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CN111069328A - Isothermal extrusion process parameter optimization method based on particle swarm optimization - Google Patents

Isothermal extrusion process parameter optimization method based on particle swarm optimization Download PDF

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CN111069328A
CN111069328A CN201911218560.3A CN201911218560A CN111069328A CN 111069328 A CN111069328 A CN 111069328A CN 201911218560 A CN201911218560 A CN 201911218560A CN 111069328 A CN111069328 A CN 111069328A
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朱成就
徐康康
杨海东
印四华
方华
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Guangdong University of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract

The invention discloses an isothermal extrusion process parameter optimization method based on a particle swarm algorithm, which aims at the problems that the relation between process parameters and metal deformation resistance is complex and unclear, and the optimal process parameter combination with qualified product quality and lower production energy consumption as constraints is difficult to realize.

Description

Isothermal extrusion process parameter optimization method based on particle swarm optimization
Technical Field
The invention relates to the technical field of metal material extrusion processing, in particular to an isothermal extrusion process parameter optimization method based on a particle swarm algorithm.
Background
In the extrusion process of metal, the setting of process parameters has great influence on the temperature distribution condition, the temperature change condition and the stress-strain state of the metal in a deformation zone, and the factors are important factors influencing the quality and the performance of the profile. Since the extrusion process is essentially a large deformation nonlinear forming process, it is difficult to measure such a nonlinear process using conventional measurement methods. However, with the deep research on computer science and mechanics theory, the numerical simulation technology and finite element analysis are introduced into the aluminum extrusion production at home and abroad by using advanced technologies and means of computers and the like, so that the distribution and change conditions of field quantities such as speed, temperature, pressure and the like of the deformed metal in the extrusion die are successfully obtained, the traditional method for determining process parameters through experiments is optimized, and the production efficiency is improved. However, most of the existing researches are focused on improving the product quality, and the influence of process parameters on the metal change rule in the extrusion process is researched by a numerical simulation method so as to analyze the influence of the process parameters on the product quality; the aim of improving the quality of the extruded product is achieved by finding the optimal process parameter combination, but the attention on the extrusion energy consumption is still low. The finite element simulation software and the energy consumption calculation model can analyze the influence rule and the influence degree of the process parameters on the extrusion forming energy consumption. However, the complex and ambiguous relationship between process parameters and metal deformation resistance makes the optimal combination of process parameters constrained by acceptable product quality and lower energy consumption for production difficult to achieve. If the numerical simulation technology is continuously adopted to replace the traditional trial extrusion method for optimizing the process parameters, although the energy cost and the raw material cost in the actual production process can be greatly reduced, the cost of consuming a large amount of time is needed, and the requirement of actual production cannot be met.
The particle swarm optimization algorithm is used for optimizing a multi-objective optimization model by numerous scholars to determine the optimal process parameters because of the advantages of easy realization, high precision and the like. At present, researches of scholars prove the superiority of the particle swarm optimization in the aspect of parameter optimization, but the particle swarm optimization cannot be directly used for the parameter optimization of the isothermal extrusion process.
In conclusion, because the relationship between the process parameters and the metal deformation resistance is complex and unclear, the optimal process parameter combination with qualified product quality and lower production energy consumption as constraints is difficult to realize, and the existing algorithm cannot be directly used for the optimization of the isothermal extrusion process parameters.
Disclosure of Invention
The invention provides an isothermal extrusion process parameter optimization method based on a particle swarm algorithm, aiming at solving the problem that the prior art cannot directly optimize the process parameters of isothermal extrusion.
In order to achieve the above purpose, the technical means adopted is as follows:
an isothermal extrusion process parameter optimization method based on a particle swarm algorithm comprises the following steps:
s1, establishing a prediction model of process parameters and forming energy consumption of isothermal extrusion and the temperature of an outlet face of a section by using a support vector machine, wherein the temperature of the outlet face of the section is used as an evaluation index of the quality of the section;
s2, constructing a multi-objective optimization model by taking the forming energy consumption and the temperature mean square error of the outlet face of the section as optimization targets;
and S3, solving the multi-target optimization model by adopting a particle swarm algorithm, thereby optimizing the process parameters of isothermal extrusion and realizing optimal profile quality and minimum forming energy consumption.
Preferably, the step S1 further includes selecting isothermal extrusion process parameters, and collecting corresponding forming energy consumption and profile outlet surface temperature data under each process parameter as a training sample set.
Preferably, after the step S1 collects the training samples, the method further includes performing normalization processing on the training samples, and scaling the value ranges of all samples in the training samples to be within [ -1,1 ]:
Figure BDA0002300166970000021
in the formula: x denotes the sample currently requiring normalization and X is the corresponding sample set.
