CN114492198A - Cutting force prediction method based on improved PSO algorithm assisted SVM algorithm - Google Patents

Cutting force prediction method based on improved PSO algorithm assisted SVM algorithm Download PDF

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CN114492198A
CN114492198A CN202210138338.8A CN202210138338A CN114492198A CN 114492198 A CN114492198 A CN 114492198A CN 202210138338 A CN202210138338 A CN 202210138338A CN 114492198 A CN114492198 A CN 114492198A
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阎春平
黄一躬
周超
倪恒欣
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Abstract

The invention discloses a cutting force prediction method based on an improved PSO algorithm assisted SVM algorithm, which is characterized in that based on historical process data, the cutting force is predicted according to the following steps, and the input and the output of a cutting force prediction model based on the SVM algorithm are determined; training an SVM parameter model; and optimizing SVM algorithm parameters by using the improved PSO algorithm. The improved PSO algorithm and the SVM algorithm are simultaneously introduced into the cutting force prediction, and the SVM model is adopted to mine the nonlinear regression relationship between the cutting force parameters and the related influence parameters, so that the cutting force prediction model is established. And model parameters are optimized by improving the PSO algorithm, the search precision is improved, the convergence is accelerated, the accuracy of the program is improved, and the prediction performance of the cutting force prediction model is further improved. The method has important significance for realizing accurate prediction of cutting force, improving the processing quality of workpieces and building intelligent workshops.

Description

Cutting force prediction method based on improved PSO algorithm assisted SVM algorithm
Technical Field
The invention belongs to the technical field of machine manufacturing, and particularly relates to a cutting force prediction method based on an improved PSO (particle swarm optimization) algorithm assisted SVM (support vector machine) algorithm.
Background
The cutting force in the machining process has important influence on the abrasion of the cutter and the machining quality of the workpiece, and is an important reference factor for selecting cutting machining parameters. The cutting process is a complex process, the cutting force is influenced by a plurality of factors, the correlation between the cutting process parameters and the cutting force is researched based on the determined workpiece material, the cutting form, the cutter structure and the like, and a roughness prediction model which meets the actual working condition under the specific condition is sought.
A Support Vector Machine (SVM algorithm for short) can seek the best compromise between the complexity and the learning capacity of a model according to limited sample information, and obtains the very complex mapping relation between dependent variables and independent variables. Researches show that main factors influencing the precision of an SVM algorithm are parameters of the SVM, a loss distance metric epsilon, a penalty parameter C and selected kernel function parameters, and the prediction method in the prior art has low optimization degree on the parameters, so that the prediction precision and the accuracy of a program are poor, the processing quality of a workpiece is difficult to guarantee, and the method is not convenient to apply to intelligent workshop construction.
Disclosure of Invention
Aiming at the defects in the prior art, the technical problems to be solved by the invention are as follows: the cutting force prediction model training parameters of the SVM algorithm are optimized by using the improved PSO algorithm, so that the prediction performance and the prediction precision of the cutting force prediction model are improved, the workpiece processing quality is improved, and the method is convenient to apply to the construction of an intelligent workshop.
In order to solve the technical problems, the invention adopts the following technical scheme:
a cutting force prediction method based on an improved PSO algorithm auxiliary SVM algorithm comprises the following steps,
1) constructing a cutting force prediction model based on an SVM algorithm, and determining input parameters and output parameters of the cutting force prediction model;
2) performing parameter model training on the cutting force prediction model;
3) optimizing parameters of the cutting force prediction model by improving a PSO algorithm;
4) and performing parameter model training by using the optimized parameters to obtain an optimized cutting force prediction model.
As optimization, the input parameters of the cutting force prediction model are processing parameters extracted from an original database, and the constraint conditions are material parameters, workpiece names, geometric characteristic parameters and equipment parameters of workpieces extracted from the original database; the output parameter is a predicted value of the cutting force.
As optimization, the process parameters are extracted from the original database by adopting a method of abnormal point clearing and normalization processing.
