An artificial neural network is a mathematical model that imitates the structure and function of a biological neural network. It has a strong self-learning ability, self-adaptive ability, generalization ability, and fault tolerance. It mainly consists of the input layer, hidden layer, and output layer.
The basis of ANN training is sufficient and reliable raw data samples. In this paper, due to the high cost of the large-scale extrusion, all data are derived from the actual production data of P91 steel pipes of the 360 MN extrusion machine in Baotou, Inner Mongolia. As for the 360 MN vertical extrusion machine, it is the largest ferrous metal extruder in the world. Its height, width, thickness, and weight are 22.5 m, 8.2 m, 8.8 m, and 3300 tons. The hydraulic system pressure is 45 MPa, the maximum extrusion speed is 70 mm/s, and the maximum extrusion force is 360 MN. As shown in , it is a P91 steel pipe manufactured by the 360 MN machine. In the current P91 steel pipe industrial production, some parameters have been relatively mature, for example, the extrusion speed is 60 mm/s. So in the ANN model, six parameters, namely the billet surface temperature before extrusion, the inner diameter of billets, the outer diameter of billets, billet length, extrusion ratio and number times of extrusion are used as the model input. The output of the network is the breakthrough extruding force. The temperature has a significant effect on the forming force, 13 especially the breakthrough extruding force, which directly affects the constitutive relationship of the material, that is, the flow stress of the billet deformation. The surface temperature of the billet before extrusion directly affects the plastic deformation. Considering the transfer of billets is operated by large mechanical equipment such as a crane in the large-scale extrusion process and the heat dissipation of billets is fast due to the large surface area, there is a big gap between the billet surface temperature before extrusion and the temperature after heating. In this case, on the one hand, the diameter and length of billets directly affect the heat dissipation speed, which affects the temperature distribution. On the other hand, these three parameters are also more in line with the actual production order needs, that is, often need to be changed according to the order requirements. Besides, the billet length directly determines the contact area between the billet and surroundings, which affects the friction that is one of the two main causes of the extruding force. When the extrusion speed is constant, the extrusion ratio is another important parameter that affects the breakthrough extruding force. What’s more, in continuous industrial production, there are inevitable factors such as the wear of container and mandrel as well as the residue of glass powder and oxide skin, etc., which are more obvious in the large-scale extrusion process. In the finite element method and theoretical solution, the influence of this part is difficult to consider, which is one of the main causes of error. This part of the factor is regarded as noises of the ANN model, which is difficult to record and measure. It will change during each extrusion process. And the accumulation of quantitative changes will lead to qualitative changes. Therefore, the extrusion times are incorporated as an additional factor in the prediction of breakthrough extruding force. shows the specific experimental results of the 360 MN extrusion test which are randomly selected from all the data and also the learning sample of the ANN model. Due to a large amount of data, only part is presented here. In the production process, according to the order requirements, the inner/outer diameter of billet of the same serial number is consistent, and the extrusion ratio is also the same. However, due to the actual operation, billet surface temperature before extrusion is bound to be different. In addition, the numbers of pipes produced with different serial numbers are also different. Besides, according to the relationship among the hidden layer, the input layer, and the output layer, 14 the number of hidden layer neurons is determined to be a natural number between 3 and 12. After calculating the influence of the number of neurons on the calculation accuracy through the enumeration method, the number of selected hidden layer neurons is 3. The error tolerance chosen for the model is 0.1 and the spread factor is 1. Therefore, a 6-3-1 RBF neural network structure is established.
Radial basis neural network can approximate any continuous function with arbitrary precision. It has the unique best approximation characteristic and there is no local minimum problem. It is the optimal forward network for completing the mapping function. Therefore, the radial basis neural network is mainly used to construct the prediction model in this paper. shows the schematic diagram of the structure of the radial basis function (RBF) neural network and is the input and output of the i-th neuron in the hidden layer. Xq represents the q-th input vector, w1i is the weight vector of the hidden layer neuron connected to the input layer and b1i is the threshold value. Gauss function is adopted as the excitation function.
Therefore, the input of the i-th hidden layer neuron:
kiq=∑j(w1ji−xjq)2×b1i
(1)
Then, the output of the i-th hidden layer neuron:
riq=radbas(kiq)=exp(−(‖w1i−Xq‖×b1i)2)
(2)
The input of the output layer is the weighted sum of the output of each hidden layer neuron, so the output is:
yq=∑i=1n(ri×w2i)
(3)
where w2i is the weight vector between the hidden layer and output layer.
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