Preferably, the process parameters include an extrusion speed of the isothermal extrusion, a billet initial temperature, and a billet temperature gradient.
Preferably, the step S1 specifically includes: and carrying out regression modeling by adopting a support vector machine, selecting a kernel function type, and adjusting the hyperparameter by adopting a K-fold cross validation method and the training sample so as to determine a prediction model and the hyperparameter of the isothermal extrusion, the forming energy consumption and the temperature of the outlet surface of the section bar, which are established by the support vector machine.
Preferably, the specific step of step S1 includes:
s11, carrying out regression modeling by adopting a support vector machine:
for a given training sample set
Figure BDA0002300166970000022
Let the regression function in the high-dimensional feature space be:
f(x)＝ω·Φ(x)+b
introduce an epsilon linear insensitive loss function:
Figure BDA0002300166970000031
in the formula: y isiDenotes xiCorresponding true value, f (x)i) Expressing the corresponding predicted value of the regression function; when the difference between the real value and the predicted value is less than or equal to epsilon, considering no loss; when the difference between the two is greater than epsilon, the error is yi-f(xi)|-ε；
Introducing a slack variable ξi,ξ′iAnd the optimization target of the regression function is converted into the following formula by introducing a penalty factor C, wherein the formula is more than or equal to 0, i is 1,2, …, and l:
Figure BDA0002300166970000032
Figure BDA0002300166970000033
introducing lagrange multiplier ηi,η′i,αi,α′iAnd establishing a Lagrange equation:
Figure BDA0002300166970000034
in the formula αi,α′i,ξi,ξ′i≥0,i＝1,2…l
According to the optimized KKT condition, the parameters of omega, b and ξ in the above formulai,ξ′iAnd (3) solving a partial derivative, and converting the partial derivative into a dual problem of the original problem:
Figure BDA0002300166970000035
Figure BDA0002300166970000036
in the formula: k (x)i,xj)＝Φ(xi)Φ(xj) Is a kernel function, where is not zero (α)i-α′i) The corresponding solution is the support vector, and the nonlinear regression function obtained by solving the above formula is:
Figure BDA0002300166970000037
Figure BDA0002300166970000038
wherein N isNSVRepresenting the number of support vectors; the kernel function selects the radial basis function, namely:
Figure BDA0002300166970000041
in the formula: sigma is a parameter to be determined and represents the width of the radial basis function;
s12, determining a prediction model established by a support vector machine:
Etotal＝fE(Δt,t,v)
ΔT＝fΔT(Δt,t,v)
in the formula: Δ t is the billet temperature gradient, t represents the billet initial temperature, and v represents the extrusion speed.
S13, determining the hyper-parameters: the parameters to be determined comprise parameters sigma of a radial basis function and a penalty factor C, and a set of parameters sigma is given firstlyi、CiThen, the parameters are trained, the accuracy of each group of parameters is calculated through a K-fold cross validation method, and the group of parameters with the highest accuracy is selected as the parameter sigma and the penalty factor C of the final radial basis kernel function.
Preferably, in step S13, K-fold cross validation is performed on σ and C within an exponential range of 2 to find an optimal parameter combination, where K value of K-fold cross validation is selected to be 5, and value ranges of σ and C of the parameters are (2)-8，28) In between, the step value takes 0.5, i.e. a total of 1024 different combinations are generated and the optimal solution is determined among the combinations.
Preferably, the multi-objective optimization model in step S2 is:
min:ΔT(Δt,t,v),Etotal(Δt,t,v)
Figure BDA0002300166970000042
Figure BDA0002300166970000043
s.t.0≤Δt≤60
460≤t≤500
3≤v≤5
wherein Δ T denotes the profile outletMean square error of surface temperature,. DELTA.t is billet temperature gradient, t denotes billet initial temperature, v denotes extrusion speed, EtotalRepresenting the energy consumption for shaping, EtRepresents the energy consumption of the filling extrusion stage, WdRepresenting the energy dissipated inside the deformation zone during the first deformation,
Figure BDA0002300166970000045
denotes the frictional power loss, W ', of each face during the first deformation'dRepresenting the energy consumed inside the deformation zone during the second deformation,
Figure BDA0002300166970000044
representing the friction power loss, λ, of the respective faces during the second deformationkDenotes the split ratio, TiIndicating the temperature of the selected node of the profile exit face;
Figure BDA0002300166970000046
representing the average temperature of the selected node of the profile outlet face; n represents the number of selected nodes.
