumption. Experimental results also show that combining a trained surrogate model with the optimization algorithm significantly improves the accuracy of performance prediction and yields more diverse Pareto front solutions, providing reliable technical support for industrial process optimization.

[0124] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0125] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A multi-objective optimization design method for auxiliary nozzles with high flow rate and low air consumption, characterized in that, include: S1: Collect performance data of the auxiliary nozzles of the air-jet loom and preprocess them; the performance data includes shape parameters and control variables; S2: Input the preprocessed performance data into the trained variational autoencoder to extract latent features; The latent features are input into a Transformer-based multilayer perceptron to obtain enhanced latent features; S3: The enhanced latent features are processed by the trained XGBoost regression model to output the optimized target variables, which include the auxiliary nozzle outlet airflow velocity and air consumption. S4: Taking the airflow velocity at the auxiliary nozzle outlet as the first objective value and the gas consumption as the second objective value, and taking maximizing the first objective value as the first objective and minimizing the second objective value as the second objective, a multi-objective optimization algorithm combining whale migration algorithm, fast non-dominated sorting optimization, elite reverse learning strategy, individual adaptive mutation and reverse perturbation strategy is used for optimization design to obtain the Pareto front solution between the airflow velocity at the auxiliary nozzle outlet and the gas consumption. S5: Design auxiliary nozzles for air-jet looms based on the Pareto front solution.

2. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 1, characterized in that, The preprocessing includes: The performance data is subjected to outlier detection, and abnormal performance data is removed. Standardize normal performance data.

3. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 1, characterized in that, The variational autoencoder includes a first input layer and an encoder, and the encoder includes a first fully connected layer and a second fully connected layer. In the trained variational autoencoder, the first input layer maps the performance data to the latent space, the first fully connected layer outputs the mean of the latent space, and the second fully connected layer outputs the log-variance of the latent space. The latent features of the performance data are obtained by reparameterizing the mean and logarithmic variance based on the latent space.

4. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 2, characterized in that, The variational autoencoder further includes a decoder, which is used to reconstruct the latent features output by the encoder and output the reconstructed value of the performance data. The training process of the variational autoencoder is as follows: with the goal of minimizing the reconstruction error and KL divergence, the variational autoencoder is hyperparameter tuned using the Bayesian optimization algorithm, and the optimal first hyperparameter combination of the variational autoencoder is selected. The first hyperparameter includes the dimension of the latent space, the batch size, and the first learning rate.

5. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 1, characterized in that, The Transformer-based multilayer perceptron includes a second input layer, a Transformer module, and an output layer. The latent features are input to the multilayer perceptron via the second input layer. The Transformer module enhances the input latent features based on a self-attention mechanism. The output layer maps the output of the Transformer module to the dimensions of each optimization target variable to obtain the enhanced latent features.

6. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 1, characterized in that, The process of obtaining the target variable for optimization includes: The enhanced latent features are then combined with the original target variables to obtain a feature set; The feature set is input into the trained XGBoost regression model, and the optimized target variable is output.

7. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 6, characterized in that, The training process of the XGBoost regression model includes: The feature set is divided into a training set and a test set; The XGBoost regression model is trained based on the training set and the predicted value is output. With the goal of minimizing the root mean square error between the predicted value and the true value, the hyperparameters of the XGBoost regression model are tuned using the Bayesian optimization algorithm. The optimal combination of the second hyperparameters of the XGBoost regression model is selected. The second hyperparameters include the tree depth, the second learning rate, and the regularization strength. The trained XGBoost regression model is evaluated based on the test set.

8. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 1, characterized in that, The process of optimization design using multi-objective optimization algorithms includes: Step 1: Generate a population using an elite reverse learning strategy. Each individual in the population consists of different enhanced latent features, a first target value, and a second target value. Each individual is assigned a randomly selected index, and the first target and the second target corresponding to each individual are calculated through a proxy model to obtain the solution corresponding to each individual. The solution includes the solution for the first target and the solution for the second target. Step 2: Perform non-dominated sorting based on the solutions corresponding to each individual, and assign a level value to each individual, where the level value represents the level of the frontier to which the individual belongs; Step 3: For any layer of the frontier, calculate the crowding degree of each individual within it; Step 4: Select the individual with the highest crowding density at the forefront of the first layer as the leader, and introduce a gradually decreasing random perturbation to the leader's position; guide other individuals to move towards the position of the leader with the random perturbation to update the positions of other individuals; Step 5: Merge the population with the second population to obtain a new population; Step 6: Perform a second non-dominated sorting based on the solutions corresponding to each individual in the new population, and assign a second-level value to each individual. The second-level value represents the level of the second frontier to which the individual belongs. Step 7: For any layer of the second frontier, calculate the second crowding degree of each individual; select the individual with the highest second crowding degree in the first layer of the second frontier as the new leader; Step 8: Perform adaptive mutation on individuals in the population to generate new individuals; Step 9: Compare the fitness of individuals before and after the mutation, and update the leader; Step 10: Before each generation update, the top k individuals with the highest level values ​​are taken as elite individuals. Each elite individual is subjected to a reverse perturbation strategy to output the corresponding solution or perturbation solution, and its solution or perturbation solution is directly passed to the next generation to improve the algorithm accuracy and convergence speed. Step 11: Iterate through steps 2-10 until the preset maximum number of iterations is reached, and obtain the Pareto front solution between the auxiliary jet outlet airflow velocity and the air consumption.

9. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 8, characterized in that, Non-dominated sorting includes: Determine the dominance relationship between individual A and individual B: If the solutions to both objective functions for individual A are better than those for individual B, then individual A dominates individual B. Otherwise, individual B dominates individual A; Individual A is a non-dominated individual when the solutions to both objective functions for individual A are better than the solutions to both objective functions for all other individuals. Multiple fronts are set up. The first front contains all non-dominated individuals, and each subsequent front contains individuals dominated by a different number of individuals. Based on the number of individuals dominating each frontier, multiple frontiers are divided into different levels; Assign a level to each individual in the frontier as its corresponding level value; the lower the level value of an individual, the higher the quality of its corresponding solution.

10. The multi-objective optimization design method for high flow rate and low air consumption of auxiliary nozzles according to claim 8, characterized in that, The strategy of applying reverse perturbation to elite individuals includes: Step 1: Subtract the solution corresponding to each elite individual from the sum of the upper and lower bounds of the solution dimension to obtain the preliminary reverse solution corresponding to each elite individual; Step 2: Calculate and compare the fitness of the preliminary reverse solution with that of the solution. If the fitness of the preliminary reverse solution is less than that of the solution, the solution is still adopted; otherwise, the preliminary reverse solution is adopted as the reverse solution of the corresponding solution. Step 3: Calculate the perturbation solution based on the solution and its inverse solution. The calculation formula is: ； in, This represents the perturbation solution corresponding to the j-th solution of the i-th elite individual; This represents the j-th solution for the i-th elite individual; This represents the reverse solution corresponding to the j-th solution of the i-th elite individual; Represents a random disturbance term; Indicates the disturbance intensity factor; Step 4: Determine whether the perturbation solution is better than the corresponding solution. If the perturbation solution is better than the corresponding solution, replace the corresponding solution with the perturbation solution; otherwise, the original solution is still used. Step 5: Iterate through steps 1-4 until the preset maximum number of iterations is reached, at which point the process terminates.

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