Condition Monitoring for Air Filters in HVAC Systems with Variable

Volume Flow

Oliver Gnepper

a

and Olaf Enge-Rosenblatt

b

Fraunhofer Institute for Integrated Circuits IIS, Division Engineering of Adaptive Systems EAS,

Zeunerstraße 38, 01069, Dresden, Germany

Keywords:

Condition Monitoring, Data Analytics, HVAC System, Air Filter, Smart Building.

Abstract:

State of the art condition monitoring systems for air ﬁlters in HVAC systems require that the HVAC system

is operated at nominal volume ﬂow. For HVAC systems with variable volume ﬂow this assumption is only

fulﬁlled in one operating point. Outside this operating point existing condition monitoring systems assess

the air ﬁlter condition in a too optimistic manner. Therefore, polluted air ﬁlters remain undetected until their

regular check, leading to unneeded energy consumption. If the true condition of an air ﬁlter is known, it could

be changed before it is clogged. So, a condition monitoring systems is needed which is also reliable in case of

HVAC systems with variable volume ﬂow. This work presents a model-based approach for such a condition

monitoring system. Therefore, a dataset from a building is used to assess an optimal model. Furthermore, the

condition monitoring systems is evaluated on that dataset.

1 INTRODUCTION

Air ﬁlters in HVAC systems are used for precipitat-

ing of dust particles from the intake air. Addition-

ally, they protect succeeding components of an HVAC

system from pollution and damage due to abrasion.

Furthermore, particles which are harmful to human’s

respiratory system should be removed from the sup-

ply air as well. Therefore, it is necessary that air ﬁl-

ters are in a good condition at any time. This is en-

sured by a professional service on a regular basis. In

(Verein Deutscher Ingenieure, 2018) a quarterly vi-

sual inspection is demanded and a semestral check of

the differential pressure of air ﬁlters in HVAC sys-

tems. For HVAC systems with a nominal volume ﬂow

of more than 1000 m

3

/h, sensors which display the

current value of the differential pressure must be in-

stalled (Verein Deutscher Ingenieure, 2018). Usually

the measured differential pressure is compared with a

ﬁxed limit to determine if an air ﬁlter is clogged and

must be changed. In principle, the differential pres-

sure measured at an air ﬁlter depends on the volume

ﬂow which passes through the air ﬁlter. So, in case

of HVAC systems with variable volume ﬂow a com-

parison of the differential pressure with a ﬁxed limit

a

https://orcid.org/0000-0001-6430-620X

b

https://orcid.org/0000-0002-6069-7423

results in an erroneous estimation of the air ﬁlter con-

dition.

The following section contains a review of the

air ﬁlter condition monitoring state of the art. It is

shown that several approaches to monitor the air ﬁl-

ter condition exist, but these approaches are either re-

stricted to be used in combination with a dedicated

HVAC system or high effort is necessary to retroﬁt

these approaches in existing HVAC systems. Further-

more, it is shown that several models of air ﬁlters exist

which could be used to estimate the air ﬁlter condi-

tion. These models are described in Section 3. For

each model the quality of ﬁt is evaluated on a dataset

from a building in Germany. This dataset is described

in Section 4. The model selection method and the

corresponding results are shown in Section 5. In Sec-

tion 6 it is shown how the selected model is used to

monitor the condition of air ﬁlters. This work is ﬁn-

ished with a conclusion in Section 7.

2 STATE OF THE ART

Detecting if air ﬁlters in HVAC systems with variable

volume ﬂow are clogged, is a problem which is ad-

dressed in different ways. A pneumatic air ﬁlter con-

dition indicator for HVAC systems which displays the

air ﬁlter condition for two different fan speeds is de-

102

Gnepper, O. and Enge-Rosenblatt, O.

Condition Monitoring for Air Filters in HVAC Systems with Variable Volume Flow.

