W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
/W
a
t
e
r s
u
pp
l
y
a
n
d
s
e
w
age
I
n
t
r
o
d
u
ct
i
on
Water
D
i
s
tributi
o
n Net
wo
r
k
(W
D
N)
m
o
delling i
s
a
s
peciali
s
ed field
w
ithin envi-
r
o
nmental engineering and W
D
N man-
agement that gained pr
o
minence t
ow
ard
s
the end
o
f the 20th centur
y
w
ith the devel-
o
pment and
s
ub
s
equent
w
ide
s
pread
ad
o
pti
o
n
o
f a m
o
delling
s
o
ft
w
are
.
Thi
s
advancement enabled re
s
earcher
s
and
engineer
s
t
o
e
x
pl
o
re ne
w
the
o
rie
s
w
hile
all
ow
ing c
o
mmercial enterpri
s
e
s
t
o
further
enhance m
o
delling capabilitie
s
.
The rapid
pr
o
gre
ss
in inf
o
rmati
o
n, c
o
mputati
o
n, and
c
o
mmunicati
o
n techn
o
l
o
gie
s
ha
s
pr
o
vided
acce
ss
t
o
va
s
t am
o
unt
s
o
f data
.
H
ow
ever,
it ha
s
al
s
o
intr
o
duced challenge
s
in han-
dling diver
s
e data t
y
pe
s
,
s
uch a
s
w
ater
meter reading
s
[
2
]
and t
o
p
o
l
o
gical data
fr
o
m
G
e
o
graphic
I
nf
o
rmati
o
n S
y
s
tem
(
G
I
S)
s
o
ft
w
are, a
s
de
s
cribed in detail b
y
D
i Nard
o
et al
.
[
3
].
The aim
o
f thi
s
article i
s
t
o
highlight
s
pecific a
s
pect
s
o
f h
y
draulic m
o
delling that
required e
x
ten
s
ive pr
o
ce
ss
ing, achieved
thr
o
ugh e
s
tabli
s
hed c
o
ncept
s
in data
s
ci-
ence
.
While the
s
e individual meth
o
d
s
ma
y
n
o
t be particularl
y
n
o
vel, their integrati
o
n
int
o
a
s
tructured heuri
s
tic frame
wo
r
k
c
o
uld
o
ffer valuable in
s
ight
s
f
o
r m
o
deller
s
, lectur-
er
s
, and
s
tudent
s
ali
k
e
.
C
a
s
e
st
u
d
y
a
r
ea
The
s
tud
y
area
s
elected f
o
r
o
ur re
s
earch
i
s
a high-pre
ss
ure
z
o
ne (HP
Z
)
w
ithin the
w
ater di
s
tributi
o
n net
wo
r
k
in Wr
o
cła
w
(
F
ig-
ure 1)
.
I
t c
o
mpri
s
e
s
five
D
i
s
trict
M
eter
A
rea
s
(
D
M
A
s
),
w
ith pre
ss
ure maintained b
y
a pumping
s
tati
o
n
.
A
lth
o
ugh there are mul-
tiple c
o
nnecti
o
n
s
t
o
o
ther
D
M
A
s
, the
s
e are
cl
o
s
ed in dail
y
o
perati
o
n
s
.
The HP
Z
w
a
s
I
mp
l
eme
n
t
i
n
g
da
t
a
sc
i
e
n
c
e
t
o
e
nh
a
n
c
e
w
a
t
e
r
d
i
st
ri
b
u
t
i
on
syst
em
m
o
de
lli
n
g
.
A
c
a
s
e
st
u
d
y
of
b
u
il
d
i
n
g
h
y
d
r
a
u
li
c
m
o
de
l
of
h
i
g
h
-
p
r
e
ss
u
r
e
z
on
e
i
n
W
r
o
cł
a
w
Wyk
o
r
z
yst
a
n
i
e
da
t
a
sc
i
e
n
c
e
d
o
u
s
p
r
a
w
n
i
e
n
i
a
m
o
de
l
o
w
a
n
i
a
h
y
d
r
a
u
li
c
z
n
eg
o
s
i
e
c
i
w
o
d
o
c
i
ąg
o
wyc
h.
P
r
z
y
pade
k
b
u
d
o
wy
m
o
de
l
u
st
r
e
f
y wys
o
k
i
eg
o
c
i
ś
n
i
e
n
i
a
w
e
W
r
o
cł
a
w
i
u
K
AR
O
L
D
Y
K
I
E
R
T, W
O
JC
I
E
CH C
I
E
Ż
A
K, P
I
O
T
R
B
R
Ó
D
K
A
DO
I 10
.
36119/15
.
2025
.
10
.
6
Thi
s
s
tud
y
pre
s
ent
s
the devel
o
pment and calibrati
o
n
o
f a h
y
draulic m
o
del f
o
r a high-pre
ss
ure
z
o
ne (HP
Z
)
w
ithin the
w
ater di
s
tributi
o
n net
wo
r
k
(W
D
N)
o
f Wr
o
cła
w.