Preferably, the step S3 specifically includes the following steps:
s31, generating an initial population;
s32, constructing a self-adaptive grid:
dividing the target space into K1×K2Each grid is divided, and the width of the t-dimension target of each grid is as follows:
Figure BDA0002300166970000051
in the formula: Δ f1、Δf2Representing the forming energy consumption and the width of the temperature mean square error dimension of the outlet surface of the section; f. of1 t、
Figure BDA0002300166970000052
Expressing the t-dimension extrusion energy consumption value of the ith particle in the external archive set and the mean square error of the temperature of the outlet surface of the profile; k1And K2The grid number of the t-dimension target division is represented;
traversing the particles in the external archive set, and calculating the number of the grid where the particle i is located:
Figure BDA0002300166970000053
counting the density of particles in the grid, wherein the smaller the density of the particles in the grid is, the larger the probability of selection is;
s33, setting an external file maintenance strategy: setting a storage scale upper limit value of the external archive, and directly storing a non-inferior solution generated by the particle swarm algorithm in the external archive when the scale of the external archive is smaller than the upper limit value during storage; when the scale of an external file is larger than or equal to an upper limit value during storage, deleting redundant particles, setting the upper limit value of the file as M for a grid M with a certain particle number larger than 1, and deleting PN particles in the grid, wherein the particle number to be deleted is PN:
Figure BDA0002300166970000054
in the formula: a. thet+1Representing the number of particles stored in the file set when iteration is carried out to t +1 generation, and grid (m) representing the number of particles contained in the grid m;
s34, selecting a global extremum: iterating to the archive set A of the t generationtAll of the superior particle i individual extremum Pi,d(t)Particle A ofk,tInto a set SiIn (1), namely:
Si＝{Ak,t|Ak,t∈At，Ak,t＞Pi,d(t)}
selecting the particles with the minimum density as a global extreme value; if the number of the determined global extreme values is more than 1, randomly selecting one global extreme value P as the particle i from the determined global extreme valuesg,d(t)；
S34, updating the particles: the particles i in the particle swarm are determined according to the determined individual extreme value Pi,d(t)And a global extremum Pg,d(t)Continuously adjusting the flight direction and the flight speed of the aircraft, and updating the formula as follows:
vi,d(t+1)＝ωvi,d(t)+c1×rand()×(Pi,d(t)-xi,d(t))+c2×rand()×(Pg,d(t)-xi,d(t))
xi,d(t+1)＝xi,d(t)+vi,d(t)
in the formula: c. C1And c2Represents a learning factor; omega is the inertial weight; rand () is a random number within the (0,1) interval; x is the number ofi,d(t) and vi,d(t) represents the position and velocity of the ith particle in the d-dimension at the t-th iteration; pi,d(t) representing the individual extreme value of the ith particle in the d-dimension in the t-th iteration, namely the best position which the ith particle has experienced at the moment is the best solution found by the particle; pg,d(t) represents the global extremum of the d-th dimension of the ith particle at the t-th iteration, i.e., the optimal solution currently found by the population.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
aiming at the problems that the relation between process parameters and metal deformation resistance is complex and unclear and the optimal process parameter combination with qualified product quality and lower production energy consumption as constraints is difficult to realize, the particle swarm algorithm-based isothermal extrusion process parameter optimization method provided by the invention adopts a support vector machine to establish a prediction model of the process parameters, isothermal extrusion forming energy consumption and section bar outlet surface temperature, adopts the mean square error of the extrusion forming energy consumption and the section bar outlet surface temperature as an optimization target to establish a multi-objective optimization model, and adopts a particle swarm algorithm to solve the multi-objective optimization model, so as to optimize the isothermal extrusion process parameters and realize an optimization scheme with optimal section bar quality and minimum forming energy consumption.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a comparison of the mean square error of the predicted temperature and the mean square error of the actual temperature for the outlet face of the profile of example 2.
FIG. 3 is a graph comparing the predicted energy consumption value and the actual energy consumption value of the extrusion in example 2.
Fig. 4 is a graph of the Pareto optimal solution set obtained in example 2.
FIG. 5 is a cloud graph of the exit face temperature of the profile under the initial process parameter combinations in example 2.
