學生 : 梁書嚴 指導教授 : 陳瑞昇 2010/12/30 1 environmental modelling & software 24...
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Optimal sampling for the estimation of dispersion parameters in soil columns using an Iterative Genetic Algorithm Federico Catania*, Ombretta Paladino
學生 :梁書嚴指導教授 :陳瑞昇2010/12/30
Environmental Modelling & Software 24 (2009) 115–123
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The dispersion coefficient
Longitudinal dispersion
Transv
erse
disp
ersio
n
T1 T2 T3
Flow
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A
B
C
D
E
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Estimation of dispersion parameters
(a) test performed in the soil column to generate
(b) breakthrough curve which is used in conjunction with a appropriate mathematical model
(c) a parameter estimation scheme to yield
(d) transport parameter of interest
(a) (b) (c) (d)
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Soil column & Optimal sampling
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The soil column experiment.
L
r
x
Spilling point
Porousmedium
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(Massabo’ et al., 2006)
( , ,0) 0C r x
1
( , , )0
r
C r x t
r
lim ( , , ) 0x
C r x t
0( ,0, ) ( ) ( )C r t C r H t∞
r=1
水流方向
2 2
2 2
1R L
C C C C Cu D D
t x r r r x
1
00
2 2 21
212
2 2 21
212
1( , , ) ( ) exp
2 2
exp4
1
2 4
exp4
1
2 4
Lk k
k
L Lk
R
kL L
R
L Lk
R
kL L
xuPeC r x t A J r
u Pe Pex
Pe
Pe u Pe terfc t
t Pe
u Pe Pex
Pe
Pe u Pe terfc
t P
Z
Z
Z
Z
Z
R
te
2 2
2 2
1
R L
C C C C Cu
t x Pe r r r Pe x
1 1
002
1
0
1
0 0
2 ( ) ( ), 1, 2,....
(
k
k
k
f J dA k
J
A f d
Z
Z
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GA
New population
Calculation fitness
select
Crossover & Mutation
Calculation end
否
是Fitness
Calculation fitness
1:設置採樣點0:不測置採樣點ㄋ
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Calculation fitness
GA
New population
Calculation fitness
select
Crossover & Mutation
Calculation end
否
是Fitness
Parameter valueNumber of strings 90Number of generations 30Cross-over probability 0.9Muation probability 0.01
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Calculation end In the experimental design problems solved for the test
case adopted, convergence was achieved with a population of 20 individuals that reproduced for a maximum of 21 generations.
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Locate of simple point X-axis grid is 0.25 R-axis is 0.5 dimensionless
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Result of the experimental design
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.
Comparison between the three optimalexperimental campaigns obtained with the three set of true.dimensionless parameter
0L
L
U LPe
D
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Testifying that longitudinal dispersion results more effective in explaining the concentration profile than the radial one.
Conclusions
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end