The
wo
r
k
f
o
cu
s
e
s
o
n advanced data pr
o
ce
ss
ing meth
o
d
s
and
calibrati
o
n technique
s
t
o
impr
o
ve m
o
del accurac
y
, dra
w
ing up
o
n e
s
tabli
s
hed c
o
ncept
s
fr
o
m b
o
th envir
o
nmental
engineering and data
s
cience
.
O
ur re
s
ult
s
indicate a ver
y
g
oo
d m
o
del fit, alth
o
ugh
w
ith min
o
r inc
o
n
s
i
s
tencie
s
regarding pipe r
o
ughne
ss
calibrati
o
n
.
The
o
verall appr
o
ach dem
o
n
s
trate
s
h
ow
the integrati
o
n
o
f
s
tati
s
tical, h
y
draulic,
and
o
ptimi
s
ati
o
n technique
s
can lead t
o
r
o
bu
s
t and reliable W
D
N m
o
delling,
s
upp
o
rting b
o
th academic and
o
perati
o
nal need
s
.
Ke
ywo
rd
s
:
w
ater di
s
tributi
o
n
s
y
s
tem m
o
delling, data
s
cience,
w
ater di
s
tributi
o
n net
wo
r
k
, ev
o
luti
o
nar
y
alg
o
rithm,
heuri
s
tic appr
o
ach, artificial intelligence
W prac
y
o
m
ów
i
o
n
o
bud
ow
ę i
k
alibrację m
o
delu h
y
draulic
z
neg
o
Stref
y
W
y
s
ok
ieg
o
Ci
ś
nienia (SWC), będącej c
z
ę-
ś
cią
s
ieci
wo
d
o
ciąg
ow
ej mia
s
ta Wr
o
cła
w.
O
pi
s
an
o
wy
brane a
s
pe
k
t
y
met
o
d
yk
i
z
z
a
k
re
s
u anali
z
y
i
o
br
ó
b
k
i dan
y
ch
w
ej
ś
ci
owy
ch (prepr
o
ce
ss
ingu), p
o
pra
w
iające d
ok
ładn
o
ś
ć m
o
delu, ba
z
ujące na r
ó
ż
n
y
ch techni
k
ach
wyko
r
z
y
s
t
yw
a-
n
y
ch
w
in
ż
y
nierii
ś
r
o
d
ow
i
s
k
a
o
ra
z
data
s
cience
.
O
tr
z
y
mane
wy
ni
k
i
w
s
k
a
z
ują na
wy
s
ok
ą ja
ko
ś
ć
k
alibracji m
o
delu
h
y
draulic
z
neg
o
, ja
kko
l
w
ie
k
z
a
o
b
s
er
wow
an
o
dr
o
bne nie
ś
ci
s
ł
o
ś
ci
w
k
alibracji chr
o
p
ow
at
o
ś
ci
w
e
w
nętr
z
n
y
ch
ś
cian
pr
z
e
wo
d
ów
wo
d
o
ciąg
owy
ch
.
O
prac
ow
ana met
o
d
yk
a p
ok
a
z
uje, i
ż
d
z
ię
k
i p
o
łąc
z
eniu met
o
d
s
tat
y
s
t
y
c
z
n
y
ch,
h
y
draulic
z
n
y
ch
o
ra
z
techni
k
o
pt
y
mali
z
ac
y
jn
y
ch
o
tr
z
y
man
y
m
o
del h
y
draulic
z
n
y
je
s
t
w
iar
y
g
o
dn
y
i
o
dp
ow
iedni
z
ar
ów
-
n
o
d
o
prac
y
nau
kow
ej ja
k
i
z
a
s
t
o
s
ow
ań pra
k
t
y
c
z
n
y
ch
.
Sł
ow
a
k
luc
z
ow
e
:
m
o
del
s
ieci
wo
d
o
ciąg
ow
ej, data
s
cience,
s
ieć
wo
d
o
ciąg
ow
a, alg
o
r
y
tm e
wo
luc
y
jn
y
, heur
y
s
t
yk
a,
s
z
tuc
z
na inteligencja
ME
ng Kar
o
l
Dyk
iert http
s
:
//
o
rcid
.o
rg/0009-0003-6168-7352
‒
M
unicipal Water and Se
w
erage C
o
mpan
y
(
M
PWiK) in Wr
o
cła
w
, P
o
land,
F
acult
y
o
f
E
nvir
o
nmental
E
ngineering, Wr
o
cła
w
Univer
s
it
y
o
f Science and Techn
o
l
o
g
y
, P
o
land,
F
acult
y
o
f
I
nf
o
rmati
o
n and C
o
mmunicati
o
n
Techn
o
l
o
g
y
, Wr
o
cła
w
Univer
s
it
y
o
f Science and Techn
o
l
o
g
y
, P
o
land
D
E
ng W
o
jciech Cie
ż
a
k
http
s
:
//
o
rcid
.o
rg/0000-0001-6210-8728
‒
F
acult
y
o
f
E
nvir
o
nmental
E
ngineering, Wr
o
cła
w
Univer
s
it
y
o
f Science and
Techn
o
l
o
g
y
, P
o
land
A
ss
o
c
.
Pr
o
f
.
