Annual Journal
Journal of
of Hydraulic
Hydraulic Engineering,
Engineering, JSCE,
JSCE, Vol.54,
Vol.54, 2010, February
Annual
ADAPTIVE EURO FUZZY IFERECE SYSTEM
APPROACH FOR PREDICTIO OF HYDRAULIC
PRESSURE CHAGE
Mebruk MOHAMMED1, Kunio WATANABE2 and Shinji TAKEUCHI3
1
Member of JSCE, M. Eng., Geosphere research Institute, Saitama University (Shimo Okubo 255, Sakura-ku,
Saitama, Japan)
2
Member of JSCE, Dr. Eng., Professor, Geosphere research Institute, Saitama University (Shimo Okubo 255,
Sakura-ku, Saitama, Japan)
3
Member of JSCE, Dr. Eng., Tono Geosciences Center, Japan Atomic Energy Agency (1-64, Yamanonichi, Akeyo,
Mizunami, Gifu, Japan)
The effect of continuous subsurface activities like tunneling, pumping, etc. on the surrounding
hydraulic pressure is usually predicted using numerical models. For numerical modeling adequate data on
the activities, hydrogeology, etc are necessary. However, these data are usually uncertain. Seeking to
circumvent these uncertainties inherent to numerical models a new approach is proposed. In this approach,
at first, by changing the hydrogeologic parameters three approximate numerical hydraulic pressure trends
are formed then adaptive neuro fuzzy inference system (ANFIS) is trained by minimizing the residual
between these numerical model trends and the measured hydraulic pressure. Finally the trained ANFIS
and the three numerical models are combined in parallel for the inferred pressure prediction. Such
modeling approach has been successfully applied to analyze the hydraulic pressure change caused by
shafts construction at Mizunami underground research laboratory (MIU) site, Japan.
Key Words: AFIS, hydraulic pressure, MIU, umerical model
1. ITRODUCTIO
Hydraulic pressure change due to construction
of any underground structure shall precisely be
predicted to monitor the construction’s effect on the
near by groundwater flow. Usually, numerical
groundwater flow analysis is conducted for such
prediction. These numerical models need precise
hydrogeologic, boundary and initial conditions
specification over a wide area. It is usually very
difficult to obtain such data. On the other hand, if
sufficient construction and measured hydraulic
pressure data are available for their training, soft
computing techniques like adaptive neuro fuzzy
inference system (ANFIS) are another alternative
method for hydraulic pressure prediction. However,
getting enough training data is a challenge for the
sole soft computing technique application.
In this study the combined use ANFIS with a
numerical groundwater flow model is discussed for
precise prediction of hydraulic pressure change.
The idea is that, at first three hydraulic pressure
trends are calculated by a numerical model for
simplified hydrogeologic conditions then ANFIS is
trained by using the three numerical models as
inputs and the measured hydraulic pressure as
output. Finally future hydraulic pressure change is
predicted using the numerical model predictions as
inputs to the trained ANFIS. ANFIS is formed from
fusion of artificial neural network (ANN) and fuzzy
logic. The fuzzy logic offers concept of fuzzy set
theory, fuzzy “if then rules” and approximate
reasoning while ANN offers learning capability.
Presently, two vertical shafts have been
excavated in the underground research laboratory at
Mizunami, Japan. Hereafter this site is referred as
the MIU site. The changes in groundwater flow
brought about by the excavation of shafts have been
monitored by observation wells. Ijiri et al.1), using
three continuous models (TOUGH2, EQUIV_FLO
and Don-Chan) analyzed the regional groundwater
flow in Tono area which encompasses MIU.
Although these models approximated the general
flow direction, the results in terms of travel time
and pathway length were found to differ by 3 and
2.5 orders of magnitude, respectively. The study
concluded that heterogeneity of the porous media is
the major cause for such uncertainty. Yanagizawa et
al.2), using a three dimensional finite element
method (FEM), analyzed the hydraulic pressure
- 43 -
change due to an excavation of 150 m long vertical
shaft in the Tono area. Despite the use of detailed
hydrogeologic investigations, there was as high as
50 m difference in the measured and simulated
hydraulic head. Therefore, there is need for
devising a method that is capable of handling such
uncertainty present in the current continuous
modeling approaches.
