**3. Numerical example**

This section numerically describes the calculation procedure as described in the previous section. **Table 1** contains an example data set with 20 records. The measured variables are Free Chlorine (CL), Turbidity (TU), pH and Conductivity (CO). These are a common water quality indicators.


The first two rows display the minimum and maximum values of each variable. These values were used to normalize the records in the left side of the table to the right side of the table. After normalization, a vector of the Euclidian Distance between each pair of records with a difference of 5 steps was calculated. This vector is the most right column in the table. The first value in this vector (located in row 6) contains the distance between record 6 to record 1. The second contains the distance between record 7 to record 2. The chart in **Figure 3** displays

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

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

39

In the following section, examples from a read data set are used to illustrate the analysis

The following examples refer to a real data set recorded at a field station with measurements, as presented in **Table 2**. The table's quality measurements include Free Chlorine (Cl measured in ppm), Turbidity (TU measured in NTU), pH, Conductivity (CO measured in mS), and pressure (PRI measured in bars). For each measurement, the algorithm dynamically calculates the minimum and maximum values of the last 48 hours. (see first two rows of **Table 1**).

**Symbol Measurement Units Minimum Maximum**

Cl Free Chlorine mA 0 2 TU Turbidity NTU 0 2 pH pH pH 6 9.5 CO Conductivity mS 0 800 PRI Pressure Bar 0 15

framework of abnormality detection and classification using this methodology.

relevant DN chart.

**Table 2.** Measurements.

**Figure 3.** Dynamic noise chart.

**4. Real data example**

**Table 1.** Data for numerical example.

Identifying Water Network Anomalies Using Multi Parameters Random Walk: Theory and Practice http://dx.doi.org/10.5772/intechopen.71566 39

**Figure 3.** Dynamic noise chart.

**Max 1 1 9.5 600**

38 Applications in Water Systems Management and Modeling

**Min 0 0 6 300**

**Table 1.** Data for numerical example.

**CL**

 0.60 0.09 7.69 536.00 0.60 0.09 0.48 0.79 0.0000 0.59 0.09 7.70 541.50 0.59 0.09 0.49 0.81 0.0000 0.60 0.08 7.70 538.00 0.60 0.08 0.49 0.79 0.0000 0.60 0.09 7.70 538.00 0.60 0.09 0.49 0.79 0.0000 0.60 0.09 7.71 538.00 0.60 0.09 0.49 0.79 0.0000 0.60 0.08 7.70 537.00 0.60 0.08 0.49 0.79 0.0003 0.60 0.09 7.70 536.00 0.60 0.09 0.49 0.79 0.0001 0.60 0.12 7.70 535.50 0.60 0.12 0.49 0.79 0.0008 0.60 0.12 7.70 536.00 0.60 0.12 0.49 0.79 0.0010 0.60 0.09 7.70 533.00 0.60 0.09 0.49 0.78 0.0002 0.60 0.09 7.70 533.00 0.60 0.09 0.49 0.78 0.0002 0.59 0.08 7.70 529.00 0.59 0.08 0.49 0.76 0.0016 0.60 0.08 7.71 529.00 0.60 0.08 0.49 0.76 0.0024 0.59 0.09 7.71 545.00 0.59 0.09 0.49 0.82 0.0017 0.59 0.09 7.71 545.00 0.59 0.09 0.49 0.82 0.0017 0.60 0.09 7.71 545.00 0.60 0.09 0.49 0.82 0.0029 0.59 0.08 7.71 544.00 0.59 0.08 0.49 0.81 0.0025 0.59 0.09 7.71 545.33 0.59 0.09 0.49 0.82 0.0000 0.59 0.08 7.71 540.00 0.59 0.08 0.49 0.80 0.0004 0.59 0.08 7.71 538.00 0.59 0.08 0.49 0.79 0.0006

**No CL TU pH CO TU pH**

**Normalized data**

**CO DN**

The first two rows display the minimum and maximum values of each variable. These values were used to normalize the records in the left side of the table to the right side of the table. After normalization, a vector of the Euclidian Distance between each pair of records with a difference of 5 steps was calculated. This vector is the most right column in the table. The first value in this vector (located in row 6) contains the distance between record 6 to record 1. The second contains the distance between record 7 to record 2. The chart in **Figure 3** displays relevant DN chart.

In the following section, examples from a read data set are used to illustrate the analysis framework of abnormality detection and classification using this methodology.
