CN114861879A - Modeling method for optimizing thermal error of electric spindle of Elman neural network based on longicorn whisker algorithm - Google Patents

Abstract

The invention belongs to the field of high-speed electric spindle thermal error analysis, and relates to an electric spindle thermal error modeling method for optimizing an Elman neural network based on a longicorn algorithm, which comprises the following steps of: collecting data, and dividing a training set and a prediction set; optimizing the temperature measuring points by utilizing K-means clustering and combining the grey correlation degree, and determining the input and the output of the model; initializing an Elman neural network model parameter and a longicorn whisker algorithm parameter; optimizing the connection weight and the threshold of each network layer of the Elman neural network by using a longicorn algorithm; and predicting and verifying the thermal error of the high-speed motorized spindle by using the BAS-Elman neural network prediction model obtained by optimization. The method optimizes the weight and the threshold of the Elman neural network by using the longicorn algorithm, improves the generalization capability and the prediction precision of the Elman neural network, and has the advantages of simple structure, high prediction precision, short running time and the like.

Description

A method for optimizing the thermal error modeling of electric spindle based on Elman neural network based on beetle algorithm

technical field

The invention relates to an electric spindle thermal error modeling method based on the Elman neural network optimization based on the long beetle algorithm, and belongs to the field of high-speed electric spindle thermal error analysis.

Background technique

As a key component of high-speed CNC machine tools, the motorized spindle generates a lot of heat during operation, which leads to thermal expansion of spindle parts or tool deformation, which affects the accuracy of the motorized spindle and even the preload of the bearing, which in turn affects the machining accuracy and service life of the machine tool. Therefore, reducing the thermal error of the high-speed motorized spindle is the key to the development of high-speed precision machining technology. The thermal error compensation method does not need to change the mechanical properties (structure, materials, etc.) of the electric spindle. Based on the establishment of a thermal error prediction model, the size of the thermal error is predicted in advance, and the error is avoided by means of compensation. It is the most economical and effective method.

Elman neural network is a dynamic recurrent neural network with a local memory unit added to the structure of the BP network. By storing the internal state, it has the function of mapping dynamic features, so that the system has the ability to adapt to time-varying characteristics and better performance. The learning ability can be used to solve problems such as rapid optimization, fitting, regression prediction, etc. It is suitable for modeling the thermal error of the electric spindle.

Elman neural network also inevitably has shortcomings such as easy to fall into local extreme value, slow convergence speed and low efficiency. In the prior art, a population evolution algorithm is combined with a neural network to optimize the weights and thresholds of the Elman neural network, but both have disadvantages such as slow convergence speed and large amount of calculation. It has the advantages of simple principle, few parameters and small amount of calculation. Therefore, it is proposed to optimize the weights and thresholds of the Elman neural network by using the long beetle algorithm, and establish a thermal error model of the electric spindle based on the long beetle algorithm to optimize the Elman neural network.

SUMMARY OF THE INVENTION

In view of the deficiencies of the existing electric spindle thermal error prediction methods, the present invention proposes an electric spindle thermal error modeling method based on the Elman neural network optimized by the beetle algorithm, which is characterized by using the beetle algorithm to optimize the weight of the Elman neural network value and threshold, the beetle algorithm has the advantages of simple implementation, fast optimization speed and strong global search ability, which makes up for the randomness defects in the selection of connection weights and thresholds of Elman neural network itself, so that Elman neural network has better performance. The strong convergence improves the learning ability and generalization ability of Elman neural network, and has higher prediction accuracy than a single neural network model.

The technical scheme adopted by the present invention to solve its technical problems is:

The invention provides a method for optimizing the thermal error modeling of Elman neural network electric spindle based on the beetle algorithm, comprising the following steps:

Step 1: Collect the temperature and thermal error data at different speeds of the high-speed motorized spindle, and divide the collected data into a training set and a test set;

Step 2: Use K-means cluster analysis and gray correlation analysis to optimize the temperature measurement points, and construct the input and output of the model;

Step 3: Initialize Elman neural network model parameters and beetle algorithm parameters;

Step 4: Optimize the connection weights and thresholds of each network layer of the Elman neural network through iterative update using the beetle of the beetle algorithm, and establish a BAS-Elman neural network electric spindle thermal error prediction model.

