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The detection of the magnetic properties of haematite plays an important role in the adjustment of the beneficiation process of haematite and the improvement of metal recovery. The existing methods for measuring the magnetic properties of iron ore either have large errors or take a long time. Therefore, it is very necessary to find a method that can quickly and accurately detect the magnetic properties of haematite. This paper presents a method to detect the magnetic properties of haematite based on the extreme learning machine based on the improved particle swarm optimization (IPSO-ELM) algorithm and spectroscopy. The improved particle swarm optimization algorithm is used to optimize the input weights, hidden layer deviations, and hidden layer nodes of the ELM network. Introducing the linear decreasing inertia weight for the particle swarm algorithm, taking into account the norm of the output weight in the particle update process and using the variation idea to change the length of the particle give the IPSO-ELM better stability and generalization ability. The experimental results show that the IPSO-ELM prediction model has a good prediction performance and has better generalization ability than that of the ELM and PSO-ELM prediction models. Compared with traditional chemical analysis methods and manual methods, this method has great advantages in terms of economy, speed, and accuracy.

Iron ore is the main raw material for production of steel, and haematite is one of the main types of iron ore. The beneficiation process of iron ore is an important process in the production process of iron ore. The choice of beneficiation process plays a decisive role in the quality of iron ore. Taking the Anshan mining area as an example, the iron content of the ore is 20–40%, with an average of 30%. Ore must be beneficiated, and the iron content after selection can reach more than 60%. For haematite, the detection of its magnetic property will play an important role in the adjustment of its beneficiation process and the improvement of metal recovery. Studies have shown that [

The extreme learning machine (ELM) neural network is a kind of single hidden layer feed-forward neural network proposed by Huang et al. in 2004, which has the advantages of fast learning and strong generalization [

However, the ELM randomly selects the input weights and hidden biases, and there will be some weights and biases of 0. This approach will cause the ELM to require a large number of hidden layer nodes to achieve the desired effect, and there will be large differences in the results of each operation. The particle swarm optimization (PSO) algorithm is a global optimization algorithm proposed by Dr. Eberhart and Dr. Kennedy in 1995 [

Therefore, the particle swarm optimization algorithm can be used to optimize the ELM input weights and hidden layer biases. In 2006, Xu and Shu proposed an extreme learning machine based on particle swarm optimization (PSO-ELM) [

The key issues that need to be solved in this paper are three aspects: data acquisition, data processing, and model building. In the data acquisition phase, haematite samples from the mining area need to be collected and subjected to spectral and chemical tests to obtain spectral data of the sample and accurate magnetic properties. In the data processing stage, high-dimensional haematite spectral data needs to be dimensioned to facilitate the establishment of the model. In the model establishment stage, it is necessary to use the spectral data after the dimension reduction and the accurate magnetic rate to establish the haematite magnetic permeability detection model based on the IPSO-ELM algorithm proposed in this paper. The test results were analyzed to verify the feasibility of detecting the magnetic properties of haematite based on spectral data and ELM algorithm.

The Anshan iron ore mine of Liaoning Province is one of the major iron ore mines in China, and the main type of iron ore in this area is haematite. Therefore, this study selected two mining areas in Anshan as experimental areas and collected haematite samples at the site. The sample is block shaped and the size is approximately 30 cm × 30 cm × 30 cm.

Core drilling and cutting are performed on the collected samples. During the processing of the experimental samples, the core is corroded along the direction of the silicon and iron formed in the ore and then cut along the direction perpendicular to the core cylinder to prepare circular lamellar experimental samples with a diameter of 6 cm and a thickness of 0.5–1 cm, as shown in Figure

The prepared experimental samples.

For the spectral test of the experimental samples, we use a SVC HR-1024 portable ground spectrometer, as shown in Figure

SVC HR-1024 portable ground object spectrometer.

In this experiment, 91 experimental samples were collected. First, the samples were chemically analyzed to obtain the accurate magnetic property of the haematite samples. There were 64 samples with their magnetic properties below 10%, 19 samples at 10–20%, and 8 samples with their magnetic properties more than 20%. Then, the spectrum test was performed. In this experiment, the sampling integration time was set to 3 s and the field of view angle was 4°. The probe of the spectrometer was 0.5 m away from the surface of the haematite sample and is perpendicular to the surface of the sample. The spectrometer (SVC HR-1024) was used to perform five spectral tests on each sample, and then the spectral data were averaged to give the spectral data of the sample (973 dimensions). After the spectrum test is completed, the data of the test spectrum of the haematite sample is obtained by performing data preprocessing operations such as roughing out and band fitting on the measured spectral data. Figure

Spectral curve of haematite samples.