D
E
ng Pi
o
tr
B
r
ó
d
k
a http
s
:
//
o
rcid
.o
rg/0000-0002-6474-0089
‒
F
acult
y
o
f
I
nf
o
rmati
o
n and C
o
mmunicati
o
n Techn
o
l
o
g
y
, Wr
o
cła
w
Univer
s
it
y
o
f Science and Techn
o
l
o
g
y
, P
o
land
.
40
A
dre
s
d
o
ko
re
s
p
o
ndencji/ C
o
rre
s
p
o
nding auth
o
r
:
k
ar
o
l
.
d
yk
iert
@
p
w
r
.
edu
.
pl
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl10/202541
W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
e
s
tabli
s
hed t
o
acc
o
mm
o
date the
s
ignificant
number
o
f high-ri
s
e apartment building
s
that
require elevated
w
ater pre
ss
ure
.
The data
s
et
pr
o
vided b
y
the
M
unicipal Water and Se
w
-
erage C
o
mpan
y
in Wr
o
cła
w
(
M
PWiK)
w
a
s
s
upplemented b
y
the temp
o
rar
y
in
s
tallati
o
n
o
f h
y
drant pre
ss
ure meter
s
f
o
r the peri
o
d
o
f
11 September 2023
–
24 September
2023, c
o
vering a t
o
tal
o
f 14 da
y
s
.
D
ue t
o
time c
o
n
s
traint
s
and vari
o
u
s
o
ther fact
o
r
s
,
h
y
drant di
s
charge te
s
t
s
w
ere n
o
t c
o
nducted
a
s
part
o
f the calibrati
o
n pr
o
ce
ss
.
Net
wo
r
k
c
o
nditi
o
n
s
w
ere a
ss
e
ss
ed pri
o
r t
o
the pre
s
-
s
ure mea
s
urement
s
thr
o
ugh
o
perati
o
nal h
y
-
drant te
s
t
s
, and
s
ub
s
equentl
y
b
y
revie
w
ing
W
D
N malfuncti
o
n and event l
o
g
s
.
The
m
o
del parameter
s
and net
wo
r
k
characteri
s
-
tic
s
are
s
ummari
s
ed in Table 1
.
M
a
t
e
ri
a
l
s
a
n
d
me
t
ho
d
s
The h
y
draulic m
o
del
w
a
s
devel
o
ped
u
s
ing the c
o
mmercial
s
o
ft
w
are
M
I
K
E
+
,
pr
o
vided b
y
M
PWiK
.
A
ll e
x
ternal data
prepr
o
ce
ss
ing
w
a
s
c
o
nducted in P
y
th
o
n,
utili
s
ing the Panda
s
[
13
]
,
[
16
]
, NumP
y
[
8
]
,
and
M
atpl
o
tlib
[
10
]
librarie
s
.
The m
o
del-
ling pr
o
ce
ss
primaril
y
f
o
ll
ow
ed the e
s
tab-
li
s
hed meth
o
d
o
l
o
g
y
o
utlined b
y
Wal
s
k
i
[
18
].
A
brief
o
vervie
w
o
f the
wo
r
k
fl
ow
i
s
pre
s
ented in
F
igure 2
.
F
o
r the purp
o
s
e
o
f m
o
del calibrati
o
n
a
ss
e
ss
ment,
w
e empl
oy
ed the
Roo
t
M
ean
Squared
E
rr
o
r (
R
M
S
E
)
[
9
]
and the c
o
effi-
cient
o
f determinati
o
n (
R
2
)
[
4
].
R
M
S
E
quantifie
s
the average deviati
o
n bet
w
een
o
b
s
erved and m
o
del-predicted value
s
,
w
hile
R
2
pr
o
vide
s
a
s
tati
s
tical mea
s
ure
o
f
h
ow
w
ell the regre
ss
i
o
n line appr
o
x
imate
s
the actual data di
s
tributi
o
n
.
The
y
are de-
fined b
y
the f
o
ll
ow
ing equati
o
n
s
:
^
ii
‒
i
Where n i
s
the number
o
f
o
b
s
ervati
o
n
s
,
y
repre
s
ent
s
mea
s
ured value
s
,
y
repre
s
ent
s
value
s
calculated b
y
the m
o
del,
y
i
s
the
mean
o
f
o
b
s
erved value
s
.
The
k
e
y
a
s
pect
s
o
f
o
ur appr
o
ach are
o
utlined bel
ow.
I
n
i
t
i
a
l
p
i
pe
r
ou
g
hn
e
ss
a
ss
e
ss
me
n
t
The initial ta
s
k
inv
o
lved a
ss
igning pre-
liminar
y
pipe r
o
ughne
ss
value
s
.
I
n acc
o
r-
dance
w
ith the e
s
tabli
s
hed te
x
tb
ook
,
w
e
empl
oy
ed re
s
earch fr
o
m 1981
[
12
]
that de-
tailed Ha
z
en-William
s
C-fact
o
r value
s
f
o
r
vari
o
u
s
material
s
,
w
ith particular empha
s
i
s
o
n ca
s
t ir
o
n pipe
s
o
f differing age
s
and
s
ubjected t
o
var
y
ing
w
ater qualit
y
level
s
,
characteri
s
ed b
y
their degree
o
f attac
k
(c
o
r-
r
o
s
ivene
ss
)
.
