research article automatic and noninvasive indoor air

Research ArticleAutomatic and Noninvasive Indoor Air QualityControl in HVAC Systems

M C Basile1 V Bruni23 F Buccolini4 D De Canditiis2 S Tagliaferri4 and D Vitulano2

1Struttura di Particolare Rilievo ldquoValorizzazione della Ricercardquo CNR 00185 Rome Italy2Istituto per le Applicazioni del Calcolo ldquoM Piconerdquo CNR 00185 Rome Italy3Dipartimento Scienze di Base e Applicate per lrsquoIngegneria Sapienza-Rome University 00161 Rome Italy4Tagliaferri srl 00191 Rome Italy

Correspondence should be addressed to V Bruni vittoriabrunisbaiuniroma1it

Received 31 March 2016 Accepted 1 June 2016

Academic Editor Ting Chen

Copyright copy 2016 M C Basile et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a methodology for assessing and monitoring the cleaning state of a heating ventilation and air conditioning(HVAC) system of a building It consists of a noninvasivemethod formeasuring the amount of dust in the whole ventilation systemthat is the set of filters and air ducts Specifically it defines the minimum amount of measurements their time table locations andacquisition conditions The proposed method promotes early intervention on the system and it guarantees high indoor air qualityand proper HVAC working conditions The effectiveness of the method is proved by some experimental results on different studycases

1 Introduction

Particulate pollution has recently drawn the attention of pub-lic institutions environmental associations and researchersin different fields like medicine engineering and so on Itconsists of a mixture of organic and inorganic substancesthat are produced during natural or human processes Theinterest in this topic is mainly due to its health hazardespecially for what concerns dust thin fraction that is PM10In fact these microscopic particles whose aerodynamicdiameter is less than or equal to 10 120583m are easily absorbedby the organism Several research studies [1ndash4] proved thatair pollution represents one of the main causes of cancerdeath In addition indoor air pollution causes several healthdamages such as asthma allergies bronchitis and generaldiseases recently denoted by Sick Building Syndrome [5 6]Despite these clear evidences indoor air quality did notreceive the same attention of outdoor air quality especiallyfor what concerns institutional rules and restrictions at bothnational andEuropean level For example even thoughWHO(World Health Organization) guidelines indicate a limit forindoor fine dust concentration equal to 10 120583gm3 the toler-ated limit in EU is 25 120583gm3 Furthermore contaminants are

responsible for bad working conditions of HVAC (heatingventilation and air conditioning) and contribute to shortenits life Scientific studies have confirmed that 50 of energyconsumption of a building is for HVAC system [7] Recentinvestigations have shown that a clean HVAC system canprovide energy saving that can be equal to 11 [8] Thisis the reason why some institutions and governments (egthe US government [9]) gave recommendations concerningsome best practices for a proper HVAC maintenance whichinvolve both filters exchange and ducts cleaning In factgood filters maintenance does not guarantee clean ductsespecially in long life plants Ducts gather dust during timethat can be released inside the building and can favour theproliferation of fungi and bacteria As a result ducts canoften be responsible for bad indoor air quality more thanfilters Nevertheless maintenance interventions are invasivetime consuming and operator-dependent In fact existingautomatic methods are devoted to filters monitoring [10ndash12] while approaches dealing with air ducts require invasiveoperations on the plant for example visual inspection bymaintenance operators [13] It is then reasonable and desir-able to have a tool for indoor air quality which automatically

Hindawi Publishing CorporationJournal of Industrial MathematicsVolume 2016 Article ID 9674387 11 pageshttpdxdoiorg10115520169674387

2 Journal of Industrial Mathematics

controls the cleaning state of the system (filters and ducts) andalerts you when it is going toward bad working conditions

The aim of this paper is to present a noninvasive proce-dure for the automatic indoor air quality assessment whichdepends on cleaning conditions of HVAC system It is basedon a mathematical algorithm that processes a few on-sitephysical measurements that are acquired by dedicated sen-sors at suitable locations with a specific time tableThe outputof the algorithm is a set of indexes that provide a snapshot ofthe system with separated zoom on filters and ducts

The development of the method started in a project par-tially funded by Provincia di Roma (Technological Promotersfor Innovation 2011) and involving Tagliaferri srl and thepublic research institute for the Applications of Calculusof the National Research Council (IAC-CNR) The methodhas been patented in Italy (Patent number 102013902196398)with PCT extension (PCTIB2014064943) with evaluationwithout observations The patent derived from a need ofthe small enterprise (Tagliaferri srl) working in the field ofHVAC installation and maintenance The collaboration withthe scientific institution allowed formulating an innovativeand successful solution having high potential future devel-opment The partnership has been promoted and managedby the research transfer office of CNR by means of spe-cific and formal agreements between small enterprise andresearch institution These agreements aimed at regulatingintellectual property rights and market exploitation modal-ities In addition the role of research transfer office hasbeen fundamental in the definition of patentable contentsand in assuring its innovative contribution The patentedprocedure has several advantages with respect to the up-to-date monitoringchecking procedures

(1) It is not an invasive approach It does not alter thestandard operation mode of the system for examplea forced temporal halt

(2) It is based on a robust and portable protocol thatmakes it practical and simple andwith low implemen-tation costs

(3) It gives the opportunity of planning maintenanceintervention by limiting it only when standard HVACworking conditions need to be restored

(4) It allows independently evaluating the cleaning stateof both plant ducts and filters

The remainder of the paper is organized as follows InSection 2 some preliminary notions are given Section 3firstly describes the proposed model and then the practicalprocedure for plant checking Section 4 presents some exper-imental results concerning two representative case studiesFinally Section 5 draws the conclusions

2 Preliminary Background

This section provides some preliminary notions and modelassumptions They are necessary for a straightforward andclear description of the whole procedure

