^{1}

^{2}

^{1}

^{1}

^{2}

For coal slurry pipeline blockage prediction problem, through the analysis of actual scene, it is determined that the pressure prediction from each measuring point is the premise of pipeline blockage prediction. Kernel function of support vector machine is introduced into extreme learning machine, the parameters are optimized by particle swarm algorithm, and blockage prediction method based on particle swarm optimization kernel function extreme learning machine (PSOKELM) is put forward. The actual test data from HuangLing coal gangue power plant are used for simulation experiments and compared with support vector machine prediction model optimized by particle swarm algorithm (PSOSVM) and kernel function extreme learning machine prediction model (KELM). The results prove that mean square error (MSE) for the prediction model based on PSOKELM is 0.0038 and the correlation coefficient is 0.9955, which is superior to prediction model based on PSOSVM in speed and accuracy and superior to KELM prediction model in accuracy.

The coal slurry as one waste is transported through pipelines to circulating fluidized bed boiler for mixed burning in gangue power plant; on the one hand, the low calorific value energy can be made full use of, and the coal slurry can be processed; on the other hand, pollution is prevented, which brings good economic and social benefits for the coal mine enterprises. At present, the coal slurry is transported through pipelines and wet transportation technology is applied, which can solve the secondary pollution problem caused by transportation process [

Artificial neural network and support vector machine (SVM) can deal well with nonlinear regression problem and have wide application in the future data prediction. But much study has found that feedforward neural network has some problems such as having slow learning speed, being easy to fall into local minimum, and being sensitive to parameter selection [

Guangbin Huang has proposed a new learning algorithm called extreme learning machine (ELM) [

ELM has shown great potential in solving problem such as data regression and classification, which overcomes some challenging limits when feedforward neural networks or other intelligent algorithms are used. Compared with the more popular Back-Propagation (BP) and Support Vector Machine (SVM), ELM not only inherits the various advantages of neural network and support vector machine (SVM) but also has a lot of outstanding characteristics.

ELM is easy to use, requiring less human intervention.

ELM has faster speed of learning. Some training learning can be done in a few seconds or minutes.

ELM has better generalization performance. In most cases, ELM can obtain a better generalization performance than BP and get close or better generalization performance than the SVM.

ELM applies to most of the nonlinear activation functions.

This algorithm is simpler. ELM is a simple algorithm with three steps that does not need to be adjusted, and simple mathematics is enough for use.

ELM cannot meet problems such as local minimum, inappropriate learning speed, and the overfitting, where traditional classical learning algorithm can be faced with.

Figure

The structure of extreme learning machine.

It can be seen that extreme learning machine still adopts three-layer feedforward neural network structure.

Different from the BP neural network, all the connection weights of BP neural network in training are constantly adjusted in the process of iteration, but initial weights of extreme learning machine can be set randomly and given well before the training; then they no longer need to be readjusted in the process of training, and only minimum weights of the output need to be solved out, which can be finished by solving the generalized inverse matrix once.

The hidden layer output of each node for extreme learning machine is shown in formula (

Formula (

There are both empirical risk and structural risk in the statistical learning theory. Extreme learning machine not only considers the experience error minimization, which is the training error minimum, but also needs to consider the structural risk minimization as well. It is easy to generate the overfitting problem if only the minimum error is considered; that is to say, although the training error is the minimum, the optimum test effect is unable to be got. So if you want to get a good model, these two kinds of risks need to be thought about compromisingly at the same time. Therefore, it is necessary to make a compromise between minimized output weights and the minimized error; then the calculation formula (

According to the KKT conditions, Lagrange function can be used to solve the above problem; that is to say, the above problem can be solved through the following formula (

So bring (

Let

So the above formulas can be combined as

In the end, formula (

So approximating function of extreme learning machine can be written as

In addition, in order to improve the nonlinear classification performance of extreme learning machine, it can be considered to combine the principle of support vector machine (SVM), and the nonlinear kernel mapping can be introduced into the extreme learning machine.

Let

The hidden layer and output of each sample

Then

It can be seen from formula (

So formula (

And

The extreme learning machine of the kernel function has more strong nonlinear approximation ability; therefore, the kernel function of support vector machines (SVM) is introduced into extreme learning machine, and the blockage prediction method for coal slurry pipeline based on kernel function extreme learning machine (KELM) is proposed in this paper.

Parameters of the kernel function are closely related to the complexity of the kernel function; generally speaking, the Gaussian kernel function is one of the preferred. When prediction based on extreme learning machine and support vector machine is made in this paper, the Gaussian function works as the kernel function, as shown in formula (

Particle swarm optimization is a kind of optimization algorithm based on group search [

Particle swarm algorithm has many advantages such as fast convergence rate and strong robustness, which is easy to implement and easy to combine with other algorithms to improve performance. In view of this, particle swarm algorithm is used to optimize the parameters from support vector machine (SVM) and extreme learning machine, and their optimization process is similar. So pressure prediction workflows based on particle swarm optimization kernel function extreme learning machine (PSOKELM) are given here, as shown in Figure

The flowchart of KELM algorithms optimized by particle swarm algorithm.