The haematite spectral data matrix exhibits a high degree of nonlinearity, and the artificial neural network has a strong adaptability when dealing with nonlinear, highly coupled data samples. Compared with other neural network algorithms, the ELM neural network has the characteristics of fast operation speed and strong generalization ability. Therefore, in this paper, the ELM neural network is combined with the principle of spectral technology to collect data, establish models, and perform prediction experiments.

The extreme learning machine is a feed-forward neural network composed of an input layer, hidden layer, and output layer. In the training process of the ELM model, the network weight and threshold parameters are randomly set before training and do not have to update with the training process. The number of hidden layer nodes is also set by experience before training. After the least squares algorithm, the ELM neural network can obtain the unique optimal solution without falling into the local optimal solution.

Suppose an extreme learning machine neural network has

Then, the output of the neural network is

The traditional ELM algorithm randomly selects input weights and hidden biases. Training this network is equivalent to solving the least-squares solution of linear system

Huang has proved that the minimum value of the least-squares solution of the linear system is as follows:

Particle swarm optimization (PSO) is a global optimization algorithm proposed by Kennedy and Eberhart, which is derived from the research on the predation behaviours of birds. The basic idea of the particle swarm algorithm is to find the optimal solution through the cooperation and information sharing among individuals in the group. Because the PSO algorithm is simple in its structure, easy to implement, and there are few parameters to adjust, it has been widely used in function optimization, neural network training, and other fields.

The particle swarm optimization algorithm is implemented as follows. In a group, each bird is abstracted as a particle and is extended to the

In each iteration, the particle passes through the best position

In the traditional ELM algorithm, the input weights and the hidden biases are randomly selected. This approach will inevitably lead to some nonoptimal or unnecessary input weights and hidden biases. The output weight matrix of the ELM network is calculated based on the input weights and the hidden biases. Therefore, randomly selecting the input weights and the hidden biases of the ELM will increase the number of nodes in the hidden layer, causing the ELM to respond to the test set slower and having poor generalization ability. Similarly, in the ELM algorithm, the number of hidden layer nodes of the network is usually selected based on experience, and the selection of the hidden layer nodes will directly affect the structure of the network and affect the performance of the ELM network.

In this paper, the improved particle swarm optimization algorithm is used to optimize the input weights, the hidden biases, and the number of hidden layer nodes of the ELM network. The details of the algorithm are as follows.

First, the swarm is randomly generated. The length of each particle in the population is

All components in the particle are randomly initialized within the range of

Second, in order to avoid overfitting the ELM, the fitness of each particle is adopted as the root mean squared error (RMSE) on the validation set.

Third, in the traditional PSO algorithm’s structure, the inertia weight is a fixed value. It has been proved that although PSO with the constant inertia weight

Fourth, as analyzed by Zhu et al. and Bartlett [

Fifth, in order to find the optimal number of hidden layer nodes, this paper introduces the idea of mutation in the update process of particles, changes the length of the particles in each update process, and then changes the number of hidden layer nodes of the ELM. Change the number of hidden layer nodes according to (

Sixth, update the speed and position of the particles. By changing the number n of hidden layer nodes in the ELM network, the next generation particle length of the particle group is

After the particle is mutated, if the length of the particle increases, the particle velocity and position adjustment rules are as follows:

After the particle is mutated, if the particle length is shortened, the

After the particle is mutated, if the particle length does not change, the particle’s velocity and position are not adjusted.

Finally, the iteration is repeated until the maximum number of iterations is reached or the searched optimal position satisfies a predefined minimum fitness value.

The ELM neural network optimized by the above improved particle swarm optimization algorithm has the best input weights, hidden biases, and hidden layer node number.

The spectral data of the haematite sample obtained by the spectral measurement is 973-dimensional, which means that the dimension is too high, and the data have a strong correlation. Therefore, the PCA method is used to reduce the dimension of the obtained spectral data. The contribution rate of the principal components is shown in Figure

Principal component contribution rate of the haematite spectral data.

