The 7th MathorCup University Mathematical Modeling Challenge in 2017
Question A Intelligent Manufacturing in Process Industry
Reproduction of the original title:
"Made in China 2025" is a national grand strategy for the upgrading of my country's manufacturing industry. The core of its technology is intelligent manufacturing, and the degree of intelligence is equivalent to the level of "German Industry 4.0". The key areas of "Made in China 2025" include not only the manufacturing industry of major equipment, but also the process industry of new energy and new material manufacturing.
In the process industry, iron and steel metallurgy, petrochemical and other industries are representative pillar industries of the national economy. The objective function of system optimization and intelligent control of its production process includes multi-objective requirements such as energy saving, high quality, low consumption, and environmental protection. In order to achieve such an optimization goal, the key technology of intelligent control of the production process must be further upgraded from the original feedback control to predictive control. That is, through the cyber physical system (Cyber Physical System) modeling of production process big data, through big data mining, determine the best way and the best parameter control range of the production process, predictively and dynamically adjust the production process control, and obtain the best production Effect.
Taking blast furnace smelting high-quality molten iron as an example, the blast furnace ironmaking process is a smelting process in which raw materials such as ore and coke are added from the top of the blast furnace in the order of feeding, and hot air is blown continuously from the bottom of the blast furnace, and coal powder is injected to adjust the furnace temperature. The smelting period is 6-8 hours from the time when the raw material is added to the top of the furnace to smelting into slag and molten iron. The blast furnace taps slag and iron every 2 hours. And the chemical composition of the molten iron and slag in this tapping was obtained by laboratory tests. Therefore, there is a correlation between the silicon content of the two furnaces, that is, the furnace temperature. The ironmaking process is a complex production process of discrete input, continuous smelting, and discrete output.
The mechanism of the ironmaking process includes not only the chemical reaction process constrained by heat balance/material balance, but also the physical movement process caused by three-phase fluid dynamic mixing. Therefore, the complete mechanism model of the smelting process is a complex mathematical model composed of algebraic equations and partial differential equations. The model equations are as follows: It is an unsolved mathematical problem to solve the optimal solution of the above mixed kinetic equations from the mechanism
. Therefore, process optimization through big data data mining technology is a feasible solution.
The process parameters collected in chronological order during the ironmaking process are a high-dimensional big data time series. There are hundreds of influencing factors. Its ultimate production indicators such as output, energy consumption, and molten iron quality are closely related to a controlling intermediate indicator in the smelting process—furnace temperature, that is, the silicon content [Si] in molten iron (mass percentage of silicon in molten iron). The prediction of the rise or fall of the blast furnace temperature after 2 hours or 4 hours, that is, the prediction of the [Si] time series, is related to the current control direction of various operating parameters of the blast furnace. Therefore, accurate predictive control modeling of [Si] has become a key technology for smelting process optimization and predictive control.
In order to simplify the problem, this project only provides a database consisting of silicon content [Si], sulfur content [S], coal injection volume PML and blast volume FL as the basis for mathematical modeling analysis and data mining. The serial number N is not only the serial number of the data sequence, but also the serial number of the blast furnace tapping time.
The requirements for the mathematical modeling of this project are:
(1) From the 1000 furnace production big data arranged in sequence [Si]-[S]-FL-PML in the given data table, independently select learning samples and algorithms, and establish [Si] ] Forecasting dynamic mathematical models, including one-step forecasting model and two-step forecasting model. A comprehensive discussion of your mathematical modeling ideas.
(2) Select verification samples independently to verify the prediction success rate of the mathematical model you have established. Including the success rate of numerical prediction and the success rate of furnace temperature rise and fall direction prediction. And discuss the feasibility of its dynamic predictive control.
(3) Taking the sulfur content [S] of the quality index molten iron as an example, the sulfur content is low and the quality of molten iron is good, which can produce high-quality steel and high-quality equipment. Try to establish the optimization mathematical model of the quality index [S], and discuss the expected effect of [Si] predictive control according to the calculation results of the optimization model.
(4) Discuss your experience in modeling complex industrial intelligent control big data.
Overview of the overall solution process (abstract)
Under the national strategy of "Made in China 2025" to upgrade my country's manufacturing industry, in order to predict and control the blast furnace ironmaking process, this paper established a neural network prediction model and a chaotic time series prediction model, and improved the neural network model based on genetic algorithm (GA). The sulfur content [S] was optimized using Particle Swarm Optimization (PSO).