The main steps are as follows:

The original data are preprocessed and divided into training set and validation set.

Initialize all particle swarm, and particle swarm algorithm is used to optimize penalty factor and kernel function

Record and save the best fitness value.

When the limit conditions (the number of iterations or fitness values) are met, terminate the iteration. Otherwise, return to step

Pressure prediction model based on PSOKELM with the best parameters is established for pipeline pressure prediction.

Coal slurry pipeline pressure is related to many factors, including traffic, coal slurry water content, pump outlet pressure, coal slurry temperature, and the distance to pump outlet. Coal slurry pipeline pressure prediction is a multivariable prediction problem. The coal slurry pipeline pressure prediction method based on kernel function extreme learning machine with particle swarm optimization (PSOKELM) is proposed in this paper, which is compared with prediction method based on support vector machine optimized by particle swarm. And accuracy and prediction speed advantage of prediction method based on PSOKELM has been verified.

The effect of the designed prediction model is generally evaluated by MSE (mean square error) and the correlation coefficient

The coal transportation system from HuangLing coal gangue power plant worked as experimental platform, PLC is the control core of the whole system, and data acquisition, centralized monitoring, and management and automatic sequence control can be realized. Based on the data record from number 2 pump in this coal transportation system, whose time is from 2012.5.26 to 5.31, blockage prediction is made. The 110 training samples and 25 test samples were randomly selected. Input variables include flow rate, the current from main pump, oil temperature, and the distance to pump outlet and water content, and output variables are the pressure from measured point. Take the pump outlet pressure prediction as an example; the computer simulation is made in MATLAB.

Kernel function is used as nonlinear mapping both for kernel function extreme learning machine (KELM) and support vector machine (SVM), and kernel function parameters and penalty factor all have certain effects on their performance. Here the effect of kernel parameter

Parameter selection 3D view of KELM.

Parameter selection 3D view of SVM.

As can be seen from Figures

In addition, the computational complexity of kernel function extreme learning machine is far lower than the support vector machine (SVM), so the calculation time of extreme learning machine should be shorter. Training time comparison has been made for the two algorithms from different training angles. PC used in simulation is Intel I3 processor, 4 GB memory. Training time comparison is shown in Figure

Training time comparison between SVM and KELM.

It can be seen from Figure

In addition, the SVM and KELM optimum parameters are optimized by the particle swarm algorithm, and the fitness curve is shown in Figure

Fitness comparison between KELM and SVM when optimized by PSO.

In order to compare the optimization effect of the particle swarm algorithm, PSOKELM and KELM without optimization algorithm are used, respectively, to forecast data sequence; the predicted results are shown in Figure

Prediction results comparison between PSOKELM and KELM.

According to the fitting degree and prediction effect of evaluation model from formula (

The MSE and

Effect evaluation | Test | |
---|---|---|

MSE |
| |

KELM | 0.00487 | 0.9428 |

PSOKELM | 0.0038 | 0.9955 |

It can be seen from Figure

In order to further contrast the prediction effect of KELM and SVM, PSOKELM and PSOSVM are used to, respectively, predict data sequence, and the prediction results are shown in Figures

The MSE and

Effect evaluation | Test | |
---|---|---|

MSE |
| |

PSOSVM | 0.0057 | 0.9228 |

PSOKELM | 0.0038 | 0.9955 |

Prediction results compassion between PSOSVM and PSOKELM.

The relative error comparison of prediction results between PSOSVM and PSOKELM.

It can be seen from Figures

The pressure prediction method for coal slurry transportation pipeline based on the particle swarm optimization kernel function extreme learning machine (PSOKELM) is studied in this paper. The following conclusions are drawn.

For pressure prediction problem of coal slurry transportation pipeline, kernel function of support vector machine is introduced into extreme learning machine, parameters are optimized by the particle swarm algorithm, and the pressure prediction method for coal slurry transportation pipeline based on PSOKELM is put forward and compared with PSOSVM prediction model and KELM prediction model.

Experiments simulation results prove that the prediction model based on PSOKELM is superior to prediction model based on PSOSVM in speed and accuracy and superior to KELM prediction model in accuracy, the prediction relative error is within 4%, then the validity of the prediction model is determined.

The research and validation of pressure prediction method for coal slurry transportation pipeline lay a foundation for the research of pipeline blocking.

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

The authors acknowledge the support provided by the National Natural Science Foundation Youth Science Fund Project. no. 51405381.