CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-43-3; ISSN 2283-9216 

Forecasting of Mine Discharge Based on Phase Space 
Reconstruction and SimpleMKL 

Xin Zhanga,b, Yinghai Guo*a, Youkuo Chena,b  
aSchool of Resources and Earth Sciences China University of Mining and Technology Xuzhou, Jiangsu 221116, China. 
bYankuang Group Company Limited, Zoucheng, Shandong 273500, China. 
teasta@163.com 
 
Forecasting of mine discharge is crucial to water disaster prevention in mines. The hydrogeological is 
complex, caused by internal and exterior factors in a mine that makes the forecasting much more difficult. The 
paper puts forward a kind of prediction method of mine discharge based on Phase Space Reconstruction and 
SimpleMKL. By analysis and studying the hydrogeology of the study field, while getting the maximal Lyapunov 
exponent 0.1844  >0 by wolf algorithm, we know mine discharge has Chaos characteristics and can find 
out the hidden evolution rule of mine discharge time series by Phase Space Reconstruction, and as 
SimpleMKL input and output parameters, so as to transform the nonlinear problem into linear solution in multi-
kernels mapping space. After choosing mine discharge date from August 2004 to February 2005 to validate, 
the results show that this method is feasible and possesses a high precision and very strong practical value. 

1. Introduction 

The reason that causes water bursting is that the natural balance of the rocks is destroyed during the process 
of mine tunnelling or face mining, surrounding water, under the action of hydrostatic pressure and mine 
ground pressure, access into face via faults, aquiclude and weak spots inside the strata(]Zhang 
C.W.et.al.(2004)).The mine groundwater system is gradually evolving with mining depth and mining area 
gradually increasing, the process of system evolution show by the original steady state to the unsteady state, 
and then reach another steady state under the system self-adjusting. The system evolution process is like an 
iterative process, each initial conditions of the iteration is different, mainly displays in the difference of 
groundwater quantity and ground water level. Due to the comprehensive effect of geologic structure, formation 
lithology, hydrometeorology and any other reasons, each initial condition shows a relative independence and 
randomness(Tang and Xiao, 2006), therefore mine discharge time series has chaos characteristics. Chaos 
Phenomena is unique because of its completely definite, simple nonlinear system model, if we can find the 
internal law of nonlinear system and establish its model, then forecasting of its uncertainty is possible. Takens’ 

Embedded Theorem provides theoretical bases for prediction of chaotic time series(Takens, 1981),many 
nonlinear prediction methods that forecasting chaotic time series were proposed(Meng and Peng, 2007), 
Adaptive Nonlinear Filtering Prediction Method(Zhang and Xiao, 2000), The Prediction Method Based on 
Neural Network(Gu and Zhai, 1995), for instance, Feed forward Neural Network Nonlinear Prediction Method 
based on Phase Space Reconstruction is able to accurately predict the low dimensional chaotic sequence, but 
due to minimized sample point error of feed-forward neural network model in training(Cui et al., 2005), ‘over-
fitting’ phenomenon is inevitable, which will lead to the model poor generalization ability.  
Support Vector Machine(SVM) now become a new hotspot after neural network, it was established on the 
basis of VC dimensional theory and structural risk minimization principle of Statistical Theory(Vapnik, 1999), 
SVM has been seen as a good replacement of traditional learning methods, especially in smallsamples, high 
dimensional nonlinear case, and has good generalization performance(Chapelle et al., 1999).  
Whereas, SVM is single kernel methods both based on individual character space. Different kernel functions 
have different characteristics, so installed performance of a kernel function varies greatly in different 
applications, and the construction or choice of kernel functions has no completely theoretical basis, at present, 
commonly used kernel functions are linearly kernel function, polynomials kernel function, Radial Basis 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651172

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Zhang X., Guo Y.H., Chen Y.K., 2016, Forecasting of mine discharge based on phase space reconstruction and 
simplemkl, Chemical Engineering Transactions, 51, 1027-1032  DOI:10.3303/CET1651172   

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Function (RBF) kernel function, Sigmoid kernel function and Gauss kernel function etc.(Genton, 2001),  in 
addition, when sample characteristics contain Heterogeneous Information(Bach F. R.(2008)), large sample  
size(Rakotomamonjy et al., 2008), multi-dimensional unnormalised data(Kingsbury et al., 2005) or non-flat 
data in high dimension space distribution characteristics(Yang et al., 2006), to deal with all samples through 
single kernel function mapping is not reasonable. To address these issues, a great deal of research about the 
method of kernel combination are come out, namely, multiple kernel learning(Bach, 2004). 
SimpleMKL can be extended to other SVM algorithms with only little changes such as regression, clustering, 
singular detection, mutli-classification etc. SimpleMKL converges in fewer times than other MKL algorithms. 
The Phase Space Reconstruction based on chaotic dynamic system are similar to machine learing, the article 
attempt to approach a method of prediction mine discharge based on Phase Space Reconstruction and 
simpleMKL, so SimpleMKL theoretical research can be applied to practical work, thus, serveing for the safety 
production of mines better. 