For problem 1, first of all, this paper preprocesses the data given in the attachment, removes outliers and normalizes them, and obtains 932 sets of valid data. Then, the BP neural network prediction model was established to predict the silicon content [Si], and the correlation among the silicon content [Si], sulfur content [S], blast volume FL and coal injection volume PML was analyzed. Secondly, the wavelet neural network prediction model and the BP neural network prediction model optimized by Genetic Algorithm (GA) are established, and the advantages and disadvantages of the three are compared. Then, 922 groups of training sample data were selected, and 10 groups of verification sample data were selected. It was found that the BP neural network prediction model and wavelet neural network prediction model optimized by the genetic algorithm had better prediction effect, but the BP neural network prediction model was poorer. Finally, the chaotic time series prediction model is established in this paper, and the chaotic local linear one-step prediction and two-step prediction are carried out for the silicon content [Si].
For the second question, first of all, this paper selects 922 sets of data as training samples and 10 sets of data as verification samples. The traditional BP neural network prediction model, wavelet neural network model prediction model, BP neural network prediction model based on genetic algorithm optimization and chaos Time series forecasting model, respectively predicting the results of silicon content [Si] in the last 10 heats and comparing with the actual value, it is calculated that the success rate of BP prediction is 20%, that of wavelet prediction is 70%, and that of GA+BP is 60%. Chaos prediction is 80%. Secondly, the results of the silicon content [Si] of the last 10 furnaces were predicted by different models, and the direction of furnace temperature rise and fall was predicted, and the calculation obtained: the success rate of BP prediction was 40%, the wavelet prediction was 100%, and the GA+BP prediction is 100%, and chaos prediction is 100%. Finally, by discussing the selection of neural network training function, the setting of neural network performance parameters and the
selection of neighborhood radius for chaotic time series prediction, the feasibility of dynamic predictive control is analyzed.
For the third question, firstly, this paper optimizes the prediction model of BP neural network according to the genetic algorithm (GA), predicts the sulfur content [S], and finds out the sulfur content [S] and silicon content [Si], blast volume The relationship between FL and the amount of coal injection PML. Then, this paper uses the particle swarm optimization algorithm (PSO) to optimize the sulfur content [S], and it is obtained that the sulfur content [S] has a minimum value when the blast volume is normalized FL=0.7012 and the coal injection volume PML=0.0809. Finally, this paper analyzes the expected effect of predicting and controlling silicon content [Si] under the optimal condition of sulfur content [S]. ] is smaller, being 0.5712.
For the fourth question, we combined the modeling background, the results obtained from solving the model and the conclusions obtained from the analysis results, and based on the significance of intelligent control in complex process industries, we briefly talked about the experience of modeling. Through big data mining, we can determine the best way and the best parameter range of the production process to obtain the best production effect.
Model assumptions:
(1) Assume that in the chaotic local linear prediction, the selection of the neighborhood ε is objective and accurate, and the subjectivity is small.
(2) Assume that in chaotic local linear prediction, local properties can accurately represent global properties.
(3) Assume that in neural network prediction, input variables are reasonably efficient as the first layer of the network.
(4) It is assumed that the data provided in the appendix and the data used are true and accurate.
(5) Assume that the data composed of silicon content [Si], sulfur content [S], coal injection volume PML and blast volume FL in molten iron can represent the blast furnace ironmaking process and reflect the blast furnace ironmaking characteristics.
problem analysis:
Analysis of Question 1: In Question 1, the title requires us to independently select learning samples and algorithms from the 1000 furnace production big data arranged in sequence [Si]-[S]-FL-PML in the given data table, and establish [ Si] forecasting dynamic mathematical models, including one-step forecasting model and two-step forecasting model. The one-step prediction model and the two-step prediction model mean that the prediction step length is 1 and 2 respectively, and there is a correlation between the silicon content of the two furnaces, that is, the furnace temperature. The learning samples here cannot be all 1000 batches of production big data, because we need to verify the prediction success rate of the established mathematical model in question 2, so we cannot choose all the data for training, but only a part of the data for learning and training. As for the modeling algorithm, it needs to be selected in combination with the problem itself.
Analysis of Question 2: In Question 2, the question requires us to independently select verification samples to verify the prediction success rate of the mathematical model we have established, including the numerical prediction success rate and the furnace temperature rise and fall direction prediction success rate. And discuss the feasibility of its dynamic predictive control. We need to select verification samples from the remaining unlearned training data in the production big data of 1000 furnaces, and verify the success rate including [Si] content and the direction of furnace temperature rise and fall. The difficulty lies in discussing the feasibility of its dynamic predictive control and how to improve the predictive success rate of the algorithm.