Azhar and Watanabe3), show a successful
application of the common ANFIS in monitoring
the daily groundwater fluctuation pattern around
Saitama city, Japan. Hong et al.4) develop a
dynamic fuzzy modeling approach, which is based
on multiple local models that are weighted using
fuzzy membership functions, to identify and predict
groundwater level fluctuations caused by storm
water infiltration around Mt. Eden area of Auckland,
New Zealand. These studies expect prediction
conditions to lie within the training condition.
Continuous underground construction results in
continuously decreasing hydraulic pressure. This
makes prediction condition to be different from the
training situation. Thus, in this paper, an approach
towards handling such differences in training and
prediction conditions using ANFIS is also proposed
and evaluated in order to arrive at conclusions
regarding the method’s efficiency in predicting
continuously decreasing hydraulic pressure caused
by construction of the shafts of MIU.
MIU
MSB-4
MIZ-1
MSB-1
MSB-3
MS
VS
N
MSB-2
DH-2
0
Fig. 1 MIU site area, Shafts and boreholes location
m diameter) are now under construction. The two
vertical shafts have been excavated in fractured
Tertiary sedimentary rock of 0.7-20 millions years
of age (Ma) that unconformably overlay a basement
rock composed of fractured Toki granite of
approximately 60-70 Ma 6).
The excavation of the vertical shafts was started
in Feb. 2005. On Oct. 27, 2005 as the fluoride
concentration of the pumped groundwater was
found to exceed the Japanese environmental
standard, the excavation was stopped6). Thus, the
water level in both shafts had started to rise. On Feb.
20, 2006, since the construction of the water
treatment facility was completed, pumping out of
the accumulated water had started. The excavation
work in the VS and MS was resumed on May 29,
and April 4, 2006, respectively (Fig. 2).
Among the six boreholes illustrated in Fig. 1,
continuous monitoring of hydraulic heads was
carried out in DH-2, MSB-1, and MSB-37). There
are five pressure sensors at different depths in
MSB-1 borehole. Fig. 2 illustrates the observed
2. MIU SITE AD AVAILABLE DATA
MIU site is located in Mizunami city, Gifu
prefecture, Japan (Fig. 1). It is a research project to
establish methods for investigating the geological
environment and develop engineering techniques
applicable in the deep underground5). Two circular
1000 m length vertical shafts (a main shaft (MS) of
6.5 m diameter and a ventilation shaft (VS) of 4.5
156
MS
VS
117.3 m amsl
130
100
72.5 m amsl
56.8 m amsl
70
40
152
148
144
140
10
05/6/23
-50
2004/12/29
05/10/27
136
06/2/20
132
2005/8/26
2006/4/23
Date
2006/12/19
2007/8/16
Fig. 2 Observed hydraulic pressure in MSB-1 borehole, excavation and water level in MS and VS
- 44 -
Hydraulic pressure (m amsl)
Water Level (m amsl) forr
MS and VS
160
-20
100m
hydraulic pressure changes in MSB-1 borehole
from Jan. 1, 2005 till Mar. 07, 2008. The hydraulic
pressure changes recorded at 117.3 m, 72.5 m and
56.8 m above mean sea level (amsl) are shown in
this Figure. From Fig. 2 it is evident that continuous
excavation and pumping results in continuous
decrease in the hydraulic pressure trend.
3. THE AFIS MODELIG APPROACH
In this model, at first, based on the limited data
available for MIU site, a simplified hydrogeologic
model with approximate boundary conditions is
created. By changing the aquifer parameters of the
hydrogeologic model, three patterns of past
(measured) and future hydraulic pressure trends are
simulated by a three dimensional Galerkin based
FEM model called TAGSAC. The TAGSAC model
results are then normalized between 0 and 1. Since
future minimum value of the measured hydraulic
pressure is unknown, its normalization is performed
based on its maximum and the average of the
predicted minimum values of the TAGSAC results.
These normalized TAGSAC and measured
hydraulic pressure trends are paired as inputs and
output, respectively, without time lag for training of
ANFIS. Finally, future hydraulic pressure change is
predicted using the normalized TAGSAC results in
the future period as inputs to the trained ANFIS.
