CN113449474B - Improved gray wolf algorithm optimized BP neural network pipe forming quality prediction method - Google Patents
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Abstract
The invention provides a pipe forming quality prediction method for optimizing a BP neural network based on an improved gray wolf algorithm, which is characterized in that the improved gray wolf algorithm, namely PGWO, is used for optimizing the weight and the threshold of the BP neural network, and searching for a complex nonlinear function relation between process parameters and forming quality indexes in the free bending forming of a pipe, so that the accuracy of an input and output neural network prediction model is improved. The invention carries out normalization processing on the data samples of the technological parameters and the forming indexes obtained by numerical simulation, determines the topological structure of the neural network according to the input and output nodes, and introduces vector speed in the parameters of the particle swarm algorithm on the basis of optimizing the BP neural network by the traditional gray wolf algorithmAnd inertial weight omega, improving the iterative updating position of the gray wolf algorithm, and training a network to construct a PGWO-BP prediction model; the process parameter prediction method provided by the invention improves the data prediction efficiency and the accuracy of analysis results.
Description
Technical Field
The invention relates to the field of neural network prediction, in particular to a prediction method for optimizing BP neural network tube forming quality based on an improved gray wolf algorithm.
Background
Because the requirements of high strength, high weight ratio and impact energy absorption can be met, the bent pipe part is increasingly applied to various high-technology industries such as aviation, aerospace, automobiles, shipbuilding and the like. In contrast to other various bending methods such as press bending, stretch bending, push bending and roll bending, the three-dimensional free bending forming technique is an important technical innovation in the field of plastic forming in recent years. However, due to multi-factor coupling and forming theory limitations, there are various forming defects such as wrinkling, excessive thinness, cross-sectional deformation, and spring back. Therefore, a great deal of work is done on the prediction of the bend forming quality by experimental, theoretical and numerical methods.
Compared with the traditional bent pipe experimental processing method, the numerical simulation has the advantages of rapidness and economy, and is widely applied, but the rapid advantage cannot be remarkably reflected due to the complex processing technology of small-radius bent pipes and various pipe fitting artworks. Aiming at the problem of free bending and forming of the pipe fitting at present, researchers predict the rebound quantity by establishing a BP neural network, but do not pay attention to the advantages and disadvantages of the pipe fitting forming result; researchers also predict the forming result and optimize the process parameters by using an optimization algorithm, but the initial weight and the threshold value of the neural network are not optimized in the study, and the high precision and the effectiveness are lacked; meanwhile, the traditional wolf algorithm has the defects of difficult coordination of exploration and development capability, low solving precision and the like, and is not ideal for optimizing the BP neural network under a specific environment to predict the result.
Therefore, in order to improve the forming defects in the three-dimensional vector free bending forming process of the pipe and improve the forming quality, the quality prediction of the pipe forming is finished by means of the economical efficiency of numerical simulation and the high efficiency of the improved and proper neural network prediction, and the efficient and high-precision three-dimensional vector free bending forming of the pipe is realized.
Disclosure of Invention
The invention aims to provide a prediction method for optimizing BP neural network pipe forming quality based on an improved wolf algorithm, so as to solve the problems in the background art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the method for predicting the forming quality of the BP neural network pipe is optimized based on an improved wolf algorithm and is characterized by comprising the following steps of:
step 1: obtaining experimental sample data of pipe forming process parameters and forming indexes through numerical simulation;
step 2: after carrying out random sequencing and normalization processing on the sample data, determining a neural network topological structure by combining an error minimum value obtained by network training through an empirical formula; the empirical formula in step 2
The formula (1):
wherein ,n1 N is the number of input layer nodes, m is the number of output layer nodes, and a is a constant of 1 to 10.
Step 3: initializing the parameters of the wolves in a pipe forming quality prediction scene, setting the number N of the wolves, the iteration number I, optimizing the dimension D and combining the network topology structure initialization parameters a, A and C;
step 4: taking the initial weight and the threshold value of the BP neural network as individual positions of the wolves, taking the fitness function as a training error value of the BP neural network, and performing iterative traversal;
step 5: surrounding the hunting object by the improved wolf and updating the position, meeting the given precision requirement or reaching the maximum iteration number, stopping the iterative optimization and outputting the optimal position of the wolf, otherwise, repeatedly executing the step 4;
step 6: and (5) performing BP neural network training to obtain a pipe forming quality prediction result, wherein the optimal position obtained in the step (5) is the optimal weight and threshold of the neural network.
The calculation formula of the step 3 is as follows (2) to (4):
a＝2-2*t/t max (2)
A＝2*a*rand 1 -a (3)
C＝2*rand 2 (4)
wherein a is a control factor, and is iterated withThe number increment is linearly decreased from 2 to 0, t is the current iteration number, t max The maximum iteration number; a and C are co-coefficient vectors, rand 1 and rand2 A random number of (0, 1).
