Intelligent Prediction of Sieving Efficiency in Vibrating Screens

Abstract

In order to effectively predict the sieving efficiency of a vibrating screen, experiments to investigate the sieving efficiency were carried out. Relation between sieving efficiency and other working parameters in a vibrating screen such as mesh aperture size, screen length, inclination angle, vibration amplitude, and vibration frequency was analyzed. Based on the experiments, least square support vector machine (LS-SVM) was established to predict the sieving efficiency, and adaptive genetic algorithm and cross-validation algorithm were used to optimize the parameters in LS-SVM. By the examination of testing points, the prediction performance of least square support vector machine is better than that of the existing formula and neural network, and its average relative error is only 4.2%.

Bin Zhang 1,2 and Jinke Gong 1 and Wenhua Yuan 2 and Jun Fu 2 and Yi Huang 1

Academic Editor:Longjun Dong

1, The State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China
2, Department of Mechanical and Energy Engineering, Shaoyang University, Shaoyang 422004, China

Received 25 November 2015; Revised 22 February 2016; Accepted 15 March 2016

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Sieving is one of the oldest physical size separation methods and has been widely used both in industries and in laboratories. Vibrating screens which include a number of types are the main sieving tool for large-scale separation and classification of solid particles by size, and they are widely used in some practical engineering such as mining, metallurgy, dry mortar, artificial sand, and agriculture production. Probability screen is a special vibrating screen for the separation and classification of fine particulate material, which exhibits problems of plugging holes and low sieving efficiency when the particle size is below 0.6 mm. Sieving efficiency is an essential evaluation indicator of sieving performance, and it is hard to be predicted based on the existing sieving design parameters in the design process of vibrating screens due to the comprehensive effect of complex particle sieving process under multiple factors, which will influence the selection or determination of these parameters. Therefore, an understanding of predicting sieving efficiency has a great practical significance.

At present, the research on the sieving efficiency of vibrating screens has also made some progress. There are lots of researchers studying the sieving process by DEM simulations like Li et al. [1], Dong et al. [2], Liu [3], Delaney et al. [4], Jiao and Zhao [5], and Li et al. [6], and qualitative relation between sieving efficiency and sieving parameters in a vibrating screen such as amplitude, vibration frequency, screen mesh size, particle size, and vibration direction angle has been analyzed, which provides references for in-depth study. But the results of DEM simulations need to be further explored and improved since particulate materials and boundary conditions of simulation are difficult to coincide with the actual conditions. Some scholars have studied the real-time monitoring of sieving efficiency in the working course of a vibrating screen by gathering its vibration signals, but their research achievements only play the role of real-time monitoring and have little effect on the design of a vibrating screen [7]. In terms of sieving efficiency fitting, Grozubinsky et al. [8] and Chen and Tong [9] have, respectively, established formulas between the sieving efficiency and sieving parameters such as amplitude, vibration frequency, vibration direction angle, particle size, and screen mesh size based on a probabilistic model and a discrete element model, but these formulas only reflect the relationship between the single parameter and sieving efficiency. Jiao et al. [10] found the mathematical formula between sieving efficiency and parameters including screen deck angle and screen mesh size based on statistical analysis of experimental data, which provides a theoretical basis for the design of vibrating screens but ignores the impact of screen length. Although some fitting function formulas of sieving efficiency have been studied, there is still no widely accepted formula to predict sieving efficiency on the basis of sieving parameters. The introduction of artificial intelligence may provide a good path to the solution of this problem [11].

Support vector machine (SVM) and neural network both can fit the nonlinear relations [12-14], whereas SVM is more suitable when the sample size is relatively small and can solve "curse of dimensionality" problems. The solution of "curse of dimensionality" can make the complexity of algorithm and the dimension of sample independent. At present, SVM has been widely and effectively used in the pattern recognition, intelligent fitting, and prediction [15-18]. However, the application of SVM to predict the sieving efficiency has not been reported in the literatures yet.

In this paper, the experimental system and results were firstly introduced and analyzed, and then intelligent fitting model of least square support vector machine (LS-SVM) and adaptive genetic algorithm were provided; finally, the contrast between the performance of the LS-SVM model, the existing formula, and the neural network was carried out.