As optimization, the sample data set of the parameter model training is set as,
{(xi,yi)∣i＝1,2,…,u} (1)
wherein x isiRepresenting the ith sample vector, and the data comprises cutting speed, feed speed, cutting depth, cutting width under preset processing conditions, yiRepresenting the predicted value of the cutting force;
as an optimization, the parametric model training comprises the steps of,
1) mapping an input feature space x of the sample data set to a high-dimensional feature space phi (x), and performing regression analysis:
f(x)＝w·φ(x)+b (2)
wherein: phi (x) is a high-dimensional feature space; w is inertia weight, w is equal to Rn(ii) a b is a bias coefficient, and b belongs to R;
2) the optimization problem of the SVM is set as follows:
Figure BDA0003505884750000021
the constraint conditions are as follows:
Figure BDA0003505884750000022
wherein ξi，
Figure BDA0003505884750000023
Is a relaxation variable; ε is a loss distance metric, C represents a penalty parameter for the degree of penalty for samples that exceed ε;
3) solving the optimization problem to obtain an SVM regression model:
Figure BDA0003505884750000031
wherein, alpha*Is a lagrange multiplier; k (x, x)i)＝φ(x)·φ(xi) Is a kernel function.
As an optimization, the method for optimizing the parameters of the cutting force prediction model by improving the PSO algorithm comprises the following steps,
1) estimating the prediction precision of the cutting force prediction model by adopting a k-fold cross validation mode, and outputting an estimated value;
2) the root mean square error value of the evaluation value is used as a fitness index for improving PSO algorithm optimization, and loss distance measurement epsilon, punishment parameter C and kernel function parameters of a cutting force prediction model trained by a parameter model are optimized;
3) inertia weight w and learning factor c of cutting force prediction model by improving PSO algorithm1、c2Carrying out optimization adjustment; wherein the learning factor c1For self-cognition factor, learning factor c2Is a social cognition coefficient.
As optimization, the adjustment of the inertia weight w adopts an adaptive adjustment method based on the inertia weight w, and adopts the following formula:
Figure BDA0003505884750000032
wherein f represents a real-time objective function value of the particle; f. ofavg，fminRespectively, the current average target value and the minimum target value of all the particles; wherein f isavgThe calculation formula is as follows：
Figure BDA0003505884750000033
As optimization, the adjustment of the learning factor adopts an adaptive adjustment method based on an acceleration factor of time change; the following formula is adopted:
Figure BDA0003505884750000034
Figure BDA0003505884750000035
where T represents the maximum number of iterations, T represents the current number of iterations, c1iAnd c2iAn initial value representing an acceleration factor, set to 1.5; c. C1fAnd c2fA final limit value representing the acceleration factor, set to 4;
then, the following steps are carried out:
1) initializing a population parameter, and setting the size of the population and the maximum iteration times;
2) calculating the fitness value of each particle, and updating the position and the speed of the particle according to the fitness function;
3) and judging the optimization termination condition of the particle swarm parameters, finishing the optimization algorithm when the iteration times reach the maximum iteration times, and outputting the optimization parameters.
Compared with the prior art, the application has the following beneficial effects:
the method can be used for predicting the cutting force, optimizes the model and further improves the prediction performance of the cutting force prediction model. The improved PSO algorithm and the SVM algorithm are simultaneously introduced into the cutting force prediction, and the SVM model is adopted to mine the nonlinear regression relationship between the cutting force parameters and the related influence parameters, so that the cutting force prediction model is established. And the SVM parameters are optimized by improving the PSO algorithm, the search precision is improved, the convergence is accelerated, the accuracy of the program is improved, and the prediction performance of the cutting force prediction model is further improved. The cutting force prediction model provided by the invention integrates the improved PSO algorithm and the SVM algorithm, and has important significance for realizing accurate prediction of cutting force, improving the processing quality of workpieces and building an intelligent workshop.
