1

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

2

The dispersion coefficient

Longitudinal dispersion

Transv

erse

disp

ersio

n

T1 T2 T3

Flow

3

A

B

C

D

E

4

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)

5

Soil column & Optimal sampling

6

7

The soil column experiment.

L

r

x

Spilling point

Porousmedium

8

(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

9

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

10

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

11

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.

12

Locate of simple point X-axis grid is 0.25 R-axis is 0.5 dimensionless

13

Result of the experimental design

14

.

Comparison between the three optimalexperimental campaigns obtained with the three set of true.dimensionless parameter

0L

L

U LPe

D

15

Testifying that longitudinal dispersion results more effective in explaining the concentration profile than the radial one.

Conclusions

16

end