ABSTRACT

It is a fundamental task of HVAC to provide occupantsa healthy and comfort environment. By far more and more attention has been paidto indoor air quality(IAQ). Excellent indoor air ensures health of occupants.It has become a worldwide problem and caused many sick building syndromes(SBS)and building related illness(BRI), which can not be ignored. Indoor air qualitywould be one of the most important problems which developers, owners, proprietorscare more about before entering 21^st century.

But up to now, due to lack of accepted internationalspecific standard and uniform method of assessment on indoor air quality, inmany cases, some index and standards in assessment on outdoor atmosphere haveto be employed when assessing indoor air quality.  Stressing on thispoint, a new assessment system, based on fuzzy mathematics, is put forward inthis paper. A full-scale assessment on indoor air quality of 6 high-risebuildings in Shanghai is carried through. All data are from measurement onsite.

1.INTRODUCTION

Thereare thousands of pollutants in building. We can not measure every pollutantthat can impat occupant health and comfort, but we can select somerepresentative pollutants as indicator for different sort of indoorcontamination. The indicator and its reference value can provide a broadassessment of IAQ. The reasons for selecting indicators and their referencevalue are discussed as follows:

CO₂: Indoor CO₂ sproduced by the occupants and can be an useful indicator of the humanbioeffluents. ASHRAE Standard 62-1989 provides a recommended maximum CO₂level of 1000 ppm, according to ASHRAE, this level is not a health risk but isa surrogate for odors produced by humans.

CO: CO is an indicator of combustionactivities because it is produced by combustion processes associated with someactivities such as cooking, smoking and so on. If the building has anunderground garage, motor vehicle operation is a potential source of CO for theoccupied portion of the building. There are no standards for maximum CO levelsfor office environments, but other guidelines are available. A maximum COconcentration of 10 ppm was selected for assessment based on the continuousexposure level recommended by the World Health Organization. If indoor levelsof CO exceed 10 ppm it could indicate a significant indoor source.

Inhalable Particles: Particles that areless than 10 micron in diameter (referred to as PM10) are of concern in termsof human health. Particles is also an indicator for occupant activities. Thereference value of a maximum short-term concentration of 0.15 mg/m³is based on the Nation Ambient Air Quality Standards set forth by EPA. Thisreference value applied to inhalable particles that are less than or equal to10 micron in diameter.

When we need investigation more detailed,other parameters can be added, such as SO₂, NO_x, andbacteria, so as to investigate the indoor combustion activities in detail.

Indoorair pollution is a major occupational health problem in occupied environments.The objective assessment of indoor air quality is usually difficult due to thecocktail effect of various pollutants. IAQ problems are often multi-factorialand difficult to analyze independent effect. Now a newobjective assessment system, based on fuzzy mathematics, is put forward in thispaper.

Thedefinition of fuzzy itself is indefinite. There is no specific finitude betweentwo opposite concepts, but some quantitative difference belonging toartificialness. The instances are very common, such as “young” and “old”, “tall”and “short”, “fat” and “thin”, “cleanness” and “pollution”, etc.. Fuzzy casesin measurement of Indoor Air Quality (IAQ) are shown in the following table.

According as criterion of CO₂ ofJapan, there is some explicit but illogical finitude after careful analysisamong the parameters above, such as, because the criterion of NO₂ is50ppb,  concentration of indoor NO₂ of 50.01ppb, exceeding thestandard, belongs to be polluted, which can not be accepted by most people.

Indoor environment includes a lot ofpollutants, so definite evaluation can’t come from one pollutant. Ifconcentration of CO is 701vppm, between the first and the second grade, and atthe same time, another pollutant lies between the second and the third grade,then how we can evaluate the indoor air synthesizing all pollutants correctly?

Fuzzy mathematics figures out thisquestion. Now the mathematics model of fuzzy mathematics evaluation isintroduced first.

2.MATHEMATICSMODEL OF FUZZY MATHEMATICS EVALUATION

(1)Assorting Factors

In the following equation; j=1,2,…,n；k=1,2,…,p；

If there are n factors in the factors unitU: U={u₁,u₂,…,u_n}。

(2)Results Unit

Results unit is aggregate ofall possible results coming from final evaluation. If there is p possibleresults, the results unit may be : V＝(v₁,v₂,……,v_p)

(3)Factors Magnitude ValueUnit

According to the importanceof all factors in the factors unit, corresponding magnitude (value changingfrom 0~1) is given to every factor. If the magnitude value of the j factor u_jis a_j, there is factors magnitude unit: A＝(a₁,a₂,……,a_n)。

The sum of all factors magnitude value is 1and all of them can not be negative.