Input air Output air

A B

Filter Ducts

HVAC

Figure 1 Sketch of HVAC system

21 Removal Efficiency of a Filter An HVAC system can besketched as in Figure 1 The air enters at point A and it isfiltered before being pumped into the building through airdistributing ducts Filters are commonly employed for multi-ple purposes [14] They allow reducing dust concentration inthe system in order to extend equipment life to reduce main-tenance costs and finally to control fine dust concentrationfor improved indoor air quality Even though particulate airpollution has different size in this paper we will focus onPM10 Air handling systems in buildings usually have twotypes of particulate air filters fibrous media filters and elec-tronic air cleanersTheymainly differ in the way they captureparticles the former act mechanically the latter use electriccharges Nonetheless they have comparable collection effi-ciency independently of particles size Based on this evidencethe removal efficiency of a filter is defined as the percentage ofPM10 that it gets hold Specifically if the upstreamPM10 con-centration is119862ext and the downstream PM10 concentration is119862int the removal efficiency of the filter is

120583119865=

119862ext minus 119862int119862ext

(1)

with 120583119865isin [0 1]

It is worth observing that filter removal efficiencyincreases over time because of its clogging Therefore byindicating with 120583

119865the removal efficiency of the unused filter

as provided by the manufacturer and with 120583(119905) the removalefficiency of the filter over time we expect that

120583 (119905) = 120583119865+ 120575120583 (119905) (2)

where 120575120583(119905) is an increasing and positive function of 119905

22 PM10 Measurements and Environmental Conditions Asconfirmed by several measurement surveys [15 16] PM10concentration depends on weather conditions such as tem-perature humidity atmospheric pressure and wind [17 18]as well as on natural and anthropic factors The pluralityof variables to be measured makes the evaluation of thecleaning state ofHVAC systems rather complex especially formonitoring purposes However since natural and anthropicfactors can be considered stable at least for a fixed timeinterval we can only deal with weather-dependent variablesIn addition their intradependencies allowus to select just twoof them as shown in the following

The relative humidity is defined as the ratio between thevapour in a given air volume and the one at saturation Asa result humidity equal to 100 means that air contains

Journal of Industrial Mathematics 3

the maximum quantity of water vapour at the measuredtemperature and atmospheric pressure The dew point 120579

119889

is the temperature to which air must be cooled at constantpressure and water content to reach saturation [19] From theMagnus-Tetens formula we have

120579119889=

119887Ω

119886 minus Ω

with Ω =119886119879

119886 + 119879+ ln(

119880

100) 119886 = 1727 119887 = 2377

∘

(3)

where 119880 is the humidity and 119879 is the temperature see[20] for further details Since the dew point 120579

119889depends on

the atmospheric pressure previous equation provides thecorrelation law between pressure temperature and humidityIt turns out that only two of them can be embedded in afunctional model that correlates PM10 concentrations withweather conditions

More precisely for fixed environmental conditions andstable wind the following time-dependent functional modelfor PM10 concentration can be assumed

119862 (119905) = 119891 (119879 (119905) 119880 (119905)) (4)

where 119862(119905) is PM10 concentration at time 119905 119879(119905) is thetemperature119880(119905) is the humidity and119891 is a suitable function

3 The Proposed Methodology

The proposed methodology consists of three steps orientedto evaluate the cleaning state of the HVAC system and toindicate which component is responsible for that state To thisaim proper physical quantities have to bemeasured at properlocations for a reliable and fast response In this section detailsabout the functional model for the involved quantities theacquisition procedure and data processing will be given

31 Model Definitions and Assumptions This section definesdata acquisition conditions and the basics for the adoptedmodel Specifically it focuses on the definition andprocessingof those quantities that are involved in the proposed alarmindexes

311 HVAC Efficiency With reference to the simplifiedHVAC model in Figure 1 (1) can be extended to the wholeHVAC system as follows

120583HVAC (119905) =119862ext (119905) minus 119862int (119905)

119862ext (119905) (5)

where 119862ext is PM10 concentration in the input (entering) airwhile 119862int is PM10 concentration in the output air that ismeasured at the inner ending of air distributing ducts

120583HVAC(119905) is a time-dependent function and representsthe global efficiency of HVAC system 120583HVAC can assumenegative values since 119862int depends on both filters retentionefficiency and ducts cleanliness As a matter of fact HVACefficiency is influenced by environment weather activity inthe building and other uncontrollable factors In order to

have a robust and reasonable estimation of HVAC efficiencyPM10 concentrations 119862int(119905) and 119862ext(119905) have to be measuredin a proper time interval [119905

1 119905119899] More precisely

(A1) [1199051 119905119899] is such that environmental and atmospheric

conditions are stable (absent or constant wind)

Under assumption (A1) the functional model in (4) forPM10 concentration holds 119891 depends on the environmentalcontext and can be estimated using on-site measurements asexplained in the next section

312 Functional Model for PM10 Concentration The relia-bility of a functional model strongly depends on the ratiobetweennumber ofmeasurements andnumber of unknownsSelecting a simple model with few parameters is then recom-mended In particular a linear model has been selected forthe function 119891 in (4) More precisely 119862(119905) is defined as

119862 (119905) = 120572119880 (119905) + 120573119879 (119905) + 120574 (6)

where the parameters (120572 120573 120574) isin 1198773 characterize the

environment and are estimated from a set of on-site timemeasurements The adequacy of such a model is supportedby the studies in [16] that experimentally validated it

Linear regression can be used for parameters estimationMore precisely let 119905

1 1199052 119905

119899be 119899 distinct and equispaced

time instants belonging to the time interval [1199051 119905119899] satisfying

assumption (A1) that is 119905119894= 1199051+ (119894 minus 1)((119905

119899minus 1199051)(119899 minus 1))

119894 = 1 2 119899 and let

C = [119862 (1199051) 119862 (119905

2) 119862 (119905

119899)] = [119862

1 1198622 119862

119899]

T = [119879 (1199051) 119879 (119905

2) 119879 (119905

119899)] = [119879

1 1198792 119879

119899]

U = [119880 (1199051) 119880 (119905

2) 119880 (119905

119899)] = [119880

1 1198802 119880

119899]

(7)

respectively be PM10 concentration temperature andhumidity measured at those time instants and at a predefinedlocation then the minimum square estimator of parameters(120572 120573 120574) is

( ) = argmin(120572120573120574)isinR3

119899

sum

119894=1

(119862119894minus 120572119880119894minus 120573119879119894minus 120574)2 (8)

