CN110472321B - PSO-GPR (particle swarm optimization-GPR) based method for predicting processing energy consumption of all-metal semi-hard shell solid rocket cabin section - Google Patents

PSO-GPR (particle swarm optimization-GPR) based method for predicting processing energy consumption of all-metal semi-hard shell solid rocket cabin section Download PDF

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CN110472321B
CN110472321B CN201910703836.0A CN201910703836A CN110472321B CN 110472321 B CN110472321 B CN 110472321B CN 201910703836 A CN201910703836 A CN 201910703836A CN 110472321 B CN110472321 B CN 110472321B
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鄢威
王正
马峰
范威
龚青山
江志刚
张华�
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Wuhan University of Science and Engineering WUSE
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Abstract

The invention discloses a PSO-GPR-based method for predicting the processing energy consumption of a solid rocket cabin section of an all-metal semi-hard shell, which comprises the following steps: 1) Collecting processing data of a solid rocket cabin section; 2) Calculating the time volume of each process influencing energy consumption by using the original data; the time volume is the product of the volume of the material removed by the workpiece and the processing time of the workpiece; 3) Establishing a prediction model; 4) And (4) inputting the sum of six total time volumes of six working procedures and six total energy consumptions of six working procedures into the model, and predicting to obtain the total energy consumption during the processing of the whole cabin section. According to the invention, two influence factors of the workpiece removal volume and the workpiece processing time are combined as prediction input, so that the accuracy of the prediction model result is improved.

Description

PSO-GPR-based solid rocket cabin section processing energy consumption prediction method for all-metal semi-hard shell
Technical Field
The invention relates to a rocket cabin section processing technology, in particular to a PSO-GPR (particle swarm optimization-GPR) based method for predicting processing energy consumption of a solid rocket cabin section of an all-metal semi-hard shell.
Background
At present, methods such as a neural network and a support vector machine are mainly adopted in the research on machine tool machining energy consumption prediction, and compared with a GPR (Gaussian process regression model), the method has the advantages of easiness in implementation, good model adaptability, super-parameter self-adaptive acquisition and the like.
However, the methods such as the neural network and the support vector machine also have the defects of long convergence time, slow speed, easy trapping to the local minimum, incapability of ensuring to obtain a global optimum value, certain randomness of a result, sensitivity to missing data and the like. Therefore, the machine tool energy consumption prediction model is established by adopting Gaussian process regression, the complexity of the model can be reduced, and real-time energy consumption prediction is realized. The PSO algorithm has the advantages of easiness in implementation, simplicity, few parameters, capability of effectively solving the problem of global optimization and the like, and the GPR model is optimized by the PSO algorithm, so that the GPR model is higher in precision and more reliable.
Disclosure of Invention
The invention aims to solve the technical problem of providing a PSO-GPR-based method for predicting the processing energy consumption of all-metal semi-hard shell solid rocket cabin sections, aiming at the defects in the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows: a PSO-GPR-based method for predicting the processing energy consumption of a solid rocket cabin section of an all-metal semi-hard shell comprises the following steps:
1) Collecting processing data of a solid rocket cabin section, wherein the processing data comprises: mass m before workpiece machining, mass m' after workpiece machining, workpiece material density rho, workpiece machining time t and machine tool machining average power
Figure BDA0002151539270000021
2) Using raw data m, m', ρ, t and
Figure BDA0002151539270000022
calculating the time volume of each process affecting energy consumption, the processes comprising: turning, milling, drilling, blanking, heat treatment and forging; the time volume is the product of the volume of the material removed by the workpiece and the processing time of the workpiece;
3) Establishing a prediction model:
3.1 Initializing a Gaussian Process Regression (GPR) model to determine a kernel function;
y＝f(X)+ε (1)
hypothesis noise
Figure BDA0002151539270000023
Obtaining a prior distribution of y:
Figure BDA0002151539270000024
wherein K (X, X) = (K) ij ) Is a covariance matrix defined by n x n order symmetry, the matrix element k ij ＝k(x i ,x j ) For measuring variable x i And variable x j The correlation between them; I.C. A n Is an n-dimensional identity matrix; sigma n Is the variance of the noise;
and the observed value y and the predicted value f * Joint bayesian prior distribution of (a):
Figure BDA0002151539270000025
wherein, K (X, X) * )＝K(x * ,X) T ，K(X,x * ) Is a test point x * An n × 1 order covariance matrix with the input X of the training set; k (x) * ,x * ) Is a test point x * (ii) its own covariance;
