Prediction of the Equivalent Radon Exhalation Rate of Uranium Ore-rock in the Course of Mine Ventila

International Journal of Nuclear Energy Science and Engineering Volume 3 Issue 4, December 2013 doi: 10.14355/ijnese.2013.0304.04

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Prediction of the Equivalent Radon Exhalation Rate of Uranium Ore-rock in the Course of Mine Ventilation Based on GA-SVM Yongjun Ye *1,2, Yali Zhao1, Dexin Ding 2, Liheng Wang1, Nanbin Fan1 School of Environmental Protection and Safety Engineering, University of South China Hengyang, Hunan421001, PR China 1

Key Discipline Laboratory for National Defense for Biotechnology in Uranium Mining and Hydrometallurgy University of South China. Hengyang, Hunan421001, PR China 2

*yongjunye@163.com Abstract The process of radon exhalation of uranium ore-rock in the course of mine ventilation is complicated, dynamic and nonlinear. The calculation basis of radon exhalation is the equivalent radon exhalation rate, which contributes to reasonably determining the ventilation air quantity in uranium mines, avoiding unnecessary cost. In fact, the equivalent radon exhalation rate is not a constant in the course of uranium mine ventilation, but a variable influenced by ventilation rate, wind pressure and other factors. In this paper, taking the ventilation rate with the corresponding wind pressure as the input vector and the equivalent radon exhalation rate as the output vector, the paper established a GA-SVM prediction model of the equivalent radon exhalation rate of uranium ore-rock during mine ventilation. Results show that it is reasonable and viable to utilize the GA-SVM model to forecast the equivalent radon exhalation rate of uranium ore-rock during mine ventilation.

Keywords Equivalent Radon Exhalation Rate; GA-SVM; Forecasting Model; Uranium Mine; Ventilation

Introduction The mechanical ventilation is an effective way to control concentrations of radon and its daughter products in underground uranium mines. The calculation basis of ventilation and radon exhalation in underground uranium mines is the equivalent radon exhalation rate, which means the radon exhalation amount of the unit equivalent emanation area. The equivalent radon exhalation rate is the ultimate characterization parameter in the process of radon exhalation of uranium ore-rock and a fundamental parameter in the uranium mine ventilation design. In Technical Regulations for Ventilation and Radon

Exhaust in Underground Uranium Mines which is a standard for nuclear industry in China, the value of equivalent radon exhalation rate is a conservative constant. However, a great deal of measured data of radon exhalation rate on the ventilation scene have shown that the value of equivalent radon exhalation rate in design is over twice higher than the measured one, causing that the measured ventilation air quantity is two times of the actual needed air quantity and that the ventilation cost accounts for about 15% of the total production cost of uranium mines, which is three times of the other metal mines . Therefore, determining the equivalent radon exhalation rate of uranium orerock in the course of mine ventilation is very important in theory and practice for reasonably determining the ventilation air quantity in uranium mines, to reduce ventilation costs and improve radiation environment in underground uranium mines.

Radon exhalation is a very complex physical process.

Recently, studies on the law of radon exhalation were mainly based on the exhalation theory of radon diffusion and permeation . According to the theory, it’s known that radon exhalation rate is influenced by many factors including emanation coefficient, permeability rate, ventilation rate and wind pressure, etc.. The fact indicates that the equivalent radon exhalation rate in the course of uranium mine ventilation is not a constant, but a variable influenced by ventilation rate, wind pressure and other factors. So in order to predict the equivalent radon exhalation rate, a GA-SVM model was established. Support Vector Machine models based on the statistical learning theory are a new class of models that can be used to predictvalues. It has been found that SVM possesses the well-known ability of being universal approximators of any multivariate function to any 103

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International Journal of Nuclear Energy Science and Engineering Volume 3 Issue 4, December 2013

desired degree of accuracy. Genetic algorithm is a random optimized method which simulates natural selection and genetic variation in the course of biological evolution. GA has a great searching ability for the whole situation which doesn’t rely on specific solving model, and it has been widely used in seeking for optimal solution.

space using a nonlinear mapping ÎŚ, and then a linear model can be constructed in the feature space as (1) where w is a m-dimensional coefficient vector and b is a bias term. Then the SVM empirical risk can be obtained as follows