DOI: 10.5220/0010405401020109

In Proceedings of the 10th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2021), pages 102-109

ISBN: 978-989-758-512-8

Copyright

c

2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

scribed in (Ladusaw, 1966). The air ﬁlter condition

is indicated by a device which ﬂoats in the air that

bypasses an air ﬁlter. The ﬂoating height is also in-

ﬂuenced by the fan speed. So, there is an indication

area for the low and the high fan speed. In (Fraden

and Rutstein, 2007) a method is described which uses

a heated wire to measure the volume ﬂow. If the lat-

ter drops below a predeﬁned limit, the air ﬁlter is de-

clared to be clogged. A similar method is claimed in

(Kang et al., 2006). Herein, the temperature gradi-

ent due to a fan speed change is measured. The air

ﬁlter condition is determined by comparing the tem-

perature gradient with a predeﬁned limit. All these

approaches have in common that they detect air ﬁlter

clogging, but they are not able to predict the remain-

ing useful life of air ﬁlters. In addition to that these

methods must be tuned for different types of air ﬁl-

ters.

An air ﬁlter model which utilizes measurements

that are already collected in HVAC system provides

a better scalability of the desired solution. In (Kang

et al., 2007) it is claimed that deviations of the to-

tal pressure difference of fans are mainly induced by

air ﬁlters. Therefore, the condition of an air ﬁlter is

assessed by comparing the measured total pressure

difference with the one which is estimated from the

characteristic fan curve. The total pressure difference

is truly affected by the condition of air ﬁlters, but this

is not the only inﬂuence. Therefore, this approach is a

good measure for anomalies in HVAC systems. This

method is designed for a particular system and does

not generalize well. Therefore, it is necessary to use a

model of air ﬁlters which represents the resistance of

air ﬁlters to the air ﬂow.

In (Saarela et al., 2014) a model which combines

different inﬂuences on the differential pressure devel-

opment of air ﬁlters for nuclear power plants is intro-

duced. Each inﬂuence is modelled separately. Hereby

the relationship between volume ﬂow

˙

V and differen-

tial pressure ∆p of an air ﬁlter is described by a model

of the form which is shown in Equation 1. This equa-

tion also includes the parameters a and n. Hereinafter

this model is called type I.

∆p = a ·

˙

V

n

(1)

In (Liu et al., 2003) such a model is also used to

estimate the reduction of empty spaces between ﬁbres

of air ﬁlters. The same model structure is also de-

scribed in (DIN Deutsches Institut f

¨

ur Normung e.V.,

2013). Whereas, (Eckhardt, 2018) uses the following

approach to model the relationship between volume

ﬂow and differential pressure of an air ﬁlter which is

subsequently denoted as type II.

∆p = a ·

˙

V

2

(2)

This modelling approach is also used in (Kruger,

2013) and in (Verein Deutscher Ingenieure, 2004).

The latter cites (L

¨

ofﬂer, 1988) which extends the sec-

ond order term with a linear term and the associated

parameter b. This yields Equation 3. The correspond-

ing model is consecutively called type III and is also

proposed in (Kanaoka and Hiragi, 1990), (Rivers and

Murphy, 2000) and (Albers, 2017).

∆p = a ·

˙

V

2

+ b ·

˙

V (3)

As shown, in the literature there is no standard

model for air ﬁlters. In addition, there is no com-

parison with other models in any of the publications.

Furthermore, there is no agreement in the literature on

the consideration of further inﬂuences on the differen-

tial pressure, such as air density or dynamic viscosity

of air as well as ﬁlter-speciﬁc parameters such as ﬁ-

bre thickness. While the models in (Verein Deutscher

Ingenieure, 2004), (L

¨

ofﬂer, 1988), (Kanaoka and Hi-

ragi, 1990) and (Rivers and Murphy, 2000) cover

any of these inﬂuences in detail, the model in (DIN

Deutsches Institut f

¨

ur Normung e.V., 2013) takes only

the inﬂuences of air density and dynamic viscosity of

air into account. On the other hand the models in

(Saarela et al., 2014), (Liu et al., 2003), (Eckhardt,

2018), (Kruger, 2013) and (Albers, 2017) neglect all

inﬂuences. Therefore, for a comparison of these mod-

els, it is necessary to unify the level of detail of the

models and to adapt all models in such a way that it

is possible to quantify the beneﬁt of further measured

variables and derived inﬂuences, such as air density

and dynamic viscosity of air.