2. Sieving Experimental System

Sieving is a process in which a certain size range of materials is separated into several products with different size through one-deck or multideck screens that have sieving mesh with uniform apertures. Theoretically, the particles whose size is larger than the mesh aperture remain on the screen surface and leave the screen surface when they pass the end of the screen, and these particles are called overflow particles; however, other smaller particles penetrate the sieving mesh through the mesh aperture and are called undersize particles. Sieving efficiency is the ratio between actual mass of undersize particles and the mass of the particles in raw materials whose size is smaller than the mesh aperture. Compared with the mesh aperture size, the smaller the particles are, the easier the penetration is, but the particles whose size is close to the mesh aperture size penetrate the screen mesh with difficulty. Probability screens have some advantages in all vibrating screens such as large sieving capacity and easy penetration because of their unique characteristics of the large mesh aperture and large inclination angle.

The repeated sieving tests are finished in an experimental system, which is illustrated in Figure 1. Sieving parameters such as inclination angle, screen length, mesh aperture size, amplitude, and vibration frequency are adjustable in this vibration sieving test bench, which is a circular experimental system and includes the multideck probability screen, storage bin of raw materials, vibrating feeder, and automatic feeding system. Samples used for measuring the sieving efficiency by Hancock's total efficiency formula are gotten when the screen is in steady working condition. The "steady working condition" means that the screen works steadily after starting the screen on the sieving test bench; meanwhile, raw materials cover the whole screen mesh surface and the feed rate of raw materials from vibrating feeder reaches a stable state. Total efficiency is the difference between the penetration probability of the particles whose size is smaller than separation size and the penetration probability of the particles whose size is larger than separation size. The schematic diagram of total efficiency calculation is shown in Figure 2.

Figure 1: Schematic diagram of the vibration sieving test bench.

[figure omitted; refer to PDF]

Figure 2: Schematic diagram of total efficiency calculation.

[figure omitted; refer to PDF]

In Figure 2, [figure omitted; refer to PDF] is the total mass of raw materials into the screen, [figure omitted; refer to PDF] is the mass of overflow particles, [figure omitted; refer to PDF] is the mass of undersize particles, [figure omitted; refer to PDF] is the percentage of the particles whose size is smaller than separation size in raw materials, [figure omitted; refer to PDF] is the percentage of the particles whose size is smaller than separation size in overflow particles, [figure omitted; refer to PDF] is the percentage of the particles whose size is smaller than separation size in undersize particles, [figure omitted; refer to PDF] is mesh aperture size of the screen mesh, [figure omitted; refer to PDF] is screen length, and [figure omitted; refer to PDF] is inclination angle of the screen surface. Total efficiency is calculated as follows [10]: [figure omitted; refer to PDF]

In test process, the screen mesh with rectangular apertures which is woven by steel wire is selected, and the common II area sands in construction industry whose particle diameter is between thick sands and fine sands are selected as raw materials. Sand properties and operating conditions are shown in Table 1, and grading curves of sands are shown in Figure 3.

Table 1: Sand properties and operating conditions.

Parameters	Actual values
Sand size/mm	0-4.75
Moisture ratio	0.3%
Fineness modulus	2.68
Sieving capacity/(t/h)	50

Figure 3: Grading curves of sands.

[figure omitted; refer to PDF]

As is shown in Figure 3, the particle diameter corresponding to the 6 data points is 0.15 mm, 0.3 mm, 0.6 mm, 1.18 mm, 2.36 mm, and 4.75 mm; the grading curve of the sand sample is almost in the middle position between the upper and lower limits of the common sand. Since the raw sands are shifted with this multideck probability screen whose separation size is 2.36 mm, 1.18 mm, and 0.6 mm, respectively, from top to bottom, and, generally, the 0.6 mm layer of this probability screen has a smallest sieving efficiency, which sieves finest materials with the particle diameter below 0.6 mm, the sieving efficiency of the 0.6 mm layer is viewed as the probability screen's one.

3. Experimental Results

According to experimental results, the sieving efficiency [figure omitted; refer to PDF] first increases with the increase of vibration amplitude [figure omitted; refer to PDF] and screen length [figure omitted; refer to PDF] and then decreases with the increase of vibration frequency [figure omitted; refer to PDF] , mesh aperture size [figure omitted; refer to PDF] , and inclination angle [figure omitted; refer to PDF] . This paper focuses on detailed analysis of [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] , and the effect of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] on the sieving efficiency is detailed in literature [7].

