Parameter Estimation in a Model for Tracer Transport in One-Dimensional Fractals - Selected Topics of Computational and Experimental Fluid Mechanics - page 239

Ta b l e 1 Comparison between original and estimated fractal parameters for different amount of
data and noise levels

40 Data 20 Data 10 Data

Parameter Original 5% 10% 5% 10% 5% 10%

α 0.75 0.744 0.743 0.746 0.775 0.749 0.789

ʸ 0.05 0.069 0.041 0.048 0.023 0.015 0.018

D ad 0.0133 0.0140 0.0166 0.0146 0.0090 0.0145 0.0125

OF 2.46 15.2 0.489 1.57 0.0643 0.314

Ta b l e 2 Percentage of relative error in the estimated fractal parameters for different amount of
data and levels of noise
40 Data 20 Data 10 Data

Parameter 5% 10% 5% 10% 5% 10%

α 0.80 0.93 0.53 3.33 0.13 5.20

ʸ 38.00 18.00 4.00 54.00 70.00 64.00

D ad 5.00 24.00 9.77 32.33 9.02 6.02

PRE 43.80 42.93 14.30 89.66 79.15 75.22

are from the original value. In this sense α and D ad are better estimated than ʸ .The

PRE values for α and D ad scarcely exceed the 5 and 30%, respectively, whereas

for slightly depends on the level of

noise compared to the other parameters. From these results it is possible to infer the
sensitivity of the model to the parameters which is in the following order:

ʸ this value achieves 60%. Estimation of α

α,

D ad ,ʸ

.

The estimation depends on the level of noise.

5.2 Sensitivity to the Amount of Data

The effect of the amount of data on the fitting can be seen in Figs. 1 and 2 by fixing
the row and changing columns. The quantitative description is deployed in Tables 1
and 2 . FromTable 1 we see that a decrement in the amount of data implies a decrement
in the OF. This is a meaningless result since the OF is proportional to the amount of
data. The PRE values in Table 2 do not have a well-defined trend, although it suggests
that the estimation is sensitive to the amount of data. As expected, the estimation of
D ad and ʸ in general improves with the amount of data.