Thi
s
c
o
n
s
iderati
o
n
w
a
s
e
s
pe-
ciall
y
critical, given that appr
o
x
imatel
y
45
%
o
f the pipe
s
in the area are c
o
mp
o
s
ed
o
f
ca
s
t ir
o
n
.
A
t the
s
ame time, the remaining
material
s
that e
x
hibit
s
caling are pre
s
ent in
c
o
n
s
iderabl
y
l
ow
er pr
o
p
o
rti
o
n
s
.
B
a
s
ed
o
n
thi
s
re
s
earch,
w
e devel
o
ped an initial frame-
wo
r
k
f
o
r the a
ss
ignment
o
f pipe r
o
ughne
ss
.
We interp
o
lated r
o
ughne
ss
value
s
c
o
rre-
s
p
o
nding t
o
m
o
derate attac
k
f
o
r ca
s
t ir
o
n
pipe
s
acr
o
ss
different diameter
s
t
o
e
s
tabli
s
h
a range
o
f a
ss
ignable value
s
(
F
igure 3)
.
F
i
g
u
r
e
1
.
Hy
d
r
a
u
li
c
m
o
de
l
of
H
P
Z
i
n
Wr
o
-
cł
a
w
.
P
i
pe
c
o
l
ou
rs
de
no
t
e
DMA
a
ss
i
g
n
me
n
ts
;
g
r
e
y
p
i
pe
s w
e
r
e
e
x
c
l
u
ded
f
r
o
m
t
h
e
f
i
n
a
l
c
a
li
b
r
a
t
i
on
st
age
(
s
ee
R
e
s
u
l
ts
).
P
r
e
ss
u
r
e
mea
s
u
r
eme
n
t st
a
t
i
on
s
a
r
e
ma
rk
ed
w
i
t
h
b
l
a
ck
d
o
ts
.
F
l
o
w w
a
s
mea
s
u
-
r
ed
a
t
DMA
e
n
try
p
o
i
n
ts
a
n
d
n
ea
r
t
h
e
p
u
mp
i
n
g
st
a
t
i
on
Rys
.
1
.
Mo
de
l
h
y
d
r
a
u
li
c
z
n
y
S
WC
w
e
Wr
o
cł
a
w
i
u.
Po
s
z
c
z
eg
ó
l
n
e
str
e
f
y
DMA
z
o
st
a
ły
z
a
z
n
a
c
z
on
e
k
o
l
o
r
am
i
.
Sz
a
r
a
str
e
f
a
n
i
e
z
o
st
a
ł
a
p
o
dda
n
a
o
st
a
t
e
c
z
n
e
j
k
a
li
b
r
a
c
ji,
c
o
z
o
st
a
ł
o
wy
j
a
ś
n
i
on
e
w Wy
n
i
-
k
a
c
h.
C
z
a
r
n
e
p
un
kty
o
z
n
a
c
z
a
j
ą
l
o
k
a
li
z
a
c
j
ę
p
un
kt
ó
w
p
o
m
i
a
r
o
-
wyc
h
F
i
g
u
r
e
2
.
A
s
u
mma
ry
of
W
D
N
m
o
de
l
de
v
e
l
o
pme
n
t
p
r
o
c
e
ss
Rys
.
2
.
U
p
r
o
s
z
c
z
on
y sc
h
ema
t
b
u
d
o
wy
m
o
de
l
u
h
y
d
r
a
u
li
c
z
n
eg
o
s
i
e
c
i
w
o
d
o
c
i
ąg
o
w
e
j
T
ab
l
e
1
.
E
l
eme
n
t c
oun
ts
i
n
H
P
Z
h
y
d
r
a
u
li
c
m
o
de
l
T
abe
l
a
1
.
K
l
u
c
z
o
w
e
pa
r
ame
try
o
b
i
e
kt
ó
w
m
o
de
-
l
u
h
y
d
r
a
u
li
c
z
n
eg
o
S
WC
E
lement t
y
pe
Number
o
f
D
M
A
s
Number
o
f juncti
o
n
s
Number
o
f pipe
s
Number
o
f cu
s
t
o
mer
s
(
w
ater demand p
o
int
s
)
T
o
tal c
o
unt
5
1247
1341
1164
Number
o
f
w
ater demand pattern
s
1034
Number
o
f pump
s
3
Number
o
f re
s
erv
o
ir
s
1
Pipe length,
k
m 68,2
A
verage t
o
tal dail
y
w
ater demand (during
14-da
y
peri
o
d), m
3
8362
Number
o
f temp
o
rar
y
pre
ss
ure mea
s
urement
s
tati
o
n
s
(TP
M
S)
30
TP
M
S
s
ampling interval, minute
s
1
Number
o
f permanent pre
ss
ure mea
s
ure-
ment
s
tati
o
n
s
(PP
M
S)
3
PP
M
S
s
ampling interval, minute
s
5
F
i
g
u
r
e
3
.
