A method for predicting the springback angle of metal material bending

Abstract

A method for predicting the springback angle of metal material bending forming comprises the following steps: establishing a bending springback finite element model, using finite element simulation software to perform virtual orthogonal tests on metal bending springback to obtain simulation data; performing range analysis on the numerical simulation data to determine the main factors that most significantly affect the bending springback angle; examining three levels of each main factor, establishing an orthogonal test table, and randomly performing an experiment on each level of the main factor; calculating the ratio of experimental data to simulation data of the springback angle under other same level conditions of the main factor, and obtaining a correction coefficient of the springback angle under each level condition of the main factor; multiplying the correction coefficient with the corresponding numerical simulation data to obtain a correction value; establishing a prediction model based on a neural network, and using the correction data under the virtual orthogonal test working condition to train and learn the neural network; using the trained neural network model to predict the bending springback angle of the metal material under the unknown working condition data.

Description

Technical Field

[0001] The invention relates to the field of metal material bending forming technology, and in particular to a method for predicting a springback angle of metal material bending forming. Background Art

[0002] At present, metal bending parts are widely used in aviation, aerospace, shipbuilding, vehicles, chemical industry, medical treatment and energy fields as gas and liquid transportation paths or structures because they can easily achieve lightweight and toughness of products and meet the requirements of low-consumption, high-efficiency and precise manufacturing.

[0003] Domestic and foreign scholars have conducted a lot of research on the springback problem of metal material bending. Currently, there are three main methods: theoretical analysis, numerical simulation and experimental research.

[0004] Theoretical analytical methods have, to some extent, revealed and solved some practical problems in the production of metal material bending, and promoted the development of bending analytical theory. However, most of them are based on a large number of assumptions and simplifications, such as assuming that metal pipes are ideal elastic-plastic materials, ignoring the displacement of the stress-strain neutral layer, ignoring the changes in material parameters such as the shrinkage strain ratio and elastic modulus during the pipe bending process, and the shear stress on the cross section of the bent pipe. They lack rigor and have large analysis errors, which limits their promotion and application in actual production.

[0005] The introduction of numerical analysis methods has made great progress in the research on the bending process of metal materials, but there is still a certain gap with the actual production. The main reason is that the bending of metal materials has both material nonlinearity, geometric nonlinearity and boundary nonlinearity, and involves the influence of many uncertain factors. It is a very complex multi-nonlinear strongly coupled deformation process, which leads to its mechanism that cannot be well understood.

[0006] In terms of experimental research, actual springback data can truly characterize the impact of many nonlinear interactive coupling factors on springback, but these methods either fail to take into account the impact of the incompleteness of the test samples on the prediction accuracy, or directly fill the sample data with the finite element simulation data, and fail to use the internal laws of the bending forming system reflected by the finite element analysis to fill in the missing data, which is still a certain distance from practical application.

[0007] In summary, among the existing research methods, the analytical calculation method contains too many assumptions and the prediction accuracy is generally not high; the numerical simulation method is still far from practical application because the bending deformation mechanism of pipes has not been well understood; the experimental research method does not take into account the incompleteness of the test samples or directly fills the sample data with finite element simulation data, and cannot achieve the effect of practical application. Summary of the invention

[0008] The present invention aims to solve the problems existing in the above-mentioned prior art and provides a method for predicting the springback angle of metal material bending forming. The method uses the internal laws of the bending forming system reflected by finite element analysis to fill in the missing data. The method has small analysis error and high prediction accuracy and can be promoted and applied in practical production.

[0009] The present invention solves the technical problem by adopting a technical solution: the method for predicting the springback angle of metal material bending forming comprises the following steps:

[0010] Step 1: Establish a finite element model of metal material bending and springback, use finite element simulation software to conduct a virtual orthogonal test on the metal material bending and springback, and obtain numerical simulation data of the metal material bending and springback angle;

[0011] Step 2: Perform range analysis on the numerical simulation data of the bending springback angle of the metal material to determine the main factors that most significantly affect the bending springback angle of the metal material;

[0012] Step 3: Each main factor is examined at three levels, and a Taguchi orthogonal test table is established. From the virtual orthogonal test table, each level of the main factor is randomly selected to conduct a real experiment to obtain the experimental data of the bending springback angle of the metal material;