FIG. 6 is a cloud chart of the temperature of the outlet surface of the profile under the optimized combination of process parameters in example 2.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The embodiment 1 provides an isothermal extrusion process parameter optimization method based on a particle swarm optimization algorithm, which includes the following steps:
before the step S1, firstly, selecting isothermal extrusion process parameters, and acquiring corresponding forming energy consumption and profile outlet surface temperature data under each process parameter as a training sample set; the process parameters selected by the embodiment comprise the extrusion speed of isothermal extrusion, the initial temperature of the blank and the temperature gradient of the blank;
in order to avoid controlling the variables with a smaller value range by the variables with a larger value range and facilitate the calculation of subsequent kernel functions, the training samples are normalized, and the value ranges of all the samples are scaled to the range of [ -1,1 ]:
Figure BDA0002300166970000071
in the formula: x denotes the sample currently requiring normalization and X is the corresponding sample set.
S1, establishing a prediction model of process parameters and forming energy consumption of isothermal extrusion and the temperature of an outlet face of a section by using a support vector machine, wherein the temperature of the outlet face of the section is used as an evaluation index of the quality of the section; the method comprises the following specific steps:
s11, carrying out regression modeling by adopting a support vector machine:
for a given training sample set
Figure BDA0002300166970000072
Let the regression function in the high-dimensional feature space be:
f(x)＝ω·Φ(x)+b
introduce an epsilon linear insensitive loss function:
Figure BDA0002300166970000073
in the formula: y isiDenotes xiCorresponding true value, f (x)i) Expressing the corresponding predicted value of the regression function; when the difference between the real value and the predicted value is less than or equal to epsilon, considering no loss; when the difference between the two is greater than epsilon, the error is yi-f(xi)|-ε；
Since there may be some sample data that cannot meet the requirement of precision ε, a slack variable ξ is introducedi,ξ′iAnd the optimization target of the regression function is converted into the following formula by introducing a penalty factor C, wherein the formula is more than or equal to 0, i is 1,2, …, and l:
Figure BDA0002300166970000081
Figure BDA0002300166970000082
introducing lagrange multiplier ηi,η′i,αi,α′iAnd establishing a Lagrange equation:
Figure BDA0002300166970000083
in the formula αi,α′i,ξi,ξ′i≥0,i＝1,2…l
According to the optimized KKT condition, the parameters of omega, b and ξ in the above formulai,ξ′iAnd (3) solving a partial derivative, and converting the partial derivative into a dual problem of the original problem:
Figure BDA0002300166970000084
Figure BDA0002300166970000085
in the formula: k (x)i,xj)＝Φ(xi)Φ(xj) Is a kernel function, where is not zero (α)i-α′i) The corresponding solution is the support vector, and the nonlinear regression function obtained by solving the above formula is:
Figure BDA0002300166970000086
Figure BDA0002300166970000087
wherein N isNSVRepresenting the number of support vectors;
wherein the kernel function can convert the training samples with linear indifference in the original solution space into the training samples with linear indivisible in the specific feature space, and calculate K (x) with a simple function in the low-dimensional spacei,xj)＝Φ(xi)Φ(xj) Replacing complex phi functions in high dimensional space. Since the radial basis function has better immunity to noise in the data, the kernel function selects the radial basis function in this embodiment, that is:
Figure BDA0002300166970000088
in the formula: sigma is a parameter to be determined and represents the width of the radial basis function;
s12, determining a prediction model established by a support vector machine:
Etotal＝fE(Δt,t,v)
ΔT＝fΔT(Δt,t,v)
in the formula: Δ t is the billet temperature gradient, t represents the billet initial temperature, and v represents the extrusion speed.
S13, determining the hyper-parameters: the parameters to be determined comprise parameters sigma of a radial basis function and a penalty factor C, and a set of parameters sigma is given firstlyi、CiThen, the parameters are trained, the accuracy of each group of parameters is calculated through a K-fold cross validation method, and the group of parameters with the highest accuracy is selected as the parameter sigma and the penalty factor C of the final radial basis kernel function.
Since the number of samples is not large, the accuracy is calculated by selecting a K-fold cross validation method in the embodiment. The K-fold cross-validation method comprises the steps of randomly dividing training samples into K mutually disjoint sets, taking (K-1) sample sets as training sets and the rest 1 sample set as test sets, solving a decision function according to the training sets, testing the test sets, and recording the accuracy; repeating the process k times; and finally, averaging the obtained k times of calculation results to obtain the final accuracy of the group of parameters.
The determination of the parameters σ and the penalty factor C of the radial basis function is essentially a discrete optimization process, and considering the training speed and the correctness of cross validation, the embodiment performs K-fold cross validation on σ and C in an exponential range of 2 to find the optimal parameter combination. The K value of the K-fold cross-validation method is generally selected to be 5, and the value ranges of the parameters sigma and C are (2)-8，28) In between, the step value takes 0.5, so a total of 1024 different combinations are generated, among which the optimal solution is determined.