Further, the first step is specifically: collecting temperature and thermal error data of several temperature measuring points at different rotational speeds of the high-speed electric spindle, and dividing the collected data into a training set and a test set according to the rotational speed;

Further, the step 2 is specifically:

(1) Using K-means cluster analysis, several temperature measurement points are divided into the required number of categories;

(2) Using the grey correlation analysis, the temperature measuring points with the greatest correlation with the thermal error are selected from each group as the temperature sensitive points;

(3) Use the screened temperature sensitive points as the input of the model, and the thermal error as the output.

Further, the third step is specifically: determining the number of _{Elman neural} network input layer, hidden layer, receiving layer and output layer _; The number of iterations T.

Before determining the positions X1 and Xr of the left and right whiskers of the beetle, the spatial position of the beetle needs to be initialized first.

Further, the number of the input layer and the output layer is determined according to the input and output parameters, and the number of the hidden layer and the successor layer is determined by the empirical formula h=(m+n) ^1/2 +a, and the trial and error method;

Among them, m is the number of input nodes, n is the number of output nodes, and a is a constant between 1 and 10.

Further, the step 4 is specifically:

a. Create a k-dimensional random vector of the direction of the beards of the beetle and normalize it. The formula is:

In the formula: rands() is a random function, and k represents the spatial dimension;

b. Create the spatial coordinates of the left and right whiskers of the beetle, the formula is:

In the formula: x _rt and x _lt represent the position coordinates of the right and left whiskers in the t-th iteration, respectively; x ^t represents the center of mass coordinates of the beetle in the t-th iteration; d ₀ represents the distance between the two whiskers. distance;

c. Determine the fitness function, using the root mean square error of the training data set as the fitness function, the formula is:

表示预测输出值，y_i表示实际值；In the formula: N is the number of training set samples;

represents the predicted output value, and y _i represents the actual value;

d. Judging the odor intensity of the left and right whiskers according to the fitness function, and determining the moving position of the beetle at the next moment, the formula is:

In the formula: δ ^t represents the step size factor in the t-th iteration, sign() is the sign function, f(x _rt ) is the fitness value of the right whisker of the beetle, f(x _lt ) is the adaptation of the left whisker of the beetle degree value;

The step size update formula of the beetle is:

δ ^t+1 = δ ^t* eta t=(0,1,2,…,n)

In the formula: eta takes the number close to 1 between [0,1];

Calculate the fitness function value corresponding to the current x ^t+1 position. If the fitness function value is better than Y _best , update X _best and Y _best , that is, replace x ^t with x ^t+1 and save it in X _best , x ^t+1 The fitness function value corresponding to the position replaces the fitness function value corresponding to the x ^t position, and is stored in Y _best ;

e. Judging whether the termination condition is met: if the current number of iterations reaches the maximum number of iterations or the training error of the network meets the accuracy requirements, the iteration is stopped and the optimization result is output, otherwise, the iterative optimization is continued;

f. Output the connection weights and thresholds of the optimized Elman network, and establish a BAS-Elman neural network electric spindle thermal error prediction model.

Among them, Y _best represents the best fitness value, and X _best represents the optimal initial weight and threshold of the neural network.

Further, it also includes step 5: using the BAS-Elman neural network electric spindle thermal error prediction model to predict and verify the thermal error of the high-speed electric spindle.

Further, the step 5 is specifically: input the training set and the test set into the BAS-Elman neural network motorized spindle thermal error prediction model, and accurately predict the thermal error of the high-speed motorized spindle; use the coefficient of determination (R ² ), the mean square Root error (RMSE) and mean absolute error (MAE) were evaluated:

Specifically, the calculation formula of the coefficient of determination of the verification part (R ² ) is:

The formula for calculating root mean square error (RMSE) is:

The formula for calculating mean absolute error (MAE) is:

表示预测输出值，y_i表示实际值。In the formula: N is the number of training set samples;

represents the predicted output value, and y _i represents the actual value.

The beneficial effects of the present invention are as follows: the present invention is a method for optimizing the thermal error modeling of the Elman neural network electric spindle based on the beard beard algorithm, and uses the K-means algorithm analysis combined with the gray correlation analysis to decouple the pre-input variables and reduce the dimension. The BAS-Elman thermal error prediction model obtained by combining the beetle algorithm and Elman neural network has the advantages of simple structure and high prediction accuracy.

