MOPSO-BP-based parameter optimization method for bending forming of stainless steel pipe with small bending radius

Abstract

The present application relates to the technical field of parameter optimization, in particular to a stainless steel small bending radius pipe push bending forming parameter optimization method based on MOPSO-BP. The method obtains process parameters to be optimized; the process parameters to be optimized are input into the MOPSO-BP neural network to obtain optimized process parameters; wherein the MOPSO-BP neural network is constructed by using a pre-trained BP neural network and a MOPSO algorithm; the process parameters to be optimized are input into the MOPSO algorithm and the multi-objective particle swarm optimization core loop processing is executed based on the pre-trained BP neural network to obtain the optimized process parameters.

Description

Technical Field

[0001] This invention relates to the field of parameter optimization technology, and in particular to a method for optimizing the parameters of push-bending forming of stainless steel tubes with small bending radii based on MOPSO-BP. Background Technology

[0002] Thin-walled tubes with small bending radii are high-performance pipes that achieve extreme bending while maintaining the advantages of a hollow pipe structure. They typically refer to bent pipe fittings with a relative bending radius (R / D) ≤ 1.5 (R is the bending radius, D is the outer diameter of the pipe) and a relatively small wall thickness (t / D). These fittings are widely used in aerospace, automotive manufacturing, and other fields, and are key components for achieving lightweight structures and compact designs. However, the low yield rate of push-bending forming of thin-walled tubes with small bending radii has consistently hindered further improvements in productivity. Push-bending is essentially a complex nonlinear process with strong coupling of multiple factors, making it difficult to establish an intuitive and effective mathematical model. Furthermore, traditional single-objective constrained multidimensional optimization methods (such as PSO) cannot accurately find the global optimal solution in its eigenspace. To address this technical problem, a parameter optimization method for push-bending forming of stainless steel thin-walled tubes based on MOPSO-BP is proposed. Summary of the Invention

[0003] To address the technical problems existing in the prior art, this invention provides a method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP.

[0004] To achieve the above objectives, the embodiments of the present invention provide the following technical solutions: In a first aspect, in one embodiment of the present invention, a method for optimizing the bending forming parameters of stainless steel tubes with small bending radii based on MOPSO-BP is provided, the method comprising the following steps: Obtain the process parameters to be optimized; The process parameters to be optimized are input into the MOPSO-BP neural network to obtain optimized process parameters. The MOPSO-BP neural network is constructed using a pre-trained BP neural network and the MOPSO algorithm. The process parameters to be optimized are input into the MOPSO algorithm, and a multi-objective particle swarm optimization core loop is executed based on the pre-trained BP neural network to obtain the optimized process parameters.

[0005] As a further aspect of the present invention, the step of inputting the process parameters to be optimized into the MOPSO algorithm and performing multi-objective particle swarm optimization core loop processing based on the BP neural network to obtain the optimized process parameters includes: the pre-trained BP neural network, which includes seven input layer neurons, ten first hidden layer neurons, six second hidden layer neurons, and four output layer neurons, wherein the ten first hidden layer neurons and two of the output layer neurons form a first network, and the six second hidden layer neurons and the other two output layer neurons form a second network.

[0006] As a further aspect of the present invention, the activation function of the hidden layer of the BP neural network is the hyperbolic tangent function.

[0007] As a further aspect of the present invention, the activation function of the output layer of the BP neural network is a purely linear function.

[0008] As a further aspect of the present invention, the loss function of the BP neural network is the regularized mean square error.

[0009] As a further aspect of the present invention, the training method of the BP neural network includes: The original dataset is divided into training and testing sets, and then the features and target variables are normalized. A dual-branch, multi-task network structure is constructed. Through multiple rounds of silent optimization, the network is iteratively trained using the trainbr algorithm, and the weights and biases are continuously updated. The global best initial weights are selected and cached based on the comprehensive weighted score. The dual-branch multi-task network structure is trained using the optimal initial weights, and then predictions are made on the test set. The dimensionless prediction results are inversely normalized to restore them to physical quantities, and the model performance is verified. The final result is then output to complete the training.

[0010] As a further aspect of the present invention, the step of dividing the original dataset into a training set and a test set, and then normalizing the features and target variables, includes: The mapminmax algorithm is used to normalize the features and target variables.