ANFIS models behave as a universal function
approximate and can possibly take into account any
non-linearity in a relationship8). For this reason, it is
used in the present study with an aim of capturing
any possible non-linearity in the functional
relationship of the TAGSAC model results and the
measured hydraulic pressure data.
The excavation and pumping data in both shafts
are in days to weeks of interval. However, in this
study six hour time interval was selected for the
hydraulic pressure analysis. Thus, the TAGSAC
model is used to change the excavation and
pumping data to six hour interval hydraulic pressure
trends that can be used as inputs to ANFIS.
The shafts have been excavated in deep
saturated fractured rock mass5). Therefore, three
dimensional saturated TAGSAC model was adopted.
The site is essentially composed of sedimentary and
granite rocks7),9). The measured hydraulic pressure
trend in MSB-1 borehole has shown a change in its
usual slope around June 23, 2005 (Fig. 2). This
change in hydraulic pressure trend may be due to
the entrance of the excavation from the low
permeable region to high permeable region. Thus, a
two layer model as illustrated in Fig. 3 was adopted
as the conceptual hydrogeologic model.
To include the natural hydraulic boundaries like
rivers and groundwater divides nearby MIU, the
analyzed domain was extended beyond the site
boundary (Fig. 3). This area was discretized into
20046 nodes that form 37196 triangular prism
elements. The main- and ventilation shafts were
represented by pile elements. The sizes of the
elements around the shafts were the smallest and
are gradually increasing towards the boundary of
the area. The hydraulic pressure sensors locations in
MSB-1 were represented by nodes.
Hydraulic conductivity and specific storage
measured for the rock of this site are widely
distributed9),10). For this reason, different
combination of horizontal (KH) and vertical (KV)
hydraulic conductivities and specific storage (Ss)
were assumed to form the hydrogeologic models.
As for the boundary conditions; the ground
surface was treated as a free seepage face. A
recharge rate of 0.28 mm/day, which is an average
infiltration rate estimated in the vicinity of the Tono
Mine9) was assigned at the top surface. A constant
head equal to the average water level of the Toki
and the Hiyoshi rivers was assigned to the nodes
representing the rivers. For the nodes along the
mountain ridges a no-flow boundary was assigned
to represent the groundwater divide11). The side of
the entire model domain is assumed as no flow
boundary to represent a streamline created by the
groundwater divide along the rivers and the ridge11).
The minimum excavation level in the analysis
period was 0.7 m amsl in VS and -30.3 m amsl in
MS. Hence, assuming a no flow boundary at -500 m
amsl was expected to have a small effect across the
entire groundwater flow domain. Transient
boundary condition was assigned for the shaft
nodes. During excavation groundwater level in the
shafts was equal to the bottom of the excavated
shaft. Thus the transient groundwater level was
assigned as changing constant head boundary over
the shaft nodes near by the shaft’s excavation level.
- 45 -
Hiyoshi
River
Ridge
MIU site
70m amsl
-500m amsl
Toki River
Fig. 3 Analyzed area and conceptual hydrogeologic model
assumed
In the TAGSAC model analysis, first, arbitrary
combinations of KV and KH were assigned in the
two-layer hydrogeologic model. Then a dynamic
steady-state hydraulic pressure distribution was
calculated for the initial condition11) estimation i.e.
before the construction of the shafts commenced.
Hydraulic pressure measured in MSB-1 borehole
before construction of the shafts was compared with
the calculated values. KV and KH values of the two
layers with better approximation were selected.
Then a transient simulation was analyzed using the
obtained initial condition, KV and KH values. In this
analysis, the Ss value was adjusted to approximate
the measured hydraulic pressure trend.
By using different combination of KV, KH and
Ss values for the two layers in Fig. 3, three different
hydrogeologic models were formed. Table 1
summarizes the set of parameter values obtained for
the three TAGSAC model results (FEMA, FEMB,
and FEMC). The top and bottom layers in the table
mainly represent the sedimentary and the granite
rocks, respectively.
The next step in this ANFIS modeling approach
is normalization. Normalization involves separately
rescaling the entire dataset, TAGSAC and measured
hydraulic pressure values, in the range of 0 and 1 as
in Eq. 1 and Eq. 2.