In view of the advantages of GA-SVM, taking the ventilation rate with the corresponding wind pressure as the input vector and the equivalent radon exhalation rate as the output vector, the paper established a GASVM predicting model of the equivalent radon exhalation rate of uranium ore-rock in the course of mine ventilation. The prediction model was applied to forecast the equivalent radon exhalation rate of uranium ore-rock in the course of mine ventilation in a uranium mine gallery 317. And the results of GA-SVM model have been discussed in this paper.

where đ?œ†đ?œ† is a regularization constant and the cost function defined by

(2)

(3)

is also called Vapnik’s ℰ-insensitive loss function, where ℰ is a positive hyper-parameter. It can be shown that the minimizing function has the following form

(4)

and the kernel with function k(xi, x) describes the inner product in the Ddimensional feature space

Introduction of GA-SVM

(5)

Principle of SVM SVM is a novel learning machine introduced first by Vapnik based on the structural risk minimization principle from computational learning theory. The basic idea of SVM is the following: the nonlinear transformation defined by an inner product function transforms the input space to a high dimensional feature space in which a nonlinear relationship is examined between the input variable and the output variable. Fig. 1 is the sketch of SVM. ÎŁ

Prediction results

K(x2, x)

K(x1, x)

ÎŚ(x1)

ÎŚ(x2)

x1

X2

K(xn, x)

ÎŚ(x)

ÎŚ(xn)

Xn x

Inner product kernel function

Nonlinear mapping

It is important to note that the features ÎŚ need not be computed; rather what is needed is the kernel function that is very simple and has a known analytical form.

The only condition required is that the kernel function has to satisfy Mercer’s condition. Some of the mostly used kernels include polynomial, Gaussian, and sigmoidal. In this paper, the focus is put on the widely used radial basis function (RBF), which is defined as (6) where Ďƒ is the kernel parameter that is always greater than zero.

Note also that for Vapnik’s ℰ-insensitive loss function, the Lagrange multipliers are sparse, i.e. they result in nonzero values after the optimization (2) only if they are on the boundary, which means that they satisfy the Karush–Kuhn–Tucker conditions. The coefficients are obtained by maximizing the following form

Support vectors Vector to predict

FIG. 1 THE SKETCH OF SVM

(7) subject to

.

Standard SVM Algorithm

where C is a positive hyper-parameter that is usually called regularization parameter.

The main objective of regression is to approximate a function g(x) from a given noisy set of samples , where is an input vector, and is its corresponding desired output. The input vector is first mapped into a high dimensional feature

Only a number of coefficients will be different from zero, and the data points associated to them are called support vectors. Parameters C and ℰ are free and have to be decided by the user. Computing b requires a more direct use of the Karush–Kuhn–Tucker

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conditions that lead to the quadratic programming problems stated above. The key idea is to pick those values for a point xk on the margin, i.e. or in the open interval (0, C). One xk would be sufficient but for stability purposes, it is recommended that one takes the average over all points on the margin. More detailed description of SVM for regression can be found in Refs. .

Genetic Algorithm Since the SVM performance heavily depends on the right setting of the regularization factor C, the insensitive parameter ε, and the kernel functional parameter σ, these three parameters need to be set properly by the user. According to the experience from numerical experiments, C, ε and σ exhibit a (strong) interaction. As a consequence, they should be optimized simultaneously, rather than separately.

GA is an adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic. The basic concept of GA is designed to simulate processes in natural system necessary for evolution, specifically those that follow the principles first laid down by Charles Darwin of survival of the fittest. As such, they represent an intelligent exploitation of a random search within a defined search space to solve the problem. First pioneered by John Holland in the 60s, GA has been widely studied, experimented with and applied in many fields in engineering worlds. Not only does GA provide an alternative methods to solve problem, it consistently outperforms other traditional methods in most of the problems link. Many of the real world problems involved finding optimal parameters, which might prove difficult for traditional methods but ideal for GA.

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are the value of the input vector, and ventilation rate and the corresponding wind pressure, respectively; is the corresponding output vector, representing the equivalent radon exhalation rate. GA helps to find out the optimization of C, ε, and σ.

Start GA-SVM Define: Initial range of C, ε, and σ; Size of population; Rcros, Fcros , Pmut; Maximum generations

Create initial population

Perform SVM on each chromosome in population Yes Max. Generation?

