A prediction method for predicting rolling force by a neural network based on the K-means clustering algorithm

Abstract

The present invention discloses a prediction method for predicting rolling force by a neural network based on the K-means clustering algorithm. It belongs to the field of computer technology, and the specific steps are as follows: determine the input and output layers of the RBF neural network; estimate the number of nodes in the input, output layers and hidden nodes of the non-linear multi-layer forward RBF neural network; construct the hidden layer space; determine appropriate data centers, and determine the expansion constants of the hidden nodes according to the distances between the centers; train the artificial neural network, learn and correct the errors, and complete the construction of the artificial neural network; and use this artificial neural network for presetting the rolling force for production use. Compared with the traditional non-linear multi-layer forward neural network, the present invention has a faster operation speed, the model is easy to maintain, and at the same time, it avoids the disadvantages of setting inappropriate numbers of hidden layers and hidden layer nodes of the neural network according to the personal experience of the designer, and being unable to locate the accurate data centers of each basis function, etc., and has a higher accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of computer technology and relates to a method for predicting the rolling force of a bar rolling mill by a neural network based on the K-means clustering algorithm. Background Art

[0002] The rolling pressure is an important process parameter in the rolling process and plays an important role in formulating the reduction schedule, analyzing the process load, and checking the equipment strength. In the process of bar production, since the deformation process of the rolled piece in the pass belongs to three-dimensional non-uniform deformation, its deformation law is difficult to master, and the theoretical research on the rolling pressure model is not deep. In actual work, the prediction of the rolling pressure often relies on traditional empirical formulas. In order to obtain the force and energy parameters in the rolling process, it is first necessary to use certain detection methods and data acquisition software to collect the real-time data at the production site. The research on the force and energy parameter model in bar rolling is still not very mature theoretically. In actual production, the calculation of the rolling force of the bar rolling mill generally uses empirical formulas for calculation. Due to the change of the production situation, the calculation results often have large errors. Therefore, it is necessary to study the rolling force model of the bar rolling mill based on a new neural network algorithm on the basis of the existing rolling theory to predict the rolling force; the above defects are what the researchers in this field hope to overcome. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to provide a method for predicting the rolling force of a bar rolling mill by a neural network based on the K-means clustering algorithm. This method is theoretically faster in operation speed than the traditional non-linear multi-layer forward neural network, the model is easy to maintain, and at the same time, it avoids the disadvantages of setting inappropriate hidden layer numbers and hidden layer node numbers of the neural network according to the designer's personal experience, and not being able to locate the data centers of accurate basis functions, etc., and has higher accuracy.

[0004] Technical Solution: The prediction method for predicting the rolling force by a neural network based on the K-means clustering algorithm described in the present invention has the following specific operation steps:

[0005] (1.1) Analyze and calculate the SIMS formula of the hot rolling force to obtain multiple sets of comprehensive data of the hot continuous rolling force of the bar rolling mill. Among them, each set of comprehensive data of the hot continuous rolling force of the bar rolling mill obtained after analysis and processing includes n most relevant influencing factors of the hot continuous rolling force, and there are m results of the hot continuous rolling force to be predicted. Take the influencing factors of the hot continuous rolling force of the bar rolling mill as the input data of the non-linear multi-layer forward RBF neural network, and take the results of the hot continuous rolling force of the bar rolling mill to be predicted as the output data of the multi-non-linear multi-layer forward RBF neural network, so as to determine the input and output layers of the RBF neural network;

[0006] (1.2) Estimate the number of nodes in the input layer, output layer, and hidden nodes of the non-linear multi-layer forward RBF neural network;

[0007] (1.3) Establish a radial basis function based on function approximation and interpolation, use it as the "basis" of the hidden unit, and then use it as the activation function of the hidden node to form the hidden layer space;

[0008] (1.4) Use the K-means self-organizing clustering algorithm to determine the appropriate data center for the radial basis function of the hidden layer nodes, and determine the expansion constant of the hidden nodes according to the distance between the centers;

[0009] (1.5) Use a supervised learning algorithm to train the output layer weights. From the relationship composed of the interpolation matrix, coefficient vector, and expected output vector, obtain the output weight matrix W through matrix transformation, where ω jk (j = 1, 2,…,M; k = 1,2…l) is the synaptic weight between the j-th node of the hidden layer and the k-th node of the output layer, T = (T 1 , T 2 ,…, T l ) T is the output layer threshold vector. The output layer neurons use a linear activation function to train the artificial neural network, learn and correct the error, and use an adaptive momentum gradient descent supervised learning algorithm to complete the construction of the artificial neural network. After that, the artificial neural network can be used for rolling force presetting for production.

[0010] Further, in the step (1.1), the specific process of analyzing the SIMS formula is as follows:

[0011] First, decompose the SIMS formula of the hot rolling force model for the bar mill.

[0012] Among them, the SIMS formula is based on the Orovan internal force balance theory in the deformation zone and assumes that there is no relative sliding on the contact surface between the roll and the workpiece during hot rolling, which is suitable for calculating the hot rolling pressure. The rolling pressure model of the SIMS formula adopts the following basic form:

[0013] P = Bl c KQ p (1)

[0014] In formula (1): B represents the width of the workpiece; l c represents the horizontal projection length of the contact arc after considering the reduction; K represents the deformation resistance; Q p represents the stress state coefficient;

[0015] Among them, l c is expressed as:

[0016]

[0017] In Equation (2): R c represents the working radius of the roll; Δh represents the reduction;

[0018] Substitute Equation (2) into Equation (1) to solve for the rolling force P; therefore, an iterative method is used to calculate the rolling force during rolling force calculation; now, the rolling force formula is processed by introducing the roll radius R to avoid iteration during calculation; the solution process is as follows:

[0019]

[0020] Let μ = KQ p , and after rearranging Equation (3), we get:

[0021] P 2 - 0.22μ 2 BRP - μ 2 B 2 RΔh = 0 (4)

[0022] Solving from Equation (4):

[0023]

[0024] From Equation (5), μ, R, B, and Δh can be obtained, and then the rolling force P can be calculated;

[0025] Since the stress state and its distribution in the deformation zone during rolling depend on the geometry of the deformation zone, the stress state coefficient derived from the SIMS formula based on the Orowan internal force balance formula in the deformation zone is complex to calculate and cannot be applied to computer on-line control:

[0026]

[0027] In Equation (6), ε represents the reduction ratio; h represents the height of the rolled piece after rolling; h y represents the instantaneous average height of the rolled piece in the deformation zone.