The dependence of PM10 concentration on environment isthen given by the following formula

119862 (119905) = 119880 (119905) + 119879 (119905) + (9)

with estimated as in (8)It is worth observing that

(i) in order to prevent unreliable parameters estimationin the presence of wiggly data it might be advanta-geous to regularize their time profiles before usingthem in (8) The integration of time profiles is afeasible regularization and it is used in this paper

(ii) a long term monitoring promotes the reliability ofparameters estimation and a better characterizationof the plant


313 Data Collection Points According to (5) the evaluationof plant efficiency requires at least two data collection points[21] An exhaustive and feasible study led to the followingsetting

(A2) An external point located outside the building andfar from the air treatment unit no more than 10 cman interior point located at no more than 10 cm faraway from the air vent of a room which in turn isfar enough away from the air treatment unit

In fact the external point has to capture the air that entersthe system If it is too far from the input of the system it couldbe influenced by other external factors The same happensfor the internal point As it will be shown in Section 4inner room activity and bad cleaning conditions can affectmeasurements leading to not consistent predictions Theconfiguration in (A2) guarantees the acquisition of morerobust and reliable data

32 Plant Checking Procedure This section presents thedetailed procedure for the assessment of the cleaning state ofthe HVAC system It consists of the determination of threecleaning indexes The first one alerts in case of very criticalconditions the others respectively refer to filters and ducts

321 Ducts Cleaning Index Poor Conditions Alert Withreference to Figure 2 the first step of HVAC checkingprocedure is devoted to the inspection of plant ducts Thisstep aims at giving a prompt alert in case of very criticalHVAC working conditions Only inner PM10 concentrationis then processed

Let Cnight = [119862(1199051) 119862(119905

119899)] Tnight = [119879(119905

1) 119879(119905

119899)]

and Unight = [119880(1199051) 119880(119905

119899)] 119905119894isin Δ1198791 respectively denote

PM10 concentration temperature and humidity measuredduring the time interval Δ119879

1at the internal point satisfying

(A2) The components of the vector Cnight are estimated as(9) using Tnight and Unight components Δ119879

1includes a long

lapse time during which the system is switched off (usuallyall the night) Let set

119875 =10038171003817100381710038171003817Cnight

10038171003817100381710038171003817infin (10)

119875 is expected to be recorded right after HVAC switching onIn fact a chimney effect is expected in HVAC ducts after sys-tem switching off Chimney effect is a phenomenon of naturalventilation inside the building and it is caused by the differ-ence between indoor and outdoor night temperature If thedifference between outdoor and indoor temperature is nega-tive indoor air is sucked by the ducts It turns out that whenHVAC is switched on the maximum concentration of PM10that is 119875 in (10) is the sum of two contributions the averageconcentration of dust ldquosucked inrdquo during the night from theroom and the dust sediment which is in HVAC ducts Moreprecisely let 119905 be the switching on time and let 119905

119904le 119905 then

119875 = 119878 + DCI (11)

where

119878 =1

119905119904minus 1199051

int

119905119904

1199051

119862 (119905) 119889119905 (12)

is the average of PM10 ldquosucked inrdquo by HVAC ducts duringthe night ([119905

1 119905119904] isin Δ119879

1) while DCI represents the amount

of PM10 transferred from the ducts to the air blown into theroom

DCI stands for Duct Cleaning Index and it is expectedthat

DCI = 119875 minus 119878 gt 0 (13)

Unfortunately in real cases it can be negative due to differentand uncontrollable causes This is the reason why recordingsuch measurements in a clean room where windows are closedis recommended As a result if DCI lt 0 the measurementsare inadequate and need to be recollected otherwise DCIis compared with a fixed alarm threshold TOLL

1 If DCI gt

TOLL1 then ducts need to be cleaned otherwise further

investigation is required

322 Filters Cleaning Index In order to assess the cleaningstate of the filters (1) and (5) will be employed Thereforeboth acquisition points in (A2) will be considered Let

119864 =1

1003816100381610038161003816Δ1198792

1003816100381610038161003816

intΔ1198792

119862ext (119905) 119889119905 (14)

be the average of external PM10 concentration estimated asin (9) in the time interval Δ119879

2 Similarly

119868 =1

1003816100381610038161003816Δ1198793

1003816100381610038161003816

intΔ1198793

119862int (119905) 119889119905 (15)

is the average of internal PM10 concentration estimated as in(9) in the time intervalΔ119879

3Δ1198793must start nomore than one

hour later thanΔ1198792ending Hence in agreement with (5) the

current global HVAC efficiency is

120583HVAC =119864 minus 119868

119864 (16)

As discussed in Section 311 119868 is the sumof two contributions(i) (1minus120583)119864 which represents the external PM10 concentrationwhich has not be retained by the filter and (ii) 119862duct whichrepresents the contribution given by the remaining part of thesystem Therefore

120583HVAC =119864 minus 119868

119864=

119864 minus [(1 minus 120583) 119864 + 119862duct]

119864

= 120583 minus119862duct119864

(17)

Hence if 119862duct is negligible (ducts are clean) and 120583 sim 120583119865

(filters are clean) 120583HVAC sim 120583119865

The deviation of 120583HVAC from 120583119865declares an inadequate

HVAC maintenance due to filters clogging andor fouledducts In particular since 119862duct(119905) ge 0 by definition and120583 ge 120583

119865 as observed in Section 21 the following conclusions

can be drawn

(i) If 120583HVAC ge 120583119865 then ducts are clean while filters are

not


A

Yes

Yes

No

No

Performing a plurality of powder concentration

measurements in a first predetermined time period

ΔT1 of plant inactivity inside said room at said air

vent


measurements in a second predetermined time

period ΔT2 at the starting of the plant inside said

room at said air vent

Calculating an average S of such plurality ofmeasurements

Extracting a maximum concentration value P fromsaid series of measurements

Calculating a duct cleaning indexDCI = P minus S

DCI ge 0Inadequate

measurements

Ductsunder critical

conditions Ductsunder not critical

conditions

DCI ge TOLL1

Performing a plurality of powder concentrationmeasurements in a third predetermined time periodΔT3 of plant activity outside said room at an airtreatment unit of said plant placed in the outerenvironment upstream of the filtering system of saidplant

