© Acta hydrotechnica 20/33 (2002), Ljubljana
ISSN 0352-3551
351
UDK / UDC: 004.8:628.32 Prejeto / Received: 17.7.2002
Izvirni znanstveni prispevek – Original scientific paper Sprejeto / Accepted: 28.12.2002
UPORABA ODLOČ ITVENIH DREVES PRI MODELIRANJU
Č ISTILNE NAPRAVE ZA ODPADNO VODO
THE USE OF DECISION TREES IN THE MODELLING OF A
WASTEWATER TREATMENT PLANT
Nataša ATANASOVA, Boris KOMPARE
Č istilne naprave (Č N) za odpadno vodo so dinamič ni in kompleksni sistemi, katerih vodenje lahko
izboljšamo z različ nimi pristopi k modeliranju in napovedovanju delovanja Č N. V nalogi smo
poskušali zgraditi uporabne modele za napoved delovanja č istilne naprave z orodji strojnega
uč enja, toč neje z odloč itvenimi drevesi. Podatkovna baza, iz katere smo modele gradili, je
sestavljena iz enodnevnih povpreč nih merjenih podatkov na Č N. Poleg kvantitativnih podatkov je
baza sestavljena iz številnih kvalitativnih ocen, kakor tudi iz obsežne mikrobiološke analize.
Dosedanja obdelava podatkov je obsegala klasifikacijo podatkov z Linneo+ postopkom. Temu smo
dodali izgradnjo preprostih, a dovolj natanč nih modelov, ki predvidevajo funkcionalno stanje Č N
na podlagi merjenih (kvantitativnih) vhodnih podatkov. Za izgradnjo modelov smo uporabili
programski paket WEKA, ki ima vgrajeno več ino popularnih algoritmov strojnega uč enja.
Ključ ne besede: odpadna voda, č istilna naprava, modeliranje, strojno uč enje, odloč itvena drevesa
Wastewater treatment plants (WWTP) are dynamic and complex systems, the management of which
can be improved by different approaches to modeling and predicting their operation. Machine
learning tools (decision trees) were used to build useful prediction models for wastewater treatment
plant operation. The data base used for building the models is composed of measured quantitative
as well as qualitative data on the WWTP. We were also provided with a microbiological analysis.
The data are presented as a one-day situation of the plant operation. So far, classification of the
data was made using the Linneo+ methodology. We extended the knowledge gained by
classification by analyzing the classified data and constructing useful models that predict WWTP
operation from inflow data. The WEKA program package, which includes most of the popular
machine learning algorithms, was used for constructing the models.
Key words: wastewater, wastewater treatment plant, modeling, machine learning, decision trees
1 . UVOD
Biološko č išč enje odpadne vode predstavlja
vrsto procesov, s katerimi se odstranjujejo
nezaželene snovi iz vode – organsko
onesnaženje, dušik, fosfor. Procese izvajajo
različ ne vrste mikroorganizmov, ki za svoj
metabolizem (razvoj) uporabljajo onesnaženje
v vodi. Za uspešen potek č išč enja mora biti
zagotovljena ustrezna koncentracija mikro-
organizmov v bioreaktorju ter ustrezni pogoji,
v katerih lahko delujejo.
1 . INTRODUCTION
Biological treatment of wastewater is
composed of numerous complex processes by
which organic matter, nitrogen and phosphorus
are removed from water. The processes are
carried out by many different microorganisms,
using the compounds to be removed for their
metabolism. Adequate concentration and
conditions for growth of microorganisms must
be achieved in the bioreactor for successful
cleaning of wastewater.

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
352
Izredna kompleksnost in obč utljivost
procesov č išč enja vode otežuje optimalno
dimenzioniranje in vodenje č istilne naprave.
Modeliranje postaja nepogrešljivo orodje za
simulacijo in vodenje č istilne naprave. V svetu
se več inoma uporabljajo matematič ni modeli.
Toda dejavnike, kot so spremenljiva sestava
odpadne vode, ki doteka na č istilno napravo,
številne vrste mikroorganizmov, ki sodelujejo
pri procesu č išč enja, ter spremenljivi pogoji
delovanja č istilne naprave, je tako rekoč nemogoč e zajeti v matematič ne enač be brez
več jih poenostavitev in številnih predpostavk.
Tako imamo ali preveč sofisticirane modele, s
številnimi parametri, ali pa preproste modele,
ki pa imajo omejeno uporabnost.
Po drugi strani so tu orodja strojnega
uč enja, s katerimi lahko dobimo uporabne
preproste konceptualne modele (Kompare,
1995) na podlagi merjenih podatkov. Ti
modeli imajo svojo največ jo uporabnost pri
odkrivanju novega znanja med podatki ter
simulaciji (napovedi) novih situacij. Pri
strojnem učenju moramo ločiti med
pridobivanjem novega znanja iz podatkov in
izdelavo uporabnih modelov. V prvem primeru
nam algoritem sam ponuja soodvisnosti med
podatki in pravzaprav ne potrebujemo znanja s
področ ja uporabe (pridobivamo novo znanje).
Pri izdelavi uporabnih modelov pa moramo
vedeti, kaj želimo dobiti. Skrbno moramo
izbirati atribute, iz katerih bo model zgrajen,
ter paziti, da bo še dovolj natanč no
napovedoval.
V literaturi smo zasledili navedbe uporabe
nekaterih tehnik strojnega uč enja na merskih
podatkih na Č N za odpadno vodo. Dosedanja
analiza in obdelava teh podatkov je potekala v
smislu klasifikacije podatkov (Sanchez et al.,
1997; Comas et al., 1999) in odkrivanja
novega znanja in soodvisnosti med podatki z
različ nimi metodami umetne inteligence (Roda
et al., 1998; Comas et al., 2001, Belanche et.
al., 1999). Klasifikacija podatkov je bila
narejena s programom Linneo+, kateri so
avtorji potem kot področni strokovnjaki
dopisali funkcionalna stanja, tj. opis stanja, v
katerem deluje Č N. Zgrajen je bil model, ki
povezuje tako vhodne kot izhodne
spremenljivke s posamezno klasifikacijo.
Due to the complexity and sensibility of the
cleaning processes it is difficult to maintain
optimal operational conditions in a WWTP.
Therefore modelling is becoming a very useful
and commonly used tool for simulation and
control of a WWTP. Usually mathematical
models are used for modelling of a WWTP.
Since we are dealing with a dynamic and
complex process, the equations in every
mathematical model are more or less
simplified, meaning that they contain more or
less parameters which need to be estimated.
The complexity of the mathematical models
can vary. Thus, we have either too
sophisticated models with many parameters,
difficult to be estimated, or else simple models
with limited use.
On the other hand, machine learning tools
offer simple conceptual models (Kompare,
1995) built from a data set. This approach is
most suitable for discovering new knowledge
among measured data or predicting situations
in a specific domain. A distinction should be
made between knowledge acquisition and
constructing prediction models. In the first
case, the learning algorithm discovers
connections and dependencies among
measured data and we do not really need
specific knowledge of the domain. We are
gaining new knowledge . I f w e w a n t t o
construct useful prediction models then we
need to carry out the measurements in a proper
way and to make a choice of relevant data in
the domain, so that the models are built from
suitable attributes and predict the situations
with satisfactory accuracy.
The WWTP data set used in this paper was
found in the literature. So far analysis of the
data set includes classification of data
(Sanchez et al., 1997; Comas et al. 1999), and
knowledge discovery with different machine
learning tools (Roda et al., 1998; Comas et al.,
2001; Belanche et. al., 1999). Classification of
data, by which several clusters were obtained,
was made with Linneo+. Domain experts then
characterised and identified each cluster with a
different state or situation on the WWTP. New
knowledge was discovered by building a
decision tree, which is composed of
quantitative and qualitative data. The model
predicts situations obtained on the WWTP

