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

Modeling method for optimizing thermal error of electric spindle of Elman neural network based on longicorn whisker algorithm Download PDF

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CN114861879A
CN114861879A CN202210480474.5A CN202210480474A CN114861879A CN 114861879 A CN114861879 A CN 114861879A CN 202210480474 A CN202210480474 A CN 202210480474A CN 114861879 A CN114861879 A CN 114861879A
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李兆龙
朱波
祝文明
王庆海
王宝东
戴野
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Harbin University of Science and Technology
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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

Modeling method for optimizing thermal error of electric spindle of Elman neural network based on longicorn whisker algorithm
Technical Field
The invention relates to an electric spindle thermal error modeling method for optimizing an Elman neural network based on a longicorn whisker algorithm, and belongs to the field of high-speed electric spindle thermal error analysis.
Background
The electric spindle is used as a key part of a high-speed numerical control machine tool, a large amount of heat is generated in the operation process, so that the thermal expansion of spindle parts or the deformation of a cutter is caused, the precision of the electric spindle and even the pretightening force of a bearing are influenced, and further the machining precision and the service life of the machine tool are influenced. Therefore, reducing the thermal error of the high-speed motorized spindle is the key for the development of high-speed precision machining technology. The thermal error compensation method does not need to change the mechanical properties (structure, material and the like) of the electric spindle, and is the most economical and effective method for predicting the thermal error in advance and avoiding the error by a compensation means on the basis of establishing a thermal error prediction model.
The Elman neural network is a dynamic recurrent neural network with a local memory unit added on the basis of the structure of a BP network, and has the function of mapping dynamic characteristics by storing internal states, so that the system has the capability of adapting to time-varying characteristics and better learning capability, can be used for solving the problems of quick optimization, fitting, regression prediction and the like, and is suitable for modeling of the thermal error of the motorized spindle.
The Elman neural network also has the inevitable defects of easy falling into local extremum, low convergence speed, low efficiency and the like. In the prior art, a population evolution algorithm is combined with a neural network to optimize the weight and the threshold of the Elman neural network, but the population evolution algorithm has the defects of low convergence rate, large calculated amount and the like, and the longicorn algorithm is a single body searching algorithm and has the advantages of simple principle, few parameters, small calculated amount and the like. Therefore, the weight and the threshold of the Elman neural network are optimized by using the longicorn algorithm, and the electric spindle thermal error model for optimizing the Elman neural network based on the longicorn algorithm is established.
Disclosure of Invention
Aiming at the defects of the existing electric spindle thermal error prediction method, the invention provides an electric spindle thermal error modeling method for optimizing an Elman neural network based on a longicorn algorithm, which is characterized in that the weight and the threshold of the Elman neural network are optimized by using the longicorn algorithm, the longicorn algorithm has the advantages of simplicity in implementation, high optimization speed, strong global search capability and the like, and the randomness defect existing in the problems of selection of the self-connection weight and the threshold of the Elman neural network is overcome, so that the Elman neural network has strong convergence, the learning capability and the generalization capability of the Elman neural network are improved, and compared with a single neural network model, the electric spindle thermal error modeling method has higher prediction accuracy.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the invention provides a method for optimizing Elman neural network electric spindle thermal error modeling based on a longicorn whisker algorithm, which comprises 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.
Further, the first step specifically comprises: 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 speed; .
Further, the second step is specifically:
(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.
Further, the third step is specifically: 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.
Before the positions Xl and Xr of the left and right whiskers of the longicorn are determined, the spatial position of the longicorn needs to be initialized.
Furthermore, 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 by 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.
Further, the fourth step is specifically:
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:
Figure BDA0003627405610000031
in the formula: rands () is a random function, k represents the spatial dimension;
b. creating a space coordinate of the left and right longicorn whiskers, wherein the formula is as follows:
Figure BDA0003627405610000032
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 Representing the barycentric coordinates of the longicorn 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:
Figure BDA0003627405610000033
in the formula: n is the number of samples in the training set;
Figure BDA0003627405610000034
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:
Figure BDA0003627405610000035
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 beard of the 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 The preparation method comprises the following steps of (1) performing;
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.
Wherein, Y best Representing the best fitness value, X best Initial weight values and threshold values representing the neural network optimization.
Further, the method also comprises the following step five: and predicting and verifying the thermal error of the high-speed motorized spindle by using a BAS-Elman neural network motorized spindle thermal error prediction model.