[0013] Step 4: Divide the experimental data of the springback angle of the metal material under a certain level of the main factor by the numerical simulation data to obtain the correction coefficient of the springback angle under the level of the main factor; calculate the ratio of the experimental data of the springback angle under other same level conditions of the main factor to the numerical simulation data in turn to obtain the correction coefficient of the springback angle under each level of the main factor;

[0014] Step 5: Multiply the correction coefficients of the main factors at each level by the corresponding numerical simulation data to obtain the correction values ​​of the virtual orthogonal test under each working condition;

[0015] Step 6: Establish a prediction model for the bending springback angle of metal materials based on artificial neural networks. After training the neural network with the correction data under the virtual orthogonal test working conditions, input the unknown working condition data of the bending springback of metal materials, and obtain the predicted value of the bending springback angle of the metal material under the unknown working condition through neural network calculation.

[0016] For further improvement, the metal material includes profiles, pipes, plates, etc.

[0017] In order to further improve it, the metal material is Q235 pipe. The phase transformation of Q235 carbon steel is generally composed of ferrite and pearlite. It has low strength and hardness, good plasticity and toughness, and is a good cold bending processing material.

[0018] Further improvement, the stress to which the metal material is subjected when it is bent is:

[0019]

[0020] Among them, σ is the actual stress, σs is the yield limit, E is the Young's modulus, ε is the actual strain, K is the hardening coefficient of the material, and n is the hardening index of the material.

[0021] Furthermore, the influencing factors of the springback angle of metal materials include the bending angle, relative bending radius, relative wall thickness, and friction coefficient.

[0022] Furthermore, before performing step 6, the correction value in step 5 is normalized.

[0023] Furthermore, the normalization formula is:

[0024]

[0025] Among them, Xij is the j-th value of the i-th input / output parameter after normalization, max(xi) and min(xi) are the upper and lower bound values of this parameter respectively; xNmin and xNmax are the normalized boundary values, 0 < xNmin < xNmax < 1, and xNmin = 0.1 and xNmax = 0.9 are taken.

[0026] Furthermore, the artificial neural network described in step 6 is one or a combination of multiple of a BP neural network, a particle swarm optimization algorithm, and a hybrid particle swarm algorithm.

[0027] The beneficial effects of the present invention are as follows: The present invention adopts the orthogonal test method, selects the test influencing factors as the bending angle, relative bending radius, relative wall thickness, and friction coefficient, each influencing factor takes 3 levels respectively, and takes the size of the springback angle as the test index. The orthogonal test has balanced dispersion and neat comparability, so that the number of tests is small, the effect is good, it is simple and convenient, and the efficiency is high; through the orthogonal test, on the basis of the finite element model of the bent pipe, the ABAQUS software is used to simulate the bending forming process and unloading springback process of the pipe fitting, and the simulation experiment data and real experiment data are obtained through the orthogonal experiment, so as to obtain the correction coefficient and correction value of the springback angle under each level of the main factors. Finally, after training and learning the neural network, input the unknown working condition data of the metal material bending springback, and through the calculation of the neural network, the predicted value of the metal material bending springback angle under this unknown working condition can be obtained. Description of the Drawings

[0028] Figure 1 It is the finite element model of the bent pipe in the present invention;

[0029] Figure 2 It is the simplified finite element model of the bent pipe in the present invention;

[0030] Figure 3 Set the reference point for the rigid body;

[0031] Figure 4 This is the error curve of neural network training based on the simulated experimental correction data;

[0032] Figure 5 Fitting curves for neural network samples based on simulated experimental correction data;

[0033] Figure 6 A state diagram for neural network training based on simulated experimental correction data;

[0034] Figure 7 Regression analysis of neural network training samples based on simulated experimental correction data;

[0035] Figure 8 Output error curves for neural network training samples based on simulated experimental correction data;

[0036] Fig. 9 It is the flow chart of hybrid particle swarm algorithm;

[0037] Fig.10 A knowledge mining model for catheter bending rebound;

[0038] Fig.11 This is the error curve of neural network training based on the original data of simulation experiment;

[0039] Fig.12 Fitting curve for neural network samples based on the original data of simulation experiment;

[0040] Fig.13 This is the error curve of the neural network fitting based on the original data of the simulation experiment.

