Control method for variable curvature arc bending of roll bending machine

Abstract

A precise control method for variable curvature arc bending torque of roll bending machine is provided by combining genetic algorithm, backpropagation neural network and particle swarm optimization algorithm. [Solution] The method collects and preprocesses data, initializes the network structure, determines parameters such as the number of nodes in the input layer, hidden layer, and output layer of the backpropagation neural network based on the training sample data, encodes the weight values ​​and thresholds of the backpropagation neural network into individuals in the population based on the set encoding rule, initializes the population based on the set population size and initialization method, performs iterative operations according to the genetic algorithm (GA)-particle swarm optimization (PSO) algorithm, initializes the backpropagation neural network parameters, trains the backpropagation neural network, and applies the model to actual control.

Description

[Technical Field]

[0001] The present invention belongs to the technical field of industrial production control, and particularly relates to a method for controlling variable curvature arc bending in a roll bending machine. [Background technology]

[0002] Roll bending is a metal processing method in which a metal plate or tube is rolled along its axis using a roll bending machine. As a common metal forming technique, it is widely used in fields such as aviation, rockets, ships, automobiles, and construction.

[0003] Roll bending Variable curvature arc bending The principle is to roll a metal plate or pipe material The three The roll shaft is made up of one or more metal rollers, and their arrangement can be adjusted as needed to achieve flexible, semi-flexible, or rigid roll bending. Three Rollers pass through metal material Let When bending, the rollers apply a certain force and bend the metal, while simultaneously adjusting the position and angle of the roll axis to control the degree and shape of the metal bending. Conventional roll bending machine tools are all manually controlled and require repeated forming and adjustment to meet requirements, which is not only inefficient but also costly. Furthermore, the processing process for producing variable curvature profile parts is complicated. Currently, roll bending of large-sized and asymmetric cross-section profile parts is still in the theoretical research stage, with relatively little effective equipment and mature experience. At the current stage, variable curvature roll bending profile processing is difficult to control the forming radius, and smooth transition between different curvature profiles cannot be achieved. Summary of the Invention

[0004] The objective of the present invention is to provide a control method for variable curvature arc bending of a roll bending machine, and to solve the technical problems in the prior art that the processing forming radius of variable curvature roll bending profiles is difficult to control and smooth transition between profiles of different curvatures cannot be realized.

[0005] The technical solution adopted by the present invention is a control method for variable curvature arc bending of a roll bending machine, which is specifically implemented by the following steps: Step 1: Collect the operation data of the roll bending machine and pre-process the data. Step 2: The number of nodes in the input layer, hidden layer, and output layer of the backpropagation neural network is determined based on the data after preprocessing in Step 1. Step 3: Encode the weight values ​​and thresholds of the backpropagation neural network into individuals of the population according to the real number encoding rule, and initialize the population according to the set population size and random initialization method. Step 4: The population obtained in Step 3 is subjected to iterative operations according to the GA-PS0 algorithm rules to obtain the globally optimal individual. Step 5: The globally optimal individual obtained in step 4 is decoded to restore the structural information of the backpropagation neural network, and then substituted into the backpropagation neural network to obtain the initial weights and thresholds of the backpropagation neural network. Step 6: Based on the preset gradient descent supervised learning method and backpropagation learning algorithm, the backpropagation neural network is repeatedly trained to obtain an optimized backpropagation neural network. Step 7: The backpropagation neural network model after being optimized in Step 6 is applied to the actual control system to accurately control the variable curvature arc bending of the roll bending section.

[0006] Further features of the present invention are as follows. Specifically, the preprocessing in step 1 is as follows. The operation data of the roll bending machine during a certain time period is collected as a training sample, and the training sample includes torque To, roller pressure Pr, roller position Pot, feed rate V, and material temperature Te, and the torque value and roller position Pot2 of the roll bending machine during time period t2 are predicted based on the torque value and roller position Pot1 of the roll bending machine during time period t1, where the time lengths of t1 and t2 are equal. The final input vector P(Tot1, Prt1, Pot1, Vt1, Tet1) and output vector T(Pot2) are obtained through preprocessing.

