Energy Consumption Optimization of the Aluminum Industrial Production Based on Pattern Recognition

The basic energy consumption situation in 1 ton of aluminum production is addressed in this paper for the current aluminum industry from mining to the aluminum processing. In order to save energy of the aluminum industrial production, the K-means algorithm and threshold cluster analysis algorithm from the pattern recognition are proposed, and the classification of the energy consumption data of the aluminum industrial production is completed by using C++. The two algorithms are compared in terms of minimum total energy consumption and the actual production requirements. A class is found with more data number and smaller total energy consumption data, and such class heart is used as an input to save the aluminum industrial production. Further-more the feasibility and the effectiveness of the algorithms are verified.


Introduction
Energy consumption of the aluminum industrial processes has always been a problem affecting people, which have been continually studied and explored.Despite many successes, there are still many gaps to do.Pattern recognition theory and methods have been a widespread attention in many science and technology fields.It has promoted the development of artificial intelligence system, and has expanded the areas of computer applications.For years, pattern recognition research has already made great achievements.This paper is aimed to classify the energy consumption data of the aluminum industrial production, extracting the implicit rules, and guiding the practical production, so as to save energy.This paper introduces the relevant knowledge of pattern recognition and cluster analysis, extracts the energy consumption situation of the aluminum industrial production, and proposes two cluster analysis algorithms for a large number of energy consumption data in the aluminum industrial production.The energy consumption data is classified by using C++, and an energy saving way is found.

Pattern recognition
Pattern recognition is a process that describes, identifies, classifies and explains the thing or phenomenon, through analyzing all the information which indicates the thing or phenomenon.Its main application fields include such subjects as image analysis, voice recognition, sound classification, communication, computer aided diagnosis, data mining and so on.According to the property of the problem and the method solving the problem, pattern recognition can be divided into classification with supervision and classification without supervision.The major difference between them is that whether the categories of the experimental specimens are known in advance.Generally speaking, the classification with supervision is often necessary to provide a large number of samples whose categories are known, but in actual problems, it often has certain difficulties.It is often needed to research the classification without supervision(Li Jing-jiao translate, 2006).There are two basic pattern recognition methods, statistical pattern recognition method and structural pattern recognition method.The statistical pattern recognition method is based on the probability density function for the distribution of the pattern set in the character space, then do some research on the general character, cluster analysis is a kind of classification without supervision.Bo, 2008) The process of dividing the physical or abstract objects into a group of classes or domains is called clustering.The class generated by clustering is a collection of objects, which are similar to the objects of the same class, and different to the objects of the other class.So in many applications, the data objects of the same class can be treated as a whole.

Cluster analysis (Yin
The mathematical description of clustering process is as follows (Yang Xiao-bing, 2005): Define the sample set to be studied as , and a non-empty subset of class , that is, and .
The ultimate goal of clustering is to divide the sample set into partitions , there may be some objects not belonging to any partition, which is defined to belong to the noise .The union of all the partitions and noise is the sample set , and there is no intersection between these partitions, that is: (For any ) The partitions are clustering.The second condition says that each sample of the sample set belongs to one class.

Cluster analysis algorithm
Cluster analysis algorithm depends on the data type, the purpose and the application of the cluster analysis.This paper proposes two cluster analysis algorithms as follows.
3.1 The threshold cluster analysis algorithm (Sun Ji-xiang, 2001) 1) The terms and conventions Set up the pattern set to be classified as , select the within-class distance threshold T.

2) Algorithm idea
Calculate the distance from the pattern feature vector to the cluster center, and compare it with the threshold T , then decide which class it belongs to or if a new class center is needed to establish.Using Euclidean Distance in the algorithm: Set , .Euclidean Distance: 3) The principle and steps of the algorithm (1)Take any pattern feature vector as the first cluster center.For example, command is the center of class .
(2)Calculate the distance from the next pattern feature vector to .If , then establish a new class , with its center being ; if , then .
(3)Assuming cluster centers have been , calculate the distance from the unsettled pattern feature vector to each cluster center .If , then set as the center of a new class , ; Otherwise, if the then . Check whether all of the patterns are finished.If finished, then come to the end; otherwise return to (3).Jie-gu, & Cai Guo-lian, 1986) K-means algorithm makes the sum of the squared distance from all the samples in the domain to the cluster center minimum, which is based on the criterion function of the sum of the squared error.K-means algorithm consists of the following steps:

K-means algorithm with error limit(Li
1) Define K value and error limit, arbitrarily choose K initial cluster centers .Usually select the first K samples from the given sample set as the initial cluster centers.
2) The th iteration.If , , then the cluster center, it is the sample set of .Repeat this step until each sample is distributed to the K cluster domains.
3) Results from the second step, calculate the new cluster center , Which leads to the criterion function of the minimum sum of the squared error.
, When the gap between the calculated new cluster center and the original cluster center is greater than the pre-defined error limit, then update the cluster center, otherwise maintain the original cluster center.

4) If
, algorithm converges, and the program ends.Otherwise, go to the second step.Count the data number of each class when classifying.

Cluster analysis algorithms applied to the aluminum industrial production
Aluminum industrial production system includes mining plant, alumina plant, electrolytic aluminum plant and aluminum processing plant.Each procedure consumes a lot of energy.
Mining plant is mainly to transport mine.The current alumina production use bauxite, nepheline, and alunite [6] .For example, alunite has the alumina content of 37%( Wang Yan-ming, Yan Ding-ou, Yang Chong-yu, & Gao Shou-ye translate, 1987). 1 ton of aluminum production needs approximately 5.1 tones of alunite.According to the present fossil fuel consumption of transportation, transporting so much alunite about 1 km consumes fuel at cost 0.25 Yuan.
Alumina plant: Comprehensive energy consumption of 1 ton of alumina production is shown in Table 1 (Wu Jin-wei, 2003).According to the chemical expression of alumina, 1 ton of aluminum production probably needs 2 tons of alumina, we can get the energy consumption of standard coal in 1 ton of aluminum production, as shown in Table 2.The alumina plant in the production of 1 ton of aluminum requires energy is shown in Table 3. Electrolytic aluminum plant is mainly carried out through the electrolytic cell.In the electrolytic cell, the expression of the energy consumption (W) is (Dong Shi-yi, Liu Yong-qiang, & Li Wei-bo, 2007): Where V is the average voltage of the electrolytic cell, η is the current efficiency.According to (Yang Yun-bo, & Dong Chun-ming, 2009), the average current efficiency of Chinese advanced aluminum plant is 94.9%.Reference (Yang Ling, 2008) points out that the current average voltage of electrolytic aluminum plant is 4.22V.Therefore, through (1), the energy consumption in the production of 1 ton of aluminum is calculated as 13251.4kWh.The coefficient of standard coal for electric is 0.407 according to Table 1.Thus the energy consumption of the electrolytic aluminum plant in the production of 1 ton of aluminum is calculated as 5393.3kgstandard coal.
In the aluminum processing plant, the main production processes include casting, forging, oxidation of color, etc (Xiao Cui-ping, 2005).The energy consumption of Chinese major aluminum processing plant is given in Table 4(Xiao Cui-ping, 2005).
For the aluminum processing plant that has only three processes and the products of each process (Xiao Cui-ping, 2005), energy consumption of the aluminum processing plant can be simplified as the energy consumption in the production of ingot, aluminum alloy plate and oxidation coloring material.
As the foregoing analysis, the situation of energy consumption in the production of 1 ton of aluminum, including mining plant, alumina plant, electrolytic aluminum plant and aluminum processing plant, is listed in Table 5.There are 10 factors (component 1-10) affecting the total energy consumption.
A batch of stochastic data is generated by Matlab according to Table 5.It is based on certain distributions in Table 6.N means normal distribution, U means continuous uniform distribution.Finally each data vector has 11 components.See the first 10 components in Table 5.The last component is the sum of the first 10 components, the total energy consumption.