The concrete steps of the improved wolf in the step 5 for surrounding the prey and updating the position are as follows:
step 5.1: after finishing initialization of the wolf group and determining individual fitness values, introducing an idea of memorizing and storing a particle swarm algorithm particle self-movement speed optimal solution, and increasing inertia factors omega to finish position updating of alpha, beta and delta wolves;
step 5.2: at the same time, adding a velocity vector to the mathematical model of the current gray wolf position updateI.e., to enable the wolf individual to memorize the optimal solution during the hunting traversal.
The mathematical model in the step 5.1 is represented by the following formulas (5) to (7):
wherein ,respectively represent the distances between the time points alpha, beta and delta and other individuals, and the +.>Respectively representing the current positions of alpha, beta and delta at the moment t, C 1 、C 2 、C 3 Is a random vector +.>For the gray wolf position at time t, ω is a non-negative inertia factor, which is selected as equation (8):
ω＝0.5+rand/2 (8)
where rand is the random number between (0, 1).
The mathematical model in the step 5.2 is as follows:
wherein the formulas (9) - (11) are the step length and the direction of the progress of the individual wolves towards alpha, beta and delta, A 1 、A 2 、A 3 As random vector, rand (N, D) is random matrix of N x D dimension (0, 1) of number N of wolves and optimization dimension D, and (13) is position of individual wolves at next moment, r i A random number of (0, 1).
Compared with the prior art, the invention has the following advantages:
the invention adopts the neural network to predict the forming quality of the three-dimensional vector free forming of the pipe, is quicker and more efficient than the traditional numerical simulation to analyze and predict, provides a model foundation for the subsequent optimized process parameters, and can realize the visualization of the forming result. Meanwhile, the BP neural network is optimized by using the improved gray wolf algorithm, the defect that the gray wolf algorithm has premature convergence in the optimization process is overcome, the coordination global search in the optimization process is realized, the local development capacity is improved, and the improved and optimized neural network has higher-precision prediction performance.
Drawings
FIG. 1 is a schematic flow chart of the pipe free bending forming quality prediction of the present invention;
fig. 2 is a flow chart of the improved wolf algorithm of the present invention.
Detailed Description
The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by persons skilled in the art without making creative efforts based on the embodiments in the present invention are all within the protection scope of the present invention.
The method for predicting the forming quality of the BP neural network pipe is optimized based on an improved wolf algorithm and is characterized by comprising the following steps of:
step 1: obtaining experimental sample data of free bending forming process parameters and forming indexes of the pipe through numerical simulation, wherein the experimental sample data are three-input three-output 25 groups of orthogonal experimental samples;
step 2: after the sample data is randomly ordered and normalized, the sample data is processed through an empirical formula
wherein ,n1 N is the number of nodes in the input layer, m is the number of nodes in the output layer, and a is a constant of 1-10. Obtaining n 1 Take the value of [3,12 ]]Combining with network training to obtain error values of different hidden node numbers, when n 1 Taking the training error value at 7, the training error value is minimum, and the neural network topology structure is determined to be 3×7×3, and the result is shown in the following table 1:
TABLE 1 BP network training errors for different hidden node numbers
Step 3: initializing the wolf parameters in a process parameter prediction scene, setting the number of the wolves N=50, the iteration number I=20, and the optimization dimension D=3, and combining the network topology initialization parameters a, A and C, wherein the calculation formulas are as shown in (2) to (4):
a＝2-2*t/t max (2)
A＝2*a*rand 1 -a (3)
C＝2*rand 2 (4)
wherein a is a control factor, linearly decreases from 2 to 0 along with the increase of the iteration number, t is the current iteration number, and t max The maximum iteration number; a and C are co-coefficient vectors, rand 1 and rand2 A random number of (0, 1).
Step 4: taking the initial weight and the threshold value of the BP neural network as individual positions of the wolves, taking the fitness function as a training error value of the BP neural network, and performing iterative traversal;
step 5: and (3) surrounding the hunting object by the improved wolf and updating the position, meeting the given precision requirement or reaching the maximum iteration number, stopping the iterative optimization and outputting the optimal position of the wolf, otherwise, repeatedly executing the step (4). The method comprises the following specific steps:
step 5.1: after finishing initialization of the wolf group and determining individual fitness values, introducing an idea of memorizing and storing a particle swarm algorithm particle self-movement speed optimal solution, and increasing inertia factors omega to finish position updating of alpha, beta and delta wolves;
step 5.2: at the same time, adding a velocity vector to the mathematical model of the current gray wolf position updateNamely, the gray wolf individuals can memorize the optimal solution in the hunting traversal process;
the mathematical model in step 5.1 is represented by the following formulas (5) to (7):
wherein ,respectively represent the distances between the time points alpha, beta and delta and other individuals, and the +.>Respectively representing the current positions of alpha, beta and delta at the moment t, C 1 、C 2 、C 3 Is a random vector +.>For the gray wolf position at time t, ω is a non-negative inertia factor, which is selected as equation (8):
ω＝0.5+rand/2 (8)
where rand is the random number between (0, 1).
