Which size of the subgroup in Identification the source of contamination in water distribution network is better?

01 January 2019 3 5K Report

Hi all,

in the [De sanctic et al 2010], [prapato 2007,2010] for Identification the source of contamination in water distribution network , had determined the subgroup of nodes that maybe a source of contamination.

I used two different methods to find the best sensor locations, I also find subgroups that may be sources.

Suppose that the answer of the first method is solution1, and the answer of the second method is solution2.

In the solution1,, the size of the subgroups is as follows

An eight-member subgroup

A two-dimensional subgroup

And ten single-member subgroups

*******************

In the solution2, the size of the subgroups is as follows

A four-member subgroup

A three-member subgroup

Three two-member subgroup

And seven single-member subgroups.

******************

The meaning of the subgroup size is as follows:

If a subgroup is single-member, the source is identified precisely.

If a subgroup is two-member,( for example, {A ,B} be a subgroup) , that is, it may َA or may B was the source. (We doubt the two nodes).

If a subgroup is three members. {A, B, C} That is, we do not know exactly whether A or B or C was the source. There is doubt between 3 nodes. Similarly, other sizes mean.

I want to know which answer is better?

Which solution is better (solution1 or solution2)?

Is it better the size of the largest subgroup,To be smaller?(Like the second answer ,solution2)

Or the size of the largest subgroup be larger, but the number of single-member subgroup is larger?

thanks

Abdelhalim Zekry

Dear Mary,

welcome,

I think with you.

You can estimate a contamination identification probability by

calculating a global probability to detect a contamination in the whole network as:

P= (No of single nodes S + .5 x two member nodes D + 3 nodes groups T/ 3 + ...+ n nodes groups /n)/ Total number of nodes,

According to this scheme as the number of single nodes increases the dtection probability increases.

Best wishes

Mary Flores

Hi @Abdelhalim Zekry , thanks for your answer. Do you mean solution 1 is better? Right?

Because

For solution1

P=(10+(1/2)+(1/8))÷20=0.53

And for solution 2

P=(7+(3/2)+(1/3)+(1/4))÷20=0.45.

Did I get it right?

Thanks

Abdelhalim Zekry

Dear Mary,

Let us calculate the P for the two case according to your groups classification.

In the first pattern

P= (10 x1 + .5 + 1/8)/20 = 10. 625/20,

The second pattern:

P= (7x1 + 3x0.5 + 1/3 +1/4)/20= 9.08 /20,

Accordingly the first case solution 1 will be more decisive than solution 2.

Best wishes

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