[0041] Description of the accompanying drawings: 1. pipe, 2. mold. DETAILED DESCRIPTION

[0042] The present invention will be further described below in conjunction with the accompanying drawings:

[0043] Referring to the accompanying drawings: In this embodiment, a method for predicting the springback angle of a metal material during bending forming includes the following steps:

[0044] Step 1: Establish a pipe bending machine based on the experiment Figure 1The finite element model of the pipe bending shown in the figure first uses the UG NX software produced by SiemensPLM Software to establish the three-dimensional model of each pipe bending mold, and then imports it into the ABAQUS software to establish the pipe model, add the Assembly assembly module for assembly, and establish the finite element model of the pipe bending for subsequent analysis. The finite element simulation software is used to perform a virtual orthogonal test on the bending springback of the metal material to obtain the numerical simulation data of the bending springback angle of the metal material;

[0045] like Figure 2 As shown in the figure, for thin-walled tubes, the following assumptions are made: ① The wall thickness of thin-walled tubes is very small, radial stress can be ignored, and the tube is considered to be in a plane stress state; ② The mold is considered to be a rigid body and cannot be deformed; ③ The material is considered to obey the Mises yield criterion, isotropic and isotropically strengthened. Based on the above assumptions, this study further simplifies the finite element model for analysis. For example, the thin-walled tube is considered as a shell, the mold is considered as a discrete rigid body, and the tube forming mold is simplified into a cavity surface that can achieve the same constraint function, and a simplified finite element model of the bent tube is established;

[0046] like Figure 3 As shown in the figure, the Q235 pipe with outer diameter D = 42mm, wall thickness t = 5mm, and length l = 3380mm is taken as an example, and the steps of geometric modeling, defining analysis steps and outputs, defining interactions, defining boundary conditions, dividing meshes, bending simulation and unloading springback are carried out in sequence. Among them, the reference point is set as the rotation center of the bending die and the jaws during geometric modeling, and various performance parameters remain unchanged when the rigid body moves around it;

[0047] When defining the analysis steps and interactions, in addition to defining the original analysis steps, two analysis steps, Step-1 bending and Step-2 springback, are also defined. Step-1 is the rotation of the jaws and the bending die around their reference points. The contact between the pipe and the jaws and the bending die is set to rough. The contact between the pipe and the follower die is initially set to 0.1, and the time length is set to 1. Step-2 is the displacement vector after unloading, and the time length is set to 3. The contact between the pipe and the jaws and the bending die is set to failure, that is, there is no constraint between them, so that the springback process can be simulated. In view of the complexity of the pipe bending deformation process, ABAQUS / explicit display algorithm is used for bending simulation and unloading springback analysis.

[0048] In order to obtain the simulation data of the springback angle of the pipe bending, it is necessary to use ABAQUS software to simulate the pipe bending forming process and the unloading springback process. After the two process simulations are completed, the springback angle can be obtained by subtracting the forming angle before springback from the forming angle after springback;

[0049] Step 2: Perform range analysis on the numerical simulation data of the bending springback angle of the metal material to determine the main factors that most significantly affect the bending springback angle of the metal material;

[0050] Step 3: Combine the four main factors that affect the springback angle of tube bending: bending angle θ, relative bending radius R / D, relative wall thickness D / t, and tube die (follower die) friction coefficient t. The test index examined is the size of the springback angle; each influence is examined at 3 levels, as shown in Table 3-3 below. Select L9 (34) Taguchi orthogonal table, design the experimental plan, and randomly select a real experiment for each level of the main factor from the virtual orthogonal test table to obtain the experimental data of the springback angle of metal material bending, forming 9 experiments, and obtain the numerical simulation value of the springback angle according to the above steps, as shown in Table 3-4 below:

[0051] Table 3-3 Factor level table

[0052]

[0053] Table 3-4 Orthogonal test scheme and springback angle numerical simulation test data

[0054]

[0055] Step 4: Use furnace-cooled Q235 carbon steel pipe fittings with the chemical composition of w(C) 0.14%, w(Si) 0.16%, w(Mn) 0.70%, w(P) 0.015%, and w(S) 0.008%. For low-carbon steel pipes with an outer diameter of 42 mm and a wall thickness of 4.6 mm, tensile Q235 pipe specimens are designed according to the national standard GB / T228.1-2010 "Tensile Test of Metallic Materials Part 1: Room Temperature Test Method". A unidirectional tensile test is carried out at a rate of 1 mm / min using an AG-X 100kN microcomputer-controlled electronic universal testing machine, and the power exponential hardening model is used to fit the stress-strain relationship in the plastic stage.

