Data-driven prediction model for adjusting burden distribution matrix of blast furnace based on improved multilayer extreme learning machine

Abstract

Reasonable burden distribution matrix is one of important requirements that can realize low consumption, high efficiency, high quality and long campaign life of the blast furnace. This paper proposes a data-driven prediction model of adjusting the burden distribution matrix based on the improved multilayer extreme learning machine (ML-ELM) algorithm. The improved ML-ELM algorithm is based on our previously modified ML-ELM algorithm (named as PLS-ML-ELM) and the ensemble model. It is named as EPLS-ML-ELM. The PLS-ML-ELM algorithm uses the partial least square (PLS) method to improve the algebraic property of the last hidden layer output matrix for the ML-ELM algorithm. However, the PLS-ML-ELM algorithm may have different results in different trails of simulations. The ensemble model can overcome this problem. Moreover, it can improve the generalization performance. Hence, the EPLS-ML-ELM algorithm is consisted of several PLS-ML-ELMs. The real blast furnace data are used to testify the data-driven prediction model. Compared with other prediction models which are based on the SVM algorithm, the ELM algorithm, the ML-ELM algorithm and the PLS-ML-ELM algorithm, the simulation results demonstrate that the data-driven prediction model based on the EPLS-ML-ELM algorithm has better prediction accuracy and generalization performance.

Appendixes

In Appendixes, the proposed EPLS-ML-ELM algorithm is verified by using standard data sets. The ELM algorithm, the ML-ELM algorithm and the PLS-ML-ELM algorithm are also used to compare with the proposed EPLS-ML-ELM algorithm. There are two parts. Appendix A is for the regression problem, and Appendix B is for the classification problem.

Table 6 Information of simulation data for regression problem

Table 7 Comparison of prediction results using different algorithms for regression problem

Table 8 Information of simulation data for classification problem

1.1 Appendix A

For regression problem, the Abalone data set (UCI 1995) and the California Housing data set (StatLib 1997) are used to testify. The benchmark problems are shown in Table 6. The number of hidden layer nodes for the ELM algorithm is 100. The numbers of the whole hidden layers nodes for the ML-ELM algorithm with three hidden layers are 200, 150 and 100, respectively. For PLS-ML-ELM, the number of hidden layers and the number of every hidden layer nodes are same with ML-ELM’s, respectively. For EPLS-ML-ELM, the number of the whole PLS-ML-ELMs is 10. Each PLS-ML-ELM has same number of hidden layers and same number of every hidden layer nodes with ML-ELM’s. In addition, all the experiments are carried out 50 trials. In this part, the root mean square error (RMSE) is used as the evaluation criterion, and the representation is shown as

$$\begin{aligned} {\text {RMSE}} = \sqrt{\frac{{\sum \nolimits _{i = 1}^n {{{({X_i} - \mathop {{X_i}}\limits ^ \wedge )^2}}}}}{n}}, \end{aligned}$$

(36)

where n is the total number of testing data; $X_i$ and $\mathop {{X_i}}\nolimits ^ \wedge$ are actual data and prediction data at the ith sample.

The comparison results are shown in Table 7. These comparison results illustrate that the proposed EPLS-ML-ELM algorithm has better generalization performance than other algorithms.

1.2 Appendix B

For classification problem, the image segmentation data set (UCI 1990), the letter data set (UCI 1991) and the MNIST data set (LeCun et al. 1998) are used to testify. The benchmark problems are shown in Table 8. All the experiments are carried out 50 trials. The comparison results are shown in Tables 9,  10 and Fig. 8. These comparison results illustrate that the proposed EPLS-ML-ELM algorithm has better generalization performance than other algorithms.

Table 9 Comparison of prediction results using different algorithms for classification problem

Table 10 Comparison of prediction results using different algorithms on MNIST data set

Fig. 8

Results of different data sets based on different algorithms. a Accuracy for image segmentation data set based on different algorithms. b Accuracy for letter data set based on different algorithms

For the letter data set, the parameter set of the whole algorithms is different from Appendix A. The number of hidden layer nodes for the ELM algorithm is 200. The numbers of nodes for the whole hidden layers for the ML-ELM algorithm with three hidden layers are 200, 200 and 400, respectively. For PLS-ML-ELM, the number of hidden layers and the number of every hidden layer nodes are same with ML-ELM’s in Appendix B, respectively. For EPLS-ML-ELM, the number of the whole PLS-ML-ELMs is 10, and each PLS-ML-ELM has same number of hidden layers and same number of every hidden layer nodes with ML-ELM’s in Appendix B.

For the MNIST data set, the parameter set of the whole algorithms is also different from Appendix A. The number of hidden layer nodes for the ELM algorithm is, respectively, set as 1000, 1500 and 2000. For ML-ELM with three hidden layers, the numbers of nodes for the whole hidden layers are, respectively, set as $\left[ {700\mathrm{{ - }}700\mathrm{{ - }}1000} \right]$, $\left[ {700\mathrm{{ - }}700\mathrm{{ - }}1500} \right]$ and $\left[ {700\mathrm{{ - }}700\mathrm{{ - }}2000} \right]$. For PLS-ML-ELM, the number of hidden layers and the number of every hidden layer nodes are same with ML-ELM’s in Appendix B, respectively. For EPLS-ML-ELM, the number of the whole PLS-ML-ELMs is 5, and each PLS-ML-ELM has the same number of hidden layers and the same number of every hidden layer nodes with ML-ELM’s in Appendix B. In addition, the whole MNIST data set is used in each PLS-ML-ELM of EPLS-ML-ELM.