FEM n − Min n , n = A, B, C
(1)
fem =
n
Max n − Min n
P =
PM − Min M
Max M − Min M
(2)
where, Minn and Maxn are the minimum and
maximum values of the FEMn trend. MaxM is the
maximum of the measured hydraulic pressure (PM).
From Fig. 2 it is evident that the measured
hydraulic pressure is continuously decreasing, this
makes its future value unknown. Thus, the MinM in
Input
If-part
µ1 A
femA
Rules
Table 1 Aquifer parameters obtained
Model
Layer
Top
FEMA
FEMB
FEMC
KH(m/s)
3.65E-07
KV(m/s)
1.0E-10
Ss( )
3.0E-4
Bottom
1.0E-07
5.0E-06
6.0E-6
Top
3.65E-07
1.0E-10
5.0E-4
Bottom
1.0E-07
5.0E-06
6.0E-6
Top
3.65E-07
1.0E-10
1.05E-3
Bottom
1.0E-07
5.0E-06
3.0E-7
Eq. 2 was approximated as an average of the
minimums of the TAGSAC model results (Eq. 3).
Min A + MinB + MinC
(3)
MinM =
3
A six layered ANFIS (Fig. 4) trained by
backpropagation algorithm have been adopted. The
three normalized TAGSAC model results are used
as input to ANFIS model. The Output layer has one
node to represent the measured hydraulic pressure.
ANFIS need additional four layers. The number of
nodes in these layers is dependant on the number of
membership functions used for each input. Since
we have used three membership functions for each
input, the If-part will have nine nodes. The
maximum number of rules formed by taking three
membership functions (one from each input) at a
time will be 27. Hence the number of nodes in Rule,
orm and Then-part layers will be 27. The ANFIS
used here is based on first order Sugeno type fuzzy
model with Gaussian membership function (GMF),
product inference rule, and weighted average
defuzzifier expressed as a typical rule Rj:
If fem A is µ Ai and femB is µ Bk and femC is µ Cm then (4)
f j = a 0 j + a Aj × fem A + a Bj × femB + aCj × femC
In which a0j, aAj, aBj, and aCj are real numbers to be
optimized during training of the ANFIS.
Norm
Then-part
W1
W1
f1
W2
Wj
fj
µ2 A
Output
µ3 A
µ1 B
femB
µ2 B
µ
femC
∑
3
µ
1
µ
2
B
C
C
µ3 C
f27
W 27
W27
femA
Fig. 4 Architecture of the ANFIS model
- 46 -
femB
femC
O
The input node passes normalized TAGSAC
results (femn) to If-part of a rule. The If-part
specifies the degree to which the given femn
satisfies the GMF, µi (Eq. 5). The Rules and orm
layers node output specifies the firing strength of a
rule (Eq. 6) and the normalized firing strength of a
rule (Eq. 7), respectively. The Then-part calculates
the weighted consequent value of a rule (Eq. 4).
The Output layer of the system sums all incoming
values from the Then-part as in Eq. 8.
  fem − c i
n
n
µ ( fem n ) = exp − 
σ ni
 
i
n




2



W j = µ Ai × µ Bk × µ Cm
Wj
∑W
(6)
(7)
j
27
(8)
O = ∑W j f j
j =1
where i = k = m =1,2,3; j =1,2, 3…, 27; n = A,B,C;
cin and σin are parameter sets to be adjusted during
training of the ANFIS.
The fuzzy logic system, once represented as the
equivalent input-output feed forward network (Fig.
4), it can be trained using any suitable training
algorithm such as the standard backpropagation
algorithm. In backpropagation algorithm, it is
standard practice to divide the dataset (the
TAGSAC results and measured hydraulic pressure)
into two phases: training and test phases, the former
is used for training (optimizing the ANFIS
parameters) of the model, and the later set is used to
check the accuracy of trained model.
While training ANFIS, values of the Output
node are compared with the normalized measured
hydraulic pressure data in the training phase and the
Mean square error (MSE) is calculated. If MSE is
within acceptable limit the process is terminated
otherwise feed backward pass is carried out for
updating cin and σin in Eq. 5 and alj in Eq. 4. See
Palit et al.12) for the detail approach.