covariance function, i.e. kernel function:
Figure BDA0002151539270000031
where, Σ = diag (1) 2 ) And 1 is a variance scale, wherein,
Figure BDA0002151539270000032
is the signal variance;
parameter set
Figure BDA0002151539270000033
Is a hyper-parameter;
for test set samples
Figure BDA0002151539270000034
The corresponding predicted values and the gaussian distributions obeyed by the predicted values can be obtained according to the bayesian principle as follows:
Figure BDA0002151539270000035
wherein the mean value
Figure BDA0002151539270000036
Sum variance cov (f) * ) Respectively as follows:
Figure BDA0002151539270000037
Figure BDA0002151539270000038
the formulas (4), (6) and (7) form a Gaussian process regression model;
3.2 Carrying out automatic optimal hyperparameter search on a GPR regression model in a sample training process by adopting a PSO algorithm to obtain optimal hyperparameters of the GPR regression model and determine the GPR regression model;
4) And inputting the sum of six total time volumes of the six procedures and six total energy consumptions of the six procedures into the model, and predicting to obtain the total energy consumption during the processing of the whole cabin.
According to the scheme, the specific steps of obtaining the optimal hyperparameter of the GPR regression model in the step 3.2) are as follows:
3.2.1 Initializing network parameters of PSO, including determining particle swarm scale, iteration times and particle random solution, wherein each particle vector represents a GPR model, and different models correspond to different GPR model parameters;
3.2.2 Randomly dividing the sample into a learning sample and a testing sample, and reading the learning sample, the testing sample and a GPR model hyper-parameter population into the PSO-GPR model; training the model, and predicting a prediction sample after obtaining prediction capability;
3.2.3 Calculate the fitness value f of each particle individual according to the PSO algorithm fitness function id The fitness function is:
Figure BDA0002151539270000041
in the formula: g (x) i ) The predicted value of the ith test sample during model training is obtained; y is i The number of the test samples is m;
3.2.4 Will step (d)3.2.3 Adapted value f) calculated in id With the best fit value f (p) of the particle in the history of previous iterations id ) Comparing, if the former is smaller than the latter, replacing f (p) of the previous round with a new adaptive value id ) Replacing the particles of the previous round with new particles;
3.2.5 The best fit value f (pid) of each particle is compared with the best fit values f (p) of all particles gd ) A comparison is made. If f (p) id )＜f(p gd ) Replacing the original global optimum adaptive value with the optimum adaptive value of the particle, and simultaneously saving the current state of the particle;
3.2.6 Finishing the program when the network meets the preset iteration step number and returning the particles with the minimum current adaptive value to find an optimal solution; and if not, performing a new iteration, updating the position and the speed of the particle by adopting an adjustment equation, namely generating a new particle, returning to the step 3.2.3) until the maximum iteration step is met, finishing the algorithm, returning to the optimal hyperparameter of the GPR model, and determining the GPR model.
According to the scheme, in the step 3.2.6), the adjustment equation is as follows:
Figure BDA0002151539270000051
in the formula (I), the compound is shown in the specification,
Figure BDA0002151539270000052
is the velocity of the ith particle in the d-dimension in the kth iteration,
Figure BDA0002151539270000053
is the position of the ith particle in the d-dimension in the kth iteration; p is a radical of id Is the individual historical optimum position, p, in the d-dimension of the ith particle gd The best position all particles experience; c. C 1 And c 2 For learning factors, in general c 1 ＝c 2 ＝1.8～2.0；r 1 、r 2 Is a uniformly distributed random number between (0, 1); w is the inertial weight, linearly decreasing according to:
Figure BDA0002151539270000054
in the formula: w is a max 、w min Maximum and minimum inertial weights, respectively; t is the current iteration number, t max Is the maximum number of iterations.
The invention has the following beneficial effects:
1. the energy consumption prediction model established from the view point of various working procedures can be suitable for various processing techniques, and the complex problem is greatly simplified;
2. the two influence factors of the workpiece removal volume and the workpiece processing time are combined to be used as sample data input, so that the sample data set is closer to the real condition, and the accuracy of the prediction model result is indirectly improved;
3. the energy consumption prediction model is established by adopting Gaussian process regression, and the particle swarm optimization model is used, so that the model avoids the defects that the neural network-genetic algorithm, the support vector machine-genetic algorithm and the like excessively depend on preset training samples, the artificial setting parameters are more and the like, is simpler and more accurate, and has higher reliability.