[0007] Step 2 may specifically be as follows: Step 2.1: The number of nodes in the input layer matches the number of features in the training samples, and each input layer node corresponds to one feature. Step 2.2: The number of nodes in the output layer is determined based on whether the problem being solved is a classification or regression problem. For classification problems, the number of nodes in the output layer is equal to the number of categories. For regression problems, the number of output nodes is one. The output of the kth neuron in the output layer is as follows:

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[0008] The number of nodes in the hidden layer in step 2.3 is determined by the following empirical formula: (3)

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[0009] Step 4 may specifically be as follows: Step 4.1: Initialize the backpropagation neural network parameters with the mutation probability P m , the crossover probability P c , particle maximum velocity V max , the inertia constant ω, the learning factors c1 and c2, the number of iterations epoch, and the calculated accuracy value E are set in advance. Step 4.1.1: Equation (4) and Equation (5) We design the crossover operator as shown in a.Position crossing operation:

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[0010] Step 4.2: Initialize the population, set the population size N and particle dimension n, initialize the particle speed and position using a random initialization method, encode the particle speed and position information according to a preset encoding rule, obtain the initial population, calculate the individual fitness values ​​of the particle group using a fitness function, and update the individual extreme values ​​of the particles and the global extreme values ​​of the particle group.

[0011] Step 4.3: The particle swarm algorithm iterates through Equations (8) and (9) The particle positions and velocities are updated according to the above equation, and the movement of the particle swarm is subjected to the joint attraction of the local optimum and the global optimum, and finally converges to the global optimum.

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[0012] Step 4.4: A particle swarm crossover operation is performed by using a roulette selection operator to select particles with high fitness values ​​from the particle swarm, and then using a velocity crossover operator and a position crossover operator to select particles with high fitness values ​​from the particle swarm using a crossover probability P c Based on this, a crossover operation is performed, the fitness values ​​of the particles of the two generations before and after the crossover operation are compared, and particles with high fitness are selected and put into the particle group to proceed to the next iteration.

[0013] Step 4.5: A particle swarm mutation operation is performed by selecting particles with low fitness values ​​from the particle swarm and using a velocity mutation operator and a position mutation operator to set the mutation probability P m A mutation operation is performed according to the result, and the particles obtained by the mutation operation are added to the population.

[0014] Step 4.6: Calculate the fitness value of the particle swarm and the particle individual extreme value pbest i and find the global extremum gbest of the particle swarm. i Update.

[0015] Step 4.7: Determine whether the algorithm is complete. Determine whether the particle evolution algebra satisfies the set maximum evolution algebra, or whether the particle swarm fitness value meets the target value. If it does, the algorithm ends and the global extremum gbest of the particle swarm is output. This is the optimal solution to the optimization target problem. If it does not, proceed to step 4.3.

[0016] Step 5 may specifically be as follows: Based on the encoding rules, a reverse decoding operation is performed to restore the structural information of the backpropagation neural network, including the number of nodes in the input layer, hidden layer, and output layer, as well as connection method information, and the decoded weight values ​​and thresholds are reconstructed into corresponding weight matrices and threshold vectors. Below is the backpropagation process of the output error. The sample goes through a forward propagation calculation process to obtain the output value of the backpropagation neural network, and the output error of the backpropagation neural network is used to perform learning correction on the weight value and threshold value of the backpropagation neural network. The error function is:

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[0017] The repeated learning in step 6 specifically repeats the process of forward transmission of the input mode and backpropagation of the output error, and verifies whether the output error of the backpropagation neural network reaches a predetermined expected accuracy value. If the expected accuracy value is reached, the learning can be terminated; if not, the cycle can be continued.

[0018] The beneficial effects of the present invention are as follows: The variable curvature arc bending control method of the present invention combines a genetic algorithm (GA), a backpropagation neural network (BP), and a particle swarm optimization algorithm (PSO) to achieve accurate control of the variable curvature arc bending torque of a roll bending machine. By optimizing the controller parameters, the control performance and robustness of the system are improved, enabling the roll bending machine to achieve stable and rapid torque control even under conditions of relatively large curvature changes. The present invention can effectively meet the control requirements under complex operating conditions, improve production efficiency and product quality, and has good prospects for engineering applications. The present invention provides significant optimization effects for the variable curvature arc bending torque control of a roll bending machine, solving the technical problems of the prior art, such as the difficulty in controlling the forming radius of variable curvature roll bending sections and the inability to achieve smooth transitions between sections with different curvatures. This has important practical significance and value for popular application. [Brief explanation of the drawings]