[0011] As a further aspect of the present invention, the step of inputting the process parameters to be optimized into the MOPSO algorithm and performing multi-objective particle swarm optimization core loop processing based on a pre-trained BP neural network to obtain optimized process parameters includes: With the particle swarm optimization algorithm as the core, the Pareto optimal solution set is continuously searched through steps such as initializing the population, calling the BP model to predict the forming quality, calculating the constrained multi-objective fitness, non-dominated sorting and crowding maintenance, and iteratively updating the particle position. At the same time, the feasibility of the process is ensured through underlying constraint correction. After the iteration terminates, the optimal solution set is sorted according to engineering preferences, and the top few sets of process parameters with the best overall performance for the current specification are output.

[0012] As a further aspect of the present invention, the process parameters include the initial length of the tube blank, the pusher stroke, the reverse thrust pressure, the polyurethane hardness, the friction mode, the relative bending radius, and the diameter-to-thickness ratio.

[0013] As a further aspect of the present invention, the output of the BP neural network is: effective elongation, thickening rate, thinning rate, and evaluation data of the geometric shape of the bent tube.

[0014] The technical solution provided by this invention has the following beneficial effects: This invention provides a method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP. The method first obtains raw data using orthogonal experimental design, then supplements the data through single-factor analysis and finite element simulation experiments to improve the generalization and prediction accuracy of the subsequent neural network model. Next, a two-branch BP neural network is constructed to better adapt to the bending process, and a suitable neural network correlation function is determined, greatly improving the model's prediction accuracy. After the neural network training is completed, a multi-objective particle swarm optimization algorithm (MOPSO) is introduced to search for the Pareto optimal solution set under the triple constraints of tube thinning rate, thickening rate, and effective elongation at the output end. Finally, the model accuracy is calibrated through a process verification closed-loop feedback mechanism, achieving high-precision and high-robust solution for key parameter combinations.

[0015] These or other aspects of the invention will become more apparent from the following description of embodiments. It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 the present invention. For those skilled in the art, other embodiments can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating an embodiment of the present invention of a method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP.

[0018] Figure 2 The diagram shows the structure of the BP neural network model in the method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP, according to an embodiment of the present invention.

[0019] Figure 3 The diagram illustrates the node structure of the input and output layers of a BP neural network in a method for optimizing the bending forming parameters of stainless steel tubes with small bending radii based on MOPSO-BP, according to an embodiment of the present invention.

[0020] Figure 4 This invention relates to a method for optimizing the bending forming parameters of stainless steel tubes with small bending radius based on MOPSO-BP, which is a dual-branch independent hidden layer architecture of a BP neural network in one embodiment of the present invention.

[0021] Figure 5 This is a training effect diagram of the BP neural network model in the method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP according to an embodiment of the present invention.

[0022] Figure 6 The flowchart of the BP neural network operation in the method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP according to an embodiment of the present invention is shown.

[0023] Figure 7 A flowchart illustrating a specific embodiment of the method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP according to one embodiment of the present invention.

[0024] Figure 8 This is a schematic diagram of a differentiated lubrication method. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content and operations / steps, nor does it necessarily have to be performed in the order described. For example, some operations / steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0027] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0028] Specifically, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0029] Please see Figure 1 , Figure 1 This is a flowchart of a method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP, as provided in an embodiment of the present invention. Figure 1 As shown, the method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP includes steps S10 to S20.

[0030] S10. Obtain the process parameters to be optimized; In embodiments of the present invention, process parameters include initial tube blank length, pusher stroke, reverse push pressure, polyurethane hardness, friction mode, tube blank bending radius, and tube blank diameter, etc.

[0031] In this embodiment of the invention, before obtaining the process parameters to be optimized, the following steps are also included: The algorithm iterates through various pipe specifications to be optimized. If all specifications are completed, the algorithm ends. If there are still specifications to be optimized, the process parameters of the pipe to be optimized are obtained.

[0032] S20. Input the process parameters to be optimized into the MOPSO-BP neural network to obtain the optimized process parameters; wherein, the MOPSO-BP neural network is constructed using a pre-trained BP neural network and the MOPSO algorithm; input the process parameters to be optimized into the MOPSO algorithm and perform multi-objective particle swarm optimization core loop processing based on the pre-trained BP neural network to obtain the optimized process parameters.