3 FILTER MODELS

During the model uniﬁcation, it must be ensured that

the resulting models can be retroﬁtted in existing

HVAC systems with as little effort as possible. In

existing HVAC systems, the ﬁlter-speciﬁc parameters

are usually unknown. Therefore, the level of detail

of the models is reduced to such an extent that they

do not contain any ﬁlter-speciﬁc parameters. Further-

more, it must be ensured that all used models can

represent the inﬂuences of air density and dynamic

viscosity of air. The following chapters describe the

model uniﬁcation procedure and the resulting models.

3.1 Exponential Model

In (DIN Deutsches Institut f

¨

ur Normung e.V., 2013)

a model is described which takes dynamic viscosity

of air and air density into account and has the same

Condition Monitoring for Air Filters in HVAC Systems with Variable Volume Flow

103

structure as model type I. Equation 4 shows the cor-

responding mathematical statement.

∆p = c · µ

2−n

· ρ

n−1

·

˙

V

n

(4)

This equation includes a resistance coefﬁcient c,

dynamic viscosity of air µ, air density ρ and an expo-

nent n. The latter is not restricted to a speciﬁc value

and changes over time as the dust load increases.

In (DIN Deutsches Institut f

¨

ur Normung e.V., 2013)

Equation 5 is used to calculate the dynamic viscosity

of air where T is measured in °C and µ in Pas.

µ =

1.455 · 10

−6

· (T + 273.15)

0.5

1 +

110.4

T + 273.15

(5)

The Equations 6 to 10 can be used to estimate

the air density which include the ambient pressure p,

the water vapour partial pressure p

w

and the relative

air humidity ϕ (DIN Deutsches Institut f

¨

ur Normung

e.V., 2013).

ρ =

0.378 · p · p

w

287.06 · (T + 273.15)

(6)

p

w

=

ϕ

100

· exp(c

1

−

c

2

T + 273.15

− c

3

· ln(T + 273.15))

(7)

c

1

= 59.484 085 (8)

c

2

= 6790.4985 (9)

c

3

= 5.028 02 (10)

The building in which the data is collected which

is used for the validation has two HVAC systems with

humidiﬁcation and one HVAC system without hu-

midiﬁcation (see Section 4). The ambient pressure

is measured in none of these HVAC systems. Addi-

tionally, the relative air humidity is only measured in

the two HVAC systems with humidiﬁcation. In order

to include the inﬂuence of the air density, it is cal-

culated in two ways. In case of the HVAC systems

with humidiﬁcation the Equations 6 to 10 are used,

but it is assumed that the ambient pressure is constant

at p = 101325Pa. Additionally, for all three HVAC

systems Equation 11 is used to estimate the air den-

sity (Albers, 2017). It is analysed which of the two

approaches provides more accurate results and thus

represents the preferred variant for similar cases (see

Section 5).

ρ = 1.275 ·

273.15

T + 273.15

(11)

3.2 Second Order Models

The model which is described in (Verein Deutscher

Ingenieure, 2004) bases on the model in (L

¨

ofﬂer,

1988) and is shown in Equation 12.

∆p =

2 · c

D

· u

2

· ρ · α · z

π · d

F

(12)

This equation includes the resistance coefﬁcient

c

D

, the ﬂow velocity u, the ﬁbre layer thickness z,

the packing density α and the ﬁbre diameter d

F

. The

last three parameters are constant. Only the pressure

coefﬁcient, the differential pressure ∆p, the air den-

sity ρ and the ﬂow velocity vary over time. The ﬂow

velocity is not measured in the analysed dataset (see

Section 4), but is replaceable by the following expres-

sion which introduces the volume ﬂow

˙

V and the ﬁlter

area A. The latter decreases over time as the dust load

increases.

u =

˙

V

A

(13)

As described above, Equation 13 is inserted in

Equation 12 which yields Equation 14. The ﬁlter-

speciﬁc parameters and the pressure coefﬁcient are

substituted by the parameter c.