2. Methodology 

2.1 Phase Space Reconstruction based on chaotic time series 

Phase Space Reconstruction is also called system reconstruction, original Phase Space Structure can be 
excavated out based on one-dimensional time series, so the intrinsic nature can be found out. At present, the 
commonly used method is time delay. The method is approached by Packard et al.( Packard N.H.et 
al.(1980)), Takens consolidated the mathematics basics. Any weight is decided by others of the system, so 
the interrelated vector information is included in any weight. 
Supposed that the time series: x={xi=1,2,…,N}, then any vector in the Phase Space Reconstruction follows: 

( 1)
{ | [ , ,..., ] , 1, 2,..., }

T

i i i i t i m t
X X X x x x i M

  
                                                                                              (1) 

Where m is the numbers of points in Phase Space Reconstruction, M=N-(m-1)t, m and t are respectively delay 
time and  embedding dimensions. Taken has proved that d is the dimensions when m2d+1, so dynamical 
system of reconstruction is equivalent to original dynamical system. 
At present, there are two kinds of method to choose the embedding dimensions m and time delay t. A sort of 
viewpoint think m and t are independence. The other viewpoint think m and t is correlate, time-window method 
or C-C method can be used to calculate them[5]. The paper using C-C method(Kim et al., 2009) to get  
embedding dimensions m and time delay t. 

2.2 Identification of Time Series Chaos  

The basic feature of chaotic motion is that the motion is very sensitive to initial conditions, it can measure the 
degree of separation. Two rail line on the close separates exponentially with time. Lyapunovi index is to 
quantitively describe the phenomenon based on whole. When the Lyapunov index is less than zero, the tracks 
shrink to point, when the Lyapunov index is greater than zero, the tracks separates, if trail has other factors, 
Chaotic Attractors will form based on the interaction. So the biggest Lyapunov index is positive is usually used 
as an important condition to judge chaos nature(Chen, 2005). 

2.3 SimpleMKL 

Kernel methods, such as support vector machines (SVM) have proved to be efficient tools for solving learning 

problems like classification or regression.Let 
1

{ , }
i i i

x y


 be the learning set, where xi is training specimen, yi is 
objective value.  
The solution of the learning problem is of the form: 

*

1

( ) ( , )
i i

i

f x a K x x b


 
                                                                                                                                  (2) 

Where ai and b* are some coefficients to be learned from examples, while K(,)is a given positive definite 
kernel, f(x) can be solved by a convex quadratic optimization. 
The multiple kernels learning are Convex Combination of classical kernel in essence. 

1

( , ') ( , ')
M

m m

m

K x x d K x x


 
 with  1

0, 1
M

m m

m

d d


 
                                                                                          (3) 

Where M is the total number of kernels. km can simply be classical kernels (such as Gaussian kernels) with 
different parameters. dm is weights of ( , )m iK x x . 

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In the SVM methodology, the decision function is a form given in Formula(2), where the optimal parameters ai 
and b* can be obtained by solving the dual of the following optimization problem Formula(4): 

2

, ,

1
min

2
i

f b
i

f C




    

. .s t     1i i iy f x b      i  

0
i
   i                                                                                                                                                          (4) 

In the MKL framework, one need look for a decision function of the form: ( ) ( )
mm

f x b f x b   ,each 
function fm associated with a kernel Km(), Rakotomamonjy A. et al. (2008) propose to address the MKL SVM 
problem by solving the following convex problem based on (Formula 4):

 

 , , ,
min

m
b df 

21 1

2 m
i

m im

f C
d




 
  

. .s t  
  1i m i ii

m

y f y bx 
 

   
 


  i  

0
i
   i       

1,
m

m

d 
0

m
d   m                                                                                                                                       (5) 

Formula (5) is the primal MKL problem, where each dm controls the squared norm of fm in the objective 
function. The MKL problem Formula (5) can equivalent to:

 
 min

d
J d   such that   

1

1,
M

m

m

d



0

m
d  ,                                                                                                            (6) 

where  


2

, ,

1 1
min

2 m
i

f b
m im

J d f C
d




  
 

. .s t
  1i m i ii

m

y f y bx 
 

   
 


  

0
i
  i                                                                                                                                                           (7)

 

The problem Formula(6) can be solved by a simple gradient method[34].The Lagrange of  Formula (7) follows: 

 
21 1

1
2 m

i i i i m i i i i

m i I m im

L f C y f x y b v
d

   