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The invention will be further described with reference to the following drawings and examples, in which:
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a flowchart of a method for determining parameters of a GPR model according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in FIG. 1, the PSO-GPR algorithm-based method for predicting the processing energy consumption of the all-metal semi-hard shell solid rocket cabin segment comprises the following steps:
1) Collecting processing data of a solid rocket cabin section, wherein the processing data comprises: mass m before workpiece machining, mass m' after workpiece machining, material density rho of workpiece, machining time t of workpiece and average power of machine tool machining
Figure BDA0002151539270000071
Collecting raw data
(1) Mass m before workpiece machining: measuring and reading out data m by using an electronic scale, and accurately measuring the data m to one decimal point;
(2) The processed mass m' of the workpiece is as follows: measuring and reading data m' by using an electronic scale, and accurately obtaining one bit after a decimal point;
(3) Workpiece material density ρ: looking up a material density table in aluminum alloy and processing handbook thereof to obtain rho;
(4) Workpiece machining time t: measuring the time t from the beginning to the end of the process by using a timer;
(5) Average power of machine tool
Figure BDA0002151539270000072
Measuring the total power P of the machine tool once every 15 seconds at the total power supply of the machine tool by using a power measuring instrument i Then by the formula of the mean value
Figure BDA0002151539270000073
Calculating the average power of machine tool
Figure BDA0002151539270000074
2) Using the raw data m, m', ρ, t and
Figure BDA0002151539270000075
calculating the time volume of each process influencing energy consumption, wherein the process comprises the following steps: turning, milling, drilling, blanking, heat treatment and forging; the time volume is the product of the volume of the material removed by the workpiece and the processing time of the workpiece;
using the raw data m, m', ρ, t and
Figure BDA0002151539270000076
and (3) calculating input and output:
Figure BDA0002151539270000081
wherein d =6 means six steps.
3) Establishing a prediction model:
3.1 Initializing a Gaussian Process Regression (GPR) model to determine a kernel function;
y＝f(X)+ε (1)
hypothesis noise
Figure BDA0002151539270000082
Obtaining a prior distribution of y:
Figure BDA0002151539270000083
wherein K (X, X) = (K) ij ) A covariance matrix defined positively for n x n order symmetry, the matrix element k ij ＝k(x i ,x j ) For measuring variable x i And variable x j The correlation between them; I.C. A n Is an n-dimensional identity matrix; sigma n Is the noise variance;
and the observed value y and the predicted value f * Joint bayesian prior distribution of (a):
Figure BDA0002151539270000091
wherein, K (X, X) * )＝K(x * ,X) T ，K(X,x * ) Is a test point x * An n × 1 order covariance matrix with the input X of the training set; k (x) * ,x * ) Is a test point x * Its own covariance.
Covariance function, i.e. kernel function:
Figure BDA0002151539270000092
wherein, Σ = diag (1) 2 ) And 1 is a variance scale, 1 is,
Figure BDA0002151539270000093
is the signal variance.
Parameter set
Figure BDA0002151539270000094
Is a hyper-parameter;
for test set samples
Figure BDA0002151539270000095
The corresponding predicted values and the following gaussian distributions can be obtained according to the bayesian principle as follows:
Figure BDA0002151539270000096
wherein the mean value
Figure BDA0002151539270000097
Sum variance cov (f) * ) Respectively as follows:
Figure BDA0002151539270000098
Figure BDA0002151539270000099
the formulas (4), (6) and (7) form a Gaussian process regression model;
3.2 Adopting a PSO algorithm to perform automatic optimal hyperparametric search on a GPR regression model in a sample training process to obtain optimal hyperparameters of the GPR regression model and determine the GPR regression model;
the specific implementation steps are as follows, as shown in fig. 2:
step 1, initializing network parameters of PSO, including determining particle swarm scale, iteration times, particle random solution particle initial velocity and particle initial position, wherein each particle vector represents a GPR model, and different models correspond to different GPR model parameters.