∆p = c ·

˙

V

2

· ρ (14)

In (L

¨

ofﬂer, 1988) this model is extended by an ad-

ditional linear term. This yields Equation 15. The

parameters c

4

and c

5

in Equation 15 replace the ﬁlter-

speciﬁc constants and any immeasurable coefﬁcient

(e.g. ﬁlter area) which correspond to the dust load of

an air ﬁlter.

∆p = c

4

· µ ·

˙

V + c

5

· ρ ·

˙

V

2

(15)

The models in Equation 4, 14 and 15 have in com-

mon, that they describe the relationship between dif-

ferential pressure and volume ﬂow of an air ﬁlter, but

they differ in their structure. All three models take the

inﬂuence of the air condition (dynamic viscosity and

density) into account. The dynamic viscosity of air

is calculated as described in Equation 5. In the case

of air density, it depends on whether the relative air

humidity is measured. If this is the case, then Equa-

tions 6 to 10 are applied. If this is not the case, then

Equation 11 is used. The different models in combi-

nation with the different approaches to consider the

air density and the dynamic viscosity of air as well as

the value of exponent n in model type I give rise to

the following questions:

1. Which of the described models is most suitable

to represent the relationship between differential

pressure and volume ﬂow of an air ﬁlter?

2. Does the consideration of the dynamic viscosity

of air and air density increase a models accuracy?

3. Is it necessary to estimate the air density via the

air temperature and the relative air humidity or is

the air temperature sufﬁcient?

SMARTGREENS 2021 - 10th International Conference on Smart Cities and Green ICT Systems

104

4. How does the exponent of model type I changes

as the dust load increases?

These questions will be answered by a model compar-

ison on a real world dataset.

4 DATASET

The dataset was collected from a building in Ger-

many. This building has three HVAC systems where

an air ﬁlter is installed in every supply air duct and

every return air duct. Every year during March, the

air ﬁlters are changed. For each of these air ﬁlters

differential pressure, volume ﬂow and air temperature

are measured. The relative air humidity is only mea-

sured for the air ﬁlters of two HVAC systems, because

the third HVAC system does not include a humidiﬁ-

cation. For the air ﬁlters of the third HVAC system

the inﬂuence of the relative air humidity on the model

performance is not analysed.

The data was collected during the period of 01

August 2017 until 31 March 2020. To reduce the

data volume and velocity the data is logged on change

with a minimal distance between two samples of one

minute. Additionally, this dataset contains several in-

consistencies. In some cases the measured physical

quantity did not match with the one which is declared

in the building management system. These incorrect

matches were identiﬁed and corrected. Furthermore,

the following data preprocessing steps were carried

out:

1. Resample the data to a ﬁxed frequency of one

minute and apply a forward ﬁll to close gaps

which are induced by the log on change.

2. Remove samples which are marked as bad quality

samples by the building management system.

3. Remove parts of a time series where the wrong

physical quantity was measured.

4. Remove samples where the value jumped to 0 and

instantly back to approximately its previous value.

5. Remove samples where the value was at least

twice as high as the nominal maximal value.

6. Remove samples where the value was lower than

the nominal minimal value.

7. Set samples to 0 when the HVAC system is turned

off and the values do not reach 0 exactly.

This procedure ensures that only valid samples re-

main for the following analysis.

5 MODEL SELECTION

In order to answer the questions which are raised at

the end of Section 3, the different model variants are

compared with each other. This process is described

in the following section. The obtained results are dis-

cussed in Section 5.2.