[0033] like Figures 2-4 As shown, in this embodiment of the invention, the step of inputting the process parameters to be optimized into the MOPSO algorithm and performing multi-objective particle swarm optimization core loop processing based on the BP neural network to obtain the optimized process parameters includes: the pre-trained BP neural network, which includes seven input layer neurons, ten first hidden layer neurons, six second hidden layer neurons, and four output layer neurons, wherein the ten first hidden layer neurons and two of the output layer neurons form a first network, and the six second hidden layer neurons and the other two output layer neurons form a second network.

[0034] The activation function of the hidden layer of the BP neural network is the tansig function (hyperbolic tangent function). Compared with the traditional sigmoid function, the tansig function provides a more balanced and unbiased gradient descent path when updating weights during backpropagation, which significantly speeds up the convergence speed. Moreover, it is more suitable for the data normalization interval, as shown in the following equation (1):

[0035] In the formula, n is the independent variable; e is the natural constant.

[0036] The activation function of the output layer of the BP neural network is the purelin function (a purely linear function). The purelin function can break the absolute upper and lower bounds of the network's predicted values, ensuring that the network can accurately output continuous values ​​with macroscopic physical meaning without being forcibly truncated after inverse normalization, as shown in the following equation (2):

[0037] The loss function of the BP neural network is the regularized mean squared error (MSE). Compared with the traditional mean squared error (MSE), a weight penalty term is added. While reducing the prediction error, it will forcibly suppress excessive or useless synaptic weights, making the model insensitive to small fluctuations in input features. The fitted curve is very smooth, thus achieving better anti-overfitting ability in small sample scenarios, as shown in equations (3) to (5) below:

[0038] In the formula: N is the total number of samples; For the first The true physical label (i.e., the true value) of each sample; For the neural network to the first Forward predicted values ​​for each sample.

[0039]

[0040]

[0041] In the formula: MSW is the mean of the sum of squares of all weights and bias parameters in the network; N w The total number of all learnable weights in the network is a scalar. The specific values ​​for weights and biases constitute multidimensional data. and The scaling factor is adaptively and dynamically adjusted by the Bayesian algorithm during training.

[0042] The evaluation function of the BP neural network comprehensively utilizes the coefficient of determination (R²). 2 The mean squared error (MSE) and a weighted comprehensive scoring criterion are introduced in the optimization logic. The training set weight of 0.4 and the test set weight of 0.6 are used to force the model to show good performance on both the training set and the test set, so as to ensure that the final derived topology weight configuration has absolute stability and reliability in the actual bending process, as shown in the following formulas (6) to (7):

[0043]

[0044] In the formula: The coefficient of determination; N is the total number of samples; For the first The true physical label (i.e., the true value) of each sample; For the neural network to the first Forward predicted values ​​for each sample; The sample mean of the true values; , These are the coefficients of determination for the training set and the test set, respectively. The overall score is calculated based on the total score.

[0045] The number of hidden layers in the BP neural network is based on a classical neural network design empirical formula derived from Kolmogorov's theorem:

[0046] In the formula: h is the number of hidden layers; m is the number of nodes in the input layer; n is the number of nodes in the output layer; 'a' is an adjustment constant (usually ranging from 1 to 10).

[0047] Meanwhile, the number of hidden layer nodes was optimized based on the grid search cross-validation method. The optimal number of hidden layer nodes for the two output variables, effective elongation of the output segment and evaluation of the geometric shape of the bent pipe, which are the responsibility of the first network, was determined to be 10. The optimal number of hidden layer nodes for the two output variables, thickening rate and thinning rate, which are the responsibility of the second network, was determined to be 6.

[0048] In this embodiment of the invention, the inputs to the BP neural network are: initial length of the tube blank, pusher stroke, reverse push pressure, polyurethane hardness, friction mode, relative bending radius, and diameter-to-thickness ratio.

[0049] In this embodiment of the invention, the output of the BP neural network is: effective elongation, thickening rate, thinning rate, and evaluation data of the geometric shape of the bent tube.

[0050] like Figures 5-6 As shown, in this embodiment of the invention, the training method of the BP neural network includes: S1. Divide the original dataset into training and testing sets at 85% and 15% respectively, and then normalize the features and target variables in the interval [-1,1] to eliminate the influence of units.