Considering that the number of samples is too small, 91 samples are subjected to 10-fold cross-validation, that is, 91 samples are equally divided into 10 groups, each group is tested once, and the remaining 9 groups are used as training sets, and cross-validation is repeated 10 times. The root mean square error of the average cross-validation of 10 times is taken as a result.

To compare the performance of neural networks, in this paper, we use the ELM, PSO-ELM, and IPSO-ELM to establish a prediction model for the magnetic properties of haematite. The number of nodes in the hidden layer of the ELM is the optimal choice for multiple tests. The activation function of the hidden layer is

The simulation was conducted in the environment of MATLAB R2016a. The simulation results are shown in Figure

Prediction results of the ELM, PSO-ELM, and IPSO-ELM.

Performance comparison of the ELM, PSO-ELM, and IPSO-ELM.

Type of model | RMSE | Time consuming (s) | Number of hidden layer nodes | Norm of output matrix |
---|---|---|---|---|

ELM | 2.4502 | 0.004115 | 28 | 236.4392 |

PSO-ELM | 2.0129 | 7.912648 | 18 | 52.7091 |

IPSO-ELM | 1.8488 | 4.713289 | 18 | 20.3052 |

First, the number of hidden layer nodes required for the PSO-ELM and IPSO-ELM is 18, while the number of hidden layer nodes required for the ELM is 28. Compared with the ELM, the PSO-ELM and IPSO-ELM can obtain smaller prediction errors with fewer hidden layer nodes. Therefore, the PSO-ELM and IPSO-ELM can use a simpler network structure to achieve better prediction results.

Second, the training time of the PSO-ELM and IPSO-ELM is obviously greater than the training time of the ELM. The time is mainly spent on the selection of input weight and deviation vector. Because the IPSO-ELM optimizes the hidden layer nodes, the running speed of the algorithm is improved relative to that of the PSO-ELM.

Third, with respect to the norm of the output weight matrix, the output matrix norm of IPSO-ELM is obviously smaller than the output matrix norm of the PSO-ELM and ELM, which indicates that the IPSO-ELM has better generalization performance than PSO-ELM and ELM do.

Finally, from the root mean square error of the test set, the root mean square error of the IPSO-ELM test set is smaller than that of the ELM and PSO-ELM, which can more accurately predict the magnetic properties of the haematite.

Table

Comparison of different method of detecting magnetic properties.

Method | Accuracy | Time consuming (h) | Cost(yuan) |
---|---|---|---|

Artificial test | 60% | 4 | About 300 |

Chemical test | 100% | 72 | About 20,000 |

IPSO-ELM | 92% | 3 | About 200 |

In summary, the model for detecting the magnetic properties of haematite based on spectral data proposed in this paper is that the extreme learning machine based on the improved particle swarm optimization has the best input weighs, hidden biases, and hidden layer node numbers. Its generalization ability is better than that of the ELM and PSO-ELM, it is faster than the PSO-ELM is, and its prediction accuracy is also higher than that of the ELM and PSO-ELM. Compared with the traditional manual detection method, the method has the advantages of simple operation and high precision. Compared with chemical testing methods, the method has faster speed and lower cost.

In this paper, the model for detecting the magnetic properties of haematite based on spectral data and the IPSO-ELM network was proposed. The spectral data of 91 haematite samples were collected and analyzed using principal component analysis. The model for detecting the magnetic properties of haematite was established using the ELM and PSO-ELM. To further improve the detection accuracy and the generalization ability of the model, an extreme learning machine based on the improved particle swarm optimization was proposed in this paper. The experimental results show that the IPSO-ELM network can well detect the magnetic properties of haematite. Compared with ELM and PSO-ELM models, the IPSO-ELM network can better detect the magnetic properties of haematite and has better generalization ability. Compared with the traditional magnetic property detection method, the model for detecting the magnetic properties of haematite based on spectral data and the IPSO-ELM network has the advantages of high precision, fast detection speed, and low costs. It provides a new method for the detection of the magnetic properties of haematite.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflict of interest.

This research work is supported by National Natural Science Foundation of China (Grant Nos. 41371437, 61203214, 61473072, 61773105, 61374147, and 61733003), Fundamental Research Funds for the Central Universities (Grant Nos. N150402001 and N160404008), National Key Research and Development Plan (2016YFC0801602), and National Twelfth Five-Year Plan for Science and Technology Support (2015BAB15B01) China.