An
e
x
amp
l
e
of
C
-
f
a
ct
o
r
c
a
l
c
u
l
a
t
ed
fo
r c
a
st
i
r
on
p
i
pe
s
of
v
a
r
i
ou
s
d
i
ame
t
e
rs
Rys
.
3
.
P
r
z
ykł
ad
w
a
rt
o
śc
i
ws
p
ó
łc
z
y
nn
i
k
a
C
H
a
z
e
n
a
-
W
illi
am
s
a
o
b
li
c
z
o
-
n
eg
o
d
l
a
p
r
z
e
w
o
d
ó
w
w
o
d
o
c
i
ąg
o
wyc
h
o
r
ó
ż
n
yc
h
śr
ed
n
i
c
a
c
h
4210/2025
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl
W
The r
o
ughne
ss
value
s
f
o
r
o
ther material
s
,
including ductile ir
o
n,
s
teel, and a
s
be
s
t
o
s
cement,
w
ere
s
ub
s
equentl
y
derived
.
O
w
ing
t
o
the
s
carcit
y
o
f data
o
n the effect
s
o
f age
and
w
ater qualit
y
f
o
r the
s
e material
s
,
w
e
elected t
o
appl
y
the curve
s
devel
o
ped f
o
r
ca
s
t ir
o
n a
s
an appr
o
x
imati
o
n
.
Thi
s
deci
s
i
o
n
w
a
s
deemed acceptable given the relative-
l
y
l
ow
prevalence
o
f
o
ther material
s
in the
area, rendering them a l
ow
er pri
o
rit
y.
A
lth
o
ugh the ch
o
ice
o
f the Ha
z
en
–
Wil-
liam
s
C-fact
o
r ma
y
appear unc
o
nventi
o
nal,
given it
s
pred
o
minant applicati
o
n in the
United State
s
, the referenced
s
tud
y
[
12
]
al
s
o
empl
oy
ed thi
s
parameter and pr
o
vided
valuable in
s
ight
s
f
o
r the initial a
ss
e
ss
ment
o
f
pipe r
o
ughne
ss
and the parameteri
s
ati
o
n
o
f
the r
o
ughne
ss
calibrati
o
n alg
o
rithm
.
While
the C-fact
o
r i
s
limited t
o
turbulent fl
ow
re-
gime
s
, thi
s
limitati
o
n
w
a
s
c
o
n
s
idered ac-
ceptable, a
s
pipe r
o
ughne
ss
i
s
primaril
y
o
f
c
o
ncern under
s
uch c
o
nditi
o
n
s
.
D
e
v
e
l
o
p
i
n
g
w
a
t
e
r
dema
n
d
pa
tt
e
r
n
s
The devel
o
pment
o
f
w
ater demand
pattern
s
required particular attenti
o
n
.
A
s
the m
o
del
w
a
s
being c
o
n
s
tructed,
w
e
aimed t
o
full
y
utili
s
e the available data,
pri
o
riti
s
ing v
o
lumetric and individual de-
mand pattern
s
t
o
accuratel
y
replicate
w
a-
ter fl
ow
at the time
o
f
o
ur mea
s
urement
s
.
M
PWiK had in
s
talled
w
ater meter
s
w
ith
m
o
re frequent reading interval
s
, enabling
h
o
url
y
mea
s
urement
s
.
H
ow
ever, n
o
t all
w
ater meter
s
had been upgraded at the
time
o
f the pre
ss
ure mea
s
urement
s
.
T
o
e
x
-
pand the data
s
et,
w
e retrieved reading
s
fr
o
m June 2024, a
s
a quantitative anal
y
s
i
s
dem
o
n
s
trated a
s
tr
o
ng
s
imilarit
y
in
w
ater
c
o
n
s
umpti
o
n during thi
s
peri
o
d
.
D
e
s
pite
thi
s
appr
o
ach, a c
o
n
s
iderable number
o
f
mi
ss
ing value
s
remained f
o
r individual
w
ater meter
s
.
F
o
ll
ow
ing di
s
cu
ss
i
o
n,
w
e
decided t
o
fill mi
ss
ing value
s
f
o
r time
s
erie
s
w
here gap
s
did n
o
t e
x
ceed t
wo
da
y
s
w
ithin a 14-da
y
peri
o
d
.
T
o
achieve thi
s
,
w
e
empl
oy
ed the c
o
ncept cl
o
s
e
s
t fit
[
6
]
,
a meth
o
d that
s
egment
s
the data
s
et int
o
predefined cla
ss
e
s
and impute
s
mi
ss
ing
value
s
u
s
ing the cl
o
s
e
s
t available rec
o
rd
w
ithin the
s
ame cla
ss
.
I
n
o
ur ca
s
e, the da-
ta
s
et
w
a
s
divided int
o
72 cla
ss
e
s
,
o
btained
b
y
a
ss
igning
o
ne
o
f three label
s
–
W
o
r
k
-
da
y
, Saturda
y
,
o
r Sunda
y
–
t
o
each full
da
y
and further
s
ubdividing the
s
e categ
o
-
rie
s
b
y
the h
o
ur
o
f the da
y.