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FIG. 1 is a block flow diagram of an embodiment of the present invention;
FIG. 2 is a sample data and partial set of process examples for an embodiment of the present invention;
FIG. 3 is a graph comparing the predicted results of embodiments of the present invention with those of existing svm prediction models.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
In the specific implementation: with reference to figures 1-3 of the drawings,
a cutting force prediction method based on an improved PSO algorithm auxiliary SVM algorithm comprises the following steps,
the method comprises the following steps of firstly, constructing a cutting force prediction model based on an SVM algorithm, and determining input parameters and output parameters of the cutting force prediction model; the cutting force prediction model aims to predict the cutting force of a workpiece in a process design stage, namely outputting the predicted value of the cutting force of the workpiece; the input is the attributes determined for the process design phase: the cutting force prediction model comprises material parameters, workpiece names and geometric characteristic parameters, equipment parameters and machining process parameters, wherein the input parameters of the cutting force prediction model are the machining process parameters extracted from an original database, the material parameters, the workpiece names and the geometric characteristic parameters, the equipment parameters and the like of the workpieces extracted from the original database are used as constraint conditions, and the output parameters are predicted values of the cutting force. However, the sample obtained from the original database has useless parameters such as specific equipment numbers, specific material information, processing personnel information, environmental information and the like in addition to the above attributes, so that a sample only containing material parameters, workpiece names and geometric characteristic parameters, equipment parameters and processing process parameters needs to be constructed for training the cutting force prediction model, wherein the training is mainly realized through outlier removal and normalization.
Secondly, performing parameter model training on the cutting force prediction model;
setting the sample data set of the parameter model training as,
{(xi,yi)∣i＝1,2,…,u} (1)
wherein x isiRepresenting the ith sample vector, and the data comprises cutting speed, feed speed, cutting depth, cutting width, y under the same machining conditions such as machine tool model, cutter material, cutter coating, workpiece material, machining feature name, machining mode (milling/turning), etciIs a target value, namely a predicted value of the cutting force;
1) firstly, mapping an input feature space x of a sample data set to a high-dimensional feature space phi (x), and performing regression analysis:
f(x)＝w·φ(x)+b (2)
wherein: phi (x) is a high-dimensional feature space; w is inertia weight, w is equal to Rn(ii) a b is a bias coefficient, and b belongs to R;
2) the optimization problem of the SVM is set as follows:
Figure BDA0003505884750000051
the constraint conditions are as follows:
Figure BDA0003505884750000052
wherein ξi，
Figure BDA0003505884750000053
Is a relaxation variable; ε is a loss distance metric, C represents a penalty parameter for the degree of penalty for samples that exceed ε;
3) solving the optimization problem to obtain an SVM regression model:
Figure BDA0003505884750000061
wherein，α，α*Is a lagrange multiplier; k (x, x)i)＝φ(x)·φ(xi) The kernel function has the function of avoiding the calculation on the high-dimensional feature space phi (x) and reducing the calculation complexity. The basic kernel functions are 3 types as follows:
polynomial kernel function:
Figure BDA0003505884750000062
gaussian kernel function: k (x, x)i)＝exp(-γ||xi-x||2)； (11)
Sigmoid kernel function:
Figure BDA0003505884750000063
where γ, φ and d are all kernel function parameters.
The selection of the kernel function is determined by the actual application condition, and the kernel function type with the best effect is generally selected after one-by-one trial.
Optimizing parameters of the cutting force prediction model by improving a PSO algorithm;
1) and evaluating the prediction accuracy of the cutting force prediction model by adopting a k-fold cross validation mode, and outputting an evaluation value. Specifically, the sample data set is divided into k parts, one part is reserved as verification data of the cutting force prediction model, and the other k-1 parts are used for training the cutting force prediction model; and repeating the cross validation k times, validating each sample data set once, and taking the average prediction result of the k times as an evaluation value of the prediction accuracy of the cutting force measurement model.
2) And optimizing the loss distance measurement epsilon, the punishment parameter C and the parameters of the kernel function of the cutting force prediction model trained by the parameter model by taking the root mean square error value of the evaluation value as a fitness index for improving the PSO algorithm optimization, thereby further improving the prediction accuracy of the cutting force prediction model.
3) Inertia weight w and learning factor c of cutting force prediction model by improving PSO algorithm1、c2Carrying out optimization adjustment; wherein the learning factor c1Is self-cognition coefficient, learning factorSub c2Is a social cognition coefficient. The inertia weight w controls the cognitive part of the particles in the PSO algorithm, and the size of the inertia weight w influences the global searching capability and the local depth searching capability of the particles; learning factor c1、c2: the self-cognition capability and the social cognition capability of the algorithm individual are determined, and the population is influenced to be close to the optimal solution area.