 
       

 
    

+
( 1)

m m m

m m

d d   
                 (8) 

Where 
i

  and 
i

v  are the Lagrange multipliers, when setting to zero the gradient of the Lagrangian with 
respect to the primal variables. The dual problem of Formula (7) can be obtained 

 

 
,

1
max ,

2
i j i j m m i j i

i j m i

y y d k x x


       

with  0i i
i

y   

0
i

c    i                                                                                                                                                    (9) 

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Which is identified to the standard SVM dual formulation, only the kernel function becomes a combination of 
kernel functions:

 
( ) ( )

i j m m m i j
K x , x d K x , x                                                                                                                            (10) 

Function ( )J d  is defined as the optimal objective value of problem Formula (7). Because of strong duality, 

( )J d is also the objective value of the dual problem Formula (11): 

   * * *
,

1
,

2
i j i j m m i j i

i j m i

J d y y d k x x      
                                                                                            (11)

 

Where * can maximizes Formula(9), the objective value J(d) can be obtained by any SVM algorithm. So 
SimpleMKL can thus take advantage of any progress in single kernel algorithms.  
The algorithm in the previous section focuses on binary classification, MKL algorithm can be extended to other 

regression with only little changes, Formula (7) can be changed: 

   
2 *

, ,

1 1
min

2 mm t
m i iHf b

m im

J d f c
d

       

. .s t  i m i i
m

y f x b       

  *m i i i
m

f x b y        i  

*
0, 0

i i
    i                                                                                                                                             (12) 

The dual problem of Formula (12) follows: 

          
,

,

1
max ,

2
i i i i i i i j j m m j

i i i j m

J d y d k xi x
 

                    

 with    0i i
i

    

0 , ,c i                                                                                                                                                   (13) 

Where {I, i} are Lagrange multipliers, J(d) is differentiable, the problem can be soled by. 

2.4 Forecasting based on phase space reconstruction and SimpleMKL 

Step1 The delay time t  and the embedding dimension m  can be got by C-C methods. 
Step2 Phase Space Reconstruction 
Step3 Reconstruction matrix as training parameters, the system of prediction is developed after simpleMKL 
regression. 
Step4 The next predictive value can be got by putting the predictive value to (2) and calculating (3). 

3. Prediction for water inrush in mine and results 

3.1 Data and Analysis 

The second Liuqiao mine is located in Midwest of Huaibei coal field. The study area is a closed and 
semiclosed grid hydrogeological unit. So it can be considered that the study area is a continuous evolution 
system, in addition, due to mine discharge is the synthesis results of some factors, such as water pressure, 
the rock pressure, impermeable layer thickness, faults, underground mining etc. The interacion among these 
factors is complicated in the course of specific mine discharge(Yang and Chen, 2009). Mine discharge data 
trend in Figure (1) during January 1990 and February 2005 of Liuqiao second mine. 

 

Figure 1: Mine discharge curve 

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3.2 Mine discharge forecasting and results analysis 

The follow graph is got by using C C  algorithm (Figure 2) 

 

Figure 2: Time delay and embedding dimension based on C-C algorithm  

Table 1: The accuracy analysis 

Time Actual 
values(m3/h) 

Predictive 
values(m3/h) 

Absolute error  Relative error 

2004-8-1 462.3300 454.8056 7.5244 0.0163 
2004-9-1 482.5800 467.5854 14.9946 0.0311 
2004-10-1 406.8800 436.7100 29.8300 0.0733 
2004-11-1 425.3100 457.2013 31.8913 0.0750 
2004-12-1 420.4400 451.4993 31.0593 0.0739 
2005-1-1 424.9400 447.7985 22.8585 0.0538 
2005-2-1 454.7900 435.3154 19.4746 0.0428 

 
The first minimal point of delta △s(t): t=11, so optimal delay time t=11, the local minimum point of Scor: t =33, 
that is tw=33, according to tw=(m-1)tau the embedding dimension m=4 can be got; maximum Lyapunov 
exponent =0.1844>0 by using wolf algorithm. So historical data of mine discharge has chaotic 
characteristics. So mine discharge can be prediction based Phase Spase Reconstruction and SimpleMKL. 
A total of 179 data during January 1990 and February 2005, among them, Data during January 1990 and July 
2004 as a training sample and get the prediction model, then to predict mine discharge during August 2004 
and February 2005 and compared with the corresponding actual value, the absolute error and relative error as 
comparative indicators(Table 2). 
In so far as some specific problems, there is not a consensus to choose better kernel parameters and 
weighted coefficient, in order to require optimal parameters, using usually empirical method, experimental 
contrast method, a large range search, cross validation method and so on. 
In this test, parameters choosing as follow: 
regularization parameters C is got using cross validation method: 
regularization parameters: C=700;   
kernel parameter: =[0.01 0.06 0.11 0.16 0.5 1 2 5 7 10 12 15 20]; d=[1,2,3]; 
The algorithm of reduced gradient method is terminated when a stopping criterion is met DualGap=0.01. 
Table 1 show machine learing methods to predict mine discharge has a high precision, relative error control 
within 0.1, which further proves that the method based on Phase Space Reconstruction and SimpleMKL to 
forecast chaotic time series is feasible, processes a high precision and can be applied to practice. 