S2, constructing a multi-objective optimization model by taking the forming energy consumption and the temperature mean square error of the outlet face of the section as optimization targets;
for the isothermal extrusion process studied in this embodiment, the energy consumption for extrusion and the profile quality are two conflicting optimization targets, and over pursuing the energy consumption for extrusion may result in the reduction of the profile quality, while over pursuing the profile quality may result in the increase of the energy consumption cost. For the isothermal extrusion process, the more uniform the temperature of the outlet surface of the profile, the better the quality of the profile, so the present embodiment takes the temperature mean square deviation and the forming energy consumption of the outlet surface of the profile as optimization targets, and the multi-objective optimization model constructed by the method is as follows:
min:ΔT(Δt,t,v),Etotal(Δt,t,v)
Figure BDA0002300166970000101
Figure BDA0002300166970000102
s.t.0≤Δt≤60
460≤t≤500
3≤v≤5
where Δ T represents the temperature mean square error of the exit face of the profile, Δ T is the billet temperature gradient, T represents the billet initial temperature, v represents the extrusion speed, EtotalRepresenting the energy consumption for shaping, EtRepresents the energy consumption of the filling extrusion stage, WdRepresenting the energy dissipated inside the deformation zone during the first deformation,
Figure BDA0002300166970000103
denotes the frictional power loss, W ', of each face during the first deformation'dRepresenting the energy consumed inside the deformation zone during the second deformation,
Figure BDA0002300166970000104
representing the friction power loss, λ, of the respective faces during the second deformationkDenotes the split ratio, TiIndicating the temperature of the selected node of the profile exit face;
Figure BDA0002300166970000108
representing the average temperature of the selected node of the profile outlet face; n represents the number of selected nodes.
S3, solving the multi-target optimization model by adopting a particle swarm algorithm, thereby optimizing the process parameters of isothermal extrusion, and realizing optimal profile quality and minimum forming energy consumption:
in this embodiment, a Pareto optimal solution is introduced to describe an optimal solution obtained by optimizing extrusion energy consumption and profile quality, and a particle swarm algorithm is used to perform optimization solution on a multi-objective optimization model, and the specific steps include:
s31, generating an initial population;
s32, constructing a self-adaptive grid:
dividing the target space into K1×K2Each grid is divided, and the width of the t-dimension target of each grid is as follows:
Figure BDA0002300166970000105
in the formula: Δ f1、Δf2Representing the forming energy consumption and the width of the temperature mean square error dimension of the outlet surface of the section; f. of1 t、
Figure BDA0002300166970000106
Expressing the t-dimension extrusion energy consumption value of the ith particle in the external archive set and the mean square error of the temperature of the outlet surface of the profile; k1And K2The grid number of the t-dimension target division is represented;
traversing the particles in the external archive set, and calculating the number of the grid where the particle i is located:
Figure BDA0002300166970000107
counting the density of particles in the grid, wherein the smaller the density of the particles in the grid is, the larger the probability of selection is;
s33, setting an external file maintenance strategy: in the particle swarm algorithm, since each cycle will generate some non-inferior solutions, the most commonly adopted measure at present is to establish an external file for storing the non-inferior solutions. But an unlimited size of the file can adversely affect the operating efficiency of the algorithm. Therefore, the present embodiment selects to use a method of truncating the file to control the size of the file, and the principle is as follows: setting a storage scale upper limit value of the external archive, and directly storing a non-inferior solution generated by the particle swarm algorithm in the external archive when the scale of the external archive is smaller than the upper limit value during storage; when the scale of an external file is larger than or equal to an upper limit value during storage, deleting redundant particles, setting the upper limit value of the file as M for a grid M with a certain particle number larger than 1, and deleting PN particles in the grid, wherein the particle number to be deleted is PN:
Figure BDA0002300166970000111
in the formula: a. thet+1Representing the number of particles stored in the file set when iteration is carried out to t +1 generation, and grid (m) representing the number of particles contained in the grid m;
s34, selecting a global extremum: in the particle swarm optimization process, which one of a plurality of non-inferior solutions is the optimal solution cannot be determined. Selecting the global extremum P of the particle ig,d(t): iterating to the archive set A of the t generationtAll of the superior particle i individual extremum Pi,d(t)Particle A ofk,tInto a set SiIn (1), namely:
Si＝{Ak,t|Ak,t∈At，Ak,t＞Pi,d(t)}