5.1 Method

Equations 4, 14 and 15 form the basis for the model

comparison. According to the explanations in Sec-

tion 3, the inﬂuence of the dynamic viscosity of air

can be represented by means of Equation 5 and the

inﬂuence of the air density either by means of Equa-

tions 6 to 10 or Equation 11. With regard to the repre-

sentation of the inﬂuence of the air density, it is deci-

sive whether the relative air humidity is recorded for

the analysed HVAC system or not. If the relative air

humidity is recorded, Equation 5 and Equations 6 to

10 are added to the model equations. This set of in-

ﬂuence equations is referred to as set A in the fol-

lowing. If the relative air humidity is not recorded,

Equation 5 can still be used, but Equation 11 is used

instead of Equations 6 to 10. In the following, this

set of inﬂuence equations is referred to as set B. In

addition, the hypothetical case that the air tempera-

ture is not measured is also considered for comparison

purposes. This is realised by assuming the inﬂuences

of the air density and the dynamic viscosity of air in

Equations 4, 14 and 15 to be constant at the value 1.

So, set C contains the value 1 for the air density and

the dynamic viscosity of air. For each combination of

model type and set of inﬂuence equations the follow-

ing steps are applied.

1. Start at the beginning of the time series.

2. Deﬁne a window of the duration m days which

selects a data segment.

3. Estimate the variables c, c

4

, c

5

and n for the se-

lected data segment by conducting a least squares

ﬁt.

4. Use the air ﬁlter model, the determined variables

as well as the measured volume ﬂow, air temper-

ature and relative air humidity values to estimate

the differential pressure for each sample of the last

day of the selected data segment.

5. Move the window one day further.

6. Repeat the steps 2 to 5 until the time series end.

This process considers changing air ﬁlter conditions

as well as different usage patterns of a building during

a week. The latter is considered by setting the window

size to a value which is a whole-number multiple of 7

Condition Monitoring for Air Filters in HVAC Systems with Variable Volume Flow

105

days where the whole number-multiple is in the range

of 1 to 5. This variation is necessary to identify a

sweet spot at which the least number of samples is

used to achieve an optimal quality of ﬁt and is the

foundation for the further analysis.

As described in step 4 the model is used to cal-

culate the estimated differential pressure

c

∆p for each

sample. These values are necessary to determine the

reconstruction error of the model. As a measure for

the reconstruction error the root mean squared error

(RMSE) is used. Equation 16 shows the used deﬁni-

tion of RMSE where N is the number of samples.

RMSE =

s

1

N

N

∑

i=1

c

∆p

i

− ∆p

i

2

(16)

The RMSE values are then used to answer the

questions in Section 3. First, however, the length of

the sliding window at which the reconstruction er-

ror becomes minimal is determined. Therefore, for

each combination of model type and set the weighted

mean of the RMSE values RMSE is calculated for

each length of the sliding window according to Equa-

tion 17. Here M is the number of air ﬁlters for which

an RMSE value was calculated, w

i

is the amount of

samples which was used to calculate the RMSE value

and RMSE

i

is the RMSE value for each air ﬁlter.

RMSE =

∑

M

i=1

(w

i

· RMSE

i

)

∑

M

i=1

w

i

(17)

The RMSE values that result from using the op-

timal sliding window length are used for the further

analyses. Based on these RMSE values, it is ﬁrst de-

termined which combination of model type and set

yield the smallest RMSE value. This answers ques-

tion 1 from Section 3. Furthermore, it is investigated

whether the use of a certain set has a systematic in-

ﬂuence on the RMSE values of all model types. This

analysis provides the answers to questions 2 and 3.

Based on these analyses, the combination of model

type I and the set is selected which provides the lowest

reconstruction error. Then, for this combination, the

development of the exponents is analysed for each air

ﬁlter. These values are aggregated on monthly basis,

since the air ﬁlters are always changed in March but

never on the same day and never in the same calendar

week. This analysis answers question 4.