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
353
Model odkriva zakonitosti, kot je na primer
povezava pojava napihnjenega blata z
ustreznimi mikroorganizmi, vendar pa tak
nač in ne omogoč a napovedovanja delovanja
Č N.
Glavni namen naše naloge je z uporabo
drugih (naprednih) tehnik strojnega uč enja
izlušč iti iz obstoječ ih podatkov še več znanja,
kot je bilo to storjeno do sedaj. Cilj naloge je
torej napovedati predhodno določ ena stanja
Č N (npr. plavajoč e blato) na podlagi meritev
na vtoku Č N. Tak model bi omogoč al
upravljalcem hitrejše odkrivanje težav pri
delovanju Č N in lažje odloč anje pri vodenju
Č N.
Poudarjamo, da so podatki pridobljeni
preko osebne komunikacije z avtorji prej
navedenih člankov, v obliki, kot so jo
uporabljali oni. Vse ostale obdelave podatkov
so navedene v tem č lanku.
2. Č ISTILNA NAPRA V A
Glavni elementi biološke č istilne naprave z
aktivnim blatom so: primarni usedalnik,
biološki reaktor in naknadni ali sekundarni
usedalnik. Surova odpadna voda doteka v
primarni usedalnik 1, kjer poteka mehansko
č išč enje tj. odstranjevanje usedljivih organskih
in anorganskih primesi. Nato gre voda v
biološki reaktor, kjer mikroorganizmi
razgrajujejo preostalo (neusedljivo) organsko
onesnaženje in ga uporabljajo za svojo rast.
Tako nastalo mešanico vode in biološkega
blata vodimo nato iz reaktorja v sekundarni
usedalnik, kjer se biološko blato prič ne
usedati, preostala vodna masa pa odteka naprej
v recipient. Usedlo biološko blato več inoma
recirkuliramo nazaj v reaktor in s tem
vzdržujemo zadostno koncentracijo biološkega
blata za uč inkovit potek č išč enja v reaktorju. V
primeru, da je dotok surove vode več ji, kot ga
prenese č istilna naprava, se višek  odpadne
vode razbremenjuje po razbremenilnem kanalu
preko primarnega usedalnika (SP3) v recipient.
Ta del odpadne vode ne vpliva na uč inek
č išč enja biološkega dela Č N. Obremenitev
obravnavane Č N je znač ilna za turistič na
mesta, saj je pozimi (30 000 populacijskih
enot) bistveno manj obremenjena kot poleti
(150 000 PE). Tehnološka shema obravnavane
Č N je prikazana na sliki 1.
using all data (quantitative, qualitative and
estimations). However such a model cannot be
used for predictions, i.e. for managing of the
WWTP.
The main goal of this paper is, by using
different (advanced) ML techniques, to gain
some more knowledge from given data, than
has been gained so far. Thus, we wanted to
predict the situations on the WWTP (i.e.
bulking sludge) from measured data on the
WWTP inflow. Such models can be of help in
detecting the conditions when operational
problems on the WWTP occur and in
managing the WWTP.
At this point we wish to stress that the data
were obtained by personal communications
with the previously cited authors, and in the
form as they were using them. All additional
processing of the data is described in this
article.
2. WWTP
An activated sludge WWTP contains three
main units: primary settler, aeration tank and
secondary settler or clarifier. The inflow of
raw wastewater is in primary settler 1, where
mechanical treatment is taking place. Water is
then transported to the aeration tank, where the
microorganisms carry out the biological
treatment. The produced mixture of water and
activated sludge is finally sent to the
secondary settler, where the flocks of
microorganisms settle down and clean water is
discharged to the recipient. The settled sludge
is recycled back to the aeration tank to
maintain a satisfactory concentration of
activated sludge for a successful treatment
process in the reactor. If the inflow to the
WWTP exceeds a certain value then the
bypass is activated. Excess water is led to
primary settler 3 and then discharged to the
recipient without any biological treatment.
This part of the wastewater does not affect
biological treatment of the WWTP. The load
of the WWTP under study is typical for tourist
resorts. It is much lower during the winter (30
000 PE) and then in summer (150 000 PE).
The configuration of the WWTP is presented
in Figure 1.

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
354
prim. used.1
prim. used.3
aerac.
bazen
sekund.
usedalnik
Dotok surove
odpadne vode
Efluent
SP1
SP3
AB
AT
EMIS
vzorč evalna mesta
AS
Inflow of 
waste water
prim. settler.1 aeration tank
sec.
settler
prim. settler.3
sampling points
razbr.
overflow
Effluent
Slika 1. Tehnološka shema č istilne naprave (Č N).
Figure 1 . Scheme of the water line of WWTP.
3. OPIS PODATKOVNE BAZE
3.1 MERJENI PODATKI (ATRIBUTI)
Visoka stopnja avtomatizacije Č N omogoč a
zapisovanje in shranjevanje več ine podatkov,
ki so znač ilni za delovanje Č N. Merjeni so
kvantitativni (preglednica 1) in kvalitativni
(preglednica 2) podatki. Kvantitativni podatki
vključ ujejo pretoke, analize odpadne vode in
biološkega blata na različ nih vzorč evalnih
mestih (AB, SP1, AS, AT, SP3), medtem ko
kvalitativni podatki vključ ujejo ocene samega
delovanja čistilne naprave ter obsežno
mikroskopsko analizo, iz katere so razvidne
vrste mikroorganizmov, ki sodelujejo v
procesu.
Podatki v bazi so podani za en dan oz. en
zapis v podatkovni bazi prikazuje enodnevno
situacijo delovanja čistilne naprave.
Uporabljena podatkovna baza je sestavljena iz
243 situacij (zapisov) in 63 atributov (merjenih
kvantitativnih in kvalitativnih podatkov na
vzorč evalnih mestih).
3. DATA BASE
3.1 MEASURED DATA
The WWTP has a high level of automation
that collects all the data measured on the plant.
Thus, we are dealing with a large amount of
historical data typical for a WWTP operation.
The data set is composed of quantitative data
(Table 1), such as flow rate, wastewater and
sludge analysis at different sampling points
(AB, SP1, AS, AT, SP3) and qualitative data
(Table 2), including estimations of WWTP
operation and sludge quality as well as large
microscopic analysis revealing microorganism
species involved in the treatment process.
The data are presented as average values
during one day, i.e. one record in the data set
represents a one-day situation of the WWTP
operation. There are 243 situations and 63
attributes (measured quantitative and
qualitative data at different sampling points,
listed in Table 1 and Table 2) in the database.