Performing a plurality of powder concentrationmeasurements in a fourth predetermined time periodΔT4 of plant activity inside said room at said air vent

Calculating an average E of such plurality of possiblyregularized measurements

Calculating an average I of such plurality of possiblyregularized measurements

Calculating a filter cleaning indexFCI = [(E minus I)E] minus 120583

Figure 2 Detailed block scheme of the proposed methodology Part A

(ii) If 120583HVAC lt 120583119865 then filters are clean while ducts are

notIn fact in the first case ducts do not significantly contribute toPM10 concentration and HVAC removal efficiency substan-tially is the filter removal efficiency120583 at the check timeOn thecontrary in the last case ducts contribution is greater than thedust released from the filters that is (1 minus 120583)119864 and then theoverall system efficiency is notably lower than 120583

119865

It turns out that the Filter Cleaning Index (FCI) can bedefined as

FCI = 120583HVAC minus 120583119865 (18)

If FCI ge 0 filters are going toward bad conditionsThe level ofcriticism is given by a fixed threshold TOLL

2(see Figure 3)

On the contrary if FCI lt 0 119862duct is definitely positive andmust be quantified


SI

Ducts dirt ispredominant

Calculating a relative index ofplant cleaningRSCI = [S minus (1 minus 120583)E]S

FCI le TOLL2Low

Dirty plant

Compare RSCI to TOLL3

RSCI gt 2TOLL3High

2TOLL3 ge RSCI gt TOLL3

Med

Dirty filters

Comparing FCI to 120583

FCI gt 2TOLL2High

2TOLL2 ge FCI gt TOLL2

Med

FCI ge 0

Clean plantRSCI ge TOLL3

A

Yes No

No

Figure 3 Detailed block scheme of the proposed methodology Part B

323 Refined Ducts Cleaning Index In order to quantify andevaluate the eventual risk of having dirty ducts the followingindex is defined

RSCI =119878 minus (1 minus 120583) 119864

119878 (19)

where 119878 is the average concentration of PM10 introduced intothe building by the HVAC system as defined in (12) while(1minus120583)119864 is the amount of air which is not retained by the filter

RSCI stands for Relative State Cleaning Index and quan-tifies the percentage of PM10 which is transferred from

the plant to indoor environmentThe one not retained by thefilter is neglected

Even in this case the level of alert is given by a prefixedalarm threshold TOLL

3 as shown in Figure 3

4 Experimental Results

The proposed methodology has been tested and validatedon different buildings The results presented in this sectionaim at giving clear evidence of the need of some assumptions


0 10 20 30 40 50 60001

002

003

004

005

006

007

008

009

01

011

t

Cin

t

(a)

0 10 20 30 40 50 60002

004

006

008

01

012

014

t

Cin

t

(b)

Figure 4 (a) Indoor PM10 concentrationmeasured with changing acquisition conditions closed windows (first half) openwindows (secondhalf) (b) Indoor PM10 concentrationmeasured by putting PM10measuring device at the center of the roomThe peak denotes human activitynearby the measuring device

and constraints that have been used in the definition ofthe proposed methodology Presented results refer to tworepresentative case studies that have been employed formodel fine tuning The first one concerns an HVAC systemserving a building of large dimensions located in the cityof Rome (Italy) The HVAC system dates back to 2002 itis well functioning and it is structured in a standard waywhereby air is drawn from outside filtered through the filterheatedcooled and then conducted through the ducts to therooms of the building The second one refers to a smallerplant which is located in a different area of the city andequipped with a different filter type with smaller efficiencyThe company Tagliaferri srl has made hygrometer athermometer and a powders measuring device availableThe latter is capable of measuring PM10 concentration atpredetermined time intervals An intense measurementssurvey has been conducted Data have been acquired for along period andweather conditions have also been annotated

The first part of fine tuning procedure has been devotedto the definition of the optimal acquisition conditions andlocation Figure 4(a) shows PM10 concentration that has beenmeasured in the same roomusing two differentmodalities Inthe first part of the plot data refer to closed windows whileair conditioning is on the second part refers to openwindowswhile air conditioning is off As it can be observed the averagePM10 concentration dramatically changes from the first tothe second part of the plot The second one is influencedby external measures so that it cannot be considered as avalid indicator of indoor air quality Figure 4(b) depicts PM10concentration acquired in the middle of the room and farfrom the air vent As it can be observed there is an anomalouspeak of dust concentration at a certain time It corresponds tohuman activity nearby the measuring device Figure 5 showsanother example concerning PM10 concentration acquiredeach 10 minutes from 7 am to 7 pm As it can be observedhigher PM10 concentrations are in correspondence with the

0 10 20 30 40 50 60 70 80minus2

0

2

4

6

8

10

12

14

16

t

Cin

t

times10minus3

Figure 5 Indoor PM10 concentration measured with changingacquisition conditions closed windows (first half) open windows(second half)

lapse of time during which windows have been opened (inthe morning) Finally Figure 6 refers to a building having afilter whose retention efficiency is less than 025 The roomis characterized by relevant human activity and the contentof the room is archive material that is there are powders ofdifferent nature In this casemeasurements are very unstableThese four examples definitely support the assumptions (A1)and (A2) given in Section 31 and recommendations for acqui-sitions related to cleanliness of the room and stable weatherconditions That is why PM10 concentration temperatureand humidity have been recorded in two specific points ofthe system near the external air intake of HVAC and close tothe air vent of a room of the building


0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t

Figure 6 Indoor PM10 concentrationmeasured in a roomwith high human activity and presence of archivematerialThe retention efficiencyof the filter is less than 025