(4)Subject Value andSubject Function

If an evaluated object belongs to thefactor k, v_k, of results unit, its subject value is r_jk.

(5)The First Degree FuzzySynthetical Evaluation

Synthetical evaluation is carried out byall factors from factors unit. Evaluated by the factor j, u_j in thefactors unit, and If the evaluated object belongs to the factor k, v_k,of results unit, its subject value is r_jk, so the matrix of thefirst degree fuzzy synthetical evaluation is:

R=

there are n factors and p results

The first degree fuzzy syntheticalevaluation unit is B＝A°R

“°”is synthesis of fuzzy relationship.

3.THE FIRST DEGREE FUZZY SYNTHETICALEVALUATION OF IAQ

When evaluating indoor air quality, it isthe most important that factors unit, subject function and magnitude value arebuilt first.

(1) Factors Unit

Because of the real testing condition, weonly choose PM10 (u₁), CO₂ (u₂), CO (u₃),NO₂(u₄), and bacteria（u₅）as synthetical evaluation factors, so the factors unitis: u={u₁,u₂,u₃,u₄ , u₅}。

(2) Subject Function

Subject functionhas several form, such as triangle, trapezoid, and bell, etc., so we can chooseone by experience. Now we choose the simple and visual triangle function.

In the left graph, there is:

Variable X₁----The concentrationof cleanness;

Variable X₂----The concentrationof pollution;

Point A----random point, that is, thispoint can be considered as cleanness or pollution.

The subject function F₁(x), F₂(x)are:

F₁(x)＝ F₂(x)＝

Now except Japanese criterion of CO₂and bacteria (showing in Tab. 2 and Tab. 3), most criterion of indoor airpollutants have only one standard between polluted and unpolluted, which is notsuit for fuzzy evaluation. So on the basis of Chinese Atmosphere QualityStandard-- GB3095-96 (Tab. 4) and effect on human health of some mainpollutants, combined with the four- degree criterion put forward by World HealthOrganization in 1963, the three-degree criterion of Chinese AtmosphereQuality Standard, and Atmosphere Quality Standard (Tab.4), 定义各室内污染物的X₁、X₂of every indoor pollutants are defined as the following:

(3) Factors Magnitude ValueUnit

That is the magnitude of everypollutant in indoor air quality.

a_pm10=1/3、a_co2=1/3、a_co=1/9、a_no2=1/9、a_cfu=1/9。

According to harm on humanhealth, we consider that the most important pollutant are PM10 and CO₂,next is NO₂、CFU、CO.

4.THE FIRST DEGREE FUZZY SYNTHETICALEVALUATION OF TESTING BUILDINGS

Six buildings are tested in July andAutumn, 1999. The testing focus on the indoor air quality and many valuabledata are collected. The following is the first degree fuzzy syntheticalevaluation of testing buildings.

Evaluation resultfrom calculating program: Building D, E, F are polluted, and the other threeare clean.

5.CONCLUSION

From the first degree fuzzy syntheticalevaluation on six office buildings in Shanghai, the merit of fuzzy mathematicsevaluation is obvious, it can synthesize all undefinite elements in evaluation.But it has some shortcomings, for example, the result can not be classifiedinto several degrees for lack of clear degree standard, except for CO₂and bacteria. So, if the corresponding degree standard of several pollutants,such as NO_X, SO_2, O₃, CO, TSP, PM10, can bebuilt, the fuzzy mathematics evaluation method for IAQ will be improvedgreatly.

REFERENCE

1) Wang Fan, Fuzzy andEngineering Mathematics, Ha’ebin shipping Engineering Institute Publisher, 1988

2) Shen Jinming, Mao J., ObjectiveAssessment on IAQ in Shanghai Office Building, Journal of Ventilation andDust Control, 1995.4, p14-17

Wei Bai, Master, Department of Facility Engineering & Management, Tongji University,

Shanghai, P.R.China (200092)

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E-mail:logiccat@sina.com