[0051] In the normalization process, the mapminmax algorithm is used to linearly map the seven input variables to the closed interval [-1, 1]. The mathematical transformation equation for the forward normalization is:

[0052] In the formula: These are the original input feature values; and These are the physical maximum and minimum values ​​of the feature in the entire sample set, respectively; This is the normalized value after mapping.

[0053] For the reverse normalization of the output variable, the strict inverse operation of the forward mapping is used, and the mathematical derivation equation is as follows:

[0054] In the formula: The dimensionless predicted value is directly calculated from the output layer of the neural network; and These are the physical maximum and minimum values ​​of the actual target variable, respectively. Predicted physical values ​​for the actual engineering project after restoration.

[0055] In this embodiment of the invention, dividing the original dataset into a training set and a test set at 85% / 15% includes: Based on an orthogonal experimental design, five key process parameters for tube bending and forming—initial tube length, pusher stroke, reverse push pressure, polyurethane hardness, and friction scheme—were selected as the main influencing factors. Four gradient levels were set for each factor. Simultaneously, to ensure good generalization of the target model, finite element simulations were conducted on four different specifications of tube blanks. To further improve the model's prediction accuracy, single-factor finite element simulation experiments were added as sample data. A total of 131 samples were collected, with 85% allocated to the training set and 15% to the test set.

[0056] S2. Construct a dual-branch multi-task network structure, and train the network iteratively using the trainbr algorithm through multiple rounds of silent optimization, continuously updating the weights and biases. Using the comprehensive weighted score as the standard, select and cache the globally optimal initial weights.

[0057] In an embodiment of the present invention, step S2 involves constructing a dual-branch multi-task network structure, repeatedly training the network using the trainbr algorithm through multiple rounds of silent optimization, continuously updating the weights and biases, and selecting and caching the globally optimal initial weights based on the comprehensive weighted score. This includes: Decouple the target variable and construct a dual-branch multi-task network architecture; Initiate multi-round silent optimization computation of the dual-branch network; Optimize the weights w and biases b of the BP neural network in the current round; Input signal feedforward propagation; Error feedback propagation (using the trainbr algorithm); Judgment: The maximum number of iterations has been reached or the accuracy requirement has been met; No: Continue error feedback propagation, update the weight value w' and bias value b', return to step 7, and enter the iteration loop; Yes: Proceed to the next step; Calculate the comprehensive weighted score based on the test set and the training set; Judgment: Does the overall score break the current record? Yes: Record and cache the current optimal initial weights w and bias b, then proceed to the next step; No: Proceed directly to the next step; Judgment: The preset maximum number of optimization iterations has been reached; No: Return to the current step to optimize the weights w and biases b of the BP neural network, and continue to the next round of optimization; Yes: Proceed to the next step.

[0058] S3. Use the optimal initial weights to perform final training on the dual-branch multi-task network structure, then perform prediction on the test set, reverse normalize the dimensionless prediction results to restore them to physical quantities, and verify the model performance through metrics such as MSE and R2, and output the final results to complete the training.

[0059] The process involves training the dual-branch multi-task network structure using optimal initial weights, performing predictions on the test set, inverse normalizing the dimensionless prediction results back to physical quantities, validating the model performance using metrics such as MSE and R2, and outputting the final results to complete the training. Assign globally optimal initial weights and perform final training for the branch; input the test set signal and perform forward prediction of the network; reverse normalize the output dimensionless prediction value; calculate the mean square error (MSE) and the coefficient of determination (R2); output the final prediction result and performance index.

[0060] It should be clarified that, given that process parameters such as initial billet length, pusher stroke, back-pushing pressure, polyurethane hardness, friction method, relative bending radius, and diameter-to-thickness ratio all significantly affect the bending quality, the number of neurons in the input layer of the BP neural network is determined to be 7. Regarding bending quality, the four results—effective elongation of the output segment, thickness increase rate, thinning rate, and bending geometry evaluation—are the most critical for judging whether the bending quality is acceptable; therefore, the number of neurons in the output layer of the BP neural network is determined to be 4. Furthermore, since the output variables in the output layer have different scale characteristics—the effective elongation of the output segment and the bending geometry evaluation are macroscopic geometric features, while the thickness increase rate and thinning rate are microscopic scale features—a dual-branch hidden layer is used to conduct supervised learning separately to address gradient interference during backpropagation. The specific framework of this BP neural network model can be found in [reference needed]. Figure 2 .