[0028] Furthermore, in the step (1.1), the most relevant influencing factors of the bar hot continuous rolling force obtained by analyzing the SIMS formula specifically include: rolling temperature, rolling speed, deformation resistance, roll radius, spread coefficient, and inlet height; it is determined that the number of input nodes is 6, then the above 6 influencing factors are used as the inputs of the RBF neural network, and the rolling force is used as the output of the RBF neural network.

[0029] Further, in the step (1.2), the specific process of estimating the number of nodes in the input and output layers and the hidden nodes of the non-linear multi-layer forward RBF neural network is as follows: Set the number of nodes in the input layer as N, set the number of hidden nodes of the non-linear multi-layer forward RBF neural network as M. Since it is a single-output RBF neural network, its output node is set to 1. Among them, the training samples of the regularization network and the "basis function" are in one-to-one correspondence; when the number of samples P is very large, the computational amount of the network will be astonishingly large. In addition, when P is very large, the weight matrix is also very large, and it is easy to generate ill-conditioned problems when solving the weights of the network; Select to establish a generalized RBF network to reduce the number of hidden nodes, that is, N < M < P.

[0030] Further, in the step (1.3), by establishing a radial basis function based on function approximation and interpolation as the "basis" of the hidden unit, and then using it as the activation function of the hidden node, the specific process of constructing the hidden layer space is as follows:

[0031] First, determine the mapping from the N-dimensional input space to the one-dimensional rolling force output space in the non-linear multi-layer forward RBF neural network; Assume that there are P input vectors X in the N-dimensional space p , where p = 1, 2,..., P, and the corresponding target value in the output space is d p , p = 1, 2,..., P. The P pairs of input and output samples constitute a training sample set; A non-linear mapping function F(X) that satisfies the interpolation condition, and make it satisfy the following interpolation condition:

[0032] F(X p ) = d p , p = 1, 2,..., P (7)

[0033] In formula (7), the function F represents an interpolation surface; The so-called strict interpolation or exact interpolation is a complete interpolation, that is, the interpolation surface must pass through all training data points;

[0034] In addition, the method of using the radial basis function technology to solve the interpolation problem is: Select P basis functions, each basis function corresponds to a training data, and the forms of each basis function are as follows:

[0035]

[0036] In formula (8), the radial basis function is a non-linear function, and the training data point X p is the center; The basis function takes the distance between the point X in the input space and the center X p as the independent variable of the function; In the non-linear multi-layer forward RBF neural network, its distance is radially isotropic.

[0037] In the step (1.3), when establishing the radial basis function based on function approximation and interpolation, the interpolation function for realizing the radial basis function is defined as a linear combination of basis functions:

[0038]

[0039] Substitute Equation (7) into Equation (9) to obtain a system of linear equations with P equations regarding the unknown coefficients ω p , where p = 1, 2…, P:

[0040]

[0041] Let Then the above system of equations can be rewritten as:

[0042]

[0043] Let Φ represent a PxP interpolation matrix with elements . Let W and d represent the coefficient vector and the desired output vector respectively. Rewrite the above equation in vector form as ΦW = d, and through transformation, the coefficient vector W can be solved, that is:

[0044] W = Φ -1 d (12)

[0045] In Equation (12), the interpolation matrix Φ is invertible because X 1 , X 2 , X 3 , …, X p are all different, so the PxP interpolation matrix is invertible.

[0046] Furthermore, in the step (1.4), the operation steps of using the K-means self-organizing clustering algorithm include two stages:

[0047] First, the self-organizing clustering method determines appropriate data centers for the radial basis functions of the hidden layer nodes, and determines the expansion constants of the hidden nodes according to the distances between the centers;

[0048] Second, it is the supervised learning stage, where the weights of the output layer are trained using a supervised learning algorithm, and the adaptive momentum gradient descent supervised learning algorithm is used for training;

[0049] The specific operation steps are as follows:

[0050] (1.4.1) Before determining the positions of the data centers through clustering, it is necessary to first estimate the number M of centers; this is determined through experiments. Since the data centers obtained by clustering are not directly based on the calculated rolling force sample data X p itself, c(k) is used to represent the center at the kth iteration;

[0051] (1.4.2), Initialize and select M distinct vectors as the initial cluster centers: c 1 (0), c 2 (0), …, c m (0). When selecting, a method of assigning small random numbers to each cluster center vector is adopted;

[0052] (1.4.3), Calculate the Euclidean distance between each sample point in the input space and the cluster center points:

[0053] ||X p -c j (k)|| for p = 1, 2, …, P; j = 1, 2, …, M; (13)

[0054] (1.4.4), Similarity matching. Let j * represent the subscript of the winning hidden node in the competition. For each input sample X of the rolling force influencing factors p Determine its classification j according to its minimum Euclidean distance from the cluster center * (X p ), that is, when there is the following equation:

[0055] j * (X p ) = min j ||X p -c j (k)|| for p = 1, 2, …, P; (14)

[0056] Assign X p to the j * th class, thus dividing all samples into M subsets: u 1 (k), u 2 (k), u 3 (k), …, u m (k). Each subset forms a clustering domain with the cluster center as the typical representative;

[0057] (1.4.5), Update the cluster centers of each class and adjust them using the competitive learning rule, that is:

[0058]

[0059] In formula (15), η represents the learning rate, and 0 < η < 1;

[0060] (1.4.6), Increment the value of k by 1 and go to step (1.4.2); Repeat the above process until the change in c j is less than the required value; After determining each cluster center, the expansion constant of the corresponding radial basis function can be determined according to the distance between the centers;

[0061] Let dj = min i ||c j -c i ||, then the extended constant is obtained as:

[0062] δ j = λd j (16)

[0063] In formula (16), λ represents the overlap coefficient;

[0064] (1.4.7) After obtaining the centers and extended constants of each radial basis function by using the K-means clustering algorithm, the weights of the output layer are obtained through supervised learning in the hybrid learning, and the LMS algorithm is used to directly calculate with the pseudoinverse method; the established nonlinear multi-layer forward RBF neural network model is an RBF neural network with a single output of rolling force. When the input is X p the output of the j-th hidden node is

[0065] Then the output matrix of the hidden layer is: If the undetermined output weights of the RBF network are W = [w 1 , w 2 , …, w M , then the network output vector is:

[0066] F(X) = ΦW (17)

[0067] Let the network output vector be equal to the teacher signal d, then Φ in formula (17) is replaced by its pseudoinverse Φ + to obtain:

[0068] W = Φ + d (18)

[0069] The pseudoinverse matrix Φ + in formula (18) is:

[0070] Φ + = (Φ T Φ) -1 Φ T (19)

[0071] Furthermore, in the step (1.5), by training the artificial neural network and learning to correct the error, the specific process of constructing the artificial neural network is as follows: for the supervised learning algorithm of the data center, small random numbers are assigned to each weight vector of the output layer and normalized. The centers, extended constants, and output layer weights of the hidden node RBF functions are all trained using the supervised learning algorithm, and the adaptive momentum gradient descent learning algorithm is used as the supervised learning algorithm for this RBF network; its objective function is defined as:

[0072]

[0073] In Equation (20), P represents the number of training samples; e i represents the error signal when the i-th sample is input, and is defined as:

[0074]

[0075] The threshold is ignored in the output function of Equation (21);

[0076] To minimize the objective function, the correction amount of each parameter should be proportional to its negative gradient. The specific algorithm is as follows:

[0077]

[0078]

[0079]

[0080] The above objective function is the sum of the errors caused by all training samples. The derived parameter correction formula is a batch adjustment, that is, it is adjusted once after all samples are input once.

[0081] Beneficial effects: Compared with the prior art, the present invention provides a method for predicting rolling force based on a non-linear multi-layer forward RBF neural network using the K-means clustering algorithm. Theoretically, it has a faster operation speed than the traditional non-linear multi-layer forward neural network, the model is easy to maintain, and at the same time, it avoids the disadvantages of setting inappropriate hidden layers and the number of hidden layer nodes of the neural network according to the designer's personal experience, and not being able to locate the data centers of accurate basis functions, etc., and has a higher accuracy. Brief Description of the Drawings

[0082] Figure 1 is a schematic diagram of the operation process of the present invention;

[0083] Figure 2 is a schematic diagram of the K-means self-organizing clustering algorithm process in the present invention;

[0084] Figure 3 is a schematic diagram of the structure of the non-linear multi-layer forward RBF neural network established in this example of the present invention;

[0085] Figure 4 is a schematic diagram of the network performance of the method for predicting hot strip rolling force based on the data of factors affecting hot strip rolling force prediction by establishing a non-linear multi-layer forward RBF neural network prediction model in this example of the present invention. Detailed Embodiments

[0086] A prediction method for predicting rolling force of a neural network based on the K-means clustering algorithm according to the present invention includes the following steps: According to the decomposition of the SIMS formula of the hot rolling force model of the bar mill, especially for the important deformation resistance K and stress state coefficient Q in the formula p analysis, simplify the steps of calculating the rolling force, obtain the key influencing factor data that determines the value of the hot continuous rolling force, and determine the input of the neural network; input the obtained influencing factor data into the non-linear multi-layer forward RBF neural network model; the non-linear multi-layer forward RBF neural network model based on the K-means clustering algorithm outputs the predicted value of the hot continuous rolling force according to the input influencing factor data;

[0087] Furthermore, before inputting the obtained influencing factor data into the non-linear multi-layer forward RBF neural network model based on the K-means clustering algorithm, the method further includes: using the comprehensive data of the hot continuous rolling force of the bar mill on multiple production lines calculated by multiple groups, the K-means clustering algorithm, the LMS algorithm for obtaining the weight value of the output layer through supervised learning, and an adaptive momentum gradient descent learning algorithm suitable for a single-output RBF network to establish a non-linear multi-layer forward RBF neural network model based on the K-means clustering algorithm.

[0088] Specifically; the specific operation steps are as follows:

[0089] (1.1), obtain the comprehensive data of the hot continuous rolling force of the bar mill through analyzing and calculating the SIMS formula of the hot rolling force. Among them, each group of comprehensive data of the hot continuous rolling force of the bar mill obtained through analysis and processing includes n most relevant influencing factors of the hot continuous rolling force, and there are m results of the hot continuous rolling force to be predicted. For the universality of the model, first, both m and n are integers greater than 2. Among them, the number of n is as small as possible on the premise of ensuring the relevance of the rolling force model, making the model simple and improving the learning rate of the neural network,

[0090] Take the influencing factors of the hot continuous rolling force of the bar mill as the input data of the non-linear multi-layer forward RBF neural network, and take the results of the hot continuous rolling force of the bar mill to be predicted as the output data of the multi-non-linear multi-layer forward RBF neural network, so as to determine the input and output layers of the RBF neural network;

[0091] Specifically,

[0092] The specific process of analyzing the SIMS formula is:

[0093] First, decompose the SIMS formula of the hot rolling force model for bar mills. The SIMS formula is based on the Orovan internal force balance theory in the deformation zone and assumes that there is no relative sliding on the contact surface between the roll and the workpiece during hot rolling. It is suitable for calculating the hot rolling pressure. The rolling pressure model of the SIMS formula adopts the following basic form:

[0094] P = Bl c KQ p (1)

[0095] In formula (1): B represents the width of the workpiece; l c represents the horizontal projection length of the contact arc after considering the reduction; K represents the deformation resistance; Q p represents the stress state coefficient;

[0096] Among them, l c is expressed as:

[0097]

[0098] In formula (2): R c represents the working radius of the roll; Δh represents the reduction;

[0099] Substitute formula (2) into formula (1) to solve for the rolling pressure P; therefore, an iterative method is used to calculate the rolling pressure during rolling force calculation; now, process the rolling force formula, introduce the roll radius R, and avoid iteration during calculation; the solution process is as follows:

[0100]

[0101] Let μ = KQ p , and after arranging formula (3), we get:

[0102] P 2 -0.22μ 2 BRP - μ 2 B 2 RΔh = 0 (4)

[0103] The solution from formula (4) is:

[0104]

[0105] From formula (5), μ, R, B, and Δh can be obtained, and then the rolling pressure P can be calculated;

[0106] Because the stress state and its distribution in the deformation zone during rolling depend on the geometry of the deformation zone, and the SIMS formula is based on the Orovan internal force balance formula in the deformation zone, the calculation of the stress state coefficient is complex and cannot be applied to computer on-line control:

[0107]

[0108] In Equation (6), ε represents the reduction rate; h represents the height of the rolled piece after rolling; h y represents the instantaneous average height of the rolled piece in the deformation zone;

[0109] Thus, it can be seen that the stress state coefficient Q p is determined by four technological parameters: ε, h, h y , and R. ε is determined by the heights of the rolled piece before and after rolling, h y is determined by the width of the rolled piece in the pass and the cross-sectional area of the rolled piece, and the width of the rolled piece is related to the reduction. The reduction also indirectly determines the spread coefficient closely related to the width of the rolled piece. Since the reduction in bar rolling is smaller than that in ordinary strip and section steel rolling, the change amount in the sample data is smaller. To sum up, there are six most relevant influencing factors on the hot continuous rolling force: rolling temperature, rolling speed, deformation resistance, roll radius, spread coefficient, and entrance height. Then, it is determined that the number of input nodes is 6. These six influencing factors are used as the inputs of the RBF neural network, and the rolling force is used as the output of the RBF neural network.