The second part of fine tuning procedure has beendevoted to data processing measurements in windy dayshave been neglected Figures 7(a) and 7(c) show PM10concentration temperature and humidity profiles in a giventime interval with stable atmospheric conditions The samefigure depicts PM10 concentration that has been regularizedby means of linear regression The figure clearly shows theconsistency of the linear dependence of PM10 concentrationon temperature and humidity In order to have a more stableestimation of PM10 concentration acquired data can beregularized before using them in the linear regression Inparticular cumulative summation has been used in orderto preserve temporal information (Figures 7(b) and 7(d))As it can be observed the regularized profile of PM10concentration is more stable Figure 8 shows the globalHVAC efficiency 120583HVAC(119905) as defined in (17) As it can beobserved the direct use of raw data gives an unstable value for120583HVAC (Figure 8(a)) on the contrary regularized data providea more robust straightforward and reliable estimation ofHVAC efficiency (Figure 8(b)) It is also worth observing thatregularized data allows us to directly measure the trend ofinvolved quantities so that the current value gives the actualsnapshot of the system on the basis of its history For longterm monitoring this trend can also be used for predictingfuture states of the systemThis is useful for planning a futurecheck or future filter change or ducts cleaning

In order to validate the model PM10 concentration hasalso been measured right after filters in the HVAC systemas sketched in Figure 9 In this way the contribution of filtersand ducts in indoor air can be well separated More preciselyif this additionalintermediate measure that is the oneacquired at the point D in Figure 9 is used in (5) as 119862int then(5) gives filters efficiency On the contrary if the intermediatemeasure is used as 119862ext (5) provides ducts efficiency Thesemeasurements have been acquired before and after filterschange This intermediate measure allowed us to assess thecoherence and robustness of the proposed methodologyin addition it has been used for tuning the adopted alarm

thresholds With regard to DCI (Ducts Cleaning Index)which is related to very critical working conditions thecurrent alarm threshold for outdoor air quality has beenused Hence TOLL = 005mgm3 in agreement with theLegislative Decree August 13 2010 available at [22] For whatconcerns FCI (Filters Cleaning Index) which is specificallyrelated to filters TOLL

2depends on retention efficiency of

the original filter and then TOLL2

= 005120583119865 Furthermore

005120583119865

le FCI le 01120583119865corresponds to a soft warning (filters

are going to be clogged) FCI gt 01120583119865means that filters have

to be changed Finally with regard to RSCI (Relative StateCleaning Index) TOLL

3has been set equal to 015 Even in

this case 015 le RSCI le 030 provides a soft warning whileRSCI gt 030 provides an alarm

Due to the lack of specific restrictions for indoor airquality previous tolerance thresholds are reasonable valuessuggested by the experience of experts inHVACmaintenanceand the evaluations made during the testing phase of theproposed methodology They can obviously be changedaccording to specific local restrictions or end use of thebuilding For example it is expected to have more severerestrictions in a hospital rather than in an office

5 Conclusions

In this paper a method for the diagnosis of the cleaning stateof a heating ventilation and air conditioning (HVAC) systemhas been presented The patented methodology is based ona noninvasive intervention in HVAC system and it is alsoable to account for measures acquired at previous times Inparticular the method consists of (i) measuring fine particlesconcentration at specific points of the building and precisetime periods as well as some physical quantities (ii) properlyprocessing those measurements and finally (iii) evaluatingthree cleaning indexes The procedure returns a snapshot ofthe system which clearly indicates the healthy state of indoorair as well as the system component (filters or ducts) that


0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)

Figure 7 (a c) Plot of PM10 concentration temperature and humidity as well as the regularized profile of PM10 concentration as in (9)outdoor concentration (a b) indoor concentration (c d) PM10 concentration has been multiplied by 50 in order to show all the data in thesame figure (b d) The same measures as in (a c) but data have been preregularized before using them in (9) Cumulative summation hasbeen used for preregularization

is more responsible for that state The proposed method hasan immediate commercial fallout In fact it is usable by thecompanies that work in the field of ventilation systems asa product-service since it is extremely flexible automaticlow-cost and able to provide a complete check of the system(filters and air ducts) As a matter of fact the potential ofthe proposed method is even greater in a long term and per-manent monitoring of the system In fact the mathematicalmodel may be used for predicting and time scheduling main-tenance interventions on ducts andor filtersThis would give

a considerable contribution to the standardization of main-tenance procedures The present invention would also have akey role in the presence of laws regulating indoor air quality inboth public and private buildings Finally the energy savingprovided by a clean HVAC is not a negligible benefit

Competing Interests

The authors declare that they have no competing interests


Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)

Figure 8 HVAC global efficiency as in (5) Raw data have been used for (a) preregularized data have been used for (b)


A B

Filter Ducts

HVAC

D

Figure 9 Sketch of HVAC system where three acquisition pointshave been indicated A andB are the two points used in the proposedmethodology D is the intermediate point that has been used for thevalidation of the model

Acknowledgments

The authors would like to thank Provincia di Roma forsponsoring ldquoClean Airrdquo project and for providing a partialfunding for this study with the Technological PromotersInnovation 2011 Program The authors would also like tothank the technological promoters in Clean Air project DrElisa Rossi and Eng Daniele Pigozzi

References

[1] Agenzia Regionale per la Protezione dellrsquoAmbiente della Lom-bardia httpwww2arpalombardiaitsitesQAria layouts15QAriaIDatiaspxv=2

[2] R Beelen O Raaschou-Nielsen M Stafoggia et al ldquoEffects oflong-term exposure to air pollution on natural-cause mortalityan analysis of 22 European cohorts within the multicentreESCAPE projectrdquo The Lancet vol 383 no 9919 pp 785ndash7952014

[3] G Liguori M Bagattini F Galle M Negrone V Di Onofrioand M Triassi ldquoAutomated cleaning of fan coil units witha natural detergent-disinfectant productrdquo Annals of ClinicalMicrobiology and Antimicrobials vol 9 article 29 2010

[4] World Health Organization (WHO) ldquoIARC outdoor air pollu-tion a leading environmental cause of cancer deathsrdquo Tech Rep221 WHO 2013

[5] Sick Building Syndrome United States Environmental Protec-tion Agency (EPA) 2009

[6] J Sundell T Lindvall and B Stenberg ldquoAssociations betweentype of ventilation and air flow rates in office buildings andthe risk of SBS-symptoms among occupantsrdquo EnvironmentInternational vol 20 no 2 pp 239ndash251 1994