Compared with the current thermal error prediction method, the advantages of the present invention are as follows:

1. The model structure is simple. The present invention reduces the model input through the K-means algorithm combined with the gray correlation degree, and solves the defects of the Elman neural network training time being too long and the network information redundancy being too large due to the huge training data;

2. High prediction accuracy. The present invention optimizes the connection weights and thresholds of the Elman neural network by using the long beetle algorithm (BAS), improves the learning ability and generalization ability of the Elman neural network, and significantly improves the accuracy of the thermal error prediction model;

3. Short running time. As an efficient intelligent optimization algorithm, the beetle algorithm only needs one search individual. Compared with other swarm intelligence algorithms, it has outstanding advantages such as simple parameter setting and small calculation amount. The BAS-Elman energy consumption prediction method proposed by the invention has the advantage of short running time while ensuring the prediction accuracy.

Description of drawings

Figure 1 shows the structure of Elman neural network.

Fig. 2 is the training flow chart of optimizing Elman neural network based on beetle search algorithm.

Fig. 3 is the BAS-Elman neural network fitness change curve of the present embodiment

Figure 4 shows the BAS-Elman and Elman prediction curves at 4000 r/min;

Figure 5 shows the BAS-Elman and Elman prediction curves at 8000 r/min.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention and the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments.

The present invention relates to a method for optimizing Elman neural network electric spindle thermal error modeling based on the beetle algorithm, which specifically includes the following steps:

Step 1: Collect temperature and thermal error data at different speeds of the high-speed motorized spindle, and divide the data into training sets and test sets at the same time;

The temperature and thermal error data of ten temperature measurement points of the high-speed motorized spindle at 4000r/min, 6000r/min and 8000r/min were obtained through experiments. The input vector, the axial thermal error is used as the output vector; the 6000r/min data set is used as the training set, and the 4000r/min and 8000r/min data sets are used as the test set;

Step 2, using K-means cluster analysis combined with gray correlation analysis to optimize the temperature measurement points, and construct the input and output of the model;

K-means clustering analysis was used to divide the ten temperature measurement points into the required number of categories; using grey correlation analysis, the temperature measurement with the greatest correlation with thermal error was selected from each group as the temperature sensitive point; The points are the input to the model and the thermal error is the output.

Step 3: Initialize Elman neural network model parameters and beetle algorithm parameters;

Figure 1 shows the structure of Elman neural network. Elman neural network is a typical recurrent neural network. Because of its internal feedforward and feedback structure, it has stronger learning ability than ordinary neural networks and is very suitable for constructing thermal error prediction. Model;

The input of the model is temperature-sensitive points, and four temperature-sensitive points are selected through optimization of temperature measurement points, that is, there are 4 neurons in the input layer; the output is thermal error, that is, there is 1 neuron in the output layer; The method determines that the number of hidden layers is 9, that is, the hidden layer and the successor layer each have 9 neurons; in this embodiment, the transfer function between the input layer and the hidden layer of the neural network is set as tansig, the implicit The transfer function between the layer and the output layer is purelin; in this embodiment, the initial step size of the long beard algorithm is set to 50, the initial distance between the left and right two whiskers is 5, and the number of iterations of the long beetle algorithm is 200;

The learning algorithm of Elman neural network is as follows:

y(k)=g(ω ₃ x(k))

x(k)=f(ω ₁ x _c (k)+ω ₂ (u(k-1)))

x _c (k)=x(k-1)

The learning indicator function of Elman neural network adopts the error sum of squares function, namely:

Among them: y is the m-dimensional output node vector; x is the n-dimensional intermediate layer node unit vector; u is the r-dimensional input vector; X _c is the n-dimensional feedback state vector; ω ₁ is the connection weight between the successor layer and the hidden layer; _ω2 is the connection weight from the input layer to the hidden layer; _ω3 is the connection weight from the hidden layer to the output layer; g() is the transfer function of the output neuron, and f() is the transfer function of the intermediate layer neuron.

Step 4. The beetle algorithm optimizes the connection weights and thresholds of each network layer of the Elman neural network through iterative updating, and establishes a BAS-Elman neural network thermal error prediction model; Figure 2 shows the optimization of the Elman neural network based on the beetle search algorithm. Training flowchart. Specific steps are as follows:

a. Create a k-dimensional random vector of the direction of the beards of the beetle and normalize it. The formula is:

In the formula: rands() is a random function, k represents the space dimension, which is also the number of parameters to be optimized, the search space dimension k=M*N+N+N*1+1+N*N, M is the number of neurons in the input layer number, N is the number of neurons in the hidden layer, and the number of neurons in the output layer is 1;

b. Create the spatial coordinates of the left and right whiskers of the beetle, the formula is:

In the formula: x _rt and x _lt represent the position coordinates of the right and left whiskers in the t-th iteration, respectively; x ^t represents the center of mass coordinates of the beetle in the t-th iteration; d ₀ represents the distance between the two whiskers. distance;

c. Determine the fitness function, using the root mean square error of the training data set as the fitness function, the formula is:

表示预测输出值，y_i表示实际值；In the formula: N is the number of training set samples;

represents the predicted output value, and y _i represents the actual value;

d. Judging the odor intensity of the left and right whiskers according to the fitness function, and determining the moving position of the beetle at the next moment, the formula is:

In the formula: δ ^t represents the step size factor in the t-th iteration, sign() is the sign function, f(x _rt ) is the fitness value of the right whisker of the beetle, f(x _lt ) is the adaptation of the left whisker of the beetle degree value;

The step size update formula of the beetle is:

δ ^t+1 = δ ^t* eta t=(0,1,2,…,n)

In the formula: eta takes the number between [0, 1] close to 1; in this embodiment, eta=0.995 is set.

Calculate the fitness function value corresponding to the current x ^t+1 position. If the fitness function value is better than Y _best , update X _best and Y _best , that is, replace x ^t with x ^t+1 and save it in X _best , x ^t+1 The fitness function value corresponding to the position replaces the fitness function value corresponding to the x ^t position, and is stored in Y _best ;

e. Judging whether the termination condition is met: if the current number of iterations reaches the maximum number of iterations or the training error of the network meets the accuracy requirements, the iteration is stopped and the optimization result is output, otherwise, the iterative optimization is continued;

f. Output the optimization results, that is, the connection weights and thresholds of the optimized Elman network.

Step 5: Use the BAS-Elman neural network prediction model obtained by optimization to predict and verify the thermal error of the high-speed motorized spindle. Using the optimized BAS-Elman neural network model, the training set and test set are input into the BAS-Elman model to accurately predict the thermal error of the high-speed motorized spindle; the coefficient of determination (R2), the root mean square error (RMSE) and the average The absolute error (MAE) was evaluated.

^R2 is an indicator of how well the model fits the sample. The larger the value of R ² , the higher the fitting degree of the model to the sample; the calculation formula of R ² is as follows:

RMSE represents the root mean squared error of the regression model. The RMSE calculation formula is as follows:

MAE represents the mean absolute error of the regression model. The formula for calculating MAE is as follows:

表示预测输出值，y_i表示实际值。In the formula: N is the number of training set samples;

represents the predicted output value, and y _i represents the actual value.

FIG. 3 is a change curve of the fitness of the BAS-Elman neural network according to the present embodiment.

It can be seen from Figure 3 that the BAS algorithm can find the optimal solution after 14 iterations, and the algorithm converges quickly. The BAS algorithm iterates for 200 generations to optimize the Elman neural network model to predict the thermal error in about 39 seconds, and the running time is short. This is because the beetle algorithm, as an efficient intelligent optimization algorithm, only needs one search individual. Compared with other swarm intelligence algorithms, it has outstanding advantages such as simple parameter setting and small computational complexity.

Figures 4 and 5 are the Elman and BAS-Elman prediction curves provided by the present application at 4000 r/min and 6000 r/min, respectively.

Table 1 provides the predicted performance parameters of Elman and BAS-Elman at different speeds for this application:

By comparing the prediction curves of the BAS-Elman and Elman models at different speeds, it can be seen from Table 1 that the BAS-Elman model has a higher degree of fitting compared with the Elman model, and the root mean square error and mean absolute error are both smaller, so BAS-Elman The Elman model can improve the prediction accuracy of the Elman model, and the BAS-Elman model has a high generalization ability.

To sum up, the present invention optimizes the initial connection weight and threshold of Elman neural network through BAS algorithm, and solves the shortcomings of Elman neural network that the convergence speed is slow and it is easy to fall into local extreme values. The invention has strong practicability and accurate prediction results, and provides a convenient method for the existing thermal error prediction.

Taking the above ideal embodiments according to the present invention as inspiration, and through the above description, relevant personnel can make various changes and modifications without departing from the technical idea of the present invention. The technical scope of the present invention is not limited to the contents in the specification, and the technical scope must be determined according to the scope of the claims.