The mathematical model in step 5.2 is represented by the following formulas (9) to (13):
wherein, formulas (9) - (11) are respectively the advancing step length and the advancing direction of individual wolves towards alpha, beta and delta, A 1 、A 2 、A 3 As random vector, rand (N, D) is random matrix of N x D dimension (0, 1) of number N of wolves and optimization dimension D, and (13) is position of individual wolves at next moment, r i A random number of (0, 1).
Step 6: and 5, obtaining the optimal position which is the optimal weight and threshold of the BP neural network, and training the BP neural network to obtain a pipe forming quality prediction result.
Table 2 shows comparison of improved Hull Algorithm and other conventional Algorithm results of the optimizing experiment
| Predictive model | BP | PSO-BP | GWO-BP | PGWO-BP |
| Mean squareError (MSE) | 0.1479 | 0.0752 | 0.0125 | 0.00439 |
Table 2 different algorithms optimize BP neural network prediction error
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the foregoing embodiments, and that the foregoing embodiments and description are merely preferred embodiments of the invention, and are not intended to limit the invention, but that various changes and modifications may be made therein without departing from the novel spirit and scope of the invention, which is defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (3)
1. The method for predicting the forming quality of the BP neural network pipe is optimized based on an improved wolf algorithm and is characterized by comprising the following steps of:
step 1: obtaining experimental sample data of pipe forming process parameters and forming indexes through numerical simulation;
step 2: after carrying out random sequencing and normalization processing on the sample data, determining a neural network topological structure by combining an error minimum value obtained by network training through an empirical formula;
step 3: initializing the parameters of the wolves in a pipe forming quality prediction scene, setting the number N of the wolves, the iteration number I, optimizing the dimension D and combining the network topology structure initialization parameters a, A and C;
step 4: taking the initial weight and the threshold value of the BP neural network as individual positions of the wolves, taking the fitness function as a training error value of the BP neural network, and performing iterative traversal;
step 5: surrounding the hunting object by the improved wolf and updating the position, meeting the given precision requirement or reaching the maximum iteration number, stopping the iterative optimization and outputting the optimal position of the wolf, otherwise, repeatedly executing the step 4;
step 6: the optimal position obtained in the step 5 is the optimal weight and threshold of the neural network, BP neural network training is carried out, and a pipe forming quality prediction result is obtained;
the concrete steps of the improved wolf in the step 5 for surrounding the prey and updating the position are as follows:
step 5.1: after finishing initialization of the wolf group and determining individual fitness values, introducing an idea of memorizing and storing a particle swarm algorithm particle self-movement speed optimal solution, and increasing inertia factors omega to finish position updating of alpha, beta and delta wolves;
step 5.2: at the same time, adding a velocity vector to the mathematical model of the current gray wolf position updateNamely, the gray wolf individuals can memorize the optimal solution in the hunting traversal process;
the mathematical model in the step 5.1 is represented by the following formulas (5) to (7):
wherein ,respectively represent the distances between the time points alpha, beta and delta and other individuals, and the +.> Respectively representing the current positions of alpha, beta and delta at the moment t, C 1 、C 2 、C 3 Is a random vector +.>For the gray wolf position at time t, ω is a non-negative inertia factor, which is selected as equation (8):
ω＝0.5+rand/2 (8)
wherein rand is a random number between (0, 1);
the mathematical model in the step 5.2 is as follows:
wherein the formulas (9) - (11) are the step length and the direction of the progress of the individual wolves towards alpha, beta and delta, A 1 、A 2 、A 3 As random vector, rand (N, D) is random matrix of N x D dimension (0, 1) of number N of wolves and optimization dimension D, and (13) is position of individual wolves at next moment, r i A random number of (0, 1).
2. The improved wolf algorithm-based BP neural network pipe forming quality prediction method is characterized by comprising the following steps of: the empirical formula in the step 2 is as formula (1):
wherein ,n1 N is the number of input layer nodes, m is the number of output layer nodes, and a is a constant of 1 to 10.
3. The improved wolf algorithm-based BP neural network pipe forming quality prediction method is characterized by comprising the following steps of: the calculation formula of the step 3 is as follows (2) to (4):
a＝2-2*t/t max (2)
A＝2*a*rand 1 -a (3)
C＝2*rand 2 (4)
wherein a is a control factor, linearly decreases from 2 to 0 along with the increase of the iteration number, t is the current iteration number, and t max The maximum iteration number; a and C are co-coefficient vectors, rand 1 and rand2 A random number of (0, 1).
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