# 基于BP神经网络和拟合对收得率的预测Prediction of Yield Based on BP Neural Network and Fitting

Abstract: Deoxidation alloying in the steelmaking process is an important process link in steel smelting. In this paper, a prediction model for the carbon and manganese yield is studied and established, and the simulation optimization test is defined. The control space theorem is defined to judge the model prediction accuracy. Secondly, using BP neural network and fitting methods, the prediction models of alloy element yield in the process of deoxidizing alloying are established respectively, which shortens the learning and training time and improves the prediction accuracy of the model. The predicted values of BP neural network are both 85%. Above, the fitting prediction values are all above 82%. The results show that: 100 production times are randomly selected for simulation optimization. According to the control interval theorem, the fitting prediction accuracy rate is above 84%, and the BP neural network prediction accuracy rate is above 89%, and the BP neural network prediction model is more in line with production requirements.

1. 引言

2. 收得率预测评判标准

$合金元素\text{ }\text{ }i\text{ }\text{ }量=\frac{目标出钢含量\text{ }\text{ }i-吹止成分\text{ }\text{ }i}{元素\text{ }\text{ }i\text{ }\text{ }收得率}×\left(钢水净重-合金总质量\right)$

2.1. BP神经网络的C、Mn收得率预测模型建立

BP神经网络是一种非线性动力系统，包含输入层、隐含层、输出层三层单元。设输入向量为 $X={\left({x}_{1},{x}_{2},\cdots ,{x}_{n}\right)}^{\text{T}}$，隐含层输出向量为 $Y={\left({y}_{1},{y}_{2},\cdots ,{y}_{m}\right)}^{\text{T}}$，输出层输出向量为 $G={\left({g}_{1},{g}_{2},\cdots ,{g}_{k}\right)}^{\text{T}}$，则有期望输出向量为 $D={\left({d}_{1},{d}_{2},\cdots ,{d}_{l}\right)}^{\text{T}}$，输出层到隐含层之间的权值矩阵用V表示， $V=\left({v}_{1},{v}_{2},\cdots ,{v}_{m}\right)$，其中列向量 ${v}_{m}$ 为隐含层第m个神经元对应的权向量，隐含层到输出层之间的权值矩阵用W表示， $W=\left({w}_{1},{w}_{2},\cdots ,{w}_{i}\right)$，其中列向量 ${w}_{i}$ 为输出层第i个神经元对应的权向量 [3]。

$\left\{\begin{array}{l}{G}_{j}=f\left(ne{t}_{j}\right),j=1,2,\cdots ,k,\text{\hspace{0.17em}}输入层\\ ne{t}_{j}=\underset{i=0}{\overset{m}{\sum }}{\omega }_{ij}{g}_{i},j=1,2,\cdots ,k,\text{\hspace{0.17em}}隐含层\\ f\left(x\right)=\frac{1}{1+{\text{e}}^{-x}},\text{\hspace{0.17em}}转移函数\\ {f}^{\prime }\left(x\right)=f\left(x\right)\left[1-f\left(x\right)\right]\end{array}$

$E=\frac{1}{2}{\left(D-G\right)}^{2}=\frac{1}{2}\underset{i=1}{\overset{k}{\sum }}{\left({d}_{i}-{g}_{i}\right)}^{2}$ (1)

$\begin{array}{c}E=\frac{1}{2}\underset{i=1}{\overset{k}{\sum }}{\left[{d}_{i}-f\left(ne{t}_{i}\right)\right]}^{2}\\ =\frac{1}{2}\underset{i=1}{\overset{k}{\sum }}{\left[{d}_{i}-f\left(ne{t}_{i}=\underset{i=0}{\overset{m}{\sum }}{w}_{ij}{g}_{i}\right)\right]}^{2}\end{array}$ (2)

$\begin{array}{c}E=\frac{1}{2}\underset{i=1}{\overset{k}{\sum }}{\left\{{d}_{i}-f\left[\underset{i=0}{\overset{m}{\sum }}{w}_{ij}f\left(ne{t}_{i}\right)\right]\right\}}^{2}\\ =\frac{1}{2}\underset{i=1}{\overset{k}{\sum }}{\left\{{d}_{i}-f\left[\underset{i=0}{\overset{m}{\sum }}{w}_{ij}f\left(\underset{i=0}{\overset{n}{\sum }}{v}_{ij}{g}_{i}\right)\right]\right\}}^{2}\end{array}$ (3)