selecting the particles with the minimum density as a global extreme value; if the number of the determined global extreme values is more than 1, randomly selecting one global extreme value P as the particle i from the determined global extreme valuesg,d(t)；
S34, updating the particles: the particles i in the particle swarm are determined according to the determined individual extreme value Pi,d(t)And a global extremum Pg,d(t)Continuously adjusting the flight direction and the flight speed of the aircraft, and updating the formula as follows:
vi,d(t+1)＝ωvi,d(t)+c1×rand()×(Pi,d(t)-xi,d(t))+c2×rand()×(Pg,d(t)-xi,d(t))
xi,d(t+1)＝xi,d(t)+vi,d(t)
in the formula: c. C1And c2Represents a learning factor; omega is the inertial weight; rand () is a random number within the (0,1) interval; x is the number ofi,d(t) and vi,d(t) represents the position and velocity of the ith particle in the d-dimension at the t-th iteration; pi,d(t) representing the individual extreme value of the ith particle in the d-dimension in the t-th iteration, namely the best position which the ith particle has experienced at the moment is the best solution found by the particle; pg,d(t) represents the global extremum of the d-th dimension of the ith particle at the t-th iteration, i.e., the optimal solution currently found by the population. Thereby completing the optimization of the technological parameters of the isothermal extrusion, realizing the optimal quality of the section bar and the minimum energy consumption for forming
Example 2
In this embodiment 2, experiments based on the particle swarm optimization-based isothermal extrusion process parameter optimization method provided in embodiment 1 prove that in the experiments, HyperXtrude numerical simulation software is used to simulate the extrusion process under different process conditions, so as to study the influence of the extrusion speed and temperature on the energy consumption of isothermal extrusion forming; the proposed process parameter optimization algorithm is implemented by MATLAB programming, the compiler tool: MATLAB R2018 a. And (3) operating environment: windows 7 and above. Hardware: the client computer requires more than 3.30G of CPU and 4.0M of memory.
Implementation of support vector machine-based prediction model
The value ranges of the three sets of process parameters for isothermal extrusion selected in this example 2 are shown in table 1. Simulation was performed on a total of 27 sets of process parameter combinations of the three process parameters, and 20 sets of the three process parameters were randomly selected as training samples, as shown in table 2, and 7 sets of the three process parameters were selected as test samples, as shown in table 3.
Process parameters Extrusion speed (mm/s) Initial temperature (. degree. C.) of billet Blank temperature ladderDegree (. degree. C.)
Value range 3-5 460-500 0-60
TABLE 1 Process parameter selection Range
Figure BDA0002300166970000121
Figure BDA0002300166970000131
TABLE 2 training samples
Figure BDA0002300166970000132
TABLE 3 test specimens
In the embodiment, the parameters are trained and predicted by using a support vector machine, and the comparison result is shown in fig. 2 and fig. 3. Fig. 3 and 4 are a comparison graph of the temperature mean square error predicted by the trained support vector machine and the temperature mean square error of the outlet face of the section bar obtained through the simulation result, and a comparison graph of the predicted energy consumption value and the energy consumption value calculated by the simulation result, respectively.
The comparison error of the temperature mean square error and the comparison error of the extrusion energy consumption value are shown in table 4, and the comparison error of the prediction result and the simulation result is less than 10%, which shows that the prediction model established by the support vector machine can accurately reflect the relationship between the extrusion process parameters and the temperature mean square error of the outlet surface of the isothermal extrusion forming energy consumption profile.
Figure BDA0002300166970000133
Figure BDA0002300166970000141
TABLE 4 comparison of predicted and simulated results
Second, implementation of quality and energy consumption multi-objective optimization based on particle swarm optimization
Aiming at the multi-objective optimization model provided in embodiment 1, a fitting model of process parameters, isothermal extrusion forming energy consumption and section temperature mean square error is used as a fitness function of a particle swarm algorithm, and the optimization model is solved by combining the particle swarm algorithm. The relevant parameters are set as follows: the initial population size is 60, the maximum iteration number is 200, the upper limit value of an external file is set to be 100, the minimum inertia weight is 0.4, the maximum inertia weight is 0.9, and a learning factor c1＝c2＝2c1＝c 22. The resulting Pareto optimal solution set is shown in fig. 4 below.
After comprehensive consideration, a group of process parameter combinations are selected from the raw materials, and the extrusion speed is 4.4 mm/s; the initial temperature of the blank is 451 ℃; the blank temperature gradient is 48 ℃, and the combination of the technological parameters is subjected to simulation by using numerical simulation software and compared with the initial scheme.