5.2 Results

Table 1 shows the weighted mean RMSE values for

each sliding window. These results indicate that

model type I and model type III perform similar on

the analysed dataset. Overall, model type II per-

forms worse than the other model types even though

in some cases the weighted mean RMSE values of

model type II are similar as the ones of the other

model types. This indicates that model type II is un-

derﬁtting the data and consequently its complexity is

not high enough. In Table 1 is also visible that the

weighted mean RMSE values of each combination

of model type and set rise with an increasing slid-

ing window length. Even raising the sliding window

length from one week to two weeks results in higher

weighted mean RMSE values. This indicates that the

condition of the analysed air ﬁlters cannot be assumed

to be constant within a period of two or more weeks.

Therefore, a sliding window of one week is used for

the further studies. Furthermore, the weighted mean

RMSE values show that the most complex models (set

A) always perform worse than the other models (set B

and C). This could be caused by the missing ambient

pressure measurements or the data quality of the rel-

ative air humidity measurements. Additionally, mod-

els which are extended by set A could be too complex

and therefore overﬁt the data. The latter assumption

is supported by the fact that in case of model type I

and type III the weighted mean RMSE values of set A

increase not as fast as the ones of set B and set C when

a larger sliding window length is used to increase the

amount of samples.

As shown in Table 1 a sliding window with a

length one week yields the best results. The corre-

sponding RMSE values for each air ﬁlter as well as

the weighted mean RMSE values are shown in Ta-

ble 2. Every air ﬁlter in the analysed building is iden-

tiﬁed by a number from 1 to 6. Uneven numbers are

assigned to air ﬁlters in the supply air duct. Whereas,

even numbers are assigned to air ﬁlters in the return

air duct. In Table 2 the RMSE values of air ﬁlters with

an uneven number are always higher than the RMSE

values of air ﬁlters with an even number. In case of

model type I and III the RMSE values of air ﬁlters

with an uneven number are almost equal for each set.

Whereas, the RMSE values of air ﬁlters with an even

number rise when set A is used. This also counts for

model type II for every air ﬁlter. So, in these cases the

usage of set A leads to overﬁtting models. Whereas,

in case of the model types I and III for air ﬁlters with

an uneven number the models lack a major inﬂuence.

Due to the nearly constant RMSE values for every set

the air condition is not that inﬂuence. In addition to

these ﬁndings the weighted mean RMSE values show

that model type I in combination with set B leads to

the best results. Even though model type I in combi-

nation with set C as well as model type III in combi-

nation with set B and C lead to comparable results.

As supported by the results in Table 2 set B is used

to analyse the dust load dependency of the exponent

SMARTGREENS 2021 - 10th International Conference on Smart Cities and Green ICT Systems

106

Table 1: Weighted mean RMSE values for each sliding window length.

window length model type I model type II model type III

in weeks set A set B set C set A set B set C set A set B set C

1 5.3303 3.7005 3.7522 9.7823 6.4420 6.3621 5.3288 3.7683 3.7671

2 5.4144 3.8586 3.8769 10.2949 6.5965 6.5028 5.4120 3.9045 3.8830

3 5.4781 3.9986 3.9719 10.5604 6.6956 6.6005 5.4728 4.0093 3.9683

4 5.5352 4.0842 4.0445 10.8248 6.8014 6.7014 5.5310 4.0902 4.0392

5 5.5903 4.1695 4.1236 11.1156 6.9083 6.8011 5.5865 4.1721 4.1163

Table 2: RMSE values for a sliding window of one week.

model type I model type II model type III

air ﬁlter set A set B set C set A set B set C set A set B set C

1 6.9818 6.9788 6.9725 10.2139 9.2112 9.2019 7.0094 6.9775 6.9714

2 3.4586 2.9847 2.9725 3.7586 3.0807 3.0660 3.4542 3.0026 2.9900

3 5.5745 5.5556 5.5369 15.6732 13.7007 13.6616 5.5551 5.5554 5.5368

4 3.9553 3.3635 3.3426 4.0731 3.4121 3.4142 3.9408 3.4023 3.4003

5 - 2.3839 2.5264 - 4.8358 4.6676 - 2.5210 2.5311

6 - 2.3471 2.3207 - 2.7927 2.7995 - 2.3959 2.3932

weighted mean 5.3303 3.7005 3.7522 9.7823 6.4420 6.3621 5.3288 3.7683 3.7671

Figure 1: Development of the exponents of model type I.