[0056] Taking the above Q235 pipe as the research object, the bending springback measured data obtained on the KM-A90-CNC-E320 pipe bending machine test bench, the human-computer interaction system of the experimental device is turned on, and the pipe shape data of the experimental bending pipe is input or imported. And the processing parameters of the experimental bending pipe, such as bending radius, are set in the "Parameter Setting" interface of the upper computer human-computer interaction system. After completing the above steps, press the start button of the CNC system, and the pipe bending machine starts to complete the bending process of the conduit according to the process formula and parameters, and obtains the processed bending forming pipe fittings.

[0057] The forming angle of the bent catheter part is obtained through measurement. By subtracting it from the target forming angle of the numerical control system, the springback angle value can be obtained. According to the orthogonal test scheme in Table 3-4, corresponding physical measurement experiments are carried out to obtain the springback experiment data, as shown in Table 4-1.

[0058] Table 4-1 Experimental data of catheter bending springback

[0059]

[0060] According to the range analysis of the springback simulation data table in Table 3-4 above, among the above four investigated factors, the bending angle has a significant influence on springback. Therefore, here, the measured data of a certain bending angle is used to proportionally correct the simulation values of different parameters under the same bending angle. In the orthogonal experiment table in Table 3-4 above, a group is extracted for on-site measurement experiments for the same bending angle, and the ratio of the measured value of the springback angle to the simulated value of the springback angle is calculated. The correction coefficient is obtained as shown in Table 5-1, and the springback angle correction result is obtained as shown in Table 5-2 through the correction coefficient.

[0061] Table 5-1 Springback angle correction coefficient

[0062]

[0063] Step 5: Multiply the correction coefficient under each level condition of the main factor by the corresponding numerical simulation data to obtain the corrected values of the virtual orthogonal experiment under each working condition, as shown in Table 5-2;

[0064] Table 5-2 Springback angle correction result

[0065]

[0066] To avoid network divergence and to accelerate the convergence of the training network, the data is normalized, and the normalization method is as follows:

[0067]

[0068] Among them, Xij is the j-th value of the i-th input / output parameter after normalization, max(xi) and min(xi) are the upper and lower bound values of this parameter respectively; xNmin and xNmax are the normalized boundary values, 0 < xNmin < xNmax < 1, and xNmin = 0.1 and xNmax = 0.9 are taken.

[0069] The orthogonal simulation experiment results and the springback angle correction data are normalized according to the above formula to obtain the normalized orthogonal simulation experiment correction data, as shown in Table 5-3;

[0070] Table 5-3 Normalized orthogonal simulation experiment correction data

[0071]

[0072] Step 6: Establish a prediction model for the bending springback angle of metal materials based on artificial neural network, and extract neural network training samples according to the normalized orthogonal simulation experiment correction data in Table 5-3, as shown in Table 5-4.

[0073] BP neural network is a multi-layer feedforward network trained by the error back propagation algorithm. Theory has proved that a three-layer BP network model can realize any continuous image. The three-layer BP network model contains only one hidden layer, including input layer, hidden layer or intermediate layer, and output layer; the input layer has i nodes, the hidden layer has j nodes, and the output layer has t nodes. The neurons between the upper and lower layers are fully connected, that is, each unit in the lower layer is weightedly connected with each unit in the upper layer, and there is no connection between the neurons in each layer. The network learns in a teacher-led way. When a pair of learning patterns is provided to the network, the neuron activation value propagates from the input layer through the intermediate layers to the output layer, and each neuron in the output layer obtains the input response of the network. After that, in the direction of reducing the error between the desired output and the actual output, the connection weights are corrected layer by layer from the output layer through the intermediate layers, and finally return to the input layer.

[0074] Algorithm steps:

[0075] (1) Set the initial weight coefficient w(0) to a small random non-zero value.

[0076] (2) Given an input / output sample pair, calculate the output of the network:

[0077] Assume that the input and output of the pth group of samples are

[0078] u p =(u 1p ,u 2p ,…,u np )

[0079] d p =(d 1p , d 2p , …, d np )p=1,2,…,L

[0080] When the pth group of samples is input, the output of node i is

[0081]

[0082] In the formula, I jP ——When the pth group of samples is input, the jth input of node i; f is the activation function, the commonly used Sigmoid function, that is,

[0083]

[0084] The input of the network output layer nodes can be obtained from the input layer through the hidden layer to the output layer.