Thi
s
appr
o
ach
en
s
ured that b
o
th diurnal and h
o
url
y
varia-
ti
o
n
s
in
w
ater demand
w
ere pre
s
erved
.
The remaining n
o
de
s
w
ith pre
s
ent
w
a-
ter demand received a general pattern
ba
s
ed
o
n t
o
tal
w
ater c
o
n
s
umpti
o
n mea-
s
ured at the pumping
s
tati
o
n
.
The c
o
n
s
tant
F
o
r the purp
o
s
e
o
f calibrati
o
n,
w
e re-
average h
o
url
y
c
o
n
s
umpti
o
n
w
a
s
multi-
s
tricted the data
s
et t
o
peri
o
d
s
w
hen the
plied b
y
a percentage value in each pumping
s
tati
o
n
w
a
s
full
y
o
perati
o
nal, e
x
-
time
s
tep
.
cluding nighttime
w
hen the
s
tati
o
n
w
a
s
s
hut
d
ow
n
.
Thi
s
appr
o
ach helped eliminate
R
e
f
e
r
e
n
c
e
da
t
a
fo
r
ma
tt
i
n
g
a
n
d
p
o
tential bia
s
e
s
that c
o
uld
s
ignificantl
y
im-
r
e
s
amp
li
n
g
pact the calibrati
o
n pr
o
ce
ss
.
R
etaining
data characteri
s
ed b
y
s
ub
s
tantiall
y
l
ow
er
A
s
previ
o
u
s
l
y
menti
o
ned, the devel
o
p-pre
ss
ure and fl
ow
rate
s
c
o
uld mi
s
lead the
ment
o
f the h
y
draulic m
o
del
w
a
s
centred
o
naut
o
calibrati
o
n alg
o
rithm and c
o
mpr
o
mi
s
e
the additi
o
nal pre
ss
ure mea
s
urement
s
.
A
fterit
s
o
verall perf
o
rmance
.
M
o
re
o
ver, the
integrating the
s
e data
w
ith rec
o
rd
s
fr
o
mHa
z
en
–
William
s
C-fact
o
r applie
s
e
x
clu-
permanent pre
ss
ure and fl
ow
m
o
nit
o
ring
s
ivel
y
t
o
turbulent fl
ow
regime
s
and i
s
p
o
int
s
,
w
e c
o
n
s
tructed a data
s
et c
o
mpri
s
ingtheref
o
re un
s
uitable f
o
r the ver
y
l
ow
fl
ow
time
s
erie
s
w
ith var
y
ing time
s
tep
s
.
Thi
s
varia-rate
s
o
b
s
erved at night
.
F
igure 4
.
pre
s
ent
s
ti
o
n p
o
s
ed challenge
s
f
o
r c
o
mpari
s
o
n anda c
o
mpari
s
o
n bet
w
een the
o
riginal ra
w
m
o
del evaluati
o
n, a
s
higher-frequenc
y
datadata and the pr
o
ce
ss
ed data u
s
ed f
o
r cali-
e
x
hibited greater n
o
i
s
e and a higher num-brati
o
n, illu
s
trated a
s
a H
y
draulic
G
rade
ber
o
f
o
utlier
s
, affecting qualit
y
metric
s
andLine (H
G
L) f
o
r
o
ne
o
f the temp
o
rar
y
pre
s
-
ma
k
ing vi
s
ual repre
s
entati
o
n le
ss
interpre-
s
ure mea
s
urement
s
tati
o
n
s
.
table
.
T
o
addre
ss
thi
s
i
ss
ue,
w
e applied
a
s
m
oo
thing meth
o
d u
s
ing bin mean
s
[
7
]
,
P
i
pe
r
ou
g
hn
e
ss c
a
li
b
r
a
t
i
on
w
here each bin repre
s
ented a full h
o
ur
w
ithin the 14-da
y
mea
s
urement peri
o
d
.
The final a
s
pect requiring e
x
ten
s
ive
Sm
oo
thing b
y
bin mean
s
i
s
s
imilar t
o
the
wo
r
k
w
a
s
pipe r
o
ughne
ss
calibrati
o
n
.
Un-
c
o
ncept cl
o
s
e
s
t fit; h
ow
ever, in
s
tead
o
f fill- li
k
e
o
ther parameter
s
, pipe r
o
ughne
ss
ing in mi
ss
ing value
s
, it replace
s
all rec
o
rd
s
pre
s
ent
s
a
s
ignificant challenge due t
o
the
w
ithin a cla
ss
w
ith a
s
ingle value
.
I
n thi
s
highl
y
irregular and unpredictable nature
ca
s
e, the replacement value i
s
the mean
o
f pipe
s
caling
.
C
o
n
s
equentl
y
, the calibra-
calculated fr
o
m all data p
o
int
s
w
ithin the ti
o
n
o
f pipe r
o
ughne
ss
remain
s
an active
re
s
pective cla
ss
.