of model type I. Figure 1 shows that the exponents

of model type I varies around the value of 2 in case

of the return air ﬁlters number 2 and number 4. In

contrast, the exponents of the corresponding supply

air ﬁlters nearly always have the value 1. Whereas,

the exponents of the supply air ﬁlter number 5 are

higher than the exponents of the return air ﬁlter num-

ber 6. As shown in Table 2 the quality of ﬁt of the

supply air ﬁlters 1 and 3 is worse than the quality of

ﬁt of the corresponding return air ﬁlters 2 and 4. This

is also indicated by the values of their exponents. It

was deﬁned that the exponents cannot be lower than

1. So, the fact that the exponents of air ﬁlter 1 and

3 mostly have the value 1 also illustrates that a major

inﬂuence is lacking in the model for these air ﬁlters.

In addition to the differences between the exponents

of each air ﬁlter Figure 1 also shows the inﬂuence of

the air condition as well as the inﬂuence of the build-

ing usage. The analysed building is not that populated

during March, August and September. Therefore, the

HVAC system operates only at partial load or is turned

off during this period. Hence, the amount of samples

decreases and the quality of ﬁt decreases as well. The

inﬂuence of the air condition is indicated by a local

maxima during the summer in case of the air ﬁlters

2, 4 and 5. In the end this analysis clariﬁes why the

model type II does not perform as good as the other

models. For this model it is assumed that the expo-

nent has the value 2 which is not the case for each air

ﬁlter. The models type I and III offer the possibility to

choose other exponents, in case of model type I and a

mixture of different exponents in case of model type

III. Furthermore, this analysis also illustrates that the

air condition as well as the usage of the building affect

the results of the ﬁt.

6 CONDITION MONITORING

Model type I in combination with set B yields the best

quality of ﬁt. So, the resulting model is used here-

inafter to estimate the condition of air ﬁlters. At ﬁrst

the used condition monitoring method is described

and Section 6.2 contains the results for the dataset

which is described in Section 4.

Condition Monitoring for Air Filters in HVAC Systems with Variable Volume Flow

107

6.1 Method

The model which was selected in Section 5 is used

to estimate the differential pressure at nominal vol-

ume ﬂow

c

∆p

n

. For existing HVAC systems, the dif-

ferential pressure limit is speciﬁed for the nominal

volume ﬂow. Thus, the estimated differential pres-

sure at nominal volume ﬂow can be compared with

the already deﬁned differential pressure limit. The es-

timated differential pressure at nominal volume ﬂow

is determined as follows:

1. Start at the beginning of the time series.

2. Deﬁne a window of the duration 7 days which se-

lects a data segment.

3. Estimate the variables c and n for the selected data

segment by conducting a least squares ﬁt.

4. Use the air ﬁlter model, the determined variables

as well as the measured volume ﬂow and air tem-

perature values to estimate the differential pres-

sure at nominal volume ﬂow for the samples dur-

ing the last day of the selected data segment.

5. Move the window one day further.

6. Repeat the steps 2 to 5 until the time series end.

The estimated differential pressure at nominal volume

ﬂow can be used in two ways. On the one hand, it

can be compared with the speciﬁed differential pres-

sure limit and an error message can be returned in

the building management system if the limit is ex-

ceeded. Alternatively, the estimated differential pres-

sure at nominal volume ﬂow can be scaled in such a

way that the resulting value of the ﬁlter clogging C

has the value 0% at the initial differential pressure

of the air ﬁlter

1

and reaches 100 % when the differ-

ential pressure limit is reached (see Equation 18). In

the analysed building, several air ﬁlters from differ-

ent manufacturers are operated in parallel, which is

why the initial differential pressure at the respective

ﬁlter stage is unknown. Therefore, in this case the

minimum differential pressure after the ﬁlter change

is used as the lower limit.