No Create next population: Rank fitness scaling; Roulette wheel selection; Heuristic crossover; Uniform mutation

Optimal C, ε, and σ for SVM FIG. 2 THE PROCEDURE OF OPTIMIZATION OF C, ε And σ

Case Study Matlab7.0 is used for model implementation in this paper.

The Processing of Data Because the values of ventilation rate, wind pressure and equivalent radon exhalation rate have different units, it’s necessary to normalize these data. How to make it is as follows: Changing the data into [0,1].

According to the ability of GA, the parameters optimization course applied in this paper is illustrated in Fig. 2. In order to obtain an objective function which can reflect SVM generalization performance without the help of test data, the cross-validation technique is adopted in this work.

where is the j data in the i input or output vector , is the min variation in the i input or output vector, is the max variation in the i input or output vector.

Modelling Procedure of GA-SVM

Sampling Data and Training of GA-SVM

In specific underground uranium mine, the grade of uranium ore and uranium-radium equilibrium coefficient are determined, so the equivalent emanation area will be excluded. In this paper, the ventilation rate with the corresponding wind pressure is the input vector of the SVM prediction model, and the equivalent radon exhalation rate is the output vector. In the , is the

The sample data come from 14 groups measured data of radon exhalation rate in a uranium mine gallery 317, shown in Table 1. The average uranium ore grade of the gallery is 0.0418%, the balance coefficient of radium and uranium is 1.103, the emanation area of the gallery is 164.25m2, and the equivalent area emanation is 7.576 m2·1%. The former 12 groups measured data is input data in the model to training it,

(8)

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the later 2 groups measured data is test data. The maximum total error is 0.0001 and maximum training times is 2000. Optimal C and σ for the GA-SVM model have been shown in Table 2, which also lists the optimal C and σ for SVM model and PSO-SVM model developed for the same case.

shown in Table 3. Comparison of the forcasting results of the three models is listed in Table 4.

TABLE 3 COMPARISON OF MEAN SQUARE ERROR AND SQUARED CORRLATION COEFFICIENT

Parameter Mean squared error Squared correlation coefficient

TABLE 1 THE EQUIVALENT RADON EXHALATION RATE RESULTS OF A URANIUM MINE GALLERY 317 AFTER CLEAN-UP

Serial Number

Ventilation Rate(m3/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1.9730 2.7930 3.1030 2.7040 2.9990 1.0030 0.9590 1.6450 0.7880 1.4080 1.3700 1.3200 1.0580 1.3580

TABLE 2 OPTIMAL C AND

Parameter C σ

Wind Pressure (mmHg) 0.2800 0.4050 0.1800 0.1000 0.1800 0.2050 0.1800 0.0800 0.4500 0.0550 0.4050 0.7430 0.4800 0.1680

Equivalent Radon Exhalation Rate (108Ci/(s·m2·1%)) 0.1771 0.1888 0.4391 0.3483 0.4402 0.1398 0.0739 0.2241 0.0639 0.1725 0.1374 0.0836 0.0936 0.1936

σ FOR SVM, PSO-SVM AND GA-SVM

SVM 16 0.0206

PSO-SVM 27.6770 0.0100

GA-SVM 44.2724 0.3557

Test of Training Results All the sampling data are tested respectively by GASVM, showing that compared with the results of SVM and PSO-SVM models, the prediction data of GA-SVM are much better. Among the three prediction modles, the mean squared error value of GA-SVM model is the smallest, and the squared correlation coefficient value of GA-SVM model is the largest, which have been

1 2 3 4 5 6 7 8 9 10 11 12 13 14

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Experimental Data(10-8Ci/ (s·m2·1%)) 0.1771 0.1888 0.4391 0.3483 0.4402 0.1398 0.0739 0.2241 0.0639 0.1725 0.1374 0.0836 0.0936 0.1936

SVM Model Forecasting Value Relative (10-8Ci/(s·m2·1%)) Error(%) 0.2248 26.93 0.3395 79.82 0.4291 -2.28 0.3696 6.12 0.4101 -6.84 0.1165 -16. 67 0.1158 56.70 0.2087 -6.87 0.0634 -0.78 0.1824 5.74 0.1274 -7.28 0.0755 -9.69 0.0837 -10.58 0.1600 -17.36

PSO-SVM

GA-SVM

0.865685

0.861683

0.976276

Besides, a BP-ANN forecasting model (the number of neurons in hidden layer is preliminarily determined as five, and the stimulating function in both the hidden and output layer is Sigmoid function as .) and a multivariate nonlinear regression model ( , where Jd is equivalent radon exhalation rate, Q air quantity and h wind pressure) have ever been built for the same case. The prediction results are listed in Table 5. Obviously, the forecasting data of GA-SVM are better than that of Multivariate Nonlinear Regression Forecasting Model, but little worse than that of BP-ANN model.