Thi
s
adju
s
tment
w
a
s
nece
s
- area
o
f
s
cientific re
s
earch, primaril
y
f
o
-
s
ar
y
ow
ing t
o
the difference in time
s
tep cu
s
ed
o
n devel
o
ping and implementing
length
s
bet
w
een the
w
ater meter
s
and pre
s
- vari
o
u
s
meth
o
d
s
t
o
addre
ss
thi
s
i
ss
ue
.
s
ure meter
s
—
o
ne h
o
ur and
o
ne minute, re-
F
o
r
o
ur
s
tud
y
,
w
e ad
o
pted a meth
o
d-
s
pectivel
y.
C
o
n
s
equentl
y
, a
o
ne-h
o
ur
o
l
o
g
y
in
s
pired b
y
the
wo
r
k
o
f
Z
ha
o
et
.
al
.
time
s
tep
w
a
s
ad
o
pted f
o
r the m
o
del
.
[
20
]
,
w
ith m
o
dificati
o
n
s
tail
o
red t
o
o
ur
F
i
g
u
r
e
4
.
A
c
o
mpa
r
i
s
on
be
tw
ee
n
t
h
e
o
r
i
g
i
n
a
l
r
a
w
da
t
a
a
n
d
t
h
e
p
r
o
c
e
ss
ed
da
t
a
u
s
ed
fo
r c
a
li
b
r
a
t
i
on
,
fo
r
on
e
of
t
h
e
mea
s
u
r
eme
n
t
p
o
i
n
ts
.
N
o
t
ab
l
y
,
t
h
e
v
i
s
i
b
l
e
d
r
o
p
s
i
n
w
a
t
e
r
p
r
e
ss
u
r
e
– r
e
s
u
l
t
i
n
g
f
r
o
m
t
h
e
s
hu
t
d
o
w
n
of
t
h
e
p
u
mp
i
n
g
st
a
t
i
on
–
h
a
v
e
bee
n
r
em
ov
ed
.
F
o
r c
l
a
r
i
ty
,
t
h
e
o
r
i
g
i
n
a
l
t
i
me
st
amp
s
h
a
v
e
bee
n
r
e
t
a
i
n
ed
i
n
t
h
e
p
r
o
c
e
ss
ed
da
t
a
s
e
t
Rys
.
4
.
Po
r
ó
w
n
a
n
i
e
s
u
r
o
wyc
h
da
n
yc
h
z
da
n
y
m
i
p
r
z
y
g
o
t
o
w
a
n
y
m
i
d
o
k
a
li
b
r
a
c
ji,
d
l
a
j
ed
n
eg
o
z
p
un
k
-
t
ó
w
p
o
m
i
a
r
o
wyc
h.
Z
a
u
w
a
ż
a
l
n
y s
pade
k c
i
ś
n
i
e
n
i
a
,
wy
n
i
k
a
j
ą
cy
z
wył
ą
c
z
e
n
i
a
p
r
z
ep
o
mp
o
w
n
i,
z
o
st
a
ł
u
s
un
i
ę
ty
.
D
l
a
k
l
a
r
o
w
no
śc
i
wykr
e
s
u
o
ry
g
i
n
a
l
n
e
st
emp
l
e
c
z
a
s
o
w
e
z
o
st
a
ły
z
a
c
ho
w
a
n
e
w
p
r
z
e
li
c
z
on
y
m
s
z
e
r
eg
u
c
z
a
s
o
wy
m
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl10/202543
W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
s
pecific ca
s
e
.
We
s
elected the Shuffledacceptable pipe r
o
ughne
ss
value
s
, ba
s
ed
C
o
mple
x
E
v
o
luti
o
n (SC
E
) alg
o
rithm
[
5
]
,
o
n inf
o
rmati
o
n fr
o
m Lam
o
nt’
s
wo
r
k
[
12
].
given
w
ell-e
s
tabli
s
hed
s
ucce
ss
o
f ev
o
lu-The target
o
bjective
s
w
ere e
s
tabli
s
hed u
s
-
ti
o
nar
y
alg
o
rithm
s
in
o
ptimi
s
ati
o
n tech-ing reference data,
w
ith
w
eighting fact
o
r
s
nique
s
f
o
r
w
ater re
s
o
urce managementadju
s
ted thr
o
ugh preliminar
y
data anal
y
-
[
11
]
, including W
D
N m
o
del calibrati
o
n
s
i
s
.
I
n thi
s
pr
o
ce
ss
,
w
e reduced the
w
eight
s
[
1
]
,
[
14
]
,
[
17
]
,
[
19
]
, a
s
w
ell a
s
it
s
availabil-
o
f
o
bjective
s
affected b
y
a higher number
it
y
w
ithin the pr
o
vided m
o
delling
s
o
ft
w
are
.o
f
o
utlier
s
and an
o
malie
s
.
SC
E
i
s
a gl
o
bal
o
ptimi
s
ati
o
n meth
o
d
de
s
igned f
o
r c
o
ntinu
o
u
s
o
ptimi
s
ati
o
n pr
o
b-
R
e
s
u
l
ts
a
n
d
d
i
sc
u
ss
i
on
lem
s
and i
s
w
idel
y
applied in h
y
dr
o
l
o
gical
m
o
delling and envir
o
nmental engineering
.