[7] L Perez-Lombard J Ortiz and C Pout ldquoA review on buildingsenergy consumption informationrdquo Energy and Buildings vol40 no 3 pp 394ndash398 2008

[8] NADCA Energy Research Project ldquoSave energy (and money)clean your heating and air conditioning systemrdquo Report Status2012

[9] Energy Cost and Indoor Air Quality Project US EnvironmentalProtection Agency 2012 httpswwwepagovindoor-air-qual-ity-iaq

[10] ldquoAirflow pressure drop in HVAC ductworkrdquo CIBSE JournalAugust 2011

[11] Patent US 20030070544 System and Method for DeterminingFilterCondition 2003

[12] ldquoHVAC air filter monitor with sensor compensationrdquo Patent US20120318073 2012

[13] httpwwwenertekcompublicdocumentif0l7b9u7040610pdf[14] B Stephens A Novoselac and J A Siegel ldquoThe effects of filtra-

tion on pressure drop and energy consumption in residentialHVAC systems (RP-1299)rdquo HVAC amp R Research vol 16 no 3pp 273ndash294 2010

[15] Agenzia Regionale per la Protezione dellrsquoAmbiente della Cal-abria Monitoraggio della qualit a dellrsquoaria rete Edison diAltomonte httpwwwarpacalitallegatiEdisonRelazione2010pdf

[16] N F F Md Yusof N A Ghazali A S Yahaya N Sansuddinand W Al Madhoun ldquoCorrelation of PM10 concentration andweather parameters in conjunction with haze event in SeberangPerai Penangrdquo in Proceedings of The International Conferenceon Construction and Building Technology (ICCBT rsquo08) KualaLumpur Malaysia 2008

[17] A Afzali M Rashid B Sabariah and M Ramli ldquoPM10

pol-lution its prediction and meteorological influence in PasirGu-dang Johorrdquo IOP Conference Series Earth and EnvironmentalScience vol 18 Article ID 012100 2014


[18] K Siwek and S Osowski ldquoImproving the accuracy of predictionof PM

10pollution by the wavelet transformation and an ensem-

ble of neural predictorsrdquo Engineering Applications of ArtificialIntelligence vol 25 no 6 pp 1246ndash1258 2012

[19] J M Wallace and P V Hobbs Atmospheric Science An intro-ductory Survey Academic Press 2006

[20] D Banks An Introduction to Thermogeology Ground SourceHeating and Cooling Wiley-Blackwell 2012

[21] S Wang B Zhao B Zhou and Z Tan ldquoAn experimentalstudy on short-time particle resuspension from inner surfacesof straight ventilation ductsrdquo Building and Environment vol 53pp 119ndash127 2012

[22] httpwwwcameraitparlamleggideleghe10155dlhtm

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


controls the cleaning state of the system (filters and ducts) andalerts you when it is going toward bad working conditions

The aim of this paper is to present a noninvasive proce-dure for the automatic indoor air quality assessment whichdepends on cleaning conditions of HVAC system It is basedon a mathematical algorithm that processes a few on-sitephysical measurements that are acquired by dedicated sen-sors at suitable locations with a specific time tableThe outputof the algorithm is a set of indexes that provide a snapshot ofthe system with separated zoom on filters and ducts

The development of the method started in a project par-tially funded by Provincia di Roma (Technological Promotersfor Innovation 2011) and involving Tagliaferri srl and thepublic research institute for the Applications of Calculusof the National Research Council (IAC-CNR) The methodhas been patented in Italy (Patent number 102013902196398)with PCT extension (PCTIB2014064943) with evaluationwithout observations The patent derived from a need ofthe small enterprise (Tagliaferri srl) working in the field ofHVAC installation and maintenance The collaboration withthe scientific institution allowed formulating an innovativeand successful solution having high potential future devel-opment The partnership has been promoted and managedby the research transfer office of CNR by means of spe-cific and formal agreements between small enterprise andresearch institution These agreements aimed at regulatingintellectual property rights and market exploitation modal-ities In addition the role of research transfer office hasbeen fundamental in the definition of patentable contentsand in assuring its innovative contribution The patentedprocedure has several advantages with respect to the up-to-date monitoringchecking procedures

(1) It is not an invasive approach It does not alter thestandard operation mode of the system for examplea forced temporal halt

(2) It is based on a robust and portable protocol thatmakes it practical and simple andwith low implemen-tation costs

(3) It gives the opportunity of planning maintenanceintervention by limiting it only when standard HVACworking conditions need to be restored

(4) It allows independently evaluating the cleaning stateof both plant ducts and filters

The remainder of the paper is organized as follows InSection 2 some preliminary notions are given Section 3firstly describes the proposed model and then the practicalprocedure for plant checking Section 4 presents some exper-imental results concerning two representative case studiesFinally Section 5 draws the conclusions

2 Preliminary Background

This section provides some preliminary notions and modelassumptions They are necessary for a straightforward andclear description of the whole procedure


A B

Filter Ducts

HVAC

Figure 1 Sketch of HVAC system

21 Removal Efficiency of a Filter An HVAC system can besketched as in Figure 1 The air enters at point A and it isfiltered before being pumped into the building through airdistributing ducts Filters are commonly employed for multi-ple purposes [14] They allow reducing dust concentration inthe system in order to extend equipment life to reduce main-tenance costs and finally to control fine dust concentrationfor improved indoor air quality Even though particulate airpollution has different size in this paper we will focus onPM10 Air handling systems in buildings usually have twotypes of particulate air filters fibrous media filters and elec-tronic air cleanersTheymainly differ in the way they captureparticles the former act mechanically the latter use electriccharges Nonetheless they have comparable collection effi-ciency independently of particles size Based on this evidencethe removal efficiency of a filter is defined as the percentage ofPM10 that it gets hold Specifically if the upstreamPM10 con-centration is119862ext and the downstream PM10 concentration is119862int the removal efficiency of the filter is

120583119865=

119862ext minus 119862int119862ext

(1)

with 120583119865isin [0 1]

It is worth observing that filter removal efficiencyincreases over time because of its clogging Therefore byindicating with 120583

