Utility of Supercomputers in Trace-Back Algorithms for City-Sized Distribution Systems

Abstract

A contaminant source identification procedure intended to protect water distribution systems has to be both rapid and able to incorporate uncertainties, when identifying possible intrusion nodes (PINs). PIN identification has two major issues, the false-negative rate (failure to identify the true ingress location) and the false-positive issue (falsely identifying a location which is not the true ingress location). A data mining procedure is described and applied, which involves mining an off-line-built database, to select PINs that possess first detection times within ±m from the online sensor first detection time. The “m” value is a statistical characterization of the array of events of the offset values between online sensor first detection time under uncertainty and the one corresponding to the same intrusion event stored in the off-line database; with “m” selected, issues of controlling false negatives and positives are addressed. The approach described herein is made possible through the power of parallel computing in supercomputers, which demonstrates huge potential by simulating scenarios simultaneously. The online data mining procedure, i.e., the PIN identification, is integrated into a geographic information system toolkit for rapid emergency response. In the case studies, simulation of scenarios is reduced linearly to the number of processors applied. Results show that increasing the number of scenarios in the database can provide input to compute the “m” value, always reduce the false-negative rate of each sensor, and usually reduce the number of false-positive PINs.

Appendix

To get the probability of generating negative random numbers, the following notations are applied:

• x= random pattern factor, obeying normal distribution,

• $\ overline{x}$= original pattern factor,

• s= standard deviation,

• y=normalized random pattern factor, obeying standard normal distribution.

Pattern factor makes no sense in negative values; every original pattern factor $\ overline{x}$ is non-negative.

When $\overline{x} = 0$, $s = 0.1$, $\overline{x} = 0$, thus, the generated random number would be always zero.

When $\overline{x} > 0$,

$$y = \frac{{x - \overline{x}}}{s}$$

((21.2))

Since s equals to $0.1\,\overline{x}$, Eq. (21.2) is converted to

$$y = \frac{{x - \overline{x}}}{{0.1\overline{x}}}$$

((21.3))

Thus, the probability of generating random negative pattern factor is

$$\begin{array}{l} P\left(x < 0\right) = P\left(\overline{x}\left(0.1\,y + 1\right) < 0\right) \\ \qquad\qquad = P\left(y < - 10\right) \\ \qquad\qquad = 7.6{\textrm{E}} - 24 \\ \end{array}$$

((21.4))