Conclusion The equivalent radon exhalation rate is complex with multiple influencing factors. In this paper, through establishing the GA-SVM predicting model and comparison with other models, two conclusions come out. On one hand, the predicting ability of GA-SVM model is the best among the three SVM models. On the other hand, the prediction results of GA-SVM model are not as good as those of BP-ANN model, but much better than those of multivariate nonlinear regression model. In general, it is reasonable and viable to utilize the GA-SVM model to forecast the equivalent radon exhalation rate of uranium ore-rock in the course of mine ventilation.

TABLE 4 COMPARISON OF FORECASTING RESULTS OF

Serial Number

SVM

0.0021763 0.00208481 0.000352763

SVM, PAO-SVM AND GA-SVM MODELS

PSO-SVM Model Forecasting Value Relative (10-8Ci/(s·m2·1%)) Error(%) 0.2256 27.39 0.3290 74.26 0.4095 -6.74 0.3586 2.96 0.3931 -10.70 0.1117 -20.10 0.1101 48.99 0.2091 -6.69 0.0542 -15.18 0.1819 5.45 0.1282 -6.70 0.0761 -8.97 0.0804 -14.10 0.1597 -17.51

GA-SVM Model Forecasting Value Relative (10-8Ci/(s·m2·1%)) Error(%) 0.1673 -5.53 0.1985 5.14 0.4493 2.32 0.3583 2.87 0.4116 -6.50 0.0986 -29.47 0.0840 13.67 0.2137 -4.64 0.0744 16.43 0.1827 5.91 0.1473 7.21 0.0932 11.48 0.1223 30.66 0.1694 -12.5

International Journal of Nuclear Energy Science and Engineering Volume 3 Issue 4, December 2013

TABLE 5 COMPARISON OF FORECASTING RESULTS OF

Serial Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Experimental Data(10-8Ci/ (s·m2·1%)) 0.1771 0.1888 0.4391 0.3483 0.4402 0.1398 0.0739 0.2241 0.0639 0.1725 0.1374 0.0836 0.0936 0.1936

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MNR, BP-ANN AND GA-SVM MODELS

Multivariate Nonlinear Regression Model GA-SVM Model Forecasting Value (10Relative Forecasting Value Relative 8Ci/(s·m2·1%)) Error(%) (10-8Ci/(s·m2·1%)) Error(%) 0.1890 6.73 0.1673 -5.53 0.2621 38.86 0.1985 5.14 0.4124 -6.07 0.4493 2.32 0.3600 3.34 0.3583 2.87 0.3882 -11.81 0.4116 -6.50 0.1175 15.95 0.0986 -29.47 0.1180 59.62 0.0840 13.67 0.1988 -11.28 0.2137 -4.64 0.0770 20.58 0.0744 16.43 0.1784 3.44 0.1827 5.91 0.1142 16.91 0.1473 7.21 0.0737 -11.88 0.0932 11.48 0.0870 7.02 0.1223 30.66 0.1512 -21.95 0.1694 -12.5

BP-ANN Model Forecasting Value Relative (10-8Ci/(s·m2·1%)) Error(%) 0.1780 0.51 0.1869 -0.98 0.4402 0.26 0.3477 -0.19 0.4395 0.16 0.1345 -3.79 0.0788 6.59 0.2222 -0.84 0.0692 8.36 0.1717 0.45 0.1405 2.23 0.0790 -5.54 0.0989 5.70 0.1966 1.55

Keerthi, S. and Lin, C.-J.. “Asymptotic behaviors of support

ACKNOWLEDGMENT

This work was financially supported by Chinese National Natural Science Fund Projects (No.11105069), Hunan Provincial Natural Science Foundation of China (No. 09JJ6078) and Hunan province science and technology program (No. 2011SK3085).

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