4. Conclusion 

This paper puts forward a kind of prediction method of mine discharge based on Phase Space Reconstruction 
and SimpleMKL. 
The prediction method based Phase Space Reconstruction and simpleMKL is feasible and the precision is 
well, which can be applied to practical problem. Maximum lyapunov of mine discharge exponent =0.1844>0 
in the field , so mine discharge has chaotic characteristics, thus input and output parameters can be obtained 
by the method of Phase Space Reconstruction and trained to get the prediction model, then mine discharge 
can be predicted. 
By testing of Lorenz chaotic time series and prediction of mine discharge, it is proved that the method based 
on Phase Space Reconstruction and SimpleMKL to forecast mine discharge is feasible, prossesses good 
robustness, high precision and a strong practical value. 

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Acknowledgements 

The work was supported by a grant awarded from National Natural Science Foundation of China (NSFC) grant 
(40472146). 
 

Reference 

Bach F.R., 2008, Consistency of the group Lasso and multiple kernel learning, Journal of Machine Learning 
Research, 9: 1179-1225. 

Bach F.R., Lanckriet G.R.G., 2004, Multiple Kernel Learning, Conic Duality, and the SMO Algorithm, In: 
Proceedings of the 21st International Conference on Machine learning. 

Chen Y.F., 2005, Application of chaotic time series in Hydrological Forecastingp[D], Chang`an University, 
Cui W.Z., Zhu C.C., Bao W.X., Liu J.H.., 2005, Prediction of the chaotic time series usingsupport vector 

machines for fuzzy rule-based modeling, Acta Phys. Sin, 54(07): 3009-3018. 
Chapelle O., Haffer P., Vapnik V.N., 1999, Support vector machines for histogram-based image classification, 

IEEE Transactions on Neural Networks, 10(5): 1055-1064 
Gu W., Zhai D.H., 1995, A neural network for fast prediction of chaotic the series, Journal of Fuan 

University(Natural Science), 34(3): 262-268. 
Genton M.G., 2001, Classes of kernels for machine learing: a statistics perspective, Journal of Machine 

Learning Research, 2: 299-312. 
Kingsbury N., Tay D.B.H., Palaniswami M., 2005, Multi-scale kernel methods for classification, In: 

Proceedings of IEEE Workshop on Machine Learning for Signal Processing, 43-48. 
Kim H.S., Eykholt R., Salas J.D., 1999, Nonlinear dynamics delay times and embedding windows[J], Physica 

D, 127: 48-60. 
Meng Q.F., Peng Y.H., 2007,Improved adding weight first order local prediction method for chaotic time 

series[J], Computer Engineering and Applications, 43(35):61-64. 
Packard N.H., Crutchfietd J.P., Farmer J.D., 1980, Geometry from a time series. Phys. Rev. Lett, 45(9):712-

716. 
Rakotomamonjy A., Bach F.R., Canu S., Grandvalet Y., 2008, SimpleMKL, Journal of Machine Learning 

Research, 9: 2491-2521. 
Tang Y.M., Xiao J, 2006, Condition and mechanism about chaos formation in the evolution   process of 

groundwater system of minning area. Journal of China Coal Society, 31(1): 45-49. 
Takens F., 1981, Determing strange attractors in turbence[J],Lecture notes in Math, 898: 361-381. 
Vapnik V.N., 1999, The Nature of Statistical Learning Theory, New York: Springer-Verlag. 
Yang Z., Guo J., Xu W. Nie X.F., Wang J., Lei J.J., 2006, Multi-scale Support Vector machine for regression 

estimation, ISNN’06, LNCS, 3971:1030-1037. 
Yang Y.G., Chen Y.H., 2009, Chaotic Characteristics and Prediction for Water Inrush in Mine[J], Journal of 

China University of Geosciences, 34(2):258:262. 
Zhang C.W., Fu B., Xu Y., 2004, Research on gushing water in coal-mine[J].,Coal Technology, (5). 
Zhang J.S., Xiao X.C., 2000, Prediction of chaotic time series by using adaptive higher order nonlinear fourier 

infrared filter[J]. Acta Phys. Sin., 49(07):1221-1227. 
 

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