Further, the fifth step is specifically: inputting the training set and the test set into a BAS-Elman neural network electric spindle thermal error prediction model to accurately predict the high-speed electric spindle thermal error; using a coefficient of determination (R) 2 ) Root Mean Square Error (RMSE) and Mean Absolute Error (MAE):
specifically, the verification section decides the coefficient (R) 2 ) The calculation formula is as follows:
Figure BDA0003627405610000041
the Root Mean Square Error (RMSE) is calculated as:
Figure BDA0003627405610000051
the Mean Absolute Error (MAE) is calculated as:
Figure BDA0003627405610000052
in the formula: n is the number of samples in the training set;
Figure BDA0003627405610000053
representing the predicted output value, y i Representing the actual value.
The invention has the beneficial effects that: the invention relates to a modeling method for optimizing Elman neural network electric spindle thermal error based on a longicorn whisker algorithm, wherein K-means algorithm analysis is combined with grey correlation analysis to perform decoupling dimension reduction on a pre-input variable, and the longicorn whisker algorithm and the Elman neural network are combined to obtain a BAS-Elman thermal error prediction model which has the advantages of simple structure, high prediction precision and the like.
Compared with the current thermal error prediction method, the method has the advantages that:
1. the model has simple structure. The invention reduces the model input by combining the K-means algorithm with the grey correlation degree, and well solves the defects of overlong Elman neural network training time, overlarge network information redundancy and the like caused by huge training data;
2. the prediction precision is high. According to the method, the connection weight and the threshold of the Elman neural network are optimized by using a Beauveria root algorithm (BAS), so that the learning capability and the generalization capability of the Elman neural network are improved, and the accuracy of a thermal error prediction model is obviously improved;
3. the running time is short. The longicorn algorithm is used as an efficient intelligent optimization algorithm, only one search individual is needed, and compared with other swarm intelligent algorithms, the longicorn algorithm has the outstanding advantages of simple parameter setting, small operand and the like. The BAS-Elman energy consumption prediction method provided by the invention has the advantage of short operation time while ensuring the prediction precision.
Drawings
FIG. 1 is a diagram of the Elman neural network architecture.
Fig. 2 is a training flow chart for optimizing the Elman neural network based on the longicorn whisker search algorithm.
FIG. 3 is a BAS-Elman neural network fitness curve of the present embodiment
FIG. 4 is a BAS-Elman and Elman prediction curve at 4000 r/min;
FIG. 5 is a BAS-Elman and Elman prediction curve at 8000 r/min.
Detailed Description
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 of the specification, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
The invention relates to a method for optimizing Elman neural network electric spindle thermal error modeling based on a longicorn whisker algorithm, which specifically comprises the following steps:
collecting temperature and thermal error data of a high-speed electric spindle at different rotating speeds, and dividing the data into a training set and a test set;
temperature and thermal error data of ten temperature measuring points of the high-speed electric spindle at 4000r/min, 6000r/min and 8000r/min are obtained through experiments, firstly, the temperature measuring points are optimized, appropriate temperature sensitive points are screened out to be used as input vectors of a model, and axial thermal errors are used as output vectors; taking a 6000r/min data set as a training set, and taking 4000r/min and 8000r/min data sets as a test set;
optimizing the temperature measuring points by utilizing K-means cluster analysis and combining grey correlation analysis, and constructing input and output of a model;
dividing ten temperature measuring points into required categories by adopting K-means cluster analysis; screening out the temperature measurement with the maximum correlation degree with the thermal error from each group as a temperature sensitive point by utilizing grey correlation degree analysis; the screened temperature sensitive points are input of the model, and the thermal errors are output.
Initializing Elman neural network model parameters and longicorn whisker algorithm parameters;
FIG. 1 is a structural diagram of an Elman neural network, which is a typical recurrent neural network, and has a feed-forward and feedback structure inside, so that the Elman neural network has stronger learning ability than a common neural network, and is very suitable for constructing a thermal error prediction model;
the input of the model is temperature sensitive points, four temperature sensitive points are selected through temperature measuring point optimization, namely 4 neurons are arranged on an input layer; the output is thermal error, namely the output layer has 1 neuron; determining the number of the hidden layers to be 9 through an empirical formula and a trial and error method, namely, 9 neurons are respectively arranged in the hidden layers and the carrying layers; in this embodiment, a transfer function between an input layer and a hidden layer of a neural network is set to tan sig, and a transfer function between the hidden layer and an output layer is purelin; in this embodiment, the initial step length of the longicorn whisker algorithm is set to be 50, the initial distance between the left and right whiskers is 5, and the iteration frequency of the longicorn whisker algorithm is 200;
the learning algorithm of the 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 index function of the Elman neural network adopts a sum of squared errors function, namely:
Figure BDA0003627405610000071
wherein: y is an m-dimensional output node vector; x is an n-dimensional intermediate layer node unit vector; u is an r-dimensional input vector; x c Is an n-dimensional feedback state vector; omega 1 The weight value of the connection from the bearer layer to the hidden layer; omega 2 Connecting the input layer to the hidden layer by a weight value; omega 3 Connecting the 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 middle layer neuron.