Three types of measures of the goodness of fit
were used to check the performance of the proposed
ANFIS model; these are coefficient of efficiency
(CE), coefficient of determination (CD), and root
mean square error (RMSE). For perfect prediction
CD and CE tend to one and RMSE tends to zero13).
Six hour interval data from Jan.1, 2005 till Mar.
7, 2008 were used. After neglecting some faulty
measured data points, 70% of the total data points
were used for training and 30% for testing of the
proposed ANFIS model. The three TAGSAC and
ANFIS models results for 56.8 m amsl sensor in
MSB-1 are shown in Fig. 5. In Fig. 5 the residual
after subtracting ANFIS model value from the
measured value is also depicted. Similar results
were also obtained for other sensors in MSB-1.
For 56.8 m amsl sensor, the training phase CE,
CD and RMSE values were 0.998, 0.998 and 0.187
m, respectively. However, CE, CD and RMSE
values obtained for the best among the three
TAGSAC models were 0.982, 1.019 and 0.563 m,
respectively. In all the three measures of goodness
the ANFIS model has performed better than the best
TAGSAC model. It has been reported that models
having CE values above 0.8 are acceptable8).
According to this criterion the ANFIS model
training was successful. The performance of the
trained ANFIS model in the test phase was also
checked in terms of CE, CD and RMSE for
different test phase periods. The results were as
shown in Fig. 6. The test phase indicates the next
60 to 358 continuous days after the end of the
training phase. From Fig. 6 it is evident that the
ANFIS model performs better in shorter testing
periods. Similar results were also obtained for other
sensors in MSB-1.
TAGSAC was also adopted to analyze the
hydraulic pressure distribution around MIU10).
Hydraulic pressure (m
amsl)
154
1
FEMA
FEM C
ANFIS
150
146
FEM B
Measured
Residual
142
0.5
0
138
Residual (m)
Wj =
(5)
4. RESULTS AD DISCUSSIO
-0.5
134
130
2004/12/29
Test Phase
Training Phase
2005/10/25
2006/8/21
Date
2007/6/17
Fig. 5 The three TAGSAC and ANFIS models results
- 47 -
-1
subsurface activities.
1.6
CD
CE
RMSE
0.3
0.2
1.2
0.1
1
0.8
REFERECES
RMSE (m)
CD/CE ( )
1.4
0
60
120
180
240
300
Test phase period (days)
360
Fig. 6 CE, CD and RMSE for different test phase periods for
56.6 m amsl sensor
Despite the use of field measured hydraulic
properties, the result of the study showed as much
as 30 m difference in the measured and modeled
hydraulic pressure values10). This result is far more
than the maximum residual obtained using the
ANFIS modeling approach. The report claims lack
of enough hydraulic properties as a cause for such
magnitude of error10). On the contrary the proposed
ANFIS modeling approach did not use expensive
and time consuming hydrogeologic studies, yet it
resulted in better simulated values.
Any model that involves training need actual
(measured) data to be trained on. Lack of such data
limits the application of the proposed ANFIS
model. Therefore, having the advantages discussed
above, this model needs this critical measured
hydraulic pressure data without which the approach
will not be successful.
5. COCLUSIO
An ANFIS model was developed for the
prediction of the hydraulic pressure change at MIU
site; Japan. The model is found to have a better
prediction results than numerical models developed
under uncertainties and lack of aquifer parameters.
The measures of goodness of fit values obtained for
training and test periods are very good. This can
clearly indicate the application of the proposed
model in hydraulic pressure prediction. However,
this model need measured hydraulic pressure data
to optimize its model parameters. The results also
indicate, by modifying the usual normalization
approach, the operation range of ANFIS can be
extended. This extension of operation range creates
an advantage to apply ANFIS for prediction of
continuously decreasing hydraulic pressure.
Although the dynamicity of the groundwater
flow pattern in MIU project area is complex due to
construction of two shafts, the proposed ANFIS
modeling approach have shown very good result.
Therefore, this modeling approach would also have
good results if it is applied in case of analyzing
hydraulic pressure changes caused by other
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- 48 -
(Received September 30, 2009)