[0110] (1.2) Estimate the number of nodes in the input, output layers and hidden nodes of the non-linear multi-layer forward RBF neural network;

[0111] The specific process is as follows: Set the number of nodes in the input layer to N, and set the number of hidden nodes of the non-linear multi-layer forward RBF neural network to M. Since it is a single-output RBF neural network, its output node is set to 1. Among them, the training samples of the regularization network and the "basis function" are in one-to-one correspondence; when the number of samples P is very large, the computational amount of implementing the network will be extremely large. In addition, when P is very large, the weight matrix is also very large, and it is easy to generate ill-conditioned problems when solving the weights of the network; choose to establish a generalized RBF network to reduce the number of hidden nodes, that is, N < M < P.

[0112] (1.3) Establish a radial basis function based on function approximation and interpolation as the "basis" of the hidden unit, and then use it as the activation function of the hidden node to form the hidden layer space; the hidden layer transforms the input vector, transforming the pattern in the low-dimensional space into a high-dimensional space, so that the linearly inseparable problem in the low-dimensional space becomes linearly separable in the high-dimensional space;

[0113] Specifically, the specific process of forming the hidden layer space by establishing a radial basis function based on function approximation and interpolation is as follows:

[0114] First, determine the mapping from the N-dimensional input space to the one-dimensional rolling force output space in the non-linear multi-layer forward RBF neural network; assume that there are P input vectors X p in the N-dimensional space, where p = 1, 2,..., P, and the corresponding target value in the output space is d p, p = 1, 2, …, P, and the P pairs of input and output samples form a training sample set; satisfying the interpolation conditions, the purpose of interpolation is to find a non - linear mapping function F(X) that satisfies the following interpolation conditions:

[0115] F(X p ) = d p , p = 1, 2…, P (7)

[0116] In equation (7), the function F represents an interpolation surface; the so - called strict interpolation or exact interpolation is a complete interpolation, that is, the interpolation surface must pass through all training data points;

[0117] In addition, the specific operation method of using the radial basis function technique to solve the interpolation problem is: select P basis functions, so that each basis function corresponds to a training data, and the forms of each basis function are as follows:

[0118]

[0119] In equation (8), the radial basis function represents a non - linear function, and the training data point X p represents the center; the basis function takes the distance between the point X in the input space and the center X p as the independent variable of the function;

[0120] In the non - linear multi - layer forward RBF neural network, the distance is radially isotropic;

[0121] In the establishment of the radial basis function based on function approximation and interpolation, the interpolation function for realizing the radial basis function is defined as a linear combination of basis functions:

[0122]

[0123] Substituting equation (7) into equation (9), we get a system of P linear equations about the unknown coefficients ω p , p = 1, 2…, P:

[0124]

[0125] Let Then the above - mentioned system of equations can be rewritten as:

[0126]

[0127] Let Φ represent a PxP - order interpolation matrix with elements , W and d represent the coefficient vector and the desired output vector respectively. Rewrite the above formula into the vector form ΦW = d, and through transformation, the coefficient vector W can be solved, that is:

[0128] W = Φ-1 d (12)

[0129] In formula (12), the interpolation matrix Φ is invertible because X 1 , X 2, X 3 , …, X p are all different, so the PxP order interpolation matrix is invertible.

[0130] (1.4), Use the K-means self-organizing clustering algorithm to determine suitable data centers for the radial basis functions of the hidden layer nodes, and determine the expansion constants of the hidden nodes according to the distances between the centers;

[0131] Specifically, using the K-means self-organizing clustering algorithm to determine suitable data centers for the radial basis functions of the hidden layer nodes is to find the relationship with the center and the training data points X p , and determine the expansion constants of the hidden nodes according to the distances between the centers. The self-organizing selection of the data centers uses a dynamic clustering algorithm to self-organize the selection of the data centers. During the learning process, the position of the data centers needs to be adjusted dynamically. Here, the K-means clustering algorithm is used. Its advantage is that it can determine the expansion constants of each hidden node according to the distances between the clustering centers; its task is divided into two stages. The first stage is to use the self-organizing clustering method to determine suitable data centers for the radial basis functions of the hidden layer nodes and determine the expansion constants of the hidden nodes according to the distances between the centers; the second stage is the supervised learning stage, and its task is to train the output layer weights with a supervised learning algorithm. Here, an adaptive momentum gradient descent supervised learning algorithm is used for training;

[0132] The specific operation steps are as follows:

[0133] (1.4.1), Before clustering to determine the positions of the data centers, it is necessary to first estimate the number M of centers; it is determined by experiments. Since the data centers obtained by clustering are not directly based on the rolling force sample data X p itself, c(k) is used to represent the center at the k-th iteration;

[0134] (1.4.2), Initialize and select M mutually different vectors as the initial clustering centers: c 1 (0), c 2 (0), …, c m (0). When selecting, a method of assigning small random numbers to each clustering center vector is used;

[0135] (1.4.3), Calculate the Euclidean distances between each sample point in the input space and the clustering center points:

[0136] ||x p -cj (k) || p = 1, 2…, P; j = 1, 2…, M; (13)

[0137] (1.4.4), Similarity matching, let j * represent the subscript of the winning hidden node in competition. For each input sample X of the rolling force influencing factor p determine its classification j according to its minimum Euclidean distance from the cluster center * (X p ), that is, when the following equation holds:

[0138] j * (X p ) = min j ||X p - c j (k) || p = 1, 2…, P; (14)

[0139] Classify X p into the j * th class, thus dividing all samples into M subsets: u 1 (k), u 2 (k), u 3 (k), …, u m (k), and each subset forms a clustering domain with the cluster center as the typical representative;

[0140] (1.4.5), Update the cluster centers of each class, and adjust them using the competitive learning rule, that is:

[0141]

[0142] In Equation (15), η represents the learning rate, and 0 < η < 1;

[0143] (1.4.6), Increment the value of k by 1, and go to step (1.4.2); repeat the above process until the change in c j is less than the required value; after determining each cluster center, the expansion constant of the corresponding radial basis function can be determined according to the distance between the centers;

[0144] Let d j = min i ||c j - c i ||, then the expansion constant is obtained:

[0145] δ j = λd j (16)

[0146] In Equation (16), λ represents the overlap coefficient.