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
355
Preglednica 1. Kvantitativno merjeni podatki.
Table 1 . Quantitative data.
Oznaka atributa
Attribute
Opis
Description
Enota
Unit
Vzorč evalno mesto
Sampling point
Qp r e t o k
flow rate
m3/dan
m3/day
AB, SP1, SP3
DQO kemijska potreba po kisiku
chemical oxygen demand
mg/l AB, SP1, SP3, AT, EMIS
DBO5 biokemijska potreba po kisiku
biochemical oxygen demand
mg/l AB, SP1, SP3, AT, EMIS
SST suspendirani delci
total suspended solids
mg/l AB, SP1, SP3, AT, EMIS
NKT amonijak in organski dušik
total kjeldhal nitrogen
mg/l AB, AT
N-NH4 amonijak
ammonium
mg/l AB, AT
NO2 nitrit
nitrite
mg/l AT
NO3 nitrat
nitrate
mg/l AT
PH PH log[H
+
]A B , A T
COND prevodnost
conductivity
µ Siemens/cm AB, AT
TERB motnost (NTU)
turbidity
NTU AB, AT
CL slanost
chlorine
mg/l AB, AT
V30 volumen blata po 30min usedanju
sludge volume after 30min settling
ml AT
LM-B masa vseh delcev biološkega blata
mixed liquor suspended solids
g/l AT
MLVSS masa organskega dela biološkega blata
mixed liquor volatile suspended solids
g/l AT
IVF indeks blata
sludge volume index
ml/g AT
SST-R recirkulacija blata
recirculation
m
3
/dan
m
3
/day
AT
CM obremenitev blata
food to microorganism ratio
DBO5/(MLSS*dan)
DBO5/(MLSS*day)
AT
TRC starost blata
sludge retention time
dan
day
AT

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
356
Preglednica 2. Kvalitativno ocenjeni podatki.
Table 2. Qualitative data.
Atribut
Attribute
Opis
Description
ESC-B pene v aeracijskem bazenu
presence of foam at the aeration tank
FLOC prisotnost flokul v sekundarnem usedalniku
presence of activated sludge flocs at the secondary
settler
ASP-AT ocena kvaliteta efluenta
quality of the final treated water
ASP-FLOC ocena flokul
microscopic appearance of the activated sludge floc
ZOO Zooglea
NOC Nocardia
A21N/THIO 021N/Thiothrix
A41 A41
MICO Microthrix parvicella
FILAM-DOMI dominantna vrsta nitastih bakterij
dominant filamentous bacteria
NFILAM število vrst nitastih bakterij
number of different filamentous bacteria
ASPID Aspidisca
EUPL Euplotes
VORT Vorticella
EPIST Epystylis
OPER Opercularia
CIL-CAR Carnivorous ciliates
GPROTO-DOMI Dominantna vrsta praživali
dominant protozoa-group
BIODIV-MIC št. različ nih mikroorganizmov
biodiversity of the microfauna
G-FLAG bič karji > 20µ m
flagellates > 20µ m
P-FLAG bič karji < 20µ m
flagellates < 20µ m
AMEB Amoebae
AMEB-TECA Testate Amoebae
ROTIFERS Rotifers
3.2 RAZREDI PODATKOV
Vsaka situacija v obravnavani bazi
merjenih podatkov ima določen razred.
Razredi so bili določ eni s programom Linneo+
(Sanchez et al., 1997; Comas et al., 1999), ki
uporablja koncept razdalje med objekti (zapisi
v podatkovni bazi). Klasifikacija je potekala v
dveh korakih: (1) Določ anje skupin podobnih
primerov (zapisov v bazi) na podlagi razdalje
in (2) Ovrednotenje dobljenih skupin s strani
strokovnakov. Dobljene razrede so analizirali,
3.2 CLASSIFICATION OF DATA
Linneo+ has been used for classification of
the data (Sanchez et al., 1997; Comas et al.,
1999). It is an unsupervised learning method
that determines clusters of the data. The
methodology implemented can be considered
as a two-step task: (1) Clustering, which
determines useful subsets of data using the
conventional concept of distance between
objects, and (2) Validation of the subsets by
experts. The obtained subsets are accepted or

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
357
modificirali in interpretirali strokovnjaki.
Vsaki skupini je bilo pripisano funkcionalno
stanje, v katerem deluje Č N. Dobljeni razredi
so prikazani v preglednici 3.
rejected by experts and identified with a
different state or situation on the WWTP
operation. The clusters are depicted in Table 3.
Preglednica 3. Razredi podatkov.
Table 3. Classes of data.
Opis razreda
Class description
Oznaka
Mark
Št. primerov
No. of
examples
Nornalno delovanje Č N pozimi
Normal WWTP-operation in winter days
c1 81
Normalno delovanje Č N poleti
Normal WWTP-operation in summer days
c2 55
Optimalno delovanje Č N poleti
Summer days with optimal WWTP-operation
c11 24
Deževje
Rainy days
c3 3
Nevihte
Storm days
c4 3
Podobremenitev (obdobje po dežju)
Underloading (final period of a storm)
c5 12
Nitrifikacija
Nitrification
c7 2
Denitrifikacija v sekundarnem usedalniku (dviganje blata)
Denitrification in the secondary settler (rising)
c13 7
Deflokulacija (motnost efluenta zaradi majhnih bič karjev)
Deflocculation (effluent turbidity due to small-flagellates)
c8 5
Plavajoč e blato zaradi Thiotrix-a (vpliv na efluent)
Bulking sludge due to Thiotrix (affecting the effluent)
c9 3
Zač etek in konec plavajoč ega blata zaradi Thiotrix-a
Beginning and end of a strong bulking-sludge episode due to Thiotrix
c14 2
Peneč e blato, ki ga povzroč a Mcrothrix (normalna diverziteta mikrofavne)
Foaming sludge due to Microthrix (with normal microfauna biodiversity)
c10 17
Peneč e blato, ki ga povzroč a Mcrothrix (nizka diverziteta mikrofavne in
dominairajo bič karji < 20 µ m)
Foaming sludge due to Microthrix (with very low microfauna biodiversity and
dominant < 20 µ m flagellates)
c18 1
Peneč e blato, ki ga povzroč a Mcrothrix (in plavajoč e blato zaradi Zooglee)
Foaming sludge due to Microthrix (and viscous bulking due to Zooglea)
c19 6
Peneč e blato, ki ga povzroč a Nocardia, ki vpliva na proces
Foaming sludge due to Nocardia, affecting the process
c15 4
Peneč e blato, ki ga povzroč a Nocardia, ki vpliva na proces (odplavljanje delcev)
Severe foaming sludge due to Nocardia, affecting the process (loss of solids)
c16 5
Peneč e blato, ki ga povzroč a Nocardia in zastopanje bič karjev < 20 µ m
Foaming sludge due to Nocardia with abundant < 20 µ m flagellates
c17 8
Sprememba konfiguracije Č N iz zimskega v letno obdobje
Winter-summer Plant configuration change
c20 3
Preobremenitev
Overloading
c6 1
Klorni šok
Chlorine shock
c12 1