Analysis of Question 3: In Question 3, the title requires us to take the sulfur content [S] of the quality index molten iron as an example. The sulfur content is low and the quality of molten iron is good, which can produce high-quality steel and high-quality equipment. Try to establish the optimization mathematical model of the quality index [S], and discuss the expected effect of [Si] predictive control according to the calculation results of the optimization model. Through big data mining, determine the best way and the best parameter control range of the production process, predictively and dynamically adjust the production process control, obtain the best production effect, establish an optimization model, and discuss the predictive control of [Si].
Analysis of Question 4: In Question 4, the topic requires us to discuss our experience in modeling complex process industry intelligent control big data, which needs to be discussed in combination with the results and background of our model.
Model establishment and solution Overall paper thumbnail
For all papers, please see below "Only modeling QQ business cards" Click on the QQ business card
Program code: (code and documentation not free)
The actual procedure is shown in the screenshot
1 def BP(sampleinnorm, sampleoutnorm,hiddenunitnum=3):
2 # 超参数
3 maxepochs = 60000 # 最大迭代次数
4 learnrate = 0.030 # 学习率
5 errorfinal = 0.65*10**(-3) # 最终迭代误差
6 indim = 3 # 输入特征维度3
7 outdim = 2 # 输出特征唯独2
8 # 隐藏层默认为3个节点，1层
9 n,m = shape(sampleinnorm)
10 w1 = 0.5*np.random.rand(hiddenunitnum,indim)-0.1 #8*3维
11 b1 = 0.5*np.random.rand(hiddenunitnum,1)-0.1 #8*1维
12 w2 = 0.5*np.random.rand(outdim,hiddenunitnum)-0.1 #2*8维
13 b2 = 0.5*np.random.rand(outdim,1)-0.1 #2*1维
14
15 errhistory = []
16
17 for i in range(maxepochs):
18 # 激活隐藏输出层
19 hiddenout = sigmod((np.dot(w1,sampleinnorm).transpose()+b1.transpose())).transpose()
20 # 计算输出层输出
21 networkout = (np.dot(w2,hiddenout).transpose()+b2.transpose()).transpose()
22 # 计算误差
23 err = sampleoutnorm - networkout
24 # 计算代价函数（cost function）sum对数组里面的所有数据求和，变为一个实数
25 sse = sum(sum(err**2))/m
26 errhistory.append(sse)
27 if sse < errorfinal: #迭代误差
28 break
29 # 计算delta
30 delta2 = err
31 delta1 = np.dot(w2.transpose(),delta2)*hiddenout*(1-hiddenout)
32 # 计算偏置
33 dw2 = np.dot(delta2,hiddenout.transpose())
34 db2 = 1 / 20 * np.sum(delta2, axis=1, keepdims=True)
35
36 dw1 = np.dot(delta1,sampleinnorm.transpose())
37 db1 = 1/20*np.sum(delta1,axis=1,keepdims=True)
38
39 # 更新权值
40 w2 += learnrate*dw2
41 b2 += learnrate*db2
42 w1 += learnrate*dw1
43 b1 += learnrate*db1
44
45 return errhistory,b1,b2,w1,w2,maxepochs
import numpy as np
#定义激活函数
def sigmoid(x,deriv=False):
if deriv == True:
return x*(1-x)
return 1/(1+np.exp(-x))
x = np.array([[0,0,0],[0,1,1],[1,0,1],[0,0,1],[0,0,1]])
print(x.shape)
#指定label值
y = np.array([[0],[1],[1],[0],[0]])
print(y.shape)
#指定随机化种子，使得每次随机值一样
np.random.seed(1)
#定义三层的神经网络
w0 = 2*np.random.random((3,4)) - 1
w1 = 2*np.random.random((4,1)) - 1
print(w0)
print(w1)
for j in range(6000):
l0 = x
l1 = sigmoid(np.dot(l0,w0))
l2 = sigmoid(np.dot(l1,w1))
#真实值-预测值
l2_error = y - l2
if j%1000 == 0 :
print("error"+str(np.mean(np.abs(l2_error))))
l2_delta = l2_error*sigmoid(l2,deriv=True)
l1_error = l2_delta.dot(w1.T)
l1_delta = l1_error*sigmoid(l1,deriv=True)
#更新w0 w1
w1 += l1.T.dot(l2_delta)
w0 += l0.T.dot(l1_delta)