The adjustment of the inertia weight w adopts an adaptive adjustment method based on the inertia weight w, and is adjusted by utilizing a strategy that the inertia weight of each particle is not only decreased along with the increase of the iteration times, but also increased along with the increase of the distance from the global optimal point. That is, the inertia weight possessed by each generation of particles is different, is under variation, and varies as the position of the particles changes. When the particle target solutions are consistent, the inertia weight w is increased; when the particle target solutions do not coincide, the inertia weight w is made small.
w is adjusted as follows:
Figure BDA0003505884750000071
wherein f represents a real-time objective function value of the particle; f. ofavg，fminRespectively, the current average target value and the minimum target value of all the particles; wherein f isavgThe calculation formula is as follows:
Figure BDA0003505884750000072
the adjustment of the learning factor adopts a self-adaptive adjustment method of an acceleration factor based on time change, and the population is enabled to implement different search modes at different stages in the whole algorithm operation process through the real-time change of the acceleration factor. In the early stage of the algorithm, a larger self-cognition coefficient c is set1And a smaller "social cognition" coefficient c2So that the individual thought of the algorithm is active on the whole, which is beneficial to the algorithm to search a wider new area in the early stage, and to set a smaller value in the later stage of the operation of the algorithm "Self-cognition coefficient c1And a larger "social cognition" coefficient c2Therefore, the population particle individuals can be more quickly closed to the global optimal solution area, and the convergence precision of the PSO algorithm is facilitated.
Figure BDA0003505884750000073
Figure BDA0003505884750000074
Where T represents the maximum number of iterations, T represents the current number of iterations, c1iAnd c2iAn initial value representing an acceleration factor, set to 1.5; c. C1fAnd c2fA final limit value representing the acceleration factor, set to 4;
then, the following steps are performed:
1) initializing population parameters, and setting the population size sizepop to 30 and the maximum iteration number maxgen to 1000.
2) Calculating the fitness value of each particle, and updating the position and the speed of the particle according to the fitness function; the smaller the fitness value, the better the velocity and position of the particle.
3) Judging particle swarm parameter optimization termination conditions, judging whether the iteration times reach the maximum iteration times maxgen, and if so, ending the optimization algorithm; otherwise, training and optimizing are carried out again, and optimization parameters are output after the algorithm is finished.
And step four, performing parameter model training by using the optimized parameters to obtain an optimized cutting force prediction model. Specifically, taking a high-speed dry cutting test of 30CrMnSiNi2A for aviation as an example, equipment is taken as a processing center, the model is BV8H which is produced by Baoji machine tool group Limited, and the used software is MATLAB. An example of a historical process scale is 500, some examples of which are shown in FIG. 2.
It can be seen from fig. 2 and 3 that the cutting force prediction model using the improved PSO-SVM is closer to the true value than the SVM cutting force prediction model. Therefore, the method has an obvious effect on improving the prediction accuracy of the SVM cutting force prediction model, and has important significance on realizing accurate prediction of the cutting force, improving the workpiece processing quality, improving the service life of the cutter and building an intelligent workshop.
The method can be used for predicting the cutting force, optimizes the model and further improves the prediction performance of the cutting force prediction model. The improved PSO algorithm and the SVM algorithm are simultaneously introduced into the cutting force prediction, and the SVM model is adopted to mine the nonlinear regression relationship between the cutting force parameters and the related influence parameters, so that the cutting force prediction model is established. And the SVM parameters are optimized by improving the PSO algorithm, the search precision is improved, the convergence is accelerated, the accuracy of the program is improved, and the prediction performance of the cutting force prediction model is further improved. The cutting force prediction model provided by the invention integrates the improved PSO algorithm and the SVM algorithm, and has important significance for realizing accurate prediction of cutting force, improving the processing quality of workpieces and building an intelligent workshop.
Although embodiments of the present invention have been shown and described, it will be apparent to those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents, and thus the embodiments of the present invention are intended only as illustrative examples of the invention and are not to be construed as limiting the invention in any way.

Claims (8)

1. A cutting force prediction method based on an improved PSO algorithm assisted SVM algorithm is characterized in that: comprises the following steps of (a) carrying out,
1) constructing a cutting force prediction model based on an SVM algorithm, and determining input parameters and output parameters of the cutting force prediction model;
2) performing parameter model training on the cutting force prediction model;
3) optimizing parameters of the cutting force prediction model by improving a PSO algorithm;
4) and performing parameter model training by using the optimized parameters to obtain an optimized cutting force prediction model.