119865the removal efficiency of the unused filter

as provided by the manufacturer and with 120583(119905) the removalefficiency of the filter over time we expect that

120583 (119905) = 120583119865+ 120575120583 (119905) (2)

where 120575120583(119905) is an increasing and positive function of 119905

22 PM10 Measurements and Environmental Conditions Asconfirmed by several measurement surveys [15 16] PM10concentration depends on weather conditions such as tem-perature humidity atmospheric pressure and wind [17 18]as well as on natural and anthropic factors The pluralityof variables to be measured makes the evaluation of thecleaning state ofHVAC systems rather complex especially formonitoring purposes However since natural and anthropicfactors can be considered stable at least for a fixed timeinterval we can only deal with weather-dependent variablesIn addition their intradependencies allowus to select just twoof them as shown in the following

The relative humidity is defined as the ratio between thevapour in a given air volume and the one at saturation Asa result humidity equal to 100 means that air contains



119889


120579119889=

119887Ω

119886 minus Ω

with Ω =119886119879

119886 + 119879+ ln(

119880

100) 119886 = 1727 119887 = 2377

∘

(3)


119889depends on



119862 (119905) = 119891 (119879 (119905) 119880 (119905)) (4)







119862ext (119905) (5)









119862 (119905) = 120572119880 (119905) + 120573119879 (119905) + 120574 (6)




1 1199052 119905




119899minus 1199051)(119899 minus 1))

119894 = 1 2 119899 and let

C = [119862 (1199051) 119862 (119905

2) 119862 (119905

119899)] = [119862

1 1198622 119862

119899]

T = [119879 (1199051) 119879 (119905

2) 119879 (119905

119899)] = [119879

1 1198792 119879

119899]

U = [119880 (1199051) 119880 (119905

2) 119880 (119905

119899)] = [119880

1 1198802 119880

119899]

(7)


( ) = argmin(120572120573120574)isinR3

119899

sum

119894=1



119862 (119905) = 119880 (119905) + 119879 (119905) + (9)










Let Cnight = [119862(1199051) 119862(119905

119899)] Tnight = [119879(119905

1) 119879(119905

119899)]

and Unight = [119880(1199051) 119880(119905





1includes a long


119875 =10038171003817100381710038171003817Cnight

10038171003817100381710038171003817infin (10)


119904le 119905 then

119875 = 119878 + DCI (11)

where

119878 =1

119905119904minus 1199051

int

119905119904

1199051

119862 (119905) 119889119905 (12)


1 119905119904] isin Δ119879




DCI = 119875 minus 119878 gt 0 (13)


1 If DCI gt




119864 =1

1003816100381610038161003816Δ1198792

1003816100381610038161003816

intΔ1198792

119862ext (119905) 119889119905 (14)


2 Similarly

119868 =1

1003816100381610038161003816Δ1198793

1003816100381610038161003816

intΔ1198793

119862int (119905) 119889119905 (15)





120583HVAC =119864 minus 119868

119864 (16)


120583HVAC =119864 minus 119868

119864=

119864 minus [(1 minus 120583) 119864 + 119862duct]

119864

= 120583 minus119862duct119864

(17)






can be drawn


not


A

Yes

Yes

No

No




vent








DCI ge 0Inadequate

measurements

Ductsunder critical


conditions

DCI ge TOLL1









119865


FCI = 120583HVAC minus 120583119865 (18)


2(see Figure 3)



SI



FCI le TOLL2Low

Dirty plant


RSCI gt 2TOLL3High


Med

Dirty filters


FCI gt 2TOLL2High


Med

FCI ge 0


A

Yes No

No



RSCI =119878 minus (1 minus 120583) 119864

119878 (19)









0 10 20 30 40 50 60001

002

003

004

005

006

007

008

009

01

011

t

Cin

t

(a)

0 10 20 30 40 50 60002

004

006

008

01

012

014

t

Cin

t

(b)




0 10 20 30 40 50 60 70 80minus2

0

2

4

6

8

10

12

14

16

t

Cin

t

times10minus3




0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t







= 005120583119865 Furthermore

005120583119865







5 Conclusions



0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119889


120579119889=

119887Ω

119886 minus Ω

with Ω =119886119879

119886 + 119879+ ln(

119880

100) 119886 = 1727 119887 = 2377

∘

(3)


119889depends on



119862 (119905) = 119891 (119879 (119905) 119880 (119905)) (4)







119862ext (119905) (5)









119862 (119905) = 120572119880 (119905) + 120573119879 (119905) + 120574 (6)




1 1199052 119905




119899minus 1199051)(119899 minus 1))

119894 = 1 2 119899 and let

C = [119862 (1199051) 119862 (119905

2) 119862 (119905

119899)] = [119862

1 1198622 119862

119899]

T = [119879 (1199051) 119879 (119905

2) 119879 (119905

119899)] = [119879

1 1198792 119879

119899]

U = [119880 (1199051) 119880 (119905

2) 119880 (119905

119899)] = [119880

1 1198802 119880

119899]

(7)


( ) = argmin(120572120573120574)isinR3

119899

sum

119894=1



119862 (119905) = 119880 (119905) + 119879 (119905) + (9)










Let Cnight = [119862(1199051) 119862(119905

119899)] Tnight = [119879(119905

1) 119879(119905

119899)]

and Unight = [119880(1199051) 119880(119905





1includes a long


119875 =10038171003817100381710038171003817Cnight

10038171003817100381710038171003817infin (10)


119904le 119905 then

119875 = 119878 + DCI (11)

where

119878 =1

119905119904minus 1199051

int

119905119904

1199051

119862 (119905) 119889119905 (12)


1 119905119904] isin Δ119879




DCI = 119875 minus 119878 gt 0 (13)


1 If DCI gt




119864 =1

1003816100381610038161003816Δ1198792

1003816100381610038161003816

intΔ1198792

119862ext (119905) 119889119905 (14)


2 Similarly

119868 =1

1003816100381610038161003816Δ1198793

1003816100381610038161003816

intΔ1198793

119862int (119905) 119889119905 (15)





120583HVAC =119864 minus 119868

119864 (16)