[0085] (3) Calculate the network's objective function J

[0086] Let Ep be the objective function of the network when the pth group of samples is input, and take the L2 norm, then

[0087]

[0088] Where ykp(t) is the output of the network after t weight adjustments when the p-th group of samples is input, and k is the k-th node in the output layer.

[0089] The overall objective function of the network is:

[0090]

[0091] As an evaluation of the status of online learning.

[0092] Judgment: If

[0093] J≤ε (5.6)

[0094] Where, ε is a predetermined value, ε≥0

[0095] The algorithm ends, otherwise, go to step (4).

[0096] (4) Back propagation calculation

[0097] From the output layer, the weights are adjusted layer by layer by reverse calculation based on J according to the "gradient descent method".

[0098]

[0099] Where η is the step size or learning rate.

[0100] The basic idea of ​​the particle swarm optimization algorithm is that each potential solution to the optimization problem is equivalent to a bird in the search space, called a particle. All particles have a fitness value determined by the optimization function, and each particle also has a velocity vector that determines the direction and distance of their flight. Then the particles follow the current optimal particle to search in the solution space.

[0101] PSO first initializes a group of random particles (random solutions), and then finds the optimal solution through iteration. In each iteration, the particles update themselves by tracking two "extreme values". One of the extreme values ​​is the optimal solution found by the particle itself up to the current moment, called the individual extreme value Pi; the other is the optimal solution found by the entire population up to the current moment, called the global extreme value Pg. When these two optimal values ​​are found, the particles use their own information, individual extreme values, and global extreme values ​​to update their speed and new position. It can be seen that the particle swarm optimization algorithm is also based on the cooperation and competition of individuals to complete the search for the optimal solution in a complex search space. It is an evolutionary computing technology based on swarm intelligence methods.

[0102] Suppose there are N particles in the D-dimensional search space, where the position of the i-th particle (i=1, 2, ..., N) is Xi=(xi1, xi2, ..., xiD), and the speed is Vi=(vi1, vi2, ..., viD). Substitute Xi into the objective function to calculate its fitness value, and measure the quality of Xi according to the fitness value. The optimal position searched by the i-th particle is recorded as vector Pi=(pi1, pi2, ..., piD), and the optimal position searched by the entire particle group is recorded as vector Pg=(pg1, pg2, ..., pgD). The particle state update operation is as follows:

[0103]

[0104]

[0105] Formulas (5.8) and (5.9) constitute the standard particle swarm optimization algorithm. In the formula, d = 1, 2, ..., D; k is the current iteration number; learning factors c1 and c2 are non-negative constants, ranging from 0 to 2; r1 and r2 are random numbers between [0, 1] and are independent of each other to maintain the diversity of the group; Vid∈[-Vmax, Vmax], Vmax is a constant set by the user, and the particle speed is limited to a maximum speed Vmax range; the inertia weight ω is a non-negative number, which describes the influence of the particle's previous generation speed on the current generation speed, so that the particle maintains the inertia of motion, has a tendency to expand the search space, and has the ability to explore new areas; selecting a larger value for the inertia weight is conducive to improving the algorithm's global search ability, while selecting a smaller value will enhance the algorithm's local search ability; because different problems have different requirements for the algorithm's global or local search ability, the balance between the algorithm's global search ability and local search ability is best adjusted, that is, the inertia weight can be automatically adjusted according to different problems. In order to make the algorithm have a strong exploration ability in the early stage of iteration, so that it can continuously search new areas, and then gradually enhance the development ability, so that the algorithm can search finely around the possible optimal solution, this paper adopts a linearly decreasing weight (LDW) strategy that linearly decreases the ω value with iteration.

[0106] Right now:

[0107]

[0108] In the formula, ωmax and ωmin are the maximum and minimum weights of ω, respectively, with typical values ​​of ωmax = 0.9-1.4 and ωmin = 0.4; k is the current evolutionary generation, and kmax is the maximum evolutionary generation. When the set maximum evolutionary generation is reached, or the optimal position searched by the particle swarm meets the set minimum adaptation threshold, the iteration is terminated.