2. The cutting force prediction method based on the improved PSO algorithm-assisted SVM algorithm is characterized in that: the input parameters of the cutting force prediction model are processing parameters extracted from an original database, and the constraint conditions are material parameters, workpiece names, geometric characteristic parameters and equipment parameters of workpieces extracted from the original database; the output parameter is a predicted value of the cutting force.
3. The cutting force prediction method based on the improved PSO algorithm-assisted SVM algorithm as claimed in claim 2, wherein: the process parameters extracted from the original database are processed by adopting an abnormal point clearing and normalization method.
4. The cutting force prediction method based on the improved PSO algorithm-assisted SVM algorithm is characterized in that: setting the sample data set of the parameter model training as,
{(xi，yi)|i＝1，2，...，u} (1)
wherein x isiRepresenting the ith sample vector, and the data comprises cutting speed, feed speed, cutting depth, cutting width under preset processing conditions, yiRepresenting the predicted value of cutting force.
5. The cutting force prediction method based on the improved PSO algorithm-assisted SVM algorithm is characterized in that: the parametric model training comprises the following steps,
1) mapping an input feature space x of the sample data set to a high-dimensional feature space phi (x), and performing regression analysis:
f(x)＝w·φ(x)+b (2)
wherein: phi (x) is a high-dimensional feature space; w is the inertial weight, w is the Rn(ii) a b is a bias coefficient, and b belongs to R;
2) the optimization problem of the SVM is set as follows:
Figure FDA0003505884740000021
the constraint conditions are as follows:
Figure FDA0003505884740000022
wherein ξi，
Figure FDA0003505884740000023
Is a relaxation variable; ε is a loss distance metric, C represents a penalty parameter for the degree of penalty for samples that exceed ε;
3) solving the optimization problem to obtain an SVM regression model:
Figure FDA0003505884740000024
wherein, alpha＊Is a lagrange multiplier; k (x, x)i)＝φ(x)·φ(xi) Is a kernel function.
6. The cutting force prediction method based on the improved PSO algorithm-assisted SVM algorithm is characterized in that: the method for optimizing the parameters of the cutting force prediction model by improving the PSO algorithm comprises the following steps,
1) estimating the prediction precision of the cutting force prediction model by adopting a k-fold cross validation mode, and outputting an estimated value;
2) the root mean square error value of the evaluation value is used as a fitness index for improving PSO algorithm optimization, and loss distance measurement epsilon, punishment parameter C and kernel function parameters of a cutting force prediction model trained by a parameter model are optimized;
3) inertia weight w and learning factor c of cutting force prediction model by improving PSO algorithm1、c2Carrying out optimization adjustment; wherein the learning factor c1For self-cognition factor, learning factor c2Is a social cognition coefficient.
7. The cutting force prediction method based on the improved PSO algorithm-assisted SVM algorithm as claimed in claim 6, wherein: the adjustment of the inertia weight w adopts an adaptive adjustment method based on the inertia weight w, and adopts the following formula:
Figure FDA0003505884740000025
wherein f represents a real-time objective function value of the particle; f. ofavg，fminRespectively, the current average target value and the minimum target value of all the particles; wherein f isavgThe calculation formula is as follows:
Figure FDA0003505884740000031
8. the cutting force prediction method based on the improved PSO algorithm-assisted SVM algorithm as claimed in claim 6, wherein: the adjustment of the learning factor adopts a self-adaptive adjustment method of an acceleration factor based on time change; the following formula is adopted:
Figure FDA0003505884740000032
Figure FDA0003505884740000033
where T represents the maximum number of iterations, T represents the current number of iterations, c1iAnd c2iAn initial value representing an acceleration factor, set to 1.5; c. C1fAnd c2fA final limit value representing the acceleration factor, set to 4;
then, the following steps are carried out:
1) initializing population parameters, and setting the size and the maximum iteration times of a population;
2) calculating the fitness value of each particle, and updating the position and the speed of the particle according to the fitness function;
3) and judging the optimization termination condition of the particle swarm parameters, finishing the optimization algorithm when the iteration times reach the maximum iteration times, and outputting the optimization parameters.
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