$\begin{array}{l}\Delta {w}_{ij}=-\eta \frac{\partial E}{\partial {w}_{ij}},\text{}i=0,1,2,\cdots ,n;\text{}j=1,2,\cdots ,k\\ \Delta {v}_{mi}=-\eta \frac{\partial E}{\partial {v}_{mi}},\text{}m=0,1,2,\cdots ,l;\text{}i=1,2,\cdots ,n\end{array}$ (4)

2.2. BP神经网络的C、Mn收得率预测模型求解

Figure 1. Comparison of real value and predicted value of Mn

Figure 2. Comparison of real value and predicted value of C

2.3. 拟合的C、Mn收得率预测模型求解

Table 1. 10 group year (year) and yield (%)

$y={a}_{1}+{a}_{2}x+\cdots +{a}_{n}{x}^{n-1}$ (5)

$\underset{i}{\overset{n}{\sum }}{\delta }_{i}^{2}=\mathrm{min}$

$\left\{{r}_{1}\left(x\right),{r}_{2}\left(x\right),\cdots ,{r}_{m}\left(x\right)\right\}=\left\{1,x,{x}^{2},\cdots ,{x}^{m-1}\right\}$ (6)

$\phi \left(x\right)={a}_{1}{r}_{1}\left(x\right)+{a}_{2}{r}_{2}\left(x\right)+\cdots +{a}_{m}{r}_{m}\left(x\right)$

$J\left({a}_{1},{a}_{2},\cdots ,{a}_{m}\right)=\underset{i}{\overset{n}{\sum }}{\delta }_{i}^{2}=\underset{i}{\overset{n}{\sum }}{\left[\phi \left({x}_{i}\right)-{y}_{i}\right]}^{2}=\underset{i}{\overset{n}{\sum }}{\left[\underset{k=1}{\overset{m}{\sum }}{a}_{k}{r}_{k}\left({x}_{i}\right)-{y}_{i}\right]}^{2}$ (7)

$\frac{\partial J}{\partial {a}_{k}}=0\text{}\left(k=1,\cdots ,m\right)$ (8)

$\left(\begin{array}{cccc}\left({r}_{1},{r}_{1}\right)& \left({r}_{1},{r}_{2}\right)& \cdots & \left({r}_{1},{r}_{m}\right)\\ \left({r}_{2},{r}_{1}\right)& \left({r}_{2},{r}_{2}\right)& \cdots & \left({r}_{2},{r}_{m}\right)\\ ⋮& ⋮& \ddots & ⋮\\ \left({r}_{m},{r}_{1}\right)& \left({r}_{m},{r}_{2}\right)& \cdots & \left({r}_{m},{r}_{m}\right)\end{array}\right)\left(\begin{array}{c}{a}_{1}\\ {a}_{2}\\ ⋮\\ {a}_{m}\end{array}\right)=\left(\begin{array}{c}\left(y,{r}_{1}\right)\\ \left(y,{r}_{2}\right)\\ ⋮\\ \left(y,{r}_{m}\right)\end{array}\right)$

$Q=\left[\begin{array}{ccc}{r}_{1}\left({x}_{1}\right)& \cdots & {r}_{m}\left({x}_{1}\right)\\ ⋮& \ddots & ⋮\\ {r}_{1}\left({x}_{n}\right)& \cdots & {r}_{m}\left({x}_{n}\right)\end{array}\right]$$a=\left[\begin{array}{c}{a}_{1}\\ ⋮\\ {a}_{2}\end{array}\right]$$y=\left[\begin{array}{c}{y}_{1}\\ ⋮\\ {y}_{n}\end{array}\right]$

Figure 3. Schematic diagram of the three-dimensional relationship between two impact factors and C yield

Table 2. C element fitting predicted value and true value analysis

Figure 4. Schematic diagram of a three-dimensional relationship between two factors and Mn yield

Table 3. Mn element fitting prediction value and true value analysis

3. 仿真优化检验

$合金元素\text{ }\text{ }i\text{ }\text{ }量=\frac{目标出钢含量\text{ }\text{ }i-吹止成分\text{ }\text{ }i}{元素\text{ }\text{ }i\text{ }\text{ }收得率}×\left(钢水净重-合金总质量\right)$

Table 4. Fitting the model to predict the carbon content of the alloy

Table 5. Fitting the model to predict the manganese content of the alloy

Figure 5. C, Mn simulation test chart

4. 结论

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