[0061] In the embodiments of this invention, the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm, compared to the classic Particle Swarm Optimization (PSO) algorithm, introduces three core mechanisms: an external archive mechanism, crowding distance estimation and gBest selection strategy, and non-dominated sorting and archive maintenance. When the archive overflows, dense particles are eliminated based on the aforementioned crowding distance priority, thus maintaining the optimality and diversity of solutions, as shown in the following equation:

[0062]

[0063] In the formula: and Particles In the The speed and position of the generation; The inertial weight is set to 0.7 in this study. , Cognitive and social learning factors (both set to 1.5); , A random number within the range [0, 1]; The optimal position in the particle's history is updated randomly with a 50% probability if and only if the new position and the old position have a non-dominated relationship. This is the globally optimal position for guiding the swarm's flight.

[0064]

[0065] In the formula: , These represent the particles after the cumulative update and before the update, respectively. The crowding distance (the initial value is usually set to 0 before the calculation begins for each new target m); , These represent the particle values ​​after sorting according to the m-th objective function value. The function values ​​of the two adjacent particles on the target; , These represent the maximum and minimum values ​​of the m-th target in the external archive, respectively.

[0066] It should be noted that in equations (11) and (12): each particle is a vector, and each element in the vector corresponds to a different process parameter. The velocity and position are iterated according to the formula. The initial velocity is obtained by generating four standard normal distribution random numbers and then multiplying them by a scaling factor, in order to prevent initial data oscillation. In equation (13): the function value f of the objective function is the value corresponding to the objective functions Obj1, Obj2, and Obj3 below.

[0067] In addition, a very large penalty coefficient M=10 is set for particle overshoot behavior. 6 This forces the particle swarm to quickly fly away from the high-risk process dead zone. To address the hard constraint that the geometric shape evaluation of the bent tube forming in the code cannot exceed 2, a shape penalty term is constructed as shown in formula (14). To address the constraint that the effective extension of the output section must be controlled within the range of 5mm to 7mm, an extension exceeding the limit penalty term is constructed as shown in formula (15). The overall global penalty function is shown in formula (16).

[0068]

[0069]

[0070] In the formula: P shape To construct the external penalty function; M is the penalty coefficient; `max()` is a function that takes the maximum or minimum value within the parentheses. y shape Specific numerical values ​​for geometric shape evaluation; P ext This is the penalty function for the effective elongation of the output segment. y ext This is the specific value of the effective elongation of the output segment; P total This is the global penalty function.

[0071] Finally, an independent multi-objective function is set. While ensuring that the particles do not cross the boundary, the model algorithm simultaneously pursues the minimization of the following three independent objectives: First, the macroscopic shape is given the highest priority, with the geometric shape evaluation approaching 1 and the protrusion approaching the median of 6 mm, as shown in formula (17). The absolute value of the shape evaluation is set to 10 to establish it as the highest priority. Second, the inner thickness rate is minimized, as shown in formula (18). Third, the outer thinning rate is minimized, as shown in formula (19).

[0072]

[0073]

[0074] In the formula, Obj1~Obj3 are functions of three independent objectives, corresponding to the sum of macroscopic shape, thickness increase rate, thinning rate, and penalty function, respectively. thick For the thickness increase rate, y thin This refers to the thinning rate.

[0075] In this embodiment of the invention, the step of inputting the process parameters to be optimized into the MOPSO algorithm and performing multi-objective particle swarm optimization core loop processing based on a pre-trained BP neural network to obtain optimized process parameters includes: With the particle swarm optimization algorithm as the core, the Pareto optimal solution set is continuously searched through steps such as initializing the population, calling the BP model to predict the forming quality, calculating the constrained multi-objective fitness, non-dominated sorting and crowding maintenance, and iteratively updating the particle position. At the same time, the feasibility of the process is ensured through underlying constraint correction. After the iteration terminates, the optimal solution set is sorted according to engineering preferences (prioritizing appearance quality), and the top 5 sets of process parameters with the best overall performance for the current specification are output.