Step 2, randomly dividing a sample into a learning sample and a testing sample, and reading the learning sample, the testing sample and a GPR model hyper-parameter population into the PSO-GPR model; and training the model, and predicting the prediction sample after obtaining the prediction capability.
Step 3, calculating the fitness value f of each particle individual according to the PSO algorithm fitness function id The fitness function is:
Figure BDA0002151539270000101
in the formula: g (x) i ) The predicted value of the ith test sample during model training is obtained; y is i The sample value of the ith test sample is m, and the number of the test samples is m.
Step 4. The adaptive value f calculated in step 3 id With the best fit value f (p) of the particle in the history of previous iterations id ) Comparing, if the former is smaller than the latter, replacing f (p) of the previous round with a new adaptive value id ) The new particles are substituted for the particles of the previous round.
Step 5 the optimal fitness value f (p) of each particle id ) Optimum adaptation value f (p) to all particles gd ) A comparison is made. If f (p) id )＜f(p gd ) Then the optimal adaptive value of the particle is used to replace the original global optimal adaptive value, and the current state of the particle is saved.
Step 6, when the network meets the preset iteration step number, ending the program and returning the particles with the minimum current adaptive value to find the optimal solution; and if not, carrying out a new iteration, updating the position and the speed of the particle by adopting the formula (8), namely generating a new particle, returning to the step 3 until the maximum iteration step is met, finishing the algorithm, returning to the optimal hyperparameter of the GPR model, and determining the GPR model.
Assume that in a d-dimensional search space, the state attribute parameters of the ith particle during the kth iteration are set as follows:
particle position:
Figure BDA0002151539270000111
L d 、U d the upper and lower limits of the particle position.
Particle velocity:
Figure BDA0002151539270000112
v min,d 、v max,d the upper and lower limits of the particle velocity.
Individual optimal position:
Figure BDA0002151539270000113
global optimal position:
Figure BDA0002151539270000114
the particle speed and position are continuously updated along with the increase of the iteration number k, and the adjustment equation is as follows:
Figure BDA0002151539270000121
in the formula (I), the compound is shown in the specification,
Figure BDA0002151539270000122
is the velocity of the ith particle in the d-dimension in the kth iteration,
Figure BDA0002151539270000123
is the position of the ith particle in the d-dimension in the kth iteration; p is a radical of formula id Is the individual historical optimum position, p, in the d-dimension of the ith particle gd The best position experienced by all particles; c. C 1 And c 2 For learning factors, typically c 1 ＝c 2 ＝1.8～2.0；r 1 、r 2 Is a uniformly distributed random number between (0, 1); w is an inertial weight, and in order to avoid the problem that the algorithm is difficult to converge around the global optimal solution in the later period, the value of the inertial weight is reduced along with the iteration of the algorithm,the linear reduction is generally performed according to the following equation:
Figure BDA0002151539270000124
in the formula: w is a max 、w min Maximum and minimum inertial weights, respectively; t is the current iteration number, t max For the maximum number of iterations, generally take w max ＝0.9,w min ＝0.4。
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.

Claims (3)

1. A PSO-GPR-based method for predicting the processing energy consumption of a solid rocket cabin section of an all-metal semi-hard shell is characterized by comprising the following steps:
1) Collecting solid rocket cabin processing data, wherein the processing data comprises: mass m before workpiece machining, mass m' after workpiece machining, material density rho of workpiece, machining time t of workpiece and average power of machine tool machining
Figure FDA0002151539260000011
2) Using raw data m, m', ρ, t and
Figure FDA0002151539260000012
calculating the time volume of each process affecting energy consumption, the processes comprising: turning, milling, drilling, blanking, heat treatment and forging; the time volume is the product of the volume of the material removed by the workpiece and the processing time of the workpiece;
3) Establishing a prediction model:
3.1 Initializing a GPR Gaussian process regression model and determining a kernel function;
y＝f(X)+ε (1)
hypothesis noise
Figure FDA0002151539260000013
Obtaining a prior distribution of y:
Figure FDA0002151539260000014
wherein K (X, X) = (K) ij ) Is a covariance matrix defined by n x n order symmetry, the matrix element k ij ＝k(x i ,x j ) For measuring variable x i And variable x j The correlation between them; I.C. A n Is an n-dimensional identity matrix; sigma n Is the variance of the noise;