3.1. Effect of Mesh Aperture Size on the Sieving Efficiency

The mesh aperture size can also be characterized by the ratio between mesh aperture size [figure omitted; refer to PDF] and separation size [figure omitted; refer to PDF] . [figure omitted; refer to PDF] is greater than 1 in probability screens. Figure 4 shows the effect of mesh aperture size [figure omitted; refer to PDF] on the sieving efficiency when [figure omitted; refer to PDF] is equal to 3.5 mm, [figure omitted; refer to PDF] is equal to 960 r/min, and [figure omitted; refer to PDF] is equal to 2.4 m. [figure omitted; refer to PDF] first increases and then decreases with the increase of [figure omitted; refer to PDF] . When the mesh aperture size is small, the sieving efficiency is low due to the approximate size between [figure omitted; refer to PDF] and [figure omitted; refer to PDF] and the lower penetration probability of the fine particles and a greater proportion of fine particles remained in overflow particles. When the mesh aperture size is larger, the sieving efficiency is higher due to the larger penetration probability of the fine particles. When the mesh aperture size is too large, the sieving efficiency becomes lower due to the higher penetration probability of the particles whose size is larger than separation size and undersize particles mixed with a greater proportion of larger particles. The optimum mesh aperture size is between 0.8 mm and 1.1 mm, and the maximum efficiency can reach above 80% when [figure omitted; refer to PDF] is 25°.

Figure 4: Effect of mesh aperture size on the sieving efficiency.

[figure omitted; refer to PDF]

3.2. Effect of Screen Length on the Sieving Efficiency

Figure 5 shows the effect of screen length [figure omitted; refer to PDF] on the sieving efficiency when [figure omitted; refer to PDF] is equal to 3 mm, [figure omitted; refer to PDF] is equal to 960 r/min, and [figure omitted; refer to PDF] is equal to 25°. [figure omitted; refer to PDF] increases significantly with the increase of [figure omitted; refer to PDF] , and the increase of [figure omitted; refer to PDF] becomes slow after [figure omitted; refer to PDF] reaches a certain value. However, [figure omitted; refer to PDF] decreases with the further increase of [figure omitted; refer to PDF] under the condition of larger value of [figure omitted; refer to PDF] due to the high penetration probability of the particles whose size is larger than separation size and undersize particles mixed with an increasing number of impurities. If [figure omitted; refer to PDF] is larger, the optimum [figure omitted; refer to PDF] is shorter due to the high penetration probability of the particles whose size is smaller than separation size during the beginning time of sieving. The optimum range of screen length is between 2.0 m and 2.6 m.

Figure 5: Effect of screen length on the sieving efficiency.

[figure omitted; refer to PDF]

3.3. Effect of Inclination Angle on the Sieving Efficiency

Inclination angle [figure omitted; refer to PDF] mainly affects the horizontal projection size of mesh aperture and the moving speed of particles on the screen surface. Figure 6 shows the effect of inclination angle [figure omitted; refer to PDF] on the sieving efficiency when [figure omitted; refer to PDF] is equal to 3.5 mm, [figure omitted; refer to PDF] is equal to 960 r/min, and [figure omitted; refer to PDF] is equal to 0.9 mm. [figure omitted; refer to PDF] first increases and then decreases with the increase of [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] reaches the maximum value with a certain inclination angle. When the inclination angle increases, the horizontal projection size of mesh aperture decreases and penetration probability of particles in the vertical direction decreases, which results in a lower penetration amount of the particles whose size is larger than separation size. Meanwhile, penetration and stratification capacity of the particles whose size is smaller than separation size is enhanced with increasing moving speed of particles on the screen surface. When the inclination angle increases further, the sieving efficiency becomes low due to sharp decrease of the horizontal projection size of mesh aperture, sharp increase of the moving speed of particles on the screen surface, and shorter stay time of particles on the screen surface. The optimum inclination angle is about 25° and the maximum efficiency can reach above 82% when [figure omitted; refer to PDF] is equal to 2.4 m.

Figure 6: Effect of inclination angle on the sieving efficiency.

[figure omitted; refer to PDF]

3.4. Effect of Vibration Amplitude on the Sieving Efficiency

Figure 7 shows the effect of vibration amplitude [figure omitted; refer to PDF] on the sieving efficiency when [figure omitted; refer to PDF] is equal to 0.9 mm, [figure omitted; refer to PDF] is equal to 2.4 m, and [figure omitted; refer to PDF] is equal to 25°. [figure omitted; refer to PDF] increases with the increase of [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] first increases and then decreases with the increase of [figure omitted; refer to PDF] . When [figure omitted; refer to PDF] and [figure omitted; refer to PDF] increase, the penetration probability of particles whose size is smaller than separation size becomes larger, so the sieving efficiency increases. However, when [figure omitted; refer to PDF] increases to 1000 r/min, [figure omitted; refer to PDF] decreases because larger vibration frequency can lead to larger penetration probability of particles whose size is larger than separation size. Optimum vibration amplitude and vibration frequency are 3.5 mm and 960 r/min, respectively.

