ASHRAE Journal - February 2021 - 41

TECHNICAL FEATURE

FIGURE 4 Abnormal detection results when N is 20, 60 and 90, respectively.

N = 20

Instantaneous Heat (kW)

A.
2,500

Data Value
Abnormal Data Point

2,000
1,500
1,000
500
0

6
8
10
Minutes (In Thousands)

Instantaneous Heat (kW)

2,500

Data Value
Abnormal Data Point

2,000
1,500
1,000
500
0

6
8
10
Minutes (In Thousands)
N = 90

C.
Instantaneous Heat (kW)

N = 60

2,500

Data Value
Abnormal Data Point

2,000
1,500
1,000
500
0

6
8
10
Minutes (In Thousands)

FIGURE 5 The changes of the three evaluation parameters varying with k.

P
TP
FP

300
Number of Detected Data Points

detected. When N is 90 (in the over-detection region),
the interval number is very large and the minD is so narrow that many normal data are detected as abnormal
data. When N is 60 (in the transition region), the interval
number and minD are appropriate. Most abnormal data
points are detected correctly, and only a few normal data
are regarded as abnormal data. Therefore, N in the transition region is the most appropriate choice of interval.
The changes to the three evaluation parameters varying with k are shown in Figure 5, where the value of N is
set to 60.
Figure 5 shows that the variation trend of the three
evaluation parameters with k is very similar to that in
Figure 3, which can also be divided into rising region,
transition region and over-detection region. In the rising region, the detection threshold of each interval is
low, and only a small number of abnormal data can be
detected. In the over-detection region, the detection
threshold of each interval is too high, and the normal data at the edge of the interval are misjudged as
abnormal data. In the transition region, the threshold
is more appropriate and can detect most abnormal
data points correctly, with only a few false detections.
Therefore, k in the transition region is the most appropriate choice.
From the above analysis, it can be seen that selecting N
and k in the transition region can correctly detect most
abnormal data points with acceptable false detection
results. Figure 3 and Figure 5 show that the parameters
in the transition region have the following characteristics. First, the amount of abnormal data detected
varying with N doesn't change much within the transition region. Second, there is a dramatic increase of
the amount of detected abnormal data just before the
transition region. And last, there is another obvious
increase of the amount of detected abnormal data right
after the transition region. According to these results,
values of N and k, which should be located in the transition region for the abnormal detection algorithm, can be
determined.
Note that for a new data set, it is impossible to
directly determine the location of the transition region
because it is impossible to know which data is normal
and which is abnormal, i.e., it is not known what the
speciﬁc values of TP and FP are. However, according
to the above analysis that clariﬁes the change characteristics of the P value with N and k, we develop an

250
200
150
100
50
0
10

100

algorithm to automatically determine the transitional
area N and k values based on the characteristics of the
P value.
FEBRUARY 2021

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