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
358
4. UPORABLJENE METODE
Odloč itvena drevesa so ena izmed uč nih
shem (opisov) danega pojma ali koncepta, ki
jo generira uč ni algoritem iz danih primerov
tega pojma. Primere podajamo v preglednici
tako, da je en primer (ena vrstica v
preglednici) sestavljen iz atributov t.j.
neodvisnih spremenljivk in razreda primera t.j.
odvisnih spremenljivk. Razred predstavlja
pojem, ki se ga algoritem nauč i napovedovati.
Za ponazoritev si poglejmo preprost primer.
Koncept, ki se ga želimo nauč iti, je uporaba
prevoznega sredstva. Vprašamo se, kdaj (v
kakšnih vremenskih pogojih) uporabiti kolo in
kdaj avto. V preglednici 4 je podano 9
primerov, iz katerih se bo algoritem uč il
koncepta.  Primere sestavljajo naslednji opisi
(atributi): sonč no, temperatura in dež. Zadnja
kolona v preglednici (prevozno sredstvo)
predstavlja razred primera.
4. METHODS
Decision trees are one of the learning
schemes of a given concept, generated by a
learning algorithm from given instances of that
concept. The instances are presented in a table,
each row being an instance and the column
being a description i.e. an attribute of the
instance or an independent variable. One of the
columns contains the values of the instances
class (dependant variable), which is the
concept to be learned by the algorithm. The
following example will illustrate the
methodology. Let the means of transportation
be the concept to be learned, i.e. when (under
what circumstances) to use a bike and when to
use a car as a means of transportation. There
are nine examples, depicted in Table 4, that
will be used to learn the concept. The
examples have the following descriptors
(attributes): sunny, temperature and rain. The
last column (means of transportation) contains
the values of each examples class.
Preglednica 4. Preprost primer uč enja koncepta.
Table 4. Simple example of concept learning.
Primer
Example
Sonce
Sunny
Temperatura
Temperature
Dež
Rainy
prevozno sredstvo
means of  transportation
1D a
Yes
Visoka
High
Ne
No
Kolo
Bike
2D a
Yes
Srednja
Med
Ne
No
Kolo
Bike
3D a
Yes
Nizka
Low
Ne
No
Avto
Car
4N e
No
Visoka
High
Da
Yes
Avto
Car
5N e
No
Srednja
Med
Da
Yes
Avto
Car
6N e
No
Nizka
Low
Da
Yes
Avto
Car
7N e
No
Visoka
High
Ne
No
Kolo
Bike
8N e
No
Srednja
Med
Ne
No
Kolo
Bike
9N e
No
Nizka
Low
Ne
No
Avto
Car

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
359
V obravnavani podatkovni bazi je primer
podan za posamezen dan delovanja Č N,
atributi so merjene in ocenjene količ ine na
vzorč evalnih mestih Č N, razred pa je opis
delovanja Č N, ki je odvisen od meritev na Č N,
t.j. podanih atributov za vsak primer.
Najpogosteje uporabljen algoritem za
generacijo odloč itvenih dreves je Top-Down
Induction of  Decision Trees (Quinlan, 1986;
Bratko et.al., 1999), ki se glasi:
1. Podani niz primerov (S) se razdeli na
podnize (S
i
) glede na izbrani najboljši
atribut tako, da imajo vsi primeri v podnizu
isto vrednost izbranega atributa. V
zgornjem primeru atribut dež razdeli
celotni niz na dva podniza: prvi niz so tisti
primeri, ki imajo vrednost tega atributa
DA, drugi pa tisti, ki imajo vrednost
atributa NE. Vsak podniz predstavlja
vozlišč e v drevesu. Najboljši atribut se
izbere avtomatsko z rač unanjem entropije
in pridobitvijo informacije.
2. Vsak podniz predstavlja vozlišč e drevesa.
Č e so vsi primeri v podnizu S
i
 istega
razreda, potem se ustvari list drevesa s tem
razredom, sicer pa se postopek ponovi za S
= S
i
.
Č e algoritem apliciramo na podani primer,
dobimo odloč itveno drevo na sliki 2. Drevo
ima dve vozlišč i (dež in temperatura) in štiri
liste (kvadrati). Na vrhu drevesa je atribut dež.
Č e je vrednost enaka DA, uporabljamo avto,
sicer pa se vprašamo, kakšna je temperatura.
Č e je VISOKA oz. SREDNJA, se peljemo s
kolesom, č e je NIZKA, pa z avtom. Glede na
podane primere, se je algoritem nauč il, da
sonce ne igra nobene vloge pri uporabi
prevoznega sredstva in ga zato ni vstavil v
odloč itveno drevo.
Algoritem deluje za diskretne vrednosti
atributov. Č e imamo opravka z zveznimi
vrednostmi, lahko uvedemo diskretizacijo
zveznih atributov. Postavimo mejne vrednosti
intervalov atributa, ki jih nato obravnavamo
kot diskretne vrednosti. Recimo, da ima atribut
temperatura namesto nominalnih realne
vrednosti (preglednica 5). Potem bi
odloč itveno drevo izgledalo, kot kaže slika 3.
In the presented database an example is
given for one day of WWTP operation, the
attributes are measured and the estimated data
on the sampling points and class provides a
description of a WWTP operation for each
day.
A commonly used algorithm for induction
of decision trees is Top-Down Induction of
Decision Trees (Quinlan, 1986; Bratko et.al.,
1999):
1. A given set of examples (S) is divided into
subsets (S
i
) according to the best attribute,
so that all examples in the subset have an
equal value of the chosen attribute. For
instance attribute rain in the presented
example would divide the given set of nine
examples into two subsets: the first one
having all examples with the value of
attribute rain YES, and second one
containing all examples that have the value
NO standing for the attribute rain. The best
attribute is chosen by calculating the
entropy and information gained.
2. Each subset represents a node in the tree
and if all examples in a subset have same
class, then a leaf is created, otherwise the
procedure is repeated for S = S
i
.
When applied on our example the algorithm
constructs the decision tree shown in Figure 2.
The tree has two nodes (rain and temperature)
and four leaves (ends of the branches). The
attribute rain is on top of the tree. If the value
of rain is YES, then we use a car, or else we
ask about the temperature. If it is HIGH or
MED then we ride a bike and if LOW we use a
car. According to the given examples the
algorithm has learned that the attribute sunny
is not important for the concept and therefore
can not be found in the tree.
This algorithm works for discrete attributes.
If we are dealing with continuous attributes,
then binarization of the numeric attributes can
be applied i.e. thresholding their ranges into
pairs of subintervals, that are treated as
symbols. Suppose that attribute temperature
has real (continuous) values instead of nominal
(Table 5). Then the decision tree would look
as shown in Figure 3.

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
360
(RAIN)
(TEMP)
(CAR)
(CAR) (BIKE)
DEŽ
TEMPERATURA
AVTO
KOLO
AVTO
KOLO
= DA (YES) = NE (NO)
=VISOKA =NIZKA
(BIKE)
HIGH LOW
=SREDNJA
MID
Slika 2. Odloč itveno drevo preprostega primera.
Figure 2. Decision tree of a simple example.
Preglednica 5. Primer z zveznim atributom.
Table 5. Example with continuous attribute.
Primer
Example
Sonce
Sunny
Temperatura
Temperature
Dež
Rainy
Prevozno sredstvo
Transportation means
1D a
Yes 25
Ne
No
Kolo
Bike
2D a
Yes 15
Ne
No
Kolo
Bike
3D a
Yes 5
Ne
No
Avto
Car
4N e
No 22
Da
Yes
Avto
Car
5N e
No 10
Da
Yes
Avto
Car
6N e
No 7
Da
Yes
Avto
Car
7N e
No 30
Ne
No
Kolo
Bike
8N e
No 14
Ne
No
Kolo
Bike
9N e
No 2
Ne
No
Avto
Car