Figure 7: Effect of vibration amplitude on the sieving efficiency.

[figure omitted; refer to PDF]

4. Establishment of the Intelligent Model Based on LS-SVM

It is supposed that there are lots of training points [figure omitted; refer to PDF] ( [figure omitted; refer to PDF] is the input value, [figure omitted; refer to PDF] is the output value, and [figure omitted; refer to PDF] is the total number of training points) to be fitted; according to the basic theory of SVM, these problems can be converted to the solution of the following equations: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is kernel function, [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] are the parameters which could be obtained by the solution of the optimization problem (such problem is described in the form of (2)), and [figure omitted; refer to PDF] is the penalty factor.

SVM algorithm is sensitive to noise, and its calculation speed does not depend on the dimensions of input vectors but on the sample size. The large sample size will result in complex quadratic programming problem based on SVM, slow operational speed, and the long time that the calculation will spend. Therefore, LS-SVM is introduced on the basis of the traditional theory of SVM.

According to the theory of LS-SVM, (2) can be converted to the following linear equation: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] is the unit matrix, and [figure omitted; refer to PDF] . Here, Gauss function is selected as Kernel function [figure omitted; refer to PDF] and it meets the following equation: [figure omitted; refer to PDF]

Accordingly, (3) can be converted into the following equation: [figure omitted; refer to PDF]

When LS-SVM is applied into the intelligent fitting of sieving efficiency [figure omitted; refer to PDF] , the five-dimensional input vector is [figure omitted; refer to PDF] and the one-dimensional output vector is [figure omitted; refer to PDF] . The 82 training samples come from the experimental results discussed above, and the prediction value of the LS-SVM model can be acquired finally by solving the value of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] .

In the theory of LS-SVM, the parameters needed to be optimized are the penalty factor [figure omitted; refer to PDF] and the kernel parameter [figure omitted; refer to PDF] , and the fitting performance of LS-SVM depends on the selection of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] .

Nowadays, there are many kinds of intelligent algorithm that can be used to optimize [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , such as particle swarm optimization algorithm, genetic algorithm, grid search, and chaos optimization algorithm [19, 20]. In these methods, genetic algorithm has been considered with increasing interest in a wide variety of applications, and it is widely used to solve linear and nonlinear problems by exploring all regions of state space and exploiting potential areas through mutation, crossover, and selection operations applied to individuals in the population. In this paper, adaptive genetic algorithm is applied to determine the value of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] .

5. Intelligent Prediction of Sieving Efficiency Based on LS-SVM

5.1. Optimization of Parameters by Adaptive Genetic Algorithm

The key of adaptive genetic algorithm [21] is to determine the fitness function. Here, it is described as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the expected output, [figure omitted; refer to PDF] is the actual output, and [figure omitted; refer to PDF] is a small real number, which is to prevent the situation of zero denominator; here [figure omitted; refer to PDF] .

The initial crossover probability and the initial mutation probability are determined by [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the larger fitness function value of the cross two bodies, [figure omitted; refer to PDF] is the fitness function value of individual, [figure omitted; refer to PDF] is the average fitness function value in the samples, and [figure omitted; refer to PDF] is the maximum fitness function value of individual in the samples.

Crossover probability and mutation probability change with the evolutional generation, and their changing rules are as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the genetic algebra, [figure omitted; refer to PDF] is the terminated genetic algebra, and [figure omitted; refer to PDF] is a constant; here [figure omitted; refer to PDF] .

The basic steps of "adaptive genetic algorithm" are listed as follows.

Step 1.

Generate initial population [figure omitted; refer to PDF] ; algebra is set to 0, and the number of individuals is [figure omitted; refer to PDF] .

Step 2.

Run selection operator, crossover operator, and mutation operator in proper order and calculate the fitness of individuals.

Step 3.

Sort individuals by fitness value and run the intelligent fitting model of LS-SVM once for the individual which has highest fitness value.

Step 4.

Get a new generation of population [figure omitted; refer to PDF] , and algebra increases by 1.

