ASHRAE Journal - February 2021 - 42

TECHNICAL FEATURE

where i = 2,3...m.
5. Find the first minimum value of the differential sequence dNY, and get the position of the minimum value
in dNY. The N value corresponding to the same position
in NY is the optimal interval parameter Nbest.
6. Set the value of Nbest determined in Step 5 in Algorithm 2 and set the threshold value k as a series of values
of fixed step, k1, k2... kw.
7. Repeat Step 3 through Step 7 in Algorithm 1, where
the parameters in Step 3 and Step 5 in Algorithm 1 are
N = Nbest, k = kj ( j = 1,2 w) where w is the total number of
elements in the series of k.
8. The number of outliers corresponding to w parameters of k, which is recorded as the sequence of outliers'
number, kY, can be calculated using Algorithm 1.
9. The differential sequence dkY is obtained using the
same method in Step 4 and Step 5 in Algorithm 2, and
the optimized threshold parameter kbest is obtained accordingly.
10. Two parameters, Nbest and kbest, are obtained.
In the practical application of the algorithm, it is not
necessary to determine the k and N values every time an
anomaly is detected. Instead, keep the k and N values
unchanged in one time window, and then recalculate
the two values in the next time window. Generally
speaking, the time window for calculating the k and N
values can be three days or one week.

Validation of Algorithm Based on Thermal Substation Data
Water temperature and flow rate data collected from
thermal substations are very important in the operation
42

ASHRAE JOURNAL

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FEBRUARY 2021

Data Value

Flow Rate (m3 /h)

k-Nearest Neighbor

Z-Score

60
40
20
0

6
8
10
Minutes (In Thousands)

FIGURE 7 Supply temperature at a thermal substation varying with time.

Temperature (°C)

(7)

dNYi = NYi − NYi −1

FIGURE 6 Instantaneous flow at a thermal substation varying with time.

85
80
75
70
65
60

Data Value
k-Nearest Neighbor
Z-Score
0
2
4

6
8
10
Minutes (In Thousands)

FIGURE 8 Return temperature at a thermal substation varying with time.

Temperature (°C)

Algorithm 2
1. Set the initial threshold k0, and set a series of fixed
step values, N1, N2... Nm, as the numbers of intervals. m is
the total number of elements in the series of N.
2. Repeat Step 3 through Step 7 in Algorithm 1, where
the parameters in Step 3 and Step 5 are N = Ni (i = 1,2 m)
and k = k0.
3. The total number of data points detected as abnormal, P, corresponding to m parameters of N, which is
recorded as the sequence of outliers' number, NY, can be
calculated using Algorithm 1.
4. For sequence NY, the differential sequence dNY is
obtained by the following method:

Data Value
k-Nearest
Neighbor
Z-Score

80
70
60
50
40
0

6
8
10
Minutes (In Thousands)

and regulation of heating systems. Flow rate and supply and return water temperature data on the primary
side at a thermal substation from Dec. 11, 2017, to Dec.
21, 2017, were used to verify the above abnormal detection algorithm. The three sets of data (instantaneous
flow rate, supply temperature and return temperature,
varying with time) are shown in Figures 6 through 8,
respectively.
A large change in the water supply temperature at
about 5,000 minutes, as shown in Figure 7, caused the
fluctuation of the primary water flow rate (as shown in
Figure 6) and then the fluctuation of the return water
temperature (as shown in Figure 8). Although these
abnormal data are not caused by sensor failure, they
will have a negative impact on subsequent data analysis,
such as pipe network and building characteristics identification and curve fitting. Therefore, these abnormal
data also need to be identified and cleared. These data

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ASHRAE Journal - February 2021

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