[0147] (1.4.7) After obtaining the centers and expansion constants of each radial basis function using the K-means clustering algorithm, the weights of the output layer are obtained through hybrid learning with a supervised learning algorithm. The LMS algorithm is used and directly calculated by the pseudo-inverse method. The established nonlinear multi-layer forward RBF neural network model is an RBF neural network with a single output of rolling force. When the input is X p the output of the j-th hidden node is

[0148] Then the output matrix of the hidden layer is: If the undetermined output weights of the RBF network are W = [w 1 , w 2 , …, w M , then the network output vector is:

[0149] F(X) = ΦW (17)

[0150] Let the network output vector be equal to the teacher signal d, then Φ in equation (11) is replaced by its pseudo-inverse Φ + to obtain:

[0151] W = Φ + d (18)

[0152] The pseudo-inverse matrix Φ + in equation (18) is:

[0153] Φ + = (Φ T Φ) -1 Φ T (19)

[0154] (1.5) Use a supervised learning algorithm to train the weights of the output layer. From the relationship composed of the interpolation matrix, the coefficient vector, and the desired output vector, the output weight matrix W is obtained through matrix transformation, where ω jk (j = 1, 2, …, M; k = 1, 2…1) is the synaptic weight between the j-th node of the hidden layer and the k-th node of the output layer, T = (T 1 , T 2 , …, T l ) T is the threshold vector of the output layer. The neurons of the output layer adopt a linear activation function. By training the artificial neural network, learning to correct the error, and using an adaptive momentum gradient descent supervised learning algorithm, the artificial neural network is thus constructed. After that, the artificial neural network can be used for pre-setting the rolling force for production use;

[0155] Specifically, regarding the supervised learning algorithm for the data center, small random numbers are assigned to each weight vector of the output layer and normalized. The centers, expansion constants, and output layer weights of the hidden node RBF functions are all trained using the supervised learning algorithm, that is, all parameters undergo an error correction learning process. Since the established nonlinear multi-layer forward RBF neural network model is an RBF neural network with a single output of rolling force, an adaptive momentum gradient descent learning algorithm suitable for single-output RBF networks is used as the supervised learning algorithm for this RBF network; its objective function is defined as:

[0156]

[0157] In Equation (20), P represents the number of training samples; e i represents the error signal when the i-th sample is input, and is defined as:

[0158]

[0159] The threshold is ignored in the output function of Equation (21);

[0160] To minimize the objective function, the correction amount of each parameter should be proportional to its negative gradient. The specific algorithm is:

[0161]

[0162]

[0163]

[0164] The above objective function is the sum of the errors caused by all training samples, and the derived parameter correction formula is a batch adjustment, that is, all samples are adjusted once after one round of input.

[0165] Embodiment: The present invention combines an artificial neural network with a traditional mathematical model, fully utilizes the characteristics of stable calculation of the traditional data model and high calculation accuracy of the artificial neural network, and effectively solves the problem of training data for the neural network. The prediction accuracy is theoretically significantly improved compared with the traditional rolling force model; since the neural network does not need to perform roll flattening iterative calculations, and the forward RBF neural network has a single hidden layer, its calculation speed of rolling force is fast and can respond quickly; the training data of its neural network is evenly distributed, that is, it ensures the robustness of the neural network, and to a certain extent alleviates the problem that in the bar production process, since the deformation process of the rolled piece in the pass belongs to three-dimensional non-uniform deformation, its deformation law is difficult to master, and the theoretical research on the rolling pressure model is not deep enough, and it can be applied to on-line production;

[0166] The following takes the rolling force calculation of the large bar rolling mills with specifications of Φ120mm and Φ78mm in a certain factory as an example to illustrate the above steps in detail;

[0167] In the step (1.1), first, the SIMS formula of the hot rolling force model of the bar rolling mill is decomposed. The SIMS formula is based on the internal force balance theory in the Orowan deformation zone and assumes that there is no relative sliding on the contact surface between the roll and the workpiece during hot rolling. It is suitable for calculating the hot rolling pressure. The rolling pressure model of the SIMS formula adopts the following basic form:

[0168] P = Bl c KQ p (1)

[0169] In Equation (1): B represents the width of the workpiece; l c represents the horizontal projection length of the contact arc considering the reduction; K represents the deformation resistance; Q p represents the stress state coefficient;

[0170] Among them, the horizontal projection length of the contact arc (l c ) can be expressed as:

[0171]

[0172] In Equation (2): In Equation (2): R c represents the working radius of the roll; Δh represents the reduction;

[0173] Substitute Equation (2) into Equation (1) to solve for the rolling pressure P. When calculating the rolling force, the flattening of the roll caused by the rolling force needs to be considered, and calculating the flattening radius is conditional on the rolling force; therefore, an iterative method is often used to calculate the rolling force during the rolling force calculation; to avoid cumbersome iterative calculations, the rolling force formula is now processed by introducing the roll radius R, avoiding iteration during the calculation. The solution process is as follows:

[0174]

[0175] Let μ = KQ p , and rearrange Equation (3) to obtain:

[0176] P 2 -0.22μ 2 BRP - μ 2 B 2 RΔh = 0 (4)

[0177] Solve from Equation (4):

[0178]

[0179] From Equation (5), μ, R, B, and Δh can be obtained, and then the rolling force P can be calculated;

[0180] The rolling force calculation formula derived through derivation is easy to be implemented by software, replacing the traditional commonly used iterative solution method, greatly shortening the software calculation time; and because μ is related to the deformation resistance K and the stress state coefficient Q p related, the deformation resistance K can be obtained from the hot compression experiment, and the stress state coefficient Q p is decomposed. Since the stress state and its distribution in the deformation zone during rolling depend on the geometry of the deformation zone, the stress state coefficient calculated based on the Eurovan internal force balance formula in the SIMS method is relatively complex and cannot be applied to computer on-line control:

[0181]

[0182] In formula (6), ε represents the reduction ratio; h represents the height of the rolled piece after rolling; h y represents the instantaneous average height of the rolled piece in the deformation zone;

[0183] Thus, it can be seen that the stress state coefficient Q p is determined by four process parameters: ε, h, h y , and R. ε is determined by the heights of the rolled piece before and after rolling, h y is determined by the width of the rolled piece in the pass and the cross-sectional area of the rolled piece, and the width of the rolled piece is related to the reduction. The reduction also indirectly determines the spread coefficient closely related to the width of the rolled piece. Since the reduction in bar rolling is relatively small compared to ordinary strip and section steel, the change amount in the sample data is relatively small. To sum up, the six most relevant influencing factors of the hot continuous rolling force are: rolling temperature, rolling speed, deformation resistance, roll radius, spread coefficient, and entrance height. Then, it is determined that the number of input nodes is 6. These six influencing factors are used as the input of the RBF neural network, and the rolling force is used as the output of the RBF neural network;

[0184] In step (1.2) described above, estimate the number of nodes in the input, output layer and hidden nodes of the non-linear multi-layer forward RBF neural network. Among them, set the number of nodes in the input layer to N, set the number of hidden nodes of the non-linear multi-layer forward RBF neural network to M. Since it is a single-output RBF neural network, the output node is set to 1. Since the training samples of the regularized network and the "basis function" are in one-to-one correspondence; when the number of samples P is very large, the computational amount of the network will be extremely large. In addition, when P is very large, the weight matrix is also very large, and it is easy to generate ill-conditioned problems when solving the weights of the network; to avoid this problem, here a generalized RBF network is selected, which can reduce the number of hidden nodes, that is, N < M < P; from step so1 above, the number of input nodes is 6, then the number of hidden nodes needs to be greater than 6, and the number of samples P needs to be greater than the number of hidden nodes;

[0185] In step (1.3), a radial basis function based on function approximation and interpolation is established. First, consider the mapping from an N-dimensional input space to a one-dimensional rolling force output space in the non-linear multi-layer forward RBF neural network; the number of input nodes obtained from step SO2 is 6, so here N = 6. Assume there are P rolling force input vectors X in the N-dimensional (6-dimensional) space p , where p = 1, 2,..., P, and their corresponding target values in the output space are d p , p = 1, 2,..., P. The P pairs of input-output samples form a training sample set. The purpose of interpolation is to find a non-linear mapping function F(X) that satisfies the following interpolation conditions:

[0186] F(X p ) = d p , p = 1, 2..., P (7)

[0187] In equation (7), the function F describes an interpolation surface. So-called strict interpolation or exact interpolation is a complete interpolation, that is, the interpolation surface must pass through all training data points;

[0188] The method of using radial basis function technology to solve the interpolation problem is to select P basis functions, each basis function corresponding to a training data, and the forms of the basis functions are as follows:

[0189]

[0190] In equation (8), the radial basis function represents a non-linear function, the training data point X p represents the center; the basis function takes the distance between the point X in the input space and the center X p as the independent variable of the function;

[0191] In the non-linear multi-layer forward RBF neural network, the distance is radially isotropic. The interpolation function based on radial basis function technology is defined as a linear combination of basis functions:

[0192]

[0193] Substitute equation (7) into equation (9) to obtain a system of linear equations with P unknown coefficients ω p , p = 1, 2..., P:

[0194]

[0195] Let Then the above system of equations can be rewritten as:

[0196]

[0197] Let Φ denote the PxP interpolation matrix with elements and let W and d denote the coefficient vector and the desired output vector respectively. Rewrite the above equation in vector form as ΦW = d, and the coefficient vector W can be solved from the transformed form, that is:

[0198] W = Φ -1 d (12)

[0199] In equation (12), the interpolation matrix Φ is invertible because X 1 , X 2 , X 3 , …, X p are all different, so the PxP interpolation matrix is invertible. The interpolation matrix Φ studied here must be invertible because X 1 , X 2 , X 3 , …, X p are all different, so the PxP interpolation matrix is invertible; in this case, the number of samples p is given as 8, that is, there are 8 sets of training data;

[0200] In step (1.4), the K-means self-organizing clustering algorithm is used to determine appropriate data centers for the radial basis functions of the hidden layer nodes, and the spread constant of the hidden nodes is determined according to the distances between the centers. The self-organizing selection of the data centers uses a dynamic clustering algorithm to self-organize the selection of the data centers. During the learning process, the positions of the data centers need to be adjusted dynamically. Here, the K-means clustering algorithm is used. Its advantage is that it can determine the spread constant of each hidden node according to the distances between the clustering centers; its task is divided into two stages. The first stage is that the self-organizing clustering method determines appropriate data centers for the radial basis functions of the hidden layer nodes and determines the spread constant of the hidden nodes according to the distances between the centers; the second stage is the supervised learning stage, and its task is to train the weights of the output layer using a supervised learning algorithm. Here, an adaptive momentum gradient descent supervised learning algorithm is used for training; the method of the first stage using the K-means clustering algorithm is as Figure 2 shown, including the following sub-steps:

[0201] As Figure 2 shown, the specific steps of the first stage are as follows:

[0202] Step 1: Before clustering to determine the positions of the data centers, first estimate the number of centers M (thus determining the number of hidden nodes), which generally needs to be determined through experiments. Considering the above relationships, in this case M = 7. Since the data centers obtained by clustering are not directly the rolling force sample data X p itself, c(k) is used to represent the center at the k-th iteration;

[0203] Step 2: Initialize by selecting M (7) distinct vectors as the initial clustering centers: c 1 (0), c 2 (0), …, c m (0). When selecting, a method of assigning small random numbers to each clustering center vector is adopted;

[0204] Step 3: Calculate the Euclidean distance between each sample point in the input space and the clustering center points:

[0205] ||X p - c j (k)|| for p = 1, 2, …, P; j = 1, 2, …, M; (13)

[0206] Step 4: Similarity matching. Let j * represent the subscript of the winning competitive hidden node. For each input sample X of the rolling force influencing factors p determine its classification j * (X p ) according to its minimum Euclidean distance from the clustering center, that is, when there is the following equation:

[0207] j * (X p ) = min j ||X p - c j (k)|| for p = 1, 2, …, P; (14)

[0208] Assign X p to the j * th class, thus dividing all samples into M subsets: u 1 (k), u 2 (k), u 3 (k), …, u m (k). Each subset forms a clustering domain with the clustering center as the typical representative;

[0209] Step 5: Update the clustering centers of each class and adjust them using the competitive learning rule, that is:

[0210]

[0211] In formula (15), η represents the learning rate, and 0 < η < 1;

[0212] Step 6: Increment the value of k by 1 and go to Step So2; repeat the above process until the change in c j is less than the required value. After determining each clustering center, the expansion constant of the corresponding radial basis function can be determined according to the distance between the centers. Let d j = min i ||c j - ci ||, the extended constant is obtained as follows:

[0213] δ j = λd j (16)

[0214] In Equation (16), λ represents the overlap coefficient.

[0215] The second stage follows immediately after the first stage, and the specific steps are as follows:

[0216] Step 7: After obtaining the centers and extended constants of each radial basis function using the K-means clustering algorithm, the weights of the output layer are obtained through hybrid learning using a supervised learning algorithm. The LMS algorithm is used and directly calculated using the pseudo-inverse method; this patent studies a method for predicting the rolling force of a bar rolling mill based on the K-means clustering algorithm. Therefore, the established non-linear multi-layer forward RBF neural network model is an RBF neural network with a single output of rolling force. When the input is X p at this time, the output of the j-th hidden node is

[0217] Then the hidden layer output matrix is: If the undetermined output weights of the RBF network are W = [w 1 , w 2 , …, w M , then the network output vector is:

[0218] F(X) = ΦW (17)

[0219] Let the network output vector be equal to the teacher signal d. Then, Φ in Equation (11) is replaced with its pseudo-inverse Φ + to obtain:

[0220] W = Φ + d (18)

[0221] The pseudo-inverse matrix Φ + in Equation (18) is:

[0222] Φ + = (Φ T Φ) -1 Φ T (19)

[0223] Thus, the output weights are obtained.

[0224] In step (1.5), the error is corrected by the supervised learning algorithm of the data center. In the most general case, small random numbers are assigned to each weight vector of the output layer and normalized. The centers, spread constants of the hidden node RBF functions, and the weights of the output layer are all trained using the supervised learning algorithm. That is, all parameters go through an error correction learning process. Since the established non-linear multi-layer forward RBF neural network model is an RBF neural network with a single output of rolling force, an adaptive momentum gradient descent learning algorithm suitable for single-output RBF networks is used here as the supervised learning algorithm for this RBF network. Its objective function is defined as:

[0225]

[0226] In Equation (20), P represents the number of training samples; e i represents the error signal when the i-th sample is input, and its definition is shown as follows:

[0227]

[0228] The threshold is ignored in the output function of Equation (21).

[0229] To minimize the objective function, the correction amount of each parameter should be proportional to its negative gradient. The specific algorithm is:

[0230]

[0231]

[0232]

[0233] The above objective function is the sum of the errors caused by all training samples. The derived parameter correction formula is a batch adjustment, that is, it is adjusted once after all samples are input in one round. Thus, the construction of the neural network for predicting rolling force is completed.

[0234] Figure 3 is the structural schematic diagram of the non-linear multi-layer forward RBF neural network established for this example; in the figure, taking a single input sample data as an example, the structural schematic diagram of the RBF neural network established in this example is briefly summarized.

[0235] Figure 4 is the network performance schematic diagram of the method for predicting the hot strip rolling force based on the data of the factors affecting the hot strip rolling force prediction in the example of the present invention by establishing a non-linear multi-layer forward RBF neural network prediction model. It can be seen that the non-linear multi-layer forward RBF neural network based on the K-means clustering algorithm in the example of the present invention has relatively good accuracy and network performance in predicting rolling force.