Step 5.

Judge whether it meets the optimization criterion. If it meets the criteria, the optimization process is over; else, return to Step 2.

There are two factors that may lead to the failure of LS-SVM: (1) "overfitting" issue (the objective function can reduce to a very low value during the training phase, but the testing error is relatively large); (2) "underfitting" issue (the objective function cannot reduce to a low value during the training phase). For solving these issues, "cross-validation" method is introduced [22, 23].

The basic steps of "cross-validation" are listed as follows.

Step 1.

Divide the training samples into [figure omitted; refer to PDF] subsamples and set [figure omitted; refer to PDF] .

Step 2.

Regard the [figure omitted; refer to PDF] th subsamples as the testing samples and the others as the training samples.

Step 3.

Optimize the parameters [figure omitted; refer to PDF] in LS-SVM based on the new training samples by adaptive genetic algorithm.

Step 4.

[figure omitted; refer to PDF] , and repeat Steps 1-3 till [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , [figure omitted; refer to PDF] .

In this paper, the population size is 40, the dimension of parameters to be optimized is 2, the maximum genetic algebra is 400, and the binary digit of each variable is 20. And after the optimization process, [figure omitted; refer to PDF] and [figure omitted; refer to PDF] . Error function is defined as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the actual output and [figure omitted; refer to PDF] is the expected output.

5.2. Comparison of the LS-SVM Model, the Existing Formula, and Neural Network

An existing fitting formula of sieving efficiency from literature [10] is shown as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is screen mesh size, [figure omitted; refer to PDF] is screen deck angle, and [figure omitted; refer to PDF] is sieving efficiency.

Neural network is also a usual intelligent model to fit the numerical relation besides LS-SVM; the training points in LS-SVM are still selected as training samples to optimize the parameters in neural network. The training methods of neural network have detailed descriptions in literature [24]. The prediction error between LS-SVM, BP neural network, RBF neural network, and the existing fitting formula in literature [10] is shown in Figure 8.

Figure 8: Fitting error comparison of the LS-SVM model, literature [10], and neural network.

[figure omitted; refer to PDF]

Figure 8 shows that the prediction error of selected 16 testing samples is analyzed; the average relative error of BP neural network is 7.3%, the average relative error of RBF neural network is 6.4%, the average relative error of literature [10] is 16.2%, and the average relative error of LS-SVM model is 4.2%. So the prediction performance of LS-SVM model is better than that of neural network and the existing fitting formula in literature [10].

6. Conclusions

The effects of different factors on sieving efficiency were investigated based on the vibration sieving test bench. According to experimental results, the sieving efficiency [figure omitted; refer to PDF] increases with the increase of vibration amplitude [figure omitted; refer to PDF] and screen length [figure omitted; refer to PDF] , and it first increases and then decreases with the increase of vibration frequency [figure omitted; refer to PDF] , mesh aperture size [figure omitted; refer to PDF] , and inclination angle [figure omitted; refer to PDF] .

The intelligent model to predict the sieving efficiency was established based on the experimental results, LS-SVM theory, and the adaptive genetic algorithm. The average prediction error of the LS-SVM model examined by testing points can be reduced to 4.2%, which is much less than that of neural network and the existing fitting formula. So, the LS-SVM model has a better prediction performance on sieving efficiency, which provides a theoretical basis for the optimal design and parameters selection of sieving screens.

Acknowledgments

The authors thank the National Science Foundation of China (nos. 51276056 and 51305045) for financial support.

References

[1] J. Li, C. Webb, S. S. Pandiella, G. M. Campbell, "Discrete particle motion on sieves-a numerical study using the DEM simulation," Powder Technology , vol. 133, no. 1-3, pp. 190-202, 2003.

[2] K. J. Dong, A. B. Yu, I. Brake, "DEM simulation of particle flow on a multi-deck banana screen," Minerals Engineering , vol. 22, no. 11, pp. 910-920, 2009.

[3] K. S. Liu, "Some factors affecting sieving performance and efficiency," Powder Technology , vol. 193, no. 2, pp. 208-213, 2009.

[4] G. W. Delaney, P. W. Cleary, M. Hilden, R. D. Morrison, "Testing the validity of the spherical DEM model in simulating real granular screening processes," Chemical Engineering Science , vol. 68, no. 1, pp. 215-226, 2012.

[5] H. G. Jiao, Y. M. Zhao, "Screen simuliation using a particle discrete element method," Journal of China University of Mining and Technology , vol. 36, no. 2, pp. 232-236, 2007.