Simulation results and analysis
The classification of a lot of energy consumption data of the aluminum industrial production is completed by using the two cluster analysis algorithms mentioned in subsection 3. The threshold T is determined through explore method, defines different thresholds, compare and analyze the different results.When T is larger than 550, get too many classes, when T=550,600,700 and 800, the classification results respectively are shown in Table 7, Table 8, Table 9 and Table 10.E means the total energy consumption of the class, Num means the data number of the class, and Error represents the error limit in subsection 3.
For K-means algorithm define different K values and error limits, when the error limits are defined as 0.001, 0.1 and 100, the classification results for all the different K values are the same, so for all the different K values respectively define three error limits of 0.001,10 and 100, when K= 5 and K= 20, the classification results are shown in Table 11 and Table 12, when K= 10 and K= 15, the classification results of error limit of 0.001 and 10 are the same, so the classification results are shown in Table 13 and Table 14 only have two cases.If the data number of the class is large, it shows that the class in reality is relatively easy to implement.In order to achieve energy saving of the aluminum industrial production, we need to find the class with minimum total energy consumption.
When K=20, for different error limits the largest data number are respectively 75, 69, 78, the maximum energy consumption are respectively 9.998, 9.998, 9.981, the minimum energy consumption are respectively 7.283, 7.283, 7.401; While the threshold cluster analysis algorithm when T=550, in the 18 classes, the largest data number is 159, the maximum energy consumption is 10.156, the minimum energy consumption is 7.167.When K=15, for the two cases the largest data number are both 101, the maximum energy consumption are respectively 9.848, 9.931, the minimum energy consumption are respectively 7.572, 7.600; While the threshold cluster analysis algorithm when T=600, in the 14 classes, the largest data number reach 218, the maximum energy consumption is 10.110, the minimum energy consumption is 6.990.When K=10, for the two cases the largest data number are respectively 128, 147, the maximum energy consumption are respectively 9.800, 9.699, the minimum energy consumption are respectively 7.610, 7.777; While the threshold cluster analysis algorithm when T=700, in the 11 classes, the largest data number reach 305, the maximum energy consumption is 10.074, the minimum energy consumption is 6.990.When K=5, for the three error limits the largest data number are respectively 287, 285, 267, the maximum energy consumption are respectively 9.492, 9.499, 9.409, the minimum energy consumption are respectively 7.785, 7.803, 7.865; While the threshold cluster analysis algorithm when T=800, in the 5 classes, the largest data number reach 404, the maximum energy consumption is 9.750, the minimum energy consumption is 7.473.For K-means algorithm, the more the classes, the stronger the regularity, and the classification results of different error limits are nearly the same, so the superiority is not obvious; But for the threshold cluster analysis algorithm for different thresholds the data number are far more different from each other, and the total energy consumption has a large span, so the superiority is rather obvious.As the cluster centers of the threshold cluster analysis algorithm are all from the original data, and once the cluster centers are determined, they will not change, when T=600 and T=700, we get the minimum total energy consumption 6.990, and the data number is just 1, so it's the minimum total energy consumption of the original data, therefore this algorithm can also find the minimum total energy consumption of the original data.
Contrast, and analyze the classification results, considering the actual production, in order to save energy in the aluminum industrial production, this paper chose the third class of the result when T=800, use the first 10 components of the cluster center (0.053, 0.211, 0.612, 0.227, 0.022, 0.006, 4.885, 0.396, 0.903, 0.758, 8.073) as input, which can reach the purpose of energy saving while fulfilling the task of the aluminum industrial production.

Conclusion
In this paper, energy saving of the aluminum industrial production is discussed, that is to say, the basic energy consumption situation in 1 ton of aluminum production, for the current aluminum industry from mining to the aluminum processing.The K-means algorithm and the threshold cluster analysis algorithm are proposed, and the classification of a lot of energy consumption data of the aluminum industrial production is completed by using C++.After analyzing the different classification results, it shows that for the K-means algorithm, the more the classes, the stronger the regularity, so the superiority is not obvious, but for the threshold cluster analysis algorithm, the superiority is rather obvious.When T = 800, the third class of the classification result is the best, and the total energy consumption of the class is only 8.073, with the data number of the class being 210.Using the first 10 components of the cluster center (0.053, 0.211, 0.612, 0.227, 0.022, 0.006, 4.885, 0.396, 0.903, 0.758, 8.073) as input, energy saving of the aluminum industrial production is greatly achieved.The feasibility and effectiveness of the algorithm are verified through simulations.

Table 1 .
Comprehensive energy consumption of 1 ton of alumina production

Table 3 .
Energy consumption of alumina plant in the production of 1 ton of aluminum