[0076] like Figure 7 As shown, in this embodiment of the invention, the step of inputting the process parameters to be optimized into the MOPSO algorithm and performing multi-objective particle swarm optimization core loop processing based on a pre-trained BP neural network to obtain optimized process parameters includes: Initialize the population position POP and velocity V, and apply initial boundaries and discrete constraints; The parameter matrix is ​​passed forward to the BP model, and multiple forming quality indicators are inferred forward. Calculate the fitness and penalty function of the multidimensional target, and apply out-of-bounds penalties for shape and elongation; Update the individual particle optimal solution pBest based on the non-dominance criterion; Perform a fast nondominated sort and calculate the crowding distance of frontier individuals; Update and truncate external archives based on congestion to maintain a global Pareto optimal solution set; Use roulette to select a guide from the archive, and update the population's flight speed and spatial position; The underlying constraint forced mapping correction corrects the interference length. Determine: The maximum number of iterations has been reached; if not, return to the step of passing the parameter matrix forward to the BP model, inferring multiple forming quality indicators forward, and continue the loop; if yes, proceed to the next step. External archives are sorted according to engineering preferences (highest priority: shape assessment approximation level 1); Output the top few sets of process parameters that provide the best overall performance for the current specification.

[0077] It should be noted that each particle corresponds to a set of process parameters. Physical boundary conditions are applied to prevent out-of-bounds behavior. The existence of the penalty function ensures that once a particle goes out of bounds (process parameters do not meet physical constraints), gBest is the feasible solution in the current Pareto front. This guarantees that the particle can return to the feasible region when updated again after going out of bounds, ensuring the rationality of the optimization results (process quality indicators). The evaluation criterion for Pareto dominance is the function value of the three objective functions, which must be minimized. The specifications of the billet are given by the process parameters, and the lubrication method is as follows: Figure 8 The differentiated lubrication shown is optimal, therefore the four adjustable process parameters are those in the optimization results; the method for ranking external archives in engineering preference is to multiply the objective function by a certain weight to determine the priority. Specifically, Figure 8 The scheme shown in the figure divides the tube blank into regions according to the diagram and performs differentiated lubrication. The friction coefficients of regions I to IV are 0.05, 0.1, 0.1, and 0.01, respectively.

[0078] This invention constructs a two-branch BP neural network model to mathematically model the nonlinear relationships of multiple strongly coupled factors in the push-bending process of thin-walled pipes with small bending radii. This model exhibits excellent adaptability and stability for the process, effectively saving significant time and trial-and-error costs. The MOPSO algorithm is successfully used to optimize the push-bending surrogate model trained by the BP neural network, solving the multi-output constrained multidimensional nonlinear optimization problem in the push-bending process. It outputs a set of Pareto optimal solutions from the archive, ultimately achieving the optimal combination of key process parameters in the pipe push-bending process, and its effectiveness is verified. The proposed optimization design method based on BP neural networks and the MOPSO algorithm significantly improves efficiency compared to traditional optimization methods and possesses excellent stability and reliability, contributing to the improvement of the yield rate in the push-bending process of thin-walled pipes with small bending radii.

[0079] It should be understood that although the above description follows a certain order, these steps are not necessarily executed in that order. Unless otherwise expressly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, some steps in this embodiment may include multiple steps or multiple stages, which are not necessarily completed at the same time, but may be executed at different times. The execution order of these steps or stages is not necessarily sequential, but may be performed alternately or in turn with other steps or at least a portion of the steps or stages of other steps.

[0080] It should be understood that, as used herein, the singular form "a" is intended to include the plural form as well, unless the context clearly supports an exception. It should also be understood that, as used herein, "and / or" refers to any and all possible combinations of one or more of the associatedly listed items. The embodiment numbers disclosed above are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0081] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention (including the claims) is limited to these examples. Within the framework of the invention, technical features of the above embodiments or different embodiments can be combined, and many other variations of different aspects of the invention exist, which are not provided in detail for the sake of brevity. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the protection scope of the invention.