Claims (6)

1. A modeling method for optimizing Elman neural network electric spindle thermal error based on a longicorn whisker algorithm is characterized by comprising the following steps:

the method comprises the following steps: collecting temperature and thermal error data of the high-speed motorized spindle at different rotating speeds, and dividing the collected data into a training set and a test set;

step two: optimizing the temperature measuring points by utilizing K-means cluster analysis and grey correlation degree analysis, and constructing the input and the output of a model;

step three: initializing an Elman neural network model parameter and a longicorn whisker algorithm parameter;

step four: and establishing a BAS-Elman neural network electric spindle thermal error prediction model by iteratively updating and optimizing the connection weight and the threshold of each network layer of the Elman neural network by using a longitussimus algorithm.

2. The method for optimizing Elman neural network motorized spindle thermal error modeling based on longitussimus algorithm according to claim 1, wherein the first step is specifically as follows: the method comprises the steps of collecting temperature and thermal error data of a plurality of temperature measuring points of the high-speed electric spindle at different rotating speeds, and dividing the collected data into a training set and a testing set according to the rotating speeds.

3. The method for optimizing the Elman neural network motorized spindle thermal error modeling based on the longicorn whisker algorithm as claimed in claim 2, wherein the second step is specifically as follows:

(1) dividing a plurality of temperature measuring points into required category numbers by utilizing K-means cluster analysis;

(2) screening out temperature measuring points with the maximum thermal error correlation degree from each group as temperature sensitive points by utilizing grey correlation degree analysis;

(3) and using the screened temperature sensitive points as the input of the model and the thermal error as the output.

4. The method for optimizing Elman neural network motorized spindle thermal error modeling based on longitussimus algorithm according to claim 1, wherein the third step is specifically as follows: determining the number of input layers, hidden layers, carrying layers and output layers of the Elman neural network; determining the position X of the left and right whiskers of a longicorn _l And X _r Initial step size delta of longicorn ₀ And the number of iterations T.

5. The method for optimizing Elman neural network motorized spindle thermal error modeling based on longitudian whiskers according to claim 4, wherein the number of the input layers and the number of the output layers are determined according to input and output parameters, and the number of the hidden layers and the number of the receiving layers are determined according to an empirical formula h ═ m + n ^1/2 + a, and trial and error determination;

wherein m is the number of input nodes, n is the number of output nodes, and a is a constant between 1 and 10.

6. The method for optimizing Elman neural network motorized spindle thermal error modeling based on longitussimus algorithm according to claim 1, wherein the fourth step is specifically as follows:

a. creating a k-dimensional random vector of the orientation of the longicorn stigma and carrying out normalization treatment, wherein the formula is as follows:

in the formula: rands () is a random function, k represents the space dimension;

b. creating a space coordinate of the left and right longicorn whiskers, wherein the formula is as follows:

in the formula: x is the number of _rt And x _lt Respectively representing the position coordinates of the right and left whiskers of the longicorn at the t iteration; x is the number of ^t Showing the dayThe barycentric coordinates of the cattle at the t-th iteration; d ₀ Representing the distance between two whiskers;

c. determining a fitness function, taking the root mean square error of the training data set as the fitness function, and taking the formula as follows:

in the formula: n is the number of samples in the training set;

representing the predicted output value, y _i Representing an actual value;

d. judging the left and right aftertaste odor intensity according to the fitness function, and determining the moving position of the longicorn at the next moment, wherein the formula is as follows:

in the formula: delta ^t Denotes the step-size factor at the t-th iteration, sign () being the sign function, f (x) _rt ) Is the fitness value of the right fibrous root of a longicorn, f (x) _lt ) The fitness value of the longicorn left palpus;

the step length updating formula of the longicorn is as follows:

δ ^t+1 ＝δ ^t *eta t＝(0,1,2,…,n)

in the formula: eta is a number close to 1 between [0,1 ];

calculate the current x ^t+1 The function value of the applicability degree corresponding to the position is better than Y _best Update X _best And Y _best I.e. x ^t+1 Substitution of x ^t Stored in X _best In, x ^t+1 Substituting x with position-corresponding fitness function value ^t The function value of the applicability degree corresponding to the position is stored in Y _best Performing the following steps;

e. judging whether a termination condition is met: if the current iteration times reach the maximum iteration times or the training error of the network reaches the precision requirement, stopping iteration and outputting an optimization result, otherwise, continuing iteration optimization;

f. and outputting the optimized connection weight and threshold of the Elman network, and establishing a BAS-Elman neural network electric spindle thermal error prediction model.

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