[0109] The particle swarm optimization algorithm is a global search algorithm. It converges quickly in the initial stage of global search. However, near the global optimal value, the search process of the particle swarm optimization algorithm will become very slow and sometimes stagnate. On the contrary, the gradient descent algorithm is a local search algorithm. It can achieve a faster convergence speed near the global optimal value, but it is easy to fall into the local optimal value. Combining the two can better combine the strong global search ability of the PSO algorithm and the strong local search ability of the BP algorithm.

[0110] Among the BP algorithms based on derivative optimization, the LM (Levenberg-Marquardt) optimization algorithm is one of the most successful typical algorithms. The LM algorithm is developed from the classic Newton algorithm, which uses the nonlinear least squares method to deduce derivatives. The iterative formula of the LM algorithm is as follows:

[0111]

[0112] Where I is the identity matrix and λ is a non-negative value. With the help of the amplitude change of λ, the method changes smoothly between two extreme cases: Newton's method (λ→0) and standard gradient method (when λ→∞). It can be seen that the LM algorithm actually combines the advantages of both Newton's method and standard gradient descent method.

[0113] Therefore, this paper introduces the particle swarm optimization algorithm and the LM algorithm to perform hybrid optimization on the neural network, forming the PSOLM hybrid particle swarm algorithm. The main idea of ​​the PSOLM hybrid particle swarm algorithm is to use the PSO algorithm as the main framework, first perform PSO optimization, and after several generations of evolution, randomly select individuals from the particle swarm to perform LM algorithm optimization search for several steps, and perform local depth search. Here, in order to avoid the loss of particle diversity during the PSO search process, a particle is randomly selected to perform LM search to update the particle position to increase the diversity of the particles; in order to avoid the PSO algorithm from searching slowly near the global optimal value, a heuristic algorithm from PSO search to LM search is adopted; at the same time, the minimum constant δ is introduced to improve the operability of the algorithm.

[0114] The specific steps of the algorithm are:

[0115] 1) Randomly initialize the speed and position of a set of particles;

[0116] 2) Use mean square error MSE as the fitness function of PSO to evaluate the initial fitness of each particle. The current position of each particle is used as the particle's current optimal solution Pi, and Pg is set to the position of the best particle among the initialized particles;

[0117] 3) If the algorithm runs to the maximum number of iterations, or the training error E is less than the specified error standard e, go to step 9), otherwise go to step 4);

[0118] 4) Store the current best particle, update the positions and velocities of all particles according to equations (5.8) and (5.9), and generate a new set of particles, that is, adjust the connection weights and thresholds of the neural network;

[0119] 5) Evaluate the fitness of each new particle, and the particle with the worst fitness is replaced by the stored best particle. If the new position of the i-th particle is better than the value of Pi, update the value of Pi to the position of the current particle. If the best position of all new particles is better than Pg, update Pg to the best position of all new particles;

[0120] 6) If the change in Pg value is very small (the absolute value of the difference between two consecutive generations of Pg values ​​is less than the given minimum constant δ for 10 consecutive times), use the LM algorithm to perform a local depth search near Pg for several steps. If the search result is better than Pg, use this search result to replace Pg and go to step 8). Otherwise, go to step 7);

[0121] 7) Randomly select a particle from the current particle swarm to perform LM search for one step, and replace the worst particle in the current particle swarm with the LM search result;

[0122] 8) Linearly reduce the inertia weight ω according to formula (5.10) and go to step 3);

[0123] 9) Output the optimal result Pg.

[0124] Table 5-4 Orthogonal simulation experiment correction data training samples

[0125]

[0126] The catheter bending rebound knowledge (weights and thresholds of the neural network) is obtained through the training of the neural network. The orthogonal simulation experiment correction data training samples mentioned above are used to train the neural network model using the gradient descent method with momentum. Here, the first layer transfer function of the BP network is selected as the tan-sigmoid function, and the transfer function of the output layer is the linear function. The maximum number of iterations is set to 5000 times, the target error is 10-4, and the learning rate is 0.001. Through trial calculation, the number of hidden layer units is 5, and a 4-5-1 catheter bending rebound knowledge mining model is established, as shown in Fig.10 shown.