[0019] [Figure 1] FIG. 2 is a flow diagram of the variable curvature arc bending control method for the roll bending machine of the present invention. [Figure 2] FIG. 2 is a network topology diagram of the backpropagation neural network in the variable curvature arc bending control method for a roll bending machine of the present invention; DETAILED DESCRIPTION OF THE INVENTION

[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Example 1 As shown in FIGS. 1 and 2, the variable curvature arc bending control method for a roll bending machine according to the present invention is specifically carried out according to the following steps. Step 1: Collect the operation data of the roll bending machine, preprocess the data, and extract the important feature parameters for use in building the control model through feature selection and extraction methods. Step 2: Based on the data after preprocessing in Step 1, the number of input layer nodes, hidden layer nodes, and output layer nodes of the backpropagation neural network are determined. Step 3: The weight values ​​and thresholds of the backpropagation neural network are coded into individuals in the population according to real number coding rules, and one coding information contains all the weight values ​​and thresholds of one backpropagation neural network and represents one individual in the population. The population is initialized according to the set population size and random initialization method. Step 4: Perform iterative operations on the population obtained in Step 3 according to the GA-PSO algorithm rules, and set the output error accuracy of the evolutionary algebra or backpropagation neural network as the algorithm termination condition in advance. When the algorithm meets the termination condition, a globally optimal individual is obtained, and this individual is the optimal structural parameter of the backpropagation neural network. Step 5: The globally optimal individual obtained in step 4 is decoded, the backpropagation neural network structure information is restored, and the information is substituted into the backpropagation neural network to obtain the initial weight values ​​and threshold values ​​of the backpropagation neural network. Step 6: According to the preset supervised learning method of gradient descent and the backpropagation learning algorithm, the backpropagation neural network is repeatedly trained to obtain an optimized backpropagation neural network. Step 7: The backpropagation neural network model optimized in Step 6 is applied to the actual control system to accurately control the variable curvature arc bending of the roll bending section.

[0021] This invention combines genetic algorithms, backpropagation neural networks, and particle swarm optimization to achieve accurate control of the variable curvature arc bending torque of a roll bending machine. By optimizing the controller parameters, the control performance and robustness of the system are improved, allowing the roll bending machine to achieve stable and rapid torque control when the curvature changes significantly. This invention can effectively meet the control requirements under complex operating conditions, improve production efficiency and product quality, and has relatively good prospects for engineering applications. This invention brings significant optimization effects to the variable curvature arc bending torque control of a roll bending machine, and has important practical significance and value for popular application.

[0022] Example 2 Based on Example 1, the pretreatment in step 1 is specifically as follows: The operation data of the roll bending machine during a certain time period is collected as a training sample, and the training sample includes torque To, roller pressure Pr, roller position Pot, feed rate V, and material temperature Te, and the torque value and roller position Pot2 of the roll bending machine during time period t2 are predicted based on the torque value and roller position Pot1 of the roll bending machine during time period t1, where the time lengths of t1 and t2 are equal. The final input vector P(Tot1, Prt1, Pot1, Vt1, Tet1) and output vector T(Pot2) are obtained through preprocessing.

[0023] Furthermore, step 2 is specifically as follows: Step 2.1: The number of nodes in the input layer matches the number of features in the training samples, with each input layer node corresponding to one feature. In this embodiment, the number of nodes in the input layer is 5. Step 2.2: The number of nodes in the output layer is determined based on whether the problem being solved is a classification problem or a regression problem. For classification problems, the number of nodes in the output layer is equal to the number of categories. For regression problems, the number of nodes in the output layer is one. In this example, the problem is a regression problem, so the number of nodes in the output layer is one.

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[0024] Furthermore, the GA-PSO algorithm in step 4 is specifically as follows: Step 4.1: Initialize the backpropagation neural network parameters with the mutation probability P m , the crossover probability P c , particle maximum velocity V max , the inertia constant ω, the learning factors c1 and c2, the number of iterations epoch, and the calculated accuracy value E are set in advance. Step 4.1.1: Equation (4) and Equation (5) We design the crossover operator as shown in a.Position crossing operation:

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[0025] Step 4.2: Initialize the population, set the population size N and particle dimension n, initialize the particle speed and position using a random initialization method, encode the particle speed and position information according to a preset encoding rule, obtain the initial population, calculate the individual fitness values ​​of the particle group using a fitness function, and update the individual extreme values ​​of the particles and the global extreme values ​​of the particle group.