C =

c

∆p

n

− ∆p

min

∆p

max

− ∆p

min

· 100 % (18)

6.2 Results

The process to determine the air ﬁlter condition which

is described in the previous section is applied for each

air ﬁlter in the dataset which is described in Section 4.

In Figure 2 the results for two air ﬁlters are shown

1

The initial differential pressure is usually speciﬁed by

the air ﬁlter manufacturer.

Figure 2: Filter clogging development for two air ﬁlters.

which are representative for all six analysed air ﬁlters.

Furthermore, the dates at which the air ﬁlters were

changed are marked by the dotted lines

2

.

Figure 2 shows various effects that occur for all air

ﬁlters, whereby the strength of the effect varies from

ﬁlter to ﬁlter. In the case of air ﬁlter 6, the reduction

of ﬁlter clogging after a ﬁlter change is clearly visi-

ble. Whereas in the case of air ﬁlter 2, the ﬁlter clog-

ging increases after the ﬁrst service and reduces as

expected after the second service. This effect is a con-

sequence of the use of different air ﬁlter brands. Each

air ﬁlter brand and type has a different initial differen-

tial pressure, which is why the measured differential

pressure increases after a service and thus also the cal-

culated ﬁlter clogging. This effect can be countered

by operating the HVAC system at different volume

ﬂow levels including the nominal volume ﬂow after a

service and using the measured differential pressure at

nominal volume ﬂow as a new lower limit if the initial

differential pressure of the ﬁlter brand is not known.

Furthermore, this initial test can be used to determine

the exponent n and keep it ﬁxed until the next service.

This reduces the degrees of freedom of the model and

thus reduces the overﬁtting potential.

Furthermore, in Figure 2 can be seen that the air

ﬁlter clogging for air ﬁlter 2 is approximately constant

between each service. This means that the accumu-

lated loading of the air ﬁlter with particles between

services has not led to any measurable increase of the

differential pressure at a comparable volume ﬂow. In

addition, the time series shows gaps, as can be seen

for air ﬁlter 2 in September 2018 and 2019. These are

2

Due to the COVID-19 pandemic and the lockdown in

Germany no ﬁlter change was carried out in March 2020.

SMARTGREENS 2021 - 10th International Conference on Smart Cities and Green ICT Systems

108

caused by the low utilisation of the analysed build-

ing and the associated shutdown of the HVAC system

during this period.

7 CONCLUSIONS

In this work, the approaches for modelling air ﬁlters

which are identiﬁed in Section 2 are uniﬁed in Sec-

tion 3 in such a way that they could be compared with

each other and are also available in different levels of

detail, which are suitable for a retroﬁt. The model

comparison is carried out on the dataset of a build-

ing in Germany described in Section 4. The compari-

son described in Section 5 shows that the models de-

rived from (DIN Deutsches Institut f

¨

ur Normung e.V.,

2013) and (L

¨

ofﬂer, 1988) deliver comparable results.

The former achieves the best results overall. In Sec-

tion 6 is described how this model can be used for

condition monitoring of air ﬁlters in HVAC systems

with variable volume ﬂow. In addition, it is shown

that this approach can be retroﬁtted to an existing

building and provides plausible results.

Nevertheless, following questions with focus on

condition monitoring of air ﬁlters in HVAC systems

with variable volume ﬂow are still open for further

research.

• Is it possible to truly increase the quality of the

air ﬁlter condition estimation by determining the

exponent of model type I after a ﬁlter change and

keeping it ﬁxed for the rest of the air ﬁlter life?

• If data with better quality and a higher frequency

resolution in combination with usage of relative

air humidity would be available, how does that af-

fect the performance of the analysed model types?

• Are the results independent from the analysed

building and potential systematic errors in the data

acquisition?

ACKNOWLEDGEMENTS

The authors acknowledge the ﬁnancial support by the

Federal Ministry for Economic Affairs and Energy

(project number 03ET1569).

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