[0127] Using the above network structure and parameter settings, the BP neural network was trained. After 3648 optimization calculations, it converged quickly, the CPU took 8 seconds, and the objective function reached 9.9969e-05, which achieved good results. The neural network training error curve, training sample fitting curve, training status, training sample regression analysis, and sample neural network output fitting error curve are shown in the figure below. Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 The catheter bending rebound knowledge (weight and threshold) established through training and learning is shown in Table 5-5;

[0128] Table 5-5 Knowledge of catheter bending and rebound established through training

[0129]

[0130] The rebound angle of known samples is fitted using the mined knowledge of catheter bending rebound, and the average variance of the rebound angle prediction reaches 3.66%, as shown in Table 5-6; the rebound angle of unknown samples is fitted using the mined knowledge of catheter bending rebound, and the average error of the rebound angle prediction is 10.89, as shown in Table 5-7; From Tables 5-6 and 5-7, it can be seen that the BP neural network’s learning of rebound data knowledge not only has a high convergence accuracy, but also has a certain generalization ability.

[0131] Table 5-6 Fitting results of known samples

[0132]

[0133] Table 5-7 Fitting results of unknown samples

[0134]

[0135] In order to analyze the impact of data correction methods on data mining results, first, the normalization formula is used to normalize the original data of the orthogonal simulation experiment to obtain the normalized original data of the orthogonal simulation experiment, as shown in Table 5-8. The normalized original data of the orthogonal simulation experiment is used as the learning of the neural network. The BP network adopts a 4-5-1 structure. The first layer transfer function selects the tan-sigmoid function, and the transfer function of the output layer is a linear function. The maximum number of iterations is set to 5000 times, the target error is 10-4, and the learning rate is 0.001. The gradient descent method with momentum is used to train the BP neural network.

[0136] Table 5-8 Normalized original data of orthogonal simulation experiment

[0137]

[0138] After 3226 optimization calculations, the convergence was rapid, the CPU took 9 seconds, and the objective function reached 9.9947e-05, which achieved good results. The neural network training error curve, training sample fitting curve, and neural network output fitting error curve are shown in the figure below. Fig.11 , Fig.12 , Fig.13 shown.

[0139] Table 5-9 gives the influence of different data samples on the springback angle fitting results, and Table 5-10 gives the influence of different data samples on the springback angle fitting error.

[0140] Table 5-9 The influence of different data samples on the springback angle fitting results

[0141]

[0142] It can be seen from Tables 5-9 and 5-10 that when the simulated experiment corrected data samples are used as neural network learning samples, the maximum value of the springback angle error inverted by the network output is 4.38% and the minimum value is 0.00%; the average error is 1.94%; when the simulated experiment original data samples are used as neural network learning samples, the maximum value of the springback angle error inverted by the network output is 8.54% and the minimum value is 2.90%. Among the 9 samples, the number of samples that exceed the maximum inverted error of the corrected data of 4.38% reaches 6, that is, the inverted springback angle error of 66.7% of the samples exceeds the maximum inverted error of the corrected data, and the average error is 5.43%, which is about 3 times the average inverted error of the corrected data. Therefore, the method of correcting the simulated values ​​of different parameters at the same bending angle by proportional correction of the finite element simulation experiment data according to the measured data of a certain bending angle can greatly improve the accuracy of neural network data mining.

[0143] Table 5-10 The influence of different data samples on the springback angle fitting error

[0144]

[0145] In order to verify the effectiveness and superiority of the PSOLM hybrid particle swarm algorithm, under the same conditions, the 4-5-1 structure neural network established above was trained using the BP algorithm and the PSOLM algorithm. Here, the first layer of the neural network uses a logarithmic S-type transfer function, the second layer uses a linear transfer function, and the error standard e is uniformly set to 10-4. For the BP algorithm, the fast learning algorithm improved by the momentum method is used, and the maximum number of iterations is 1000. When the PSOLM algorithm is used to train the network, the maximum number of LM local depth searches is set to 20 times, and the PSO population size is 40. During the search process, the position of each particle is clamped in the range [-2.5, 2.5], and the rate of each particle is clamped in the range [-0.15, 0.15]; the inertia weight is linearly reduced from 0.95 to 0.4; the constants c1 and c2 are both 1.49, and the sum of square errors is taken as the fitness evaluation function of the particle; the maximum training generation is 1000, and the minimum constant δ is 10-6.