[0026] Step 4.3: The particle swarm algorithm iterates through Equations (8) and (9) The particle positions and velocities are updated according to the above equation, and the movement of the particle swarm is subjected to the joint attraction of the local optimum and the global optimum, and finally converges to the global optimum.

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[0027] Step 4.4: A particle swarm crossover operation is performed by using a roulette selection operator to select particles with high fitness values ​​from the particle swarm, and then using a velocity crossover operator and a position crossover operator to select particles with high fitness values ​​from the particle swarm using a crossover probability P c Based on this, a crossover operation is performed, the fitness values ​​of the particles of the two generations before and after the crossover operation are compared, and particles with high fitness are selected and put into the particle group to proceed to the next iteration.

[0028] Step 4.5: A particle swarm mutation operation is performed by selecting particles with low fitness values ​​from the particle swarm and using a velocity mutation operator and a position mutation operator to set the mutation probability P m A mutation operation is performed according to the result, and the particles obtained by the mutation operation are added to the population.

[0029] Step 4.6: Calculate the fitness value of the particle swarm and the particle individual extreme value pbest i and find the global extremum gbest of the particle swarm. i Update.

[0030] Step 4.7: Determine whether the algorithm is complete. Determine whether the particle evolution algebra satisfies the set maximum evolution algebra, or whether the particle swarm fitness value meets the target value. If it does, the algorithm ends and outputs the global extremum gbest of the particle swarm. This is the optimal solution to the optimization target problem. If it does not, proceed to step 4.3.

[0031] Furthermore, step 5 is specifically as follows: Based on the encoding rules, a reverse decoding operation is performed to restore the structural information of the backpropagation neural network, including the number of nodes in the input layer, hidden layer, and output layer, as well as connection method information, and the decoded weight values ​​and thresholds are reconstructed into corresponding weight matrices and threshold vectors. The backpropagation process of the output error is as follows: The sample goes through a forward propagation calculation process to obtain the output value of the backpropagation neural network, and the output error of the backpropagation neural network is used to perform learning correction on the weight value and threshold value of the backpropagation neural network. The error function is:

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[0032] Furthermore, the backpropagation neural network is repeatedly trained using a predefined gradient descent supervised learning method and a backpropagation learning algorithm until the algorithm termination condition is met, at which point the final output of the GA-PSO-BP network is obtained. The final output refers to the parameters and weights obtained through training of the backpropagation neural network, which are key factors in controlling the model's behavior. The output result is a mapping result corresponding to the input data of the backpropagation neural network. The repeated training in step 6 specifically involves repeating the process of forward transmission of the input model and backpropagation of the output error. To ensure that the output error of the backpropagation neural network is sufficiently small, each set of training samples for the backpropagation neural network typically undergoes several hundred repeated training processes, allowing the backpropagation neural network to grasp the mapping relationship between the input and output data. Each time the cyclic memory training is performed, it is necessary to verify whether the output error of the backpropagation neural network reaches a predetermined expected accuracy value. If so, the training ends; otherwise, the cycle continues.

[0033] Example 3 The backpropagation neural network model has five input parameters, namely torque, roller pressure, roller position, feed rate, and material temperature, and one output parameter, namely the torque value of the roll bending machine at the next time. Therefore, the input layer has five nodes, the output layer has one node, and the number of nodes in the hidden layer in step 2.3 is calculated by the following empirical formula: (3)