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
361
DEŽ
TEMPERATURA
AVTO
AVTO
= DA (YES) = NE (NO)
<= 7
> 7
KOLO
(RAIN)
(TEMP)
(CAR)
(CAR) (BIKE)
Slika 3. Odloč itveno drevo, zgrajeno iz nominalnih in numerič nih atributov.
Figure 3. Decision tree induced from nominal and numeric attributes.
5. IZVEDENE ANALIZE
(EKSPERIMENTI)
Loč iti moramo med pridobivanjem novega
znanja in izdelavo uporabnih modelov za
napoved delovanja Č N. V prvem primeru
lahko izberemo poljubno spremenljivko za
odvisno, t.j. za razred primera, ki jo
napovedujemo na podlagi vseh podanih
atributov. Z uč nim algoritmom odkrivamo
njihovo povezanost oz. odvisnost med sabo. V
tem primeru se lahko zgodi, da odkrivamo
trivialne soodvisnosti.
Pri izdelavi uporabnih modelov pa mora biti
razred, ki ga napovedujemo, odvisna
spremenljivka, atributi, iz katerih je model
zgrajen, pa striktno neodvisne spremenljivke,
da ne bi dobili trivialnih povezav. V našem
primeru želimo kvalitativne (ocenjene)
podatke napovedati iz merjenih
(kvantitativnih), ki so na voljo.
5.1 SELEKCIJA POMEMBNEJŠIH
ATRIBUTOV
Modeli, ki jih želimo zgraditi, naj bi dali
odgovore na vprašanja, kot so: Kaj pomeni
določ en dotok na Č N? Kaj se zgodi, č e se
obremenitev poveča ali pomanjša? Kako
vplivajo karakteristike biološkega blata na
proces č išč enja? itd. Za konstrukcijo takih
modelov je treba najprej izbrati ustrezne
atribute, iz katerih bo model zgrajen. To so
predvsem kvantitativno merjeni podatki in so
5. EXPERIMENTS
A distinction should be made between
knowledge discovery from data and building
prediction models on WWTP operation. In the
first case we can pick any attribute to be a
dependent variable, i.e. the class which is
predicted from all given attributes. The
learning algorithm discovers connections and
dependencies between data, where also trivial
dependencies can be found.
If we want to construct useful prediction
models then the class which is predicted has to
be a dependent variable, while the attributes
from which the model is built need to be
independent variables. In our case, the models
should predict qualitative data from the
measured (quantitative) data that are available.
5.1 SELECTION OF RELEVANT
ATTRIBUTES
Models to be constructed should give
answers to questions like: What is the
influence of a specific inflow on WWTP
operation? What happens if the load of WWTP
increases or decreases? What is the influence
of sludge characteristics on the treatment
process? and so on. The first step in building
such models is selection of relevant attributes
(Table 6), from which the model is built.
These are mainly quantitative data, measured

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
362
upravljalcem na voljo oz. jih lahko predvidijo
za določ ena obdobja, npr. dotok na Č N poleti
ali pozimi. Izbrani atributi so prikazani v
preglednici 6.
on regular bases and usually available to the
manager. These data can also be predicted in
certain periods of the year, e.g. inflow to the
WWTP in summer or winter.
5.2 REDUKCIJA OBSTOJEČ IH
RAZREDOV
Z razvrščanjem podatkov v skupine,
upoštevajoč vseh 63 atributov, je bilo v izvirni
podatkovni bazi določeno 20 razredov
(Sanchez et al., 1997; Comas et al., 1999).
Glede na številč nost primerov, ki spadajo v
nek razred, vidimo, da od dvajsetih izstopa le
nekaj razredov: c1 (81 primerov), c2 (55
primerov), c11 (24 primerov), c10 (17
primerov). Č e pa želimo da se algoritem nauč i
nekega razreda (pojma), mora imeti dovolj
primerov (opisov) tega razreda, na podlagi
katerih se uči. Odločitveno drevo, ki
napovedujejo vse razrede, ne glede na
številčnost primerov, odkriva soodvisnosti
med atributi in razredi, vendar pa je precej
veliko in nepregledno (Comas et al., 2001).
Redukcijo smo naredili tako, da smo združili
vse razrede, ki opisujejo probleme z blatom iz
različ nih razlogov (c9, c10, c14 do c19) v en
razred cb (preglednica 7).
5.2 REDUCTION OF CLASSES
There were 20 clusters determined using the
linneo+ classification (Sanchez et al., 1997;
Comas et al., 1999). But according to the
number of instances belonging to a specific
cluster only a few clusters can be depicted: c1
(81 examples), c2 (55 examples), c11 (24
examples), c10 (17 examples). These clusters
can be easily learned by the algorithm, since
they have enough descriptions. If we want to
predict all clusters (also those which have only
one example) then we expect the decision tree
to be big and not understandable (Comas et al.,
2001). Therefore in our analysis we reduced
the number of clusters by joining all clusters
that describe sludge problems for different
reasons (c9, c10, c14 to c19) into one cluster
cb (Table 7). Now we have 46 examples
belonging to this class and we expect the
algorithm to learn to predict this class
properly.
Preglednica 6. Izbira pomembnejših atributov.
Table 6. Choice of relevant attributes.
Vzorč evalno mesto
Sampling point
Atributi
Attribute
AB Q, DQO, DBO5, SST, NKT, N-NH4, PH, COND, TERB, CL
SP1 Q, DQO, DBO5, SST
SP3 Q, DQO, DBO5, SST
PODATKI O BIOLOŠKEM BLATU
SLUDGE DATA
V30, LM-B, IVF,  MLVSS,  SST-R, CM, TRC

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
363
Preglednica 7. Reducirani razredi (z 20 na 13).
Table 7. Reduction of classes (from 20 to 1 3).
Opis razreda
Class description
Oznaka
Class
Št. Primerov
Number of examples
Nornalno delovanje Č N pozimi
Normal WWTP-operation in winter days
c1 81
Normalno delovanje Č N poleti
Normal WWTP-operation in summer days
c2 55
Optimalno delovanje Č N poleti
Summer days with optimal WWTP-operation
c11 24
Deževje
Rainy days
c3 3
Nevihte
Storm days
c4 3
Podobremenitev (obdobje po dežju)
Underloading (final period of a storm)
c5 12
Nitrifikacija
Nitrification
c7 2
Denitrifikacija v sekundarnem usedalniku (dviganje blata)
Denitrification in the secondary settler (rising)
c13 7
Problemi z biološkim blatom
Sludge problems
cb 46
Sprememba konfiguracije Č N iz zimskega v letno obdobje
Winter-summer plant configuration change
c20 3
Preobremenitev
Overloading
c6 1
klorni šok
Chlorine shock
c12 1
5.3 UPOŠTEVANJE Č ASOVNEGA
SOSLEDJA PRI MERJENIH PODATKIH
Glede na navedbe o nač inu vzorč evanja
sklepamo, da so podatki v bazi podani kot
povprečen enodnevni podatek. Prave
informacije nimamo, vendar predpostavljamo,
da so podatki v bazi podani zaporedno s
korakom en dan oz. z enodnevnim zamikom.
V izvirni podatkovni bazi je klasifikacija v
razrede opravljena glede na podane atribute za
isti dan. To pomeni, da vtoč ni parametri
vplivajo na kakovost biološkega blata še isti
dan, kar pa ne drži povsem. Č e se kakšen dan
pojavi problem plavajočega blata, je to
posledica vtoč nih parametrov merjenih pred
enim ali dvema dnevoma. Zato smo zapise v
podatkovni bazi spremenili tako, da vsak zapis
vsebuje vrednosti posameznega atributa, ki so
se pojavile pred enim oz. dvema dnevoma
(preglednica 8). Oznaka ATT-n pomeni
vrednost atributa ATT, ki se je pojavila pred n
dnevi. Npr. DQO-1 pomeni vrednost atributa
DQO pred enim dnevom.
5.3 INCORPORATING TIME DELAY
ATTRIBUTES
Data in the database are presented as one-
day average values of the measured attributes,
and one record represents a one-day situation
on the WWTP. We assume that the records are
given with a one-day step and without too
many missing days. Classes (situations) of the
records are determined with respect to the
attributes given for the same day, meaning that
sludge quality is a result of the inflow from the
same day. Based on the assumption that, in
reality, problems with bulking sludge can not
appear on the same day as they are presented
in the data set, we incorporated a one- and
two-day delay for sludge problems. Thus, we
added new attributes which describe the
obtained classes as a result of one or two days
before inflow. The records are changed so that
each record has information on values of the
specific attribute that occurred one and two
days before. In Table 8 are given the new
attributes where the sign ATT–n denotes the
value of attribute ATT that occurred n days
ago, e.g. DQO-1 denotes the value of attribute
DQO one day ago.