[0146] The performance of the two data mining algorithms, BP and PSOLM, is compared by using the orthogonal simulation experiment correction data in Table 5-4 as training samples and the unknown sample data in Table 5-7 as test samples. Table 5-11 gives the comparison of the training performance and generalization performance of the two algorithms, BP and PSOLM. It can be seen from Table 5-11 that the average training error of the PSOLM algorithm is less than 1 / 6 of that of the BP algorithm; the average test error of the PSOLM algorithm is as low as about 1 / 8 of that of the BP algorithm. It can be seen that the PSOLM algorithm spends less CPU time, but obtains higher convergence accuracy and prediction accuracy than the BP algorithm, that is, the PSOLM algorithm has better learning ability and generalization ability than the BP algorithm. In short, the PSOLM algorithm has better average performance (including average training performance, average generalization performance and average CPU time) than the BP algorithm, and has obvious algorithm stability compared with the BP algorithm, that is, the PSOLM algorithm has better learning ability than the BP algorithm, and can obtain faster convergence speed and higher convergence accuracy.

[0147] Table 5-11 Comparison of training performance and generalization performance of the two algorithms (statistical results of 20 experiments)

[0148]

[0149] In summary, the PSOLM hybrid particle swarm algorithm proposed in this paper not only has a faster convergence speed and higher convergence accuracy, but also has a stronger generalization ability, giving full play to the characteristics of PSO global search and LM local fast optimization, making up for their respective shortcomings and realizing the complementary advantages of the algorithms. The PSOLM algorithm is used to optimize the various parameters of the neural network. The modeling process is simple, with good convergence performance, avoiding falling into local minima, effectively finding the global optimal solution of the problem, and fast optimization performance, obtaining better efficiency and robustness than the BP algorithm. The experimental results verify the effectiveness and superiority of the algorithm.

[0150] Although the present invention has been shown and described with reference to preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein within the scope of the claims.

Claims

1. A method for predicting the springback angle of metal material bending, comprising the following steps: Step 1: Establish a finite element model of metal material bending and springback, use finite element simulation software to conduct a virtual orthogonal test on the metal material bending and springback, and obtain numerical simulation data of the metal material bending and springback angle; Step 2: Perform range analysis on the numerical simulation data of the bending springback angle of the metal material to determine the main factors that most significantly affect the bending springback angle of the metal material; Step 3: Each main factor is examined at three levels, and a Taguchi orthogonal test table is established. From the virtual orthogonal test table, each level of the main factor is randomly selected to conduct a real experiment to obtain the experimental data of the bending springback angle of the metal material; Step 4: Divide the experimental data of the springback angle of the metal material bending at any one of the three levels of the main factor by the numerical simulation data to obtain the correction coefficient of the springback angle at that level of the main factor; calculate the ratio of the experimental data of the springback angle at other levels of the main factor to the numerical simulation data to obtain the correction coefficient of the springback angle at each level of the main factor; Step 5: Multiply the correction coefficients of the main factors at each level by the corresponding numerical simulation data to obtain the correction values ​​of the virtual orthogonal test under each working condition; Step 6: Establish a prediction model for the bending springback angle of metal materials based on artificial neural networks. After training the neural network with the correction data under the virtual orthogonal test working conditions, input the unknown working condition data of the bending springback of metal materials, and obtain the predicted value of the bending springback angle of the metal material under the unknown working condition through neural network calculation; The main factors of the bending springback angle of the metal material include the bending angle, relative bending radius, relative wall thickness and friction coefficient.

2. The method for predicting the springback angle of metal material bending according to claim 1, characterized in that: The metal material is Q235 pipe.

3. A method for predicting the springback angle of metal material bending according to claim 1 or 2, characterized in that: The stress to which the metal material is subjected when it is bent is: Among them, σ is the actual stress, σs is the yield limit, E is Young's modulus, ε is the actual strain, K is the hardening coefficient of the material, and n is the hardening exponent of the material.

4. A method for predicting the springback angle of metal material bending according to claim 1 or 2, characterized in that: Before proceeding to step 6, the corrected value in step 5 is normalized.

5. The method for predicting the springback angle of metal material bending according to claim 4, characterized in that: The normalization formula is: Among them, Xij is the j-th value of the i-th input / output parameter after normalization, max(xi) and min(xi) are the upper and lower bound values of this parameter respectively; xNmin and xNmax are the normalized boundary values, where 0 < xNmin < xNmax < 1. Take xNmin = 0.1 and xNmax = 0.

9.

6. A method for predicting the springback angle of metal material bending according to claim 1 or 2, characterized in that: The artificial neural network in step 6 is one or more combinations of BP neural network, particle swarm optimization algorithm and hybrid particle swarm optimization algorithm.

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