120583HVAC =119864 minus 119868

119864=

119864 minus [(1 minus 120583) 119864 + 119862duct]

119864

= 120583 minus119862duct119864

(17)






can be drawn


not


A

Yes

Yes

No

No




vent








DCI ge 0Inadequate

measurements

Ductsunder critical


conditions

DCI ge TOLL1









119865


FCI = 120583HVAC minus 120583119865 (18)


2(see Figure 3)



SI



FCI le TOLL2Low

Dirty plant


RSCI gt 2TOLL3High


Med

Dirty filters


FCI gt 2TOLL2High


Med

FCI ge 0


A

Yes No

No



RSCI =119878 minus (1 minus 120583) 119864

119878 (19)









0 10 20 30 40 50 60001

002

003

004

005

006

007

008

009

01

011

t

Cin

t

(a)

0 10 20 30 40 50 60002

004

006

008

01

012

014

t

Cin

t

(b)




0 10 20 30 40 50 60 70 80minus2

0

2

4

6

8

10

12

14

16

t

Cin

t

times10minus3




0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t







= 005120583119865 Furthermore

005120583119865







5 Conclusions



0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















Let Cnight = [119862(1199051) 119862(119905

119899)] Tnight = [119879(119905

1) 119879(119905

119899)]

and Unight = [119880(1199051) 119880(119905





1includes a long


119875 =10038171003817100381710038171003817Cnight

10038171003817100381710038171003817infin (10)


119904le 119905 then

119875 = 119878 + DCI (11)

where

119878 =1

119905119904minus 1199051

int

119905119904

1199051

119862 (119905) 119889119905 (12)


1 119905119904] isin Δ119879




DCI = 119875 minus 119878 gt 0 (13)


1 If DCI gt




119864 =1

1003816100381610038161003816Δ1198792

1003816100381610038161003816

intΔ1198792

119862ext (119905) 119889119905 (14)


2 Similarly

119868 =1

1003816100381610038161003816Δ1198793

1003816100381610038161003816

intΔ1198793

119862int (119905) 119889119905 (15)





120583HVAC =119864 minus 119868

119864 (16)


120583HVAC =119864 minus 119868

119864=

119864 minus [(1 minus 120583) 119864 + 119862duct]

119864

= 120583 minus119862duct119864

(17)






can be drawn


not


A

Yes

Yes

No

No




vent








DCI ge 0Inadequate

measurements

Ductsunder critical


conditions

DCI ge TOLL1









119865


FCI = 120583HVAC minus 120583119865 (18)


2(see Figure 3)



SI



FCI le TOLL2Low

Dirty plant


RSCI gt 2TOLL3High


Med

Dirty filters


FCI gt 2TOLL2High


Med

FCI ge 0


A

Yes No

No



RSCI =119878 minus (1 minus 120583) 119864

119878 (19)









0 10 20 30 40 50 60001

002

003

004

005

006

007

008

009

01

011

t

Cin

t

(a)

0 10 20 30 40 50 60002

004

006

008

01

012

014

t

Cin

t

(b)




0 10 20 30 40 50 60 70 80minus2

0

2

4

6

8

10

12

14

16

t

Cin

t

times10minus3




0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t







= 005120583119865 Furthermore

005120583119865







5 Conclusions



0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










A

Yes

Yes

No

No




vent








DCI ge 0Inadequate

measurements

Ductsunder critical


conditions

DCI ge TOLL1









119865


FCI = 120583HVAC minus 120583119865 (18)


2(see Figure 3)



SI



FCI le TOLL2Low

Dirty plant


RSCI gt 2TOLL3High


Med

Dirty filters


FCI gt 2TOLL2High


Med

FCI ge 0


A

Yes No

No



RSCI =119878 minus (1 minus 120583) 119864

119878 (19)









0 10 20 30 40 50 60001

002

003

004

005

006

007

008

009

01

011

t

Cin

t

(a)

0 10 20 30 40 50 60002

004

006

008

01

012

014

t

Cin

t

(b)




0 10 20 30 40 50 60 70 80minus2

0

2

4

6

8

10

12

14

16

t

Cin

t

times10minus3




0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t







= 005120583119865 Furthermore

005120583119865







5 Conclusions



0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SI



FCI le TOLL2Low

Dirty plant


RSCI gt 2TOLL3High


Med

Dirty filters


FCI gt 2TOLL2High


Med

FCI ge 0


A

Yes No

No



RSCI =119878 minus (1 minus 120583) 119864

119878 (19)









0 10 20 30 40 50 60001

002

003

004

005

006

007

008

009

01

011

t

Cin

t

(a)

0 10 20 30 40 50 60002

004

006

008

01

012

014

t

Cin

t

(b)




0 10 20 30 40 50 60 70 80minus2

0

2

4

6

8

10

12

14

16

t

Cin

t

times10minus3




0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t







= 005120583119865 Furthermore

005120583119865







5 Conclusions



0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 60001

002

003

004

005

006

007

008

009

01

011

t

Cin

t

(a)

0 10 20 30 40 50 60002

004

006

008

01

012

014

t

Cin

t

(b)




0 10 20 30 40 50 60 70 80minus2

0

2

4

6

8

10

12

14

16

t

Cin

t

times10minus3




0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t







= 005120583119865 Furthermore

005120583119865







5 Conclusions



0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 60 700

001

002

003

004

005

006

007

008

009

01

t

Cin

t







= 005120583119865 Furthermore

005120583119865







5 Conclusions



0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 5 10 15 20 250

10

20

30

40

50

60

Time

Out

door

mea

sure

s

PM10T

U

PM10 reg

(a)

Time0 5 10 15 20 25

0

5

10

15

20

25

30

35

40

45

50

Indo

or m

easu

res

PM10T

U

PM10 reg

(b)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(c)

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Time

Indo

or m

easu

res

PM10T

U

PM10 reg

(d)




Competing Interests



Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Time0 5 10 15

05

055

06

065

07

075

08

085120583

HV

AC

(a)Time

0 5 10 15

065

075

085

095

07

08

09

120583H

VA

C

(b)



A B

Filter Ducts

HVAC

D


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article automatic and noninvasive indoor air

Documents