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
364
Preglednica 8. Upoštevanje č asovnega zamika pri atributih.
Table 8. Incorporated time delay among measured attributes.
Vzorč evalno mesto
Sampling point
Atributi
Attributes
AB Q, DQO, SST, COND, Q-1, DQO-1, SST-1, COND-1, Q-2, DQO-2, SST-2, COND-2
SP1 DQO, SST, DQO-1, SST-1, DQO-2, SST-2
SP3 Q, Q-1, Q-2
AT DQO, SST, NH4, NO3, DQO-1, SST-1, NH4-1, NO3-1, DQO-2, SST-2, NH4-2, NO3-2
PODATKI O BIOLOŠKEM BLATU
SLUDGE DATA
LM-B, IVF, SST-R, CM, TRC
OCENE
ESTIMATIONS
ESC-B, FLOC, ASP-AT, ESC-B-1, FLOC-1, ASP-AT-1, ESC-B-2, FLOC-2, ASP-AT-2
6. REZULTATI
Za konstrukcijo modelov smo uporabili
programski paket WEKA, ki vsebuje več ino
popularnih algoritmov strojnega uč enja. Za
indukcijo odloč itvenih dreves je bil razvit
algoritem J48.
Podatkovno bazo razdelimo na uč no
množico, na podlagi katere se model zgradi,
ter testno množico, na kateri program
ovrednoti natančnost modela. Napovedani
razredi so v listih drevesa, kjer se vidi tudi
natančnost napovedovanja posameznih
razredov. Prva številka pomeni število
primerov, uvršč enih v ta razred, druga pa
število nepravilno uvrščenih primerov.
Zgradili smo tri modele, ki imajo svojo
uporabnost pri vodenju Č N, saj napovedujejo
njeno delovanje na podlagi kvantitativnih
atributov, merjenih na vhodu Č N.
6.1 M1 – NAPOVED VSEH RAZREDOV
NA PODLAGI VHODNIH ATRIBUTOV
Prič ujoč i model naj bi napovedoval vseh 20
razredov. Vendar pa imajo nekateri razredi
premalo primerov (opisov), da bi jih lahko
napovedovali z razumljivo velikim drevesom.
Zato smo z rezanjem zgradili manjše in
razumljivejše drevo z natančnostjo 71.2
odstotka na testni množici podatkov, ki pa
napoveduje le razrede, ki imajo več primerov:
c5, c1, c10, c2 in c11 (slika 4). Model je
zgrajen iz petih atributov Q-SP3, DQO-SP1,
Q-AB, Q-SP1 in LM-B. Na vrhu drevesa se
6. RESULTS
We used the WEKA package to build the
models. WEKA incorporates most of the
popular machine learning algorithms that can
be applied to a dataset and analyses its output
to extract information about the data.
Algorithm J48 was developed for induction of
decision trees.
The data set is divided into a learning set
used to build the model (scheme), and test data
used to determine the model accuracy. In the
leaves of the tree are the predicted classes.
There are two numbers in each leaf. The first
means the number of the examples going to
the leaf and the second is for misclassified
examples. We built three models, which can
be of help in managing the WWTP, since they
predict the WWTP operation according to the
inflow data.
6.1 M1 – PREDICTING ALL CLASSES
FROM INFLOW ATTRIBUTES
Model M1 is built to predict all 20 classes.
Due to the small number of examples
describing some of the classes, the tree that
predicts all classes is not understandable.
Therefore we used the pruning option and built
an understandable and smaller tree with
71.2 % accuracy on test split, predicting only
the classes that have more descriptions: c5, c1,
c10, c2 and c11 (Figure 4). The model is built
of five attributes: Q-SP3, DQO-SP1, Q-AB,
Q-SP1 and LM-B. The model put the attribute
Q-SP3, which describes the flow rate in the

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
365
nahaja atribut Q-SP3, ki opisuje pretok po
razbremenilnem kanalu. Č e je manjši od 929,
model napove razred c1 (dobro delovanje
pozimi) in razred c2 (dobro delovanje poleti) v
veji, kjer je Q-SP3 < 929. Torej  na podlagi
vrednosti atributa Q-SP3 lahko sklepamo, ali
gre za zimski (zunaj turistič ne sezone) oz. letni
č as (v turistič ni sezoni) delovanja Č N.
bypass and on top of the tree. According to
this attribute value we can decide if the
WWTP is operating in winter or in summer
(tourist season). We can expect class c1
(normal operation in winter) if Q-SP3 < 929
according to the model. Similarly we can find
the class c2 (normal operation in summer) in
the branch where Q-SP3 > 929.
Q-SP3
DQO-SP1
Q-AB
Q-SP1
LM-B
c5
c1 
c10 
c2 
c2 c11 
<= 929
<= 270
<= 10859
<= 9197
<=
2.38
> 929
> 270 > 10859
> 9197
> 2.38
Slika 4. Odloč itveno drevo modela M1.
Figure 4. Decision tree of model M1 .
6.2 M2 – NAPOVED REDUCIRANIH
RAZREDOV
Iz istega razloga kot pri modelu M1 smo
tudi pri izgradnji modela M2 uporabili
možnost rezanja. Orodje je avtomatsko našlo
štiri najpomembnejše atribute, iz katerih je
nato zgrajen model (Q-SP3, Q-AB, Q-SP1 in
LM-B). Od podanih razredov iz preglednice 7
pa napoveduje naslednje: c1, cb, c2 in c11
(slika 5). Natanč nost, ki jo dosega, znaša 73.9
odstotka na testni množici podatkov. Torej,
dosega več jo natanč nost od modela M1. Na
vrhu drevesa se nahaja atribut Q-SP3, podobno
kot prejšnji primer.
6.2 M2 – PREDICTION OF REDUCED
CLASSES
For the same reason as with model M1 we
used the pruning option to build model M2.
The algorithm has found four important
attributes of which the model is built (Q-SP3,
Q-AB, Q-SP1 and LM-B). From the classes
given to the model (Table 7) only c1, cb, c2
and c11 are predicted (Figure 5) with accuracy
73.9 % on test split. Thus, it is a little more
accurate then M1. Similarly to M1 attribute,
Q-SP3 is on top of the tree.

