ASHRAE Journal - February 2021 - 38

TECHNICAL FEATURE

Even though this method was improved by
Ramaswamy, et al.,5 numerous parameters still need
to be assigned, which reduces the flexibility of this
method.

FIGURE 1 Common abnormal data points in a heating system.

200

A Simplified Detection Algorithm for Abnormal Data Based on k-Nearest
Neighbor
Abnormal data produced in a heating system is usually caused by two reasons. One is broken sensors or
other equipment; the other is data deviation caused by
the communication system. Abnormal data points in
heating systems are usually similar to the data shown in
Figure 1. The data set is one-dimensional, varying with
time. Therefore, the k-nearest neighbor distance can be
expressed as the sum of the difference between point p
and k-nearest neighbor:
Dk ( p) =

∑ (value

q ∈S p ,k

( p)

− value( q ) )

(2)

where Sp,k is a data set of k-nearest neighbor of point p.
The simplified k-nearest neighbor algorithm for
abnormal data detection will be based on the following
description of heating operation data.
1. In most cases, the data is time series. The normal
time series data has self-correlation, which means that
if two data are measured in a short time, their values are
usually similar.
2. The change of data with time obeys a certain rule.
For example, the accumulation of heat should increase
with time; the outdoor temperature changes periodically with the time of day, etc. By processing a variable
based on the corresponding rules, a new variable can be
obtained, the value of which is always stable in a normal
situation. For example, heat accumulation can be processed as heat consumption per day.
3. For the new variable, there will be exceptions,
which obviously drift from other normal points. This
means the differences between abnormal and normal
will be greater than the differences between normal
points. And in the value interval of the new variable,
abnormal points are located at the ends of the interval
(or on one side).
4. The number of exceptions is a minority of the total
data.
Based on the above premises and the description
of heating operation data, the simplified k-nearest
38

ASHRAE JOURNAL

ashrae.org

FEBRUARY 2021

Flow Rate (m3 /h)

160
120
80
40
0

100

Minutes

neighbor algorithm for sporadic and stochastic offset
fault detection is proposed as follows.
Algorithm 1
1. Select the data set S. There should be more than one
element in the data set.
2. Find the minimum data, minValue, and maximum
data, maxValue, of S.
3. Divide the value range (minValue, maxValue) into N sections. The range interval of each section, minD, can be
calculated using Equation 3:
minD =

(maxValue − minValue )
N

(3)

Thus, the space interval is:
Di =  minValue + (i − 1) × minD , minValue + i × minD 

(4)

where (i = 1,2...N).
4. Calculate the number of data for each interval, Di;
5. Give the abnormal number threshold, k, and classify each interval. If the number of variable objects in
an interval is less than or equal to k, this interval will be
classified as in the candidate range for abnormal points;
otherwise, the interval is within a normal range. k is an
arbitrary integer determined by observation, but the value
of k should be less than the number of data in data set S.
6. Judge the candidate range for abnormal points. The
rule should be:
distance( p,q) = value( p) − value(q) > minD ,q ∈ S(normal )

(5)

7. Based on the rules of the Step 6, judge the candidate interval to find abnormal points. If the candidate
interval is located between two normal ranges, it will be
determined a normal interval. If the candidate interval

http://ashrae.org

ASHRAE Journal - February 2021

Table of Contents for the Digital Edition of ASHRAE Journal - February 2021