**Case 4.1: Malfunctioning of sensors**

The first case shows a situation in which two of the sensors stopped functioning for a short period of time. As can be seen from **Figure 7**, the Cl and the pH dropped suddenly to zero for a short period. This may result from communication problems, which are very common with distributed I/O.

**Figure 6.** DN for normal measurements.

**Figure 5.** Normal measurements.

Identifying Water Network Anomalies Using Multi Parameters Random Walk: Theory and Practice

http://dx.doi.org/10.5772/intechopen.71566

41

**Figure 7.** Malfunctioning of sensors.

**Figure 4.** DN histogram.

Identifying Water Network Anomalies Using Multi Parameters Random Walk: Theory and Practice http://dx.doi.org/10.5772/intechopen.71566 41

**Figure 5.** Normal measurements.

Typical minimum and maximum values are shown in **Table 2**. Given these minimum and maximum values, the raw measurements are transformed into normalized measurements, as shown by Eq. (4) of Section 2. The normalized measurements are used to calculate the "Dynamic Noise", as shown in Eq. (5), with a lag difference between the records of 10 time-

As can be seen from the histogram, a value which is more than 0.25 is rare (see red arrow). Hence, the threshold for the dynamic noise was set to 0.3. In terms of Section 2 of this

The first data analysis step with regard to the dynamic noise algorithm is to estimate the normal conditions, i.e., to observe how a dynamic noise curve behavie in case of a normal data flow. **Figure 5** shows a normal period of time for the four water quality measurements. Note that pH ranges between 7.70 and 7.79; Free Chlorine ranges between 0.37 and 0.48; Conductivity usually has an average of around 520–530 with short drops to 450; and Turbidity

**Figure 6** shows the equivalent dynamic noise for the relevant measurements. As can be seen,

We will now discuss four different cases, in which the dynamic noise violation threshold is analyzed. Note please that violation of the threshold L triggers an alarm only after a delay time in which the value of the DN is above the level of L. This in order to avoid false alarms

The first case shows a situation in which two of the sensors stopped functioning for a short period of time. As can be seen from **Figure 7**, the Cl and the pH dropped suddenly to zero for a short period. This may result from communication problems, which are very common with

stamps. **Figure 4** shows the distribution of the dynamic noise values.

chapter, L = 0.3.

ranges between 0.09 and 0.12.

caused by short spikes.

distributed I/O.

**Figure 4.** DN histogram.

**Case 4.1: Malfunctioning of sensors**

the values range between 0.03 and 0.25 at the most.

40 Applications in Water Systems Management and Modeling

**Figure 6.** DN for normal measurements.

**Figure 7.** Malfunctioning of sensors.

**Figure 8** shows the resulting dynamic noise curve of the sensor's malfunctioning. As can be seen, the drop in the values of Cl and pH causes a sharp increase in the value of the dynamic noise. After a short period, when the sensors resume functioning, the value of the dynamic noise drops back to a level below the red threshold line (0.3).

Note also that if the sensors remain non-functional for a long period of time, and the algorithm stops using the values of these sensors as part of Eq. (5), the level of the dynamic noise curve will be lower during steady state, since less sensors are transmitting data.

The gray box around the area of the event depicts the shape of the dynamic noise curve as a rectangle. This is due to the sharp change in the values of certain sensors. This sharp change can only occur during sensor failure . A chemical change in water quality cannot occur within 1 minute.