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
366
Q-SP3
Q-AB
Q-SP1
LM-B
c1 
cb 
c2 
c2 
c11 
<= 929
<= 10859
<= 9197
<=
2.38
> 929
> 10859
> 9197
> 2.38
Slika 5. Odloč itveno drevo modela M2.
Figure 5. Decision tree of model M2.
6.3 M3 - UPOŠTEVANJE Č ASOVNEGA
ZAMIKA
Model je zgrajen iz atributov, ki opisujejo
časovno zakasnitev (preglednica 8) in
napoveduje reducirane razrede z natanč nostjo
kar 75.3 odstotka. V modelu (slika 6)
nastopajo le trije atributi (Q-SP3, Q-AB-2, Q-
SP1) in štirje razredi (c1, cb, c11, c2).
6.3 M3 – INCORPORATING TIME
DELAY
The model is predicting the following
classes: c1, cb, c11, and c2, using the attributes
that incorporate time delay (Table 8).
Accuracy achieved is 75.3 % on test split.
Only three attributes are needed for this
prediction: Q-SP3, Q-AB-2 and Q-SP1
(Figure 6).
Q-SP3
Q-AB-2
Q-SP1
c1 
cb
c2
c11 
<= 567
<= 10662
> 567
> 10662
<=9197
> 9197
Slika 6. Odloč itveno drevo modela M3.
Figure 6. Decision tree of model M3.

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
367
7. DISKUSIJA
Temeljni pogoj za konstrukcijo uporabnih
in natanč nih modelov na podlagi merjenih
podatkov je dovolj velika, kakovostna in
ustrezno izdelana podatkovna baza.
Obravnavana Č N ima možnost zapisovanja
velikega števila podatkov, vendar pa ima kar
nekaj težav:
1. Velikost podatkovne baze je relativno
majhna (243 zapisov) glede na število
atributov (63) in število razredov (20).
2. Nač in merjenja atributov. V tem primeru je
ena situacija delovanja Č N prirejena na
enodnevni interval, kar pomeni, da se
vpliva vtoč nih parametrov na kakovost
iztoka in kskovost blata ne vidi v celoti. To
težavo smo poskušali rešiti z upoštevanjem
ustreznega č asovnega zamika med atributi,
ki se vidi pri modelu M3. Model dosega
večjo natančnost in prispeva k več ji
informiranosti.
3. Vprašljiva je tudi konsistentnost
kvalitativnih podatkov. Atribut FLOC
opisuje stanje flokul, vendar zavzema le
problematič ne vrednosti, medtem ko opisa
dobrega delovanja ne zasledimo.
Domnevamo, da bi to lahko bile
manjkajoč e vrednosti tega atributa. Atribut
torej nima pozitivnih vrednosti in ga zato ne
moremo napovedovati, t.j. algoritem bi se
učil pojma na nepopolnih primerih.
Vprašljiv je tudi atribut ASP-FLOC, ki
podaja oceno flokul b.b. Plavajoč e blato
(fangflotant) ima enkrat oceno 1, drugič pa
oceno 2 ali več (preglednica 9).
Nekonsistentnost se pojavlja tudi v
povezavi z indeksom blata (IFV). Med
podatki zasledimo za isti dan delovanja Č N
normalno vrednost volumskega indeksa
blata IFV (100 do 150) in hkrati plavajoč e
blato. Zato smo napovedovanje
kvalitativnih atributov opustili.
4. Razredi, ki naj bi jih napovedovali, so
preveč natanč no določ eni oz. jih je bilo
preveč . Č e bi želeli napovedovati vse
razrede, bi bilo odloč itveno drevo temu
ustrezno veliko in nerazumljivo, hkrati pa
preveč specifič no (preveč prilagojeno uč ni
množici). Zato smo z izbiro rezanja zgradili
7. DISCUSSION
Preparation of data is one of the most
important, difficult and time-consuming steps
in the knowledge acquisition process. Good
quality of data is often the key to success in
making predictions. The analysed data set had
several problems:
1. The data set was quite small (243 records)
in relation to the number of measured
attributes (63) and classes (20).
2. Data preparation and measurements. Each
situation on the WWTP consists of
attributes average values during the day,
which does not reveal the complete
influence of the inflow data to outflow
characteristics and on sludge quality. We
tried to solve this problem by incorporating
a time delay among the attributes. Model
M3 has highest accuracy and contributes to
better information
3. Consistency of qualitative data. Attribute
FLOC describes the quality of flocks, but it
only has negative values and no positive
values i.e. good operation. There are a lot
of missing values, so we assume that
positive values are some of the missing
ones. Thus the attribute has no positive
values and therefore cannot be predicted
since the algorithm would learn the concept
on incomplete examples (descriptions). The
value of this attribute should be in
correlation with attribute ASP-FLOC,
which is an estimation (mark from 1 to 4)
of the flocs. But the same value of FLOC
(i.e. fangflotant) corresponds ones to mark
1 and ones to mark 2 or more (Table 9).
Attribute IFV (sludge volume index) is also
inconsistent. The value of 100 to 150
corresponds to bulking sludge. For all these
reasons we omitted prediction of the
qualitative attributes.
4. According to the number of instances
belonging to a specific cluster, the clusters
were determined too accurately. If we want
to predict all clusters (also those which
have only one example) then we expect the
decision tree to be big and not

