10 and 19 FP events needs examining. The meaning of ten false events over 9 months
is on average one false alarm every month. The meaning of 19 false alarms over
9 months is on average a false alarm every second week. In both cases, a water utility
will need a sampling team that will be ready to go out per call and take manual
samples to approve or disapprove the indication of the automatic system. Choosing
between the two options is strictly a managerial decision. However, it will be logical
to assume that in most cases an experienced manager will not let an automatic
system shut down water supply without a second manual examination of samples
from the “contaminated” area.
Obviously, if the level of false alarms in the case of a short delay of 10 min would
result in hundreds of alarms per month, the correct policy would be to set a delay of
2 h or more. In this case it seems that a selection of RHL ¼ 2.61 and delay time of
10 min seem logical.
6 Using Other Kernel Functions for RBF
As it was explained earlier in this chapter, other forms of functions may be used as a
kernel function for the RBF. In what follows three different forms of kernel functions
are examined and compared to the first functional form, which has been used until
now. These functions are:
• Run 2: Inverse quadratic – ∅ r
ð Þ ¼
1
r
• Run 3: Inverse quadratic – ∅ r
ð Þ ¼
1
1þ r
ð Þ
2
• Run 4: Inverse multi-quadratic – ∅ r
ð Þ ¼
1
ffiffiffiffiffiffiffiffiffi ffi
1þ r
ð Þ
2
p
The results and RBF chart of Run 2 are displayed in Fig. 10 and Table 4,
respectively.
Once again, the analysis of the function performance is focused on the point
where it loses the “first TP event.” This happens when the number of FP events is
18 with a delay of 10 min (see second row in Table 4). In case of a delay of 120 min,
this happens at a level of 16 FP events. As it can be seen from Fig. 10, the noise
generated by the second RBF is substantially large relative to the range of the output
of the RBF. The two red arrows in Fig. 10 show that the ratio between the noise and
the range of the RBF is in some periods 50% to 75% of the range. This is a major
disadvantage for this function.
This means that relative to the performance of Run 1 (see Table 3), the Run
2 function performed poorly.
The results and RBF chart of Run 3 are displayed in Fig. 11 and Table 5,
respectively.
Once again, the results are worse than Run 1. Losing the first TP event reduces
only four FP events and increases the delay time from 10 to 120 min. However, as it
Using Radial Basis Function for Water Quality Events Detection
157
is on average one false alarm every month. The meaning of 19 false alarms over
9 months is on average a false alarm every second week. In both cases, a water utility
will need a sampling team that will be ready to go out per call and take manual
samples to approve or disapprove the indication of the automatic system. Choosing
between the two options is strictly a managerial decision. However, it will be logical
to assume that in most cases an experienced manager will not let an automatic
system shut down water supply without a second manual examination of samples
from the “contaminated” area.
Obviously, if the level of false alarms in the case of a short delay of 10 min would
result in hundreds of alarms per month, the correct policy would be to set a delay of
2 h or more. In this case it seems that a selection of RHL ¼ 2.61 and delay time of
10 min seem logical.
6 Using Other Kernel Functions for RBF
As it was explained earlier in this chapter, other forms of functions may be used as a
kernel function for the RBF. In what follows three different forms of kernel functions
are examined and compared to the first functional form, which has been used until
now. These functions are:
• Run 2: Inverse quadratic – ∅ r
ð Þ ¼
1
r
• Run 3: Inverse quadratic – ∅ r
ð Þ ¼
1
1þ r
ð Þ
2
• Run 4: Inverse multi-quadratic – ∅ r
ð Þ ¼
1
ffiffiffiffiffiffiffiffiffi ffi
1þ r
ð Þ
2
p
The results and RBF chart of Run 2 are displayed in Fig. 10 and Table 4,
respectively.
Once again, the analysis of the function performance is focused on the point
where it loses the “first TP event.” This happens when the number of FP events is
18 with a delay of 10 min (see second row in Table 4). In case of a delay of 120 min,
this happens at a level of 16 FP events. As it can be seen from Fig. 10, the noise
generated by the second RBF is substantially large relative to the range of the output
of the RBF. The two red arrows in Fig. 10 show that the ratio between the noise and
the range of the RBF is in some periods 50% to 75% of the range. This is a major
disadvantage for this function.
This means that relative to the performance of Run 1 (see Table 3), the Run
2 function performed poorly.
The results and RBF chart of Run 3 are displayed in Fig. 11 and Table 5,
respectively.
Once again, the results are worse than Run 1. Losing the first TP event reduces
only four FP events and increases the delay time from 10 to 120 min. However, as it
Using Radial Basis Function for Water Quality Events Detection
157