and observed value y and predicted value f * Joint bayesian prior distribution of (a):
Figure FDA0002151539260000015
wherein, K (X, X) * )＝K(x * ,X) T ，K(X,x * ) Is a test point x * An nx1 order covariance matrix with the input X of the training set; k (x) * ,x * ) Is a test point x * (ii) its own covariance;
covariance function, i.e. kernel function:
Figure FDA0002151539260000021
where, Σ = diag (1) 2 ) And 1 is a variance scale, 1 is,
Figure FDA0002151539260000022
is the signal variance;
parameter set
Figure FDA0002151539260000023
Is a hyper-parameter;
for test set samples
Figure FDA0002151539260000024
The corresponding predicted values and the following gaussian distributions can be obtained according to the bayesian principle as follows:
Figure FDA0002151539260000025
wherein the mean value
Figure FDA0002151539260000026
Sum variance cov (f) * ) Respectively as follows:
Figure FDA0002151539260000027
Figure FDA0002151539260000028
the formulas (4), (6) and (7) form a Gaussian process regression model;
3.2 Adopting a PSO algorithm to perform automatic optimal hyperparametric search on a GPR regression model in a sample training process to obtain optimal hyperparameters of the GPR regression model and determine the GPR regression model;
4) And inputting the sum of six total time volumes of six working procedures and six total energy consumptions of six working procedures into a prediction model to obtain the predicted total energy consumption during the processing of the whole cabin section.
2. The PSO-GPR based solid rocket cabin processing energy consumption prediction method for all-metal semi-hard shells based on the PSO-GPR, according to the claim 1, is characterized in that the specific steps of obtaining the optimal hyperparameter of the GPR regression model in the step 3.2) are as follows:
3.2.1 Initializing network parameters of PSO, including determining particle swarm scale, iteration times, particle initial speed and particle initial position, wherein each particle vector represents a GPR model, and different models correspond to different GPR model parameters;
3.2.2 Randomly dividing a sample into a learning sample and a testing sample, and reading the learning sample, the testing sample and a GPR model hyper-parameter population into the PSO-GPR model; training the model, and predicting a prediction sample after obtaining the prediction capability;
3.2.3 ) calculating the fitness value f of each particle individual according to the PSO algorithm fitness function id The fitness function is:
Figure FDA0002151539260000031
in the formula: g (x) i ) The predicted value of the ith test sample during model training is obtained; y is i The sample value of the ith test sample is, and m is the number of the test samples;
3.2.4 C) adapting the fitness value f calculated in step 3.2.3) id With the best fit value f (p) of the particle in the history of previous iterations id ) Comparing, if the former is smaller than the latter, replacing f (p) of the previous round with a new adaptive value id ) Replacing the particles of the previous round with new particles;
3.2.5 The optimum adaptation value f (p) of each particle id ) Optimum adaptation value f (p) to all particles gd ) A comparison is made. If f (p) id )＜f(p gd ) Replacing the original global optimum adaptive value with the optimum adaptive value of the particle, and simultaneously saving the current state of the particle;
3.2.6 When the network meets the preset iteration step number, ending the program and returning the particles with the minimum current adaptive value to find the optimal solution; and if not, performing a new iteration, updating the position and the speed of the particle by adopting an adjustment equation, namely generating a new particle, returning to the step 3.2.3) until the maximum iteration step is met, finishing the algorithm, returning to the optimal hyperparameter of the GPR model, and determining the GPR model.
3. The PSO-GPR based all-metal semi-hard shell solid rocket cabin processing energy consumption prediction method according to claim 1, characterized in that in step 3.2.6), the adjustment equation is as follows:
Figure FDA0002151539260000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002151539260000042
is the velocity of the ith particle in the d-dimension in the kth iteration,
Figure FDA0002151539260000043
is the position of the ith particle in the d-dimension in the kth iteration; p is a radical of id Is the individual historical optimum position, p, in the d-dimension of the ith particle gd The best position all particles experience; c. C 1 And c 2 For learning factors, in general c 1 ＝c 2 ＝1.8～2.0；r 1 、r 2 Is a uniformly distributed random number between (0, 1); w is the inertial weight, linearly decreasing according to:
Figure FDA0002151539260000044
in the formula: w is a max 、w min Maximum and minimum inertial weights, respectively; t is the current number of iterations, t max Is the maximum iteration number.
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