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Claims

1. A roll bending machine for controlling variable curvature arc bending, which is composed of at least three rollers, the arrangement of the roll axes of the three rollers being adjusted as needed, a roll bending profile which is a metal plate or a pipe material is set between the three rollers, the roll axes move the roll bending profile forward, and the roll axes gradually bend and form the roll bending profile into a desired shape, wherein one of the three rollers is a roller to be adjusted in roller position, and with the roller positions of the remaining two rollers fixed, a method for controlling variable curvature arc bending of a roll bending machine is capable of controlling the degree and shape of bending of the roll bending profile by adjusting the roller position of one of the rollers to be adjusted in roller position, Step 1: Collect the operation data of the roll bending machine and pre-process the data; Step 2: Determine the number of nodes in the input layer, hidden layer, and output layer of the backpropagation neural network based on the preprocessed data in Step 1; Step 3: Encode the weights and thresholds of the backpropagation neural network into individuals in the population according to the real number encoding rule, and initialize the population according to the set population size and random initialization method; Step 4: Perform iterative operations on the population obtained in Step 3 according to the GA-PS0 algorithm rules to obtain the globally optimal individual; Step 5: Decode the globally optimal individual obtained in step 4, restore the structure information of the backpropagation neural network, and substitute it into the backpropagation neural network to obtain the initial weight values ​​and threshold values ​​of the backpropagation neural network; Step 6: Based on the preset supervised learning method of gradient descent and the backpropagation learning algorithm, the backpropagation neural network is repeatedly trained to obtain an optimized backpropagation neural network; Step 7: Apply the backpropagation neural network model after optimization in Step 6 to the actual control system to accurately control the variable curvature arc bending of the roll bending profile; Including the above steps, The pre-processing in step 1 is Operation data of the roll bending machine during a certain time period is collected as a training sample, and the training sample includes roller torque To, roller pressure Pr, roller position Pot, feed speed V, and material temperature Te. Based on the roller torque value and roller position Pot1 that are the control target of the roll bending machine during time period t1, the roller torque value and roller position Pot2 that are the control target of the roll bending machine during time period t2 are predicted, where the time lengths of t1 and t2 are equal, The final preprocessing step is to obtain the input vector P (Tot1, Prt1, Pot1, Vt1, Tet1) and the output vector T (Pot2). Step 2 is Step 2.1: The number of nodes in the input layer matches the number of features in the training samples, with each input layer node corresponding to one feature. Step 2.2: The number of nodes in the output layer is determined depending on whether the problem to be solved is a classification problem or a regression problem. For classification problems, the number of nodes in the output layer is equal to the number of categories. For regression problems, the number of nodes in the output layer is one. The output of the kth neuron in the output layer is as follows: [Equation 1] In equation (1), a 1k is the output of node k in the output layer, a 1i is the output of node i in the hidden layer, ω 1ki is the connection weight between node i and node k, b 1k is the threshold of node k in the output layer, and f 1 (·) is the transfer function of the output layer. Step 2.3: The number of nodes in the hidden layer is increased from a small number until the performance stabilizes, and the output of the i-th neuron in the hidden layer is: [Equation 2] In equation (2), n is the number of nodes in the input layer, P j is the input of the j-th neuron in the input layer, a 2i is the output of node i in the hidden layer, ω 2ji is the connection weight between node i and node j, b 2i is the threshold of node i in the hidden layer, and f 2 (·) is the transfer function of the hidden layer. Including the above steps, The number of nodes in the hidden layer in step 2.3 is calculated using the following empirical formula (3): [Equation 3] is determined based on where n is the number of nodes in the hidden layer, n i is the number of nodes in the input layer, n o is the number of nodes in the output layer, a is a constant between 1 and 10, and the range of n is 4 to 13. Step 4 is Step 4.1: Initializing the parameters of the backpropagation neural network, including the mutation probability P m , the crossover probability P c , the maximum particle velocity V max , the inertia constant ω, the learning factors c 1 and c 2 , the number of iterations epoch, and the calculated accuracy value E; Step 4.1.1: Design the crossover operator as shown in equations (4) and (5), a. Position crossing operation: [Equation 4] b. Speed ​​crossing operation: [Equation 5] In equations (4) and (5), α 1 and α 2 are random numbers between [0, 1], x i is the position vector of the i-th particle, x j is the position vector of the j-th particle, v i is the velocity vector of the i-th particle, and v j is the velocity vector of the j-th particle. Step 4.1.2: Design a mutation operator, and select the i-th individual to mutate as shown in Equations (6) and (7). a. Positional mutagenesis: [Equation 6] b. Rate Mutation Engineering: [Equation 7] In equations (6) and (7), X max and X min are the upper and lower limits of the particle position, respectively, V max and V min are the maximum and minimum values ​​of the velocity, respectively, r 1 , r 2 , and r 3 are random numbers in [0, 1], g is the current iteration number, x i is the position vector of the i-th particle, and v i is the velocity vector of the particle. Step 4.2: Initialize the population, set the population size N and the particle dimension n, initialize the particle speed and position using a random initialization method, encode the particle speed and position information according to a preset encoding rule, obtain an initial population, calculate the individual fitness value of the particle group using a fitness function, and update the individual extreme value of the particle and the global extreme value of the particle group; Step 4.3: In the iterative process, the particle swarm algorithm updates the particle position and velocity according to equations (8) and (9), and the movement of the particle swarm is subject to the joint attraction of the local optimum and the global optimum, and finally converges to the global optimum. [Equation 8] [Equation 9] In equations (8) and (9), ω is an inertia weighting coefficient, c 1 and c 2 are learning factors, also called acceleration constants, and their values ​​are random numbers between (0, 2), r 1 and r 2 are uniform random numbers within the range of (0, 1), x i is the position vector of the i-th particle, v i is the velocity vector of the particle, and v i+1 is the velocity vector of the particle at the next iteration. [Equation 10] where vmax is a constant that limits the particle's velocity according to user settings, pbest i is the particle's current best position, i.e., the individual extremum, and pbest i is the particle's current best position, i.e., the global extremum; Step 4.4: A particle swarm crossover operation is performed by using a roulette wheel selection operator to select some particles with high fitness values ​​from the particle swarm, and using a velocity crossover operator and a position crossover operator to perform a crossover operation based on the crossover probability P c set for the velocity and position of the particle swarm, respectively; comparing the fitness values ​​of the particles of the two generations before and after the crossover operation, selecting particles with high fitness and putting them into the particle swarm to proceed to the next iteration; Step 4.5: A mutation operation of the particle group is performed by selecting some particles with low fitness values ​​from the particle group, and using a velocity mutation operator and a position mutation operator to perform a mutation operation according to the mutation probability P m set for the velocity and position of the particle, respectively, and putting the particles obtained by the mutation operation into a population; Step 4.6: Calculate the fitness value of the particle swarm, update the particle individual extreme value pbest i , and update the particle swarm global extreme value gbest i ; Step 4.7: Determine whether the algorithm is finished, and determine whether the particle evolution algebra satisfies the set maximum evolution algebra, or whether the fitness value of the particle swarm meets the target value. If it does, the algorithm is finished, and the global extremum gbest of the particle swarm is output, that is, it is the optimal solution of the optimization target problem; if it does not, proceed to step 4.