[6] H. C. Li, Y. M. Li, Z. Tang, "Numerical simulation and analysis of vibration screening based on EDEM," Transactions of the Chinese Society of Agriculture Engineering , vol. 27, no. 5, pp. 117-121, 2011.

[7] Z. Z. Shi, Y. J. Huang, "Research on screening efficiency based on AR model of high-order cumulant LS-SVM," China Mechanical Engineering , vol. 22, no. 16, pp. 1965-1969, 2011.

[8] V. Grozubinsky, E. Sultanovitch, I. J. Lin, "Efficiency of solid particle screening as a function of screen slot size, particle size, and duration of screening," International Journal of Mineral Processing , vol. 52, no. 4, pp. 261-272, 1998.

[9] Y. H. Chen, X. Tong, "Modeling screening efficiency with vibrational parameters based on DEM 3D simulation," Mining Science and Technology , vol. 20, no. 4, pp. 615-620, 2010.

[10] H. G. Jiao, J. R. Li, Y. M. Zhao, "Test and research on optimum configuration of diameter of screen aperture and incline of screen deck," Coal Preparation Technology , vol. 35, no. 2, pp. 1-4, 2007.

[11] E. Jia-Qiang Intelligent Fault Diagnosis and Its Application , Hunan University Press, Changsha, China, 2006.

[12] S. Umehara, T. Yamazaki, Y. Sugai, "A precipitation estimation system based on support vector machine and neural network," Electronics and Communications in Japan , vol. 89, no. 3, pp. 38-47, 2006.

[13] A. Kuh, P. De Wilde, "Comments on pruning error minimization in least squares support vector machines," IEEE Transactions on Neural Networks , vol. 18, no. 2, pp. 606-609, 2007.

[14] K. Lamorski, Y. Pachepsky, C. Slawinski, R. T. Walczak, "Using support vector machines to develop pedotransfer functions for water retention of soils in Poland," Soil Science Society of America Journal , vol. 72, no. 5, pp. 1243-1247, 2008.

[15] C. H. Wang, Z. P. Zhong, R. Li, E. Jia-Qiang, "Prediction of jet penetration depth based on least square support vector machine," Powder Technology , vol. 203, no. 2, pp. 404-411, 2010.

[16] C. H. Wang, Z. P. Zhong, R. Li, J. Q. E, "Intelligent fitting of minimum spout-fluidised velocity in spout-fluidised bed," Canadian Journal of Chemical Engineering , vol. 89, no. 1, pp. 101-107, 2011.

[17] J. E, C. Qian, T. Liu, G. Liu, "Research on the vibration characteristics of the new type of passive super static vibratory platform based on the multiobjective parameter optimization," Advances in Mechanical Engineering , vol. 2014, pp. 1-8, 2014.

[18] L. J. Dong, X. B. Li, M. Xu, Q. Li, "Comparisons of random forest and support vector machine for predicting blasting vibration characteristic parameters," Procedia Engineering , vol. 26, pp. 1772-1781, 2011.

[19] E. Jiaqiang, C. Qian, H. Liu, G.-L. Liu, "Design of the _{H ∞} robust control for the piezoelectric actuator based on chaos optimization algorithm," Aerospace Science and Technology , vol. 47, pp. 238-246, 2015.

[20] E. Jiaqiang, C. Qian, T. Liu, G. Liu, "Chaos analysis on the acceleration control signals of the piezoelectric actuators in the stewart platform," Shock and Vibration , vol. 2016, 2016.

[21] K. P. Ferentinos, T. A. Tsiligiridis, "Adaptive design optimization of wireless sensor networks using genetic algorithms," Computer Networks , vol. 51, no. 4, pp. 1031-1051, 2007.

[22] L. J. Dong, X. B. Li, G. N. Xie, "Nonlinear methodologies for identifying seismic event and nuclear explosion using random forest, support vector machine, and naive bayes classification," Abstract and Applied Analysis , vol. 2014, 2014.

[23] L. J. Dong, X. B. Li, "Comprehensive models for evaluating rockmass stability based on statistical comparisons of multiple classifiers," Mathematical Problems in Engineering , vol. 2013, 2013.

[24] J. Q. E, H. Y. Zuo, Z. Q. Luo Fuzzy Inference Neural Network Intelligent Information Fusion and Its Engineering Application , China Water Power Press, Beijing, China, 2012.