Claims

1. A method for optimizing the bending forming parameters of stainless steel tubes with small bending radii based on MOPSO-BP, characterized in that, The method includes: Obtain the process parameters to be optimized; The process parameters to be optimized are input into the MOPSO-BP neural network to obtain the optimized process parameters; wherein, the MOPSO-BP neural network is constructed using a pre-trained BP neural network and the MOPSO algorithm; the process parameters to be optimized are input into the MOPSO algorithm and a multi-objective particle swarm optimization core loop is performed based on the pre-trained BP neural network to obtain the optimized process parameters. The training method for the BP neural network includes: The original dataset is divided into training and testing sets, and then the features and target variables are normalized. A dual-branch, multi-task network structure is constructed. Through multiple rounds of silent optimization, the network is iteratively trained using the trainbr algorithm, and the weights and biases are continuously updated. The global best initial weights are selected and cached based on the comprehensive weighted score. The dual-branch multi-task network structure is trained using the optimal initial weights, and then predictions are made on the test set. The dimensionless prediction results are inversely normalized to restore them to physical quantities, and the model performance is verified. The final results are then output to complete the training. To address the particle boundary crossing behavior in the MOPSO algorithm, a very large penalty coefficient is set to force the particle swarm to quickly fly away from the high-risk process dead zone. The formula for the shape penalty term is as follows: The formula for the over-limit penalty term for the extension amount is as follows: The formula for the overall global penalty function is as follows: In the formula: Pshape is the penalty function for constructing the shape; M is the penalty coefficient; `max()` is a function that takes the maximum or minimum value within the parentheses. yshape is the specific numerical value for geometric shape evaluation; Pext is the penalty function for the effective elongation of the output segment; yext is the specific value of the effective elongation of the output segment; Ptotal is the global total penalty function; Furthermore, an independent multi-objective function is set up. While ensuring that particles do not cross the boundary, the model algorithm simultaneously pursues the minimization of the following three independent objectives: First, the macroscopic shape is given the highest priority, as shown in the following formula: Second, the minimum inner thickness ratio is determined by the following formula: Thirdly, the minimum thinning rate on the outer side is achieved, as shown in the following formula: In the formula, Obj1, Obj2, and Obj3 are functions of three independent objectives, corresponding to the sum of macroscopic shape, thickening rate, thinning rate, and penalty function, respectively; ythick is the thickening rate; and ythin is the thinning rate.

2. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 1, characterized in that, The process of inputting the process parameters to be optimized into the MOPSO algorithm and performing multi-objective particle swarm optimization core loop processing based on the BP neural network to obtain the optimized process parameters includes: the pre-trained BP neural network, which includes seven input layer neurons, ten first hidden layer neurons, six second hidden layer neurons and four output layer neurons, wherein the ten first hidden layer neurons and two of the output layer neurons form a first network, and the six second hidden layer neurons and the other two output layer neurons form a second network.

3. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 1, characterized in that, The activation function of the hidden layer of the BP neural network is the hyperbolic tangent function.

4. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 3, characterized in that, The activation function of the output layer of the BP neural network is a purely linear function.

5. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 4, characterized in that, The loss function of the BP neural network is the regularized mean squared error.

6. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 1, characterized in that, The process of dividing the original dataset into training and testing sets, and then normalizing the features and target variables, includes: The mapminmax algorithm is used to normalize the features and target variables.

7. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 1, characterized in that, The process parameters to be optimized are input into the MOPSO algorithm and a multi-objective particle swarm optimization core loop is executed based on a pre-trained BP neural network to obtain optimized process parameters, including: With particle swarm optimization as the core, the algorithm initializes the population, calls the BP model to predict the forming quality, calculates the constrained multi-objective fitness, maintains non-dominated sorting and crowding, iteratively updates the particle positions, and continuously searches for the Pareto optimal solution set. At the same time, it ensures the feasibility of the process through underlying constraint correction. After the iteration terminates, the optimal solution set is sorted according to engineering preferences, and the top few sets of process parameters with the best overall performance for the current specification are output.

8. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 1, characterized in that, Process parameters include initial tube blank length, pusher stroke, reverse thrust, polyurethane hardness, friction mode, relative bending radius, and diameter-to-thickness ratio.

9. The method for optimizing the bending forming parameters of stainless steel small bending radius tubes based on MOPSO-BP as described in claim 8, characterized in that, The output of the BP neural network is: effective elongation, thickening rate, thinning rate, and evaluation data of the geometric shape of the pipe bending process.

Images