Claims

1. A prediction method for predicting rolling force of a neural network based on the K-means clustering algorithm, characterized in that, the specific operation steps are as follows: (1.1) Analyze the SIMS formula to obtain the most relevant influencing factors of the bar hot continuous rolling force, so as to determine the input and output layers of the RBF neural network; The specific process of analyzing the SIMS formula is: Decompose the SIMS formula of the hot rolling force model of the bar mill; Among them, the SIMS formula is based on the internal force balance theory in the Orowan deformation zone, assuming that there is no relative sliding on the contact surface between the roll and the workpiece in the deformation zone during hot rolling. The hot rolling force model of the bar mill of the SIMS formula adopts the following basic form: P = Bl c KQ p (1) In formula (1): B represents the width of the rolled piece; l c represents the horizontal projection length of the contact arc after considering the roll gap reduction; K represents the deformation resistance; Q p represents the stress state coefficient; where l c is expressed as: In formula (2): R c represents the working radius of the roll; Δh represents the reduction amount; Substitute Equation (2) into Equation (1) to solve the rolling pressure P; introduce the roll radius R to avoid iteration during calculation; the solution process is as follows: Let μ = KQ p , rearrange Equation (3), and thus obtain: P 2 -0.22 μ 2 BRP-μ 2 B 2 RΔh = 0 (4) Solve from Equation (4): From Equation (5), μ, R, B, and Δh can be obtained, and then the rolling force P can be calculated; In addition, since the stress state and its distribution in the deformation zone during rolling depend on the geometry of the deformation zone, the derived stress state coefficient is shown as follows: In formula (6), ε represents the reduction rate; h represents the height of the rolled piece after rolling; h y represents the instantaneous average height of the rolled piece in the deformation zone; (1.2) Estimate the number of nodes in the input, output layers and hidden nodes of the non-linear multi-layer forward RBF neural network; The specific process is: Set the number of nodes in the input layer to N, and set the number of hidden nodes of the non-linear multi-layer forward RBF neural network to M; the output node of the single-output RBF neural network is set to 1; to avoid ill-conditioned problems when solving the weights of the network when the number of samples P is very large; then choose to establish a generalized RBF network to reduce the number of hidden nodes, that is, N < M < P; (1.3) Establish a radial basis function based on function approximation and interpolation to form the hidden layer space; The specific process of forming the hidden layer space by establishing a radial basis function based on function approximation and interpolation is: Determine the mapping from the N-dimensional input space to the one-dimensional rolling force output space in the described non-linear multi-layer forward RBF neural network; assume that there are P input vectors X in the N-dimensional space p , where p = 1, 2, …, P, and the corresponding target value in the output space is d p , p = 1, 2, …, P, and the P pairs of input-output samples form a training sample set; the non-linear mapping function F(X) that satisfies the interpolation condition is shown as follows F(X p ) = d p , p = 1, 2…, P (7) In Equation (7), the function F represents an interpolation surface; this completely interpolated interpolation surface passes through all training data points; In addition, the specific operation method of using the radial basis function technology to solve the interpolation problem is: select P basis functions, so that each basis function corresponds to a training data, and the forms of each basis function are as follows: In formula (8), the radial basis function represents a non-linear function, and the training data point X p represents the center; the basis function takes the distance between the point X in the input space and the center X p as the independent variable of the function; In addition, in establishing a radial basis function based on function approximation and interpolation, the interpolation function for realizing the radial basis function is defined as a linear combination of basis functions: Substitute Equation (7) into Equation (9) to obtain a system of linear equations for the \(P\) unknown coefficients \(\omega\) p , where \(p = 1, 2, \ldots, P\): Let i = 1, 2, …, P; n = 1, 2, …, P; then the above system of equations can be rewritten as: Let Φ denote the PxP interpolation matrix with elements , and let W and d denote the coefficient vector and the desired output vector respectively. Rewrite the above equation in vector form as ΦW = d, and the coefficient vector W can be solved by transformation, i.e.: W = Φ -1 d (12) In Equation (12), the interpolation matrix Φ is invertible because X 1 , X 2 , X 3 , …, Xp are all different, so the PxP-order interpolation matrix is invertible; (1.4) Use the K-means self-organizing clustering algorithm to determine suitable data centers for the radial basis functions of the hidden layer nodes, and determine the expansion constants of the hidden nodes according to the distances between the centers; The operation steps of using the K-means self-organizing clustering algorithm include two stages: One is to use the self-organizing clustering method to determine suitable data centers for the radial basis functions of the hidden layer nodes, and determine the expansion constants of the hidden nodes according to the distances between the centers; The second is the supervised learning stage, training the weights of the output layer with a supervised learning algorithm, and using the adaptive momentum gradient descent supervised learning algorithm for training; The specific operation steps are as follows: (1.4.1) Before determining the location of the data center by clustering, first estimate the number M of centers; this is determined through experiments. Since the data centers obtained by clustering are not directly based on the calculated rolling force sample data X p itself, c(k) is used to represent the center at the k-th iteration; (1.4.2), Initialize by selecting M distinct vectors as the initial cluster centers: c 1 (0), c 2 (0), …, c m (0), and when selecting, use the method of assigning small random numbers to each cluster center vector; (1.4.3) Calculate the Euclidean distance between each sample point in the input space and the clustering center point; ||X p -c j (k)|| p = 1, 2…, P; j = 1, 2…, M; (13) (1.4.4), Similarity matching, let j * represent the subscript of the winning hidden node in the competition. For each input sample X of the rolling force influencing factors p determine its classification j according to its minimum Euclidean distance from the cluster center * (X p ), that is, when the following equation holds: j * (X p )=min j ||X p -c j (k)|| p=1,2…,P; (14) Assign X p to the j * th class, thereby dividing all samples into M subsets: u 1 (k), u 2 (k), u 3 (k), …, u m (k), and each subset forms a clustering domain with the clustering center as a typical representative; (1.4.5) Update the clustering centers of each class, and adjust them using the competitive learning rule, that is: In Equation (15), η represents the learning rate, and 0 < η < 1; (1.4.6) Increment the value of k by 1, and go to step (1.4.2); repeat the above process until the change in c j is less than the required value; after determining each cluster center, determine the expansion constant of the corresponding radial basis function according to the distances between the centers. Let d j = min i ||c j - c i ||, then the extended constant is obtained: δ j = λd j (16) In Equation (16), λ represents the overlap coefficient; (1.4.7) After obtaining the centers and spread constants of each radial basis function using the K-means clustering algorithm, the weights of the output layer are obtained through hybrid learning with a supervised learning algorithm. The LMS algorithm is adopted and directly calculated using the pseudoinverse method. The established nonlinear multi-layer forward RBF neural network model is an RBF neural network with a single output of rolling force. When the input is X p the output of the j-th hidden node is p = 1, 2…, P; j = 1, 2…, M; Then the output matrix of the hidden layer is as follows: If the undetermined output weights of the RBF network are \(W = [w 1 , w 2 , \cdots, w M \), then the network output vector is: F(X) = ΦW (17) Let the network output vector be equal to the teacher signal d, then Φ in Equation (17) is replaced by its pseudoinverse Φ + to obtain: W = Φ + d (18) The pseudo-inverse matrix Φ in Equation (18) + is as follows: Φ + = (Φ T Φ) - 1 Φ T (19); (1.5) Train the artificial neural network, learn and correct the error, so as to complete the construction of the artificial neural network; and use this artificial neural network for presetting the rolling force for production use; The specific process of completing the construction of the artificial neural network by training the artificial neural network, learning and correcting the error is: for the supervised learning algorithm of the data center, assign small random numbers to each weight vector of the output layer and perform normalization processing. The centers, expansion constants, and output layer weights of the hidden node RBF functions are all trained using the supervised learning algorithm. The adaptive momentum gradient descent learning algorithm is used as the supervised learning algorithm for this RBF network; its defined objective function is: In formula (20), P represents the number of training samples; e i represents the error signal when the i-th sample is input, and its definition is as follows: The threshold is ignored in the output function of Equation (21); To minimize the objective function, the correction amount of each parameter should be proportional to its negative gradient. The specific algorithm is: The above objective function is the sum of the errors caused by all training samples, and the derived parameter correction formula is a batch adjustment, that is, it is adjusted once after all samples are input in one round.

2. A prediction method for predicting rolling force by a neural network based on the K-means clustering algorithm according to claim 1, characterized in that, In the step (1.1), the specific factors affecting the hot continuous rolling force of bars with the highest relevance obtained by analyzing the SIMS formula include: rolling temperature, rolling speed, deformation resistance, roll radius, spread coefficient, and inlet height; it is determined that the number of input nodes is 6, then the above 6 influencing factors are used as the inputs of the RBF neural network, and the rolling force is used as the output of the RBF neural network.

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