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
368
manjše, bolj posplošene, hkrati pa
razumljive in dovolj natanč ne modele, ki pa
napovedujejo le tiste razrede, v katere sodi
več je število primerov.
understandable. So in our analysis we used
the pruning option and built smaller and
understandable trees, that predict only those
clusters with more examples.
Preglednica 9. Prikaz neustreznosti podatkov v bazi.
Table 9. Presentation of data inconsistency.
IVF SSVLM-B SST-R CM TRC ESC-B FLOC ASP-AT ASP-FLOC WWTP
194 1.49 4.5 0.31 4.81 2 fangflotant 1 2 c8
186 1.07 3.21 0.41 8.23 1 ? 2 ? c1
469 1.68 5.94 0.24 7.58 3 desfloculacio 2 2 c1
374 1.82 4.05 0.37 7.87 2 desnitrificacio 2 1 c1
?????2?2?c 1
? ? ? ? ? 1 fangflotant 2 3 c1
Kljub naštetim težavam smo zgradili nekaj
uporabnih modelov, iz katerih lahko
razberemo kar nekaj zakonitosti in informacij
pri delovanju obravnavane Č N. Najbolj oč itno
je, da se težave pojavljajo v turistič ni sezoni,
ko imamo več ji dotok na Č N in se zato
aktivira razbremenilni kanal. Vsi modeli (M1,
M2 in M3) postavljajo na vrhu drevesa atribut
Q-SP3 (pretok v razbremenilnem kanalu).
Dokler je manjši od določ ene vrednosti (926
m
3
/dan glede na modela M1 in M2 oz. 526
m
3
/dan po modelu M3), napovedujejo modeli
razred c1 (dobro delovanje pozimi). V tej veji
drevesa ne zasledimo težav z biomaso. Edino
model M1 napoveduje podobremenitev (razred
c5) v zimskem č asu in sicer č e je DQO-SP1
(koncentracija KPK) < 270 mg/l (glej sliko 4).
Težave z blatom zasledimo v veji dreves,
kjer je Q-SP3 več ji od zgoraj omenjenih
vrednosti, oz v času turistične sezone.
Turistič na sezona torej predstavlja prevelik
obremenitveni šok (hidravlič ni), ki ga naprava
rešuje z razbremenjevanjem (preko SP3).
Istočasno je koncentracija organskega
onesnaženja na Č N manjša zaradi več je porabe
vode na prebivalca v poletnem č asu. To
povzroč a, da se nitaste bakterije v flokulah
hitreje razvijejo (ker jim je hrana lažje
dostopna kot ostalim) oz. napihnjeno blato.
Obič ajno so te posledice razvidne nekaj dni
po nizko obremenjenem (biokemijsko) vtoku
na Č N. Model, ki upošteva č asovno
zakasnitev, je zelo preprost in razumljiv,
In spite of all these difficulties we
constructed three useful models that discover
certain knowledge and information about
WWTP operation. The most obvious
information revealed from the models is that
problems appear during the tourist season,
when the inflow increases and bypass is
activated. All models (M1, M2 and M3) put
the attribute Q-SP3 (flow rate in the bypass)
on the top of the tree. We can expect class c1
(normal operation in winter) until Q-SP3 is
less than certain value (929 m
3
/day according
to models M1 and M2 or 526 according to
model M3). In this branch of the trees there are
no sludge problems. Only model M1 predicts
class c5 (underloading) in winter time if DQO-
SP1 (COD concentration) < 270 mg/l (see
Figure 4).
Sludge problems can be found in the
branches where Q-SP3 is greater than 929 or
526, i.e. in summer (tourist season.). It is clear
that in summer (tourist season) the plant is
hydraulically overloaded, which is solved by
activating the overflow bypass. At the same
time organic matter concentration
(microorganisms food) decreases due to
greater water consumption per capita, i.e. the
wastewater is more diluted. This causes
bulking sludge, since the filamentous bacteria
in flocks develop faster (better food access).
These consequences are usually visible
after a few days of underloaded
(biochemically) inflow to the plant. This is

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
369
dosega pa kar veliko natanč nost. Za razliko od
modelov M1 in M2, ki napovedujta težave z
blatom na podlagi vtoka na Č N istega dne,
model M3 napoveduje problem plavajoč ega
blata v turistič ni sezoni (pri Q-SP3 > 567
m
3
/dan) na podlagi pretoka skozi AB pred
dvema dnevoma. Č e je dotok na č istilno
napravo izpred dveh dni (Q-AB-2) manjši od
10 662 m
3
/dan ter iztok iz primarnega
usedalnika 1 manjši od 9 197 m
3
/dan, potem
lahko prič akujemo težave z blatom (slika 6).
confirmed by model M3, which incorporates
time delay attributes. The model is very simple
and understandable and achieves quite high
accuracy. M3 predicts sludge problems during
the tourist season, i.e. when Q-SP3 > 567
m
3
/dan according to the flow rate through AB,
two days before. If the inflow to the WWTP
two days ago was less than 10 662 m
3
/dan and
the flow rate through point SP1 is less then
9 197 m
3
/dan, then we can expect sludge
problems (see Figure 6).
8. ZAKLJUČ KI
Iz podane podatkovne baze, merjene na Č N
za odpadno vodo, smo poskušali z
odloč itvenimi drevesi predvideti delovanje
Č N. Kljub pomankljivostim v podatkovni bazi,
smo s selekcijo relevantnih atributov
(domenski ekspert) in redukcijo razredov
uspeli zgraditi modele, ki so uporabni pri
vodenju Č N, še zlasti pa pri odkrivanju težav,
ki se pojavljajo na Č N.
Uvedba č asovne zakasnitve se je izkazala
kot dobra rešitev, saj je model zelo preprost,
dosega pa največ jo natanč nost in prispeva k
več ji informiranosti.
Nač in merjenja in klasificiranja podatkov je
bistvenega pomena za konstrukcijo uporabnih
odloč itvenih dreves. Za poveč anje natanč nosti
modelov bi bilo smiselno ustrezno poveč ati
bazo podatkov, ali pa prestrukturirati zapise v
podatkovni bazi tako, da bo en zapis
predstavljal dejansko situacijo delovanja Č N.
Podatki na iztoku iz Č N bi morali biti rezultat
vtoč nih podatkov in ne povpreč ne dnevne
vrednosti. Potrebna bi bila tudi klasificikacija
podatkov z drugo, fleksibilnejšo metodo.
ZAHV ALA
Del raziskave je nastal v okviru seminarja
“Analiza ekoloških podatkov z orodji umetne
inteligence”, katerega nosilec je bil dr. Sašo
Džeroski. Sredstva za podiplomsko
raziskovalno usposabljanje prve avtorice je
omogoč ilo Ministrstvo za šolstvo, znanost in
šport Republike Slovenije po pogodbi št.
S2-792-020/19443/99.
8. CONCLUSIONS
We used the given data set measured on
WWTP to predict WWTP operation by
constructing decision trees. By selecting
relevant attributes and reducing the classes we
built three models that can be used in
managing the plant and revealing the problems
that occur in WWTP operation.
Incorporating time delay attributes appeared
to be a good solution. Model M3 is very
simple, has the highest accuracy and extracts
more information.
Data preparation and classification is a
crucial step in constructing useful decision
trees. To increase the accuracy of the
constructed models it would be necessary to
enlarge the database or reorganise the data, so
that one record would represent the actual
situation of the treatment process. Outflow
data should be a result of the inflow data and
not average values during the day. Also the
classification of data should be done by some
other method.
ACKNOWLEDGEMENTS
Part of this research was elaborated within
the seminar “Analysis of Environmental Data
with Machine Learning Methods”, conducted
by Dr. Sašo Džeroski. The postgraduate study
of the first author was subsidised by the
Ministry of Education, Science and Sport of
the Republic of Slovenia (contract No. S2-
792-020/19443/99).

Atanasova N., Kompare B.: Uporaba odloč itvenih dreves pri modeliranju č istilne naprave za odpadno vodo
– The Use of Decision Trees in the Modelling of a Waste Water Treatment Plant
© Acta hydrotechnica 20/33 (2002), 351-370, Ljubljana
370
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Naslova avtorjev – Authors’ Addresses
mag. Nataša Atanasova
Univerza v Ljubljani – University of Ljubljana
Fakulteta za gradbeništvo in geodezijo – Faculty of Civil and Geodetic Engineering
Inštitut za zdravstveno hidrotehniko – Institute of Sanitary Engineering
Jamova 2, SI–1000 Ljubljana, Slovenia
E–mail: natanaso@fgg.uni-lj.si
izr. prof. dr. Boris Kompare
Univerza v Ljubljani – University of Ljubljana
Fakulteta za gradbeništvo in geodezijo – Faculty of Civil and Geodetic Engineering
Inštitut za zdravstveno hidrotehniko – Institute of Sanitary Engineering
Jamova 2, SI–1000 Ljubljana, Slovenia
E–mail: bkompare@fgg.uni-lj.si