The concentration of alumina in the electrolyte is of great significance during the production of aluminum; it may affect the stability of aluminum reduction cell and the current efficiency. However, the concentration of alumina is hard to be detected online because of the special circumstance in the aluminum reduction cell. At present, there is lack of fast and accurate soft sensing methods for alumina concentration and existing methods can not meet the needs for online measurement. In this paper, a novel soft sensing method based on a modified extreme learning machine (MELM) for online measurement of the alumina concentration is proposed. The modified ELM algorithm is based on the enhanced random search which is called incremental extreme learning machine in some references. It randomly chooses the input weights and analytically determines the output weights without manual intervention. The simulation results show that the approach can give more accurate estimations of alumina concentration with faster learning speed compared with other methods such as BP and SVM.

In the industrial aluminum reduction cells, the stability of the alumina concentration is the key issue to maintain high efficiency during the production of aluminum. It is easy to lead to the occurrence of the so-called “anode effect” if the alumina content in the electrolyte becomes too low (e.g., 1%–1.5%). When it occurs, cell voltage rises abruptly to 30

Figure

Experimental environment.

The main thought of the soft sensing technology is to build one model which uses variables that could be directly online measured as input and thus the variables to be estimated as output, to use many kinds of complex calculating and evaluation and to get the values of detecting variables by computer software [

So far, the widely used method of determining alumina concentration in the industrial factory is to use the spectrometer to analyze the sampled electrolyte. It is an offline method. The improved ELM method is applied to build up the soft sensing online detection approach of alumina concentration in this paper. This ELM algorithm tends to provide the best generalization performance at extremely fast learning speed. The experimental result shows that the new method can produce the best generalization performance and learn much faster than the traditional prediction models.

The following sections are organized as follows. Section

Huang proposed extreme learning machine (ELM) algorithm; ELM was originally proposed for the single-hidden-layer feedforward neural networks (SLFNs) and then it extends to the generalized SLFNs. ELM can randomly generate the input weights and the bias of hidden nodes. It uses the theory of least squares to get the output weights. The learning speed of ELM can be thousands of times faster than traditional feedforward network learning algorithms like backpropagation (BP) algorithm while obtaining better generalization performance and smaller training error [

SLFN network architecture.

Considering there are

The fact that standard SLFNs with

The above

The minimal norm least squares method instead of the standard optimization method was used in the original implementation of ELM:

Assign arbitrary input weighs

Calculate the hidden layer output matrix

Calculate the output weights

Ridge Regression, which was proposed by Horel and Kennard in

Consider

Consider

Hoerl and Kennard had proved that Ridge Regression has less mean square error than the ordinary regression under the proper ridge parameter. It is as follows:

So, when

From the above equations,

The Error Minimized Extreme Learning Machine algorithm starts from a small size of ELM hidden layer and adds random hidden node (nodes) to the hidden layer, while the output weights are updated incrementally.

Suppose a SLFN,

Huang had proved

Consider

In order to facilitate the calculation, the inversion is substituted as follows:

So

Similarly, we get

Now, a new hidden layer output matrix is obtained which has less output error. Then, we can update the output weight matrix based on the new hidden layer output matrix.

In the aluminum production, through referring to relative documents and soliciting experts opinion, there are many factors that affect the alumina concentration, such as alumina feeding speed, cell voltage, series current, current of anode rod, voltage between anode rod and cathode bar, and bath temperature [

It is necessary to do the data denoising preprocessing before using the algorithm, because the process of data collection may introduce noise, where data collection is affected by interference and influence of all kinds of noise signal. At present, there are two denoising methods, the traditional filtering method and the wavelet denoising method. Traditional denoising method is based on Fourier analysis and can always be used in the environment where signal and noise are very small. While wavelet analysis is known as the “microscope” of mathematical analysis, it is a time-frequency analysis method of signal, with the characteristics of multiresolution analysis [

In this paper, we select voltage between anode rod and cathode bar as model input and alumina concentration in the electrolyte below the anode rod as model output.

First, ELM algorithm is applied to build soft sensing method model of alumina concentration. In general, active functions play an important role in computing of neural networks. Widely used active functions in the ELM algorithm are

Data in this paper came from a 350 kA prebaked aluminum reduction cell in the ZunYi aluminium electrolysis factory; Figure

The voltage between number 20 anode rod and cathode bar and the alumina concentration in the electrolyte below the anode rod.

The voltage between number 21 anode rod and cathode bar and the alumina concentration in the electrolyte below the anode rod.

The ELM, BP, and SVM soft sensing models are trained by the same sample set. All the data are preprocessed before training and simulating in the algorithm. For the purpose of comparing the three models quantitatively, we substitute ten

Simulation alumina concentration results of three models.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|

Actual value (%) | 1.94 | 2.37 | 2.03 | 1.95 | 2.16 | 2.02 | 1.99 | 1.94 | 2.64 | 2.94 |

Output of ELM (%) | 1.8164 | 2.0641 | 2.0739 | 2.1544 | 1.9423 | 1.9065 | 1.9166 | 2.047 | 2.6761 | 2.6443 |

Output of BP (%) | 1.7551 | 2.015 | 1.9953 | 2.4558 | 1.9594 | 1.9047 | 1.9510 | 2.0183 | 3.0956 | 2.9993 |

Output of SVM (%) | 1.9176 | 2.003 | 2.006 | 2.0917 | 1.8828 | 1.8834 | 1.8979 | 1.8833 | 2.301 | 2.3042 |

The comparison of performance indicators.

Training Time (s) | Testing Time (s) | Training RMSE | Testing RMSE | ARE (%) | |
---|---|---|---|---|---|

ELM | 0 | 0 | 0.0926 | 0.1784 | 6.78 |

BP | 28.3281 | 0.0156 | 0.1698 | 0.2626 | 9.17 |

SVM | 0.0156 | 0 | 0.2635 | 0.2797 | 8.83 |

Experimental aluminum reduction cell and anode rod.

Sampled electrolyte.

From Figure

Simulation result of ELM model.

Actual alumina concentration values and simulation results.

Alumina concentration is very important in the aluminum electrolysis, which may affect the performance of aluminum reduction cell. It is difficult to measure the alumina content due to the complicated environment of aluminum reduction cell. This paper proposes a novel soft sensing method of alumina concentration in the electrolyte based on extreme learning machine (ELM) and builds the relationship between alumina concentration and voltage between anode rod and cathode bar. Through the simulation results and comparison of BP model and SVM model, we can see the validity and advantage of the proposed method. This method is able to effectively achieve rapid and reliable estimation of alumina concentration in a relatively short time.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work has been supported by the National High Technology Research and Development Program (“863” Program) of China (Grant no. 2013AA040705).