The temperature cloud charts of the outlet surface of the section are shown in fig. 5 and 6, the comparison results are shown in table 5, and the comparison results show that the mean square deviation of the temperature of the optimized process parameter combination is 0.485, which is 21.7% lower than that of the initial scheme; the extrusion energy consumption value is 1.1590 multiplied by 103kJ, 1.6% lower than the energy consumption of the initial solution for extrusion. The optimized scheme can produce the section bar with better quality than the original scheme and lower energy consumption for extrusion forming.
Figure BDA0002300166970000142
TABLE 5 comparison of initial and optimized solutions
The terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (9)

1. An isothermal extrusion process parameter optimization method based on a particle swarm algorithm is characterized by comprising the following steps:
s1, establishing a prediction model of process parameters and forming energy consumption of isothermal extrusion and the temperature of an outlet face of a section by using a support vector machine, wherein the temperature of the outlet face of the section is used as an evaluation index of the quality of the section;
s2, constructing a multi-objective optimization model by taking the forming energy consumption and the temperature mean square error of the outlet face of the section as optimization targets;
and S3, solving the multi-target optimization model by adopting a particle swarm algorithm, thereby optimizing the process parameters of isothermal extrusion and realizing optimal profile quality and minimum forming energy consumption.
2. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 1, wherein the step S1 further comprises selecting isothermal extrusion process parameters, and collecting corresponding forming energy consumption and profile outlet surface temperature data under each process parameter as a training sample set.
3. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 2, wherein after the step S1 of collecting training samples, the method further comprises performing normalization on the training samples to scale the value ranges of all samples to be within [ -1,1 ]:
Figure FDA0002300166960000011
in the formula: x denotes the sample currently requiring normalization and X is the corresponding sample set.
4. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 1, wherein the process parameters comprise an extrusion speed of isothermal extrusion, a billet initial temperature and a billet temperature gradient.
5. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 3, wherein the step S1 specifically comprises: and carrying out regression modeling by adopting a support vector machine, selecting a kernel function type, and adjusting the hyperparameter by adopting a K-fold cross validation method and the training sample so as to determine a prediction model and the hyperparameter of the isothermal extrusion, the forming energy consumption and the temperature of the outlet surface of the section bar, which are established by the support vector machine.
6. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 3, wherein the specific steps of the step S1 comprise:
s11, carrying out regression modeling by adopting a support vector machine:
for a given training sample set
Figure FDA0002300166960000021
Let the regression function in the high-dimensional feature space be:
f(x)＝ω·Φ(x)+b
introduce an epsilon linear insensitive loss function:
Figure FDA0002300166960000022
in the formula: y isiDenotes xiCorresponding true value, f (x)i) Expressing the corresponding predicted value of the regression function; when the difference between the real value and the predicted value is less than or equal to epsilon, considering no loss; when the difference between the two is greater than epsilon, the error is yi-f(xi)|-ε；
Introducing a slack variable ξi,ξ′iAnd the optimization target of the regression function is converted into the following formula by introducing a penalty factor C, wherein the formula is more than or equal to 0, i is 1,2, …, and l:
Figure FDA0002300166960000023
Figure FDA0002300166960000024
introducing lagrange multiplier ηi,η′i,αi,α′iAnd establishing a Lagrange equation:
Figure FDA0002300166960000025
in the formula αi,α′i,ξi,ξ′i≥0,i＝1,2…l
According to the optimized KKT condition, the parameters of omega, b and ξ in the above formulai,ξ′iAnd (3) solving a partial derivative, and converting the partial derivative into a dual problem of the original problem:
Figure FDA0002300166960000026
Figure FDA0002300166960000027
in the formula: k (x)i,xj)＝Φ(xi)Φ(xj) Is a kernel function, where is not zero (α)i-α′i) The corresponding solution is the support vector, and the nonlinear regression function obtained by solving the above formula is:
Figure FDA0002300166960000031
Figure FDA0002300166960000032
wherein N isNSVRepresenting the number of support vectors;
the kernel function selects the radial basis function, namely:
Figure FDA0002300166960000033
in the formula: sigma is a parameter to be determined and represents the width of the radial basis function;
s12, determining a prediction model established by a support vector machine:
Etotal＝fE(Δt,t,v)
ΔT＝fΔT(Δt,t,v)
in the formula: Δ t is the billet temperature gradient, t represents the billet initial temperature, v represents the extrusion speed;
s13, determining the hyper-parameters: the parameters to be determined comprise parameters sigma of a radial basis function and a penalty factor C, and a set of parameters sigma is given firstlyi、CiThen, the parameters are trained, the accuracy of each group of parameters is calculated through a K-fold cross validation method, and the group of parameters with the highest accuracy is selected as the parameter sigma and the penalty factor C of the final radial basis kernel function.
7. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 6, wherein in the step S13, the K-fold cross validation is performed on σ and C within an exponential range of 2 to find the optimal parameter combination, wherein the K value of the K-fold cross validation is selected to be 5, and the values of the parameters σ and C are within a range of (2)-8，28) In between, the step value takes 0.5, i.e. a total of 1024 different combinations are generated and the optimal solution is determined among the combinations.
8. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 1, wherein the multi-objective optimization model in step S2 is:
min:ΔT(Δt,t,v),Etotal(Δt,t,v)
Figure FDA0002300166960000041
Figure FDA0002300166960000042
s.t.0≤Δt≤60
460≤t≤500
3≤v≤5
where Δ T represents the temperature mean square error of the exit face of the profile, Δ T is the billet temperature gradient, T represents the billet initial temperature, v represents the extrusion speed, EtotalRepresenting the energy consumption for shaping, EtRepresents the energy consumption of the filling extrusion stage, WdRepresenting the energy dissipated inside the deformation zone during the first deformation,
Figure FDA0002300166960000043
denotes the frictional power loss, W ', of each face during the first deformation'dRepresenting the energy consumed inside the deformation zone during the second deformation,
Figure FDA0002300166960000044
representing the friction power loss, λ, of the respective faces during the second deformationkDenotes the split ratio, TiIndicating the temperature of the selected node of the profile exit face;
Figure FDA0002300166960000045
representing the average temperature of the selected node of the profile outlet face; n represents the number of selected nodes.
9. The particle swarm optimization-based isothermal extrusion process parameter optimization method according to claim 1, wherein the step S3 specifically comprises the following steps:
s31, generating an initial population;
s32, constructing a self-adaptive grid:
dividing the target space into K1×K2Each grid is divided, and the width of the t-dimension target of each grid is as follows:
Figure FDA0002300166960000046
in the formula: Δ f1、Δf2Representing the forming energy consumption and the width of the temperature mean square error dimension of the outlet surface of the section; f. of1 t、
Figure FDA0002300166960000047
Expressing the t-dimension extrusion energy consumption value of the ith particle in the external archive set and the mean square error of the temperature of the outlet surface of the profile; k1And K2The grid number of the t-dimension target division is represented;
traversing the particles in the external archive set, and calculating the number of the grid where the particle i is located:
Figure FDA0002300166960000048
counting the density of particles in the grid, wherein the smaller the density of the particles in the grid is, the larger the probability of selection is;
s33, setting an external file maintenance strategy: setting a storage scale upper limit value of the external archive, and directly storing a non-inferior solution generated by the particle swarm algorithm in the external archive when the scale of the external archive is smaller than the upper limit value during storage; when the scale of an external file is larger than or equal to an upper limit value during storage, deleting redundant particles, setting the upper limit value of the file as M for a grid M with a certain particle number larger than 1, and deleting PN particles in the grid, wherein the particle number to be deleted is PN:
Figure FDA0002300166960000051
in the formula: a. thet+1Representing the number of particles stored in the file set when iteration is carried out to t +1 generation, and grid (m) representing the number of particles contained in the grid m;
s34, selecting a global extremum: iterating to the archive set A of the t generationtAll of the superior particle i individual extremum Pi,d(t) particles Ak,tInto a set SiIn (1), namely:
Si＝{Ak,t|Ak,t∈At，Ak,t＞Pi,d(t)}
selecting the particles with the minimum density as a global extreme value; if the number of the determined global extreme values is more than 1, randomly selecting one global extreme value P as the particle i from the determined global extreme valuesg,d(t)；
S34, updating the particles: the particles i in the particle swarm are determined according to the determined individual extreme value Pi,d(t) and a global extremum Pg,d(t) continuously adjusting the flight direction and the flight speed of the aircraft, wherein the updating formula is as follows:
vi,d(t+1)＝ωvi,d(t)+c1×rand()×(Pi,d(t)-xi,d(t))+c2×rand()×(Pg,d(t)-xi,d(t))
xi,d(t+1)＝xi,d(t)+vi,d(t)
in the formula: c. C1And c2Represents a learning factor; omega is the inertial weight; rand () is a random number within the (0,1) interval; x is the number ofi,d(t) and vi,d(t) represents the position and velocity of the ith particle in the d-dimension at the t-th iteration; pi,d(t) representing the individual extreme value of the ith particle in the d-dimension in the t-th iteration, namely the best position which the ith particle has experienced at the moment is the best solution found by the particle; pg,d(t) represents the global extremum of the d-th dimension of the ith particle at the t-th iteration, i.e., the optimal solution currently found by the population.
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