3. Including the above steps, Step 5 is Perform a reverse decoding operation according to the encoding rules to restore the structural information of the backpropagation neural network, including the number of nodes in the input layer, hidden layer, and output layer, as well as connection method information, and reconstruct the decoded weight values ​​and thresholds into corresponding weight matrices and threshold vectors; The backpropagation process of the output error is as follows: The sample goes through the forward propagation calculation process to obtain the output value of the backpropagation neural network, and then uses the output error of the backpropagation neural network to perform learning correction on the weight value and threshold of the backpropagation neural network; The error function is: [0011] In equation (11), t k is the desired output, a 2k is the actual output of the network, E is the error function, In the weight value correction of the output layer, the weights from the i-th input to the k-th output are as follows: [0012] [0013] [0014] In equations (12), (13) and (14), η is the learning coefficient, E is the error criterion function, ω 2ki is the connection weight between node i and node k, a 1i is the output of node i in the hidden layer, δ ki is the local gradient of the i-th neuron in the k-th set of samples, and f 2 ′ is the first derivative of the transfer function of the output layer. In the hidden layer weight value correction, the weight values ​​from the jth input to the ith output are as follows: [Equation 15] [0016] [Equation 17] In equations (15), (16) and (17), η is the learning coefficient, E is the error criterion function, ω 1ij is the connection weight between node i and node j, δ ij is the local gradient of the jth neuron of the ith set of samples, p j is the input of the jth neuron in the input layer, ω 2ki is the connection weight between node i and node k, and f 1 ' is the first derivative of the transfer function of the hidden layer. The output deviation of the backpropagation neural network is propagated from the output layer to the hidden layer and then to the input layer, and the weight values ​​of each layer of the backpropagation neural network are modified. The threshold is regarded as the connection weight of one neuron whose input is 1, and is involved in the adjustment of the weight values. The repeat learning in step 6 repeats the process of forward transmission of input mode and back propagation of output error, and verifies whether the output error of the back propagation neural network reaches a predetermined expected accuracy value. If the expected accuracy value is reached, the learning is terminated; if not, the cycle is continued.

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