Step four, the longicorn whisker algorithm establishes a BAS-Elman neural network thermal error prediction model by iteratively updating and optimizing the connection weight and the threshold of each network layer of the Elman neural network; fig. 2 is a training flow chart for optimizing the Elman neural network based on the longicorn whisker search algorithm. The method comprises the following specific steps:
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:
Figure BDA0003627405610000072
in the formula: rands () is a random function, k represents a space dimension and is also the number of parameters to be optimized, k is a search space dimension k, M is N + N is 1+1+ N, M is the number of neurons in an input layer, N is the number of neurons in a hidden layer, and the number of neurons in an output layer is 1;
b. creating a space coordinate of the left and right longicorn whiskers, wherein the formula is as follows:
Figure BDA0003627405610000081
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 Representing the barycentric coordinates of the longicorn 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:
Figure BDA0003627405610000082
in the formula: n is the number of samples in the training set;
Figure BDA0003627405610000084
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:
Figure BDA0003627405610000083
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 beard of the 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 ]; in this embodiment, eta is set to 0.995.
Calculate the current x t+1 Position pairThe function value of the applicable degree 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 an optimization result, namely the optimized connection weight and threshold of the Elman network.
And fifthly, predicting and verifying the thermal error of the high-speed motorized spindle by using the BAS-Elman neural network prediction model obtained through optimization. Inputting the training set and the testing set into the BAS-Elman model by utilizing the BAS-Elman neural network model obtained by optimization, and accurately predicting the thermal error of the high-speed motorized spindle; evaluation was performed using a coefficient of determination (R2), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE).
R 2 Is an indicator of how well the model fits to the sample. R 2 A larger value of (d) indicates a higher degree of fit of the model to the sample; r 2 The calculation formula is as follows:
Figure BDA0003627405610000091
RMSE represents the root mean square error of the regression model. The RMSE calculation formula is as follows:
Figure BDA0003627405610000092
MAE represents the mean absolute error of the regression model. The MAE is calculated as follows:
Figure BDA0003627405610000093
in the formula: n is the number of samples in the training set;
Figure BDA0003627405610000094
representing the predicted output value, y i Representing the actual value.
FIG. 3 is a BAS-Elman neural network fitness curve of the present embodiment.
From fig. 3, the BAS algorithm finds the optimal solution through 14 iterations, and the algorithm converges quickly. The BAS algorithm iterates 200 generations of optimized Elman neural network models, only about 39 seconds are needed for predicting the thermal error, and the running time is short. The longicorn algorithm is used as an efficient intelligent optimization algorithm, only one search individual is needed, and compared with other swarm intelligent algorithms, the longicorn algorithm has the outstanding advantages of simple parameter setting, small operand and the like.
FIGS. 4 and 5 are graphs of Elman and BAS-Elman predictions provided herein at 4000r/min and 6000r/min, respectively.
Table 1 provides predicted performance parameters for Elman and BAS-Elman at different speeds as provided herein:
Figure BDA0003627405610000101
by comparing the prediction graphs of the BAS-Elman model and the Elman model at different rotating speeds, analysis table 1 shows that the BAS-Elman model has higher fitting degree with the Elman model, the root mean square error and the average absolute error are smaller, so that the BAS-Elman model can improve the prediction accuracy of the Elman model, and has higher generalization capability.
In conclusion, the invention optimizes the initial connection weight and the threshold of the Elman neural network through the BAS algorithm, and solves the defects that the Elman neural network has low convergence speed and is easy to fall into local extremum. The method has the advantages of strong practicability and accurate prediction result, and provides a simple method for the conventional thermal error prediction.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and 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:
Figure FDA0003627405600000021
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:
Figure FDA0003627405600000022
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:
Figure FDA0003627405600000023
in the formula: n is the number of samples in the training set;
Figure FDA0003627405600000024
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:
Figure FDA0003627405600000025
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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