The
s
ucce
ss
ful devel
o
pment and cali-
The alg
o
rithm
o
perate
s
b
y
ev
o
lving multiple brati
o
n
o
f the HP
Z
h
y
draulic m
o
del
w
ere
p
o
pulati
o
n
s
(c
o
mple
x
e
s
)
o
f p
o
tential
s
o
lu- achieved thr
o
ugh the applicati
o
n
o
f the
ti
o
n
s
thr
o
ugh iterative
s
huffling and ev
o
lu- af
o
rementi
o
ned meth
o
d
s
.
The u
s
e
o
f the
ti
o
n
s
tep
s
.
I
n the m
o
delling
s
o
ft
w
are, m
o
del c
o
ncept
o
f cl
o
s
e
s
t fit all
ow
ed nearl
y
88
%
fitne
ss
i
s
a
ss
e
ss
ed b
y
c
o
mputing an aggre-
o
f all
w
ater demand p
o
int
s
(1024
o
ut
o
f
gated
o
bjective functi
o
n
–
a
w
eighted
s
um 1164
w
ater demand pattern
s
) t
o
receive
o
f
o
bjective
s
s
pecified b
y
the m
o
deller
.
individual
w
ater demand pattern
s
, en-
B
uilding
o
n previ
o
u
s
re
s
earch
[
20
]
and abling an accurate recreati
o
n
o
f
w
ater
net
wo
r
k
anal
y
s
i
s
,
w
e devel
o
ped a meth- fl
ow
during the
s
elected calibrati
o
n peri
o
d
.
o
d
o
l
o
g
y
f
o
r parameteri
s
ing SC
E
.
The al-
F
igure 5
.
s
h
ow
s
a c
o
mpari
s
o
n bet
w
een the
g
o
rithm’
s
s
tandard parameter
s
w
ere im- fl
ow
mea
s
ured at the pumping
s
tati
o
n and
plemented acc
o
rding t
o
rec
o
mmendati
o
n
s
the calculated fl
ow.
fr
o
m the
o
riginal re
s
earch
[
5
].
D
eci
s
i
o
nPr
o
ce
ss
ing the reference data pr
o
vided
variable
s
w
ere defined ba
s
ed
o
n t
wo
cri- deeper in
s
ight
s
int
o
e
s
tabli
s
hed pattern
s
,
teria
:
pipe diameter (
D
) and
D
M
A
, re
s
ult- all
ow
ing f
o
r the refinement
o
f vari
o
u
s
pa-ing
in a t
o
tal
o
f 27 deci
s
i
o
n variable
s
.
E
ach rameter
s
,
s
uch a
s
the
w
eight
s
a
ss
igned t
o
deci
s
i
o
n variable
w
a
s
a
ss
igned a range
o
f deci
s
i
o
n variable
s
.
R
egarding m
o
del fit-
2
ne
ss
, the
R
M
S
E
value
s
calculated f
o
r all
reference
w
ater pre
ss
ure data ranged fr
o
m
0,29 t
o
1,3 m H
O
,
w
hile the
R
2
varied
bet
w
een 0,92 and 0,99
.
The median
R
M
S
E
acr
o
ss
all mea
s
urement p
o
int
s
w
a
s
0,46,
w
hile the median
R
2
value
w
a
s
0,98,
further reinf
o
rcing the
o
verall accurac
y
o
f
the m
o
del
.
F
igure 6
.
s
h
ow
s
the c
o
mpari
s
o
n
bet
w
een calculated and mea
s
ured value
s
f
o
r
o
ne
o
f the mea
s
urement p
o
int
s
.
The
s
e re
s
ult
s
indicate a ver
y
g
oo
d
m
o
del fit,
w
ith the maj
o
rit
y
o
f the data
s
et
e
x
hibiting minimal deviati
o
n fr
o
m
o
b-
s
erved value
s
.
Several fact
o
r
s
c
o
ntributed
t
o
di
s
crepancie
s
bet
w
een the m
o
del and
the reference data, including
:
l
D
ifference
s
in net
wo
r
k
depth bet
w
een
the m
o
del and the actual
s
y
s
tem, re
s
ult-
ing fr
o
m the u
s
e
o
f a
D
igital
E
levati
o
n
M
o
del a
s
a data
s
o
urce f
o
r n
o
de ele-
vati
o
n,
l
A
pipe bur
s
t cau
s
ing a
s
ignificant pre
s
-
s
ure dr
o
p at
o
ne
o
f the temp
o
rar
y
pre
s
-
s
ure mea
s
urement
s
tati
o
n
s
,
l
O
ther min
o
r an
o
malie
s
that
w
ere diffi-
cult t
o
accuratel
y
implement in the
m
o
del
.
The c
o
mplete li
s
t
o
f deci
s
i
o
n variable
s
u
s
ed f
o
r pipe r
o
ughne
ss
calibrati
o
n i
s
pre-
s
ented in Table 2
.
O
ne
o
f the
k
e
y
element
s
requiring
clarificati
o
n i
s
the n
o
table variati
o
n in the
range
o
f C-fact
o
r
s
a
ss
igned t
o
deci
s
i
o
n
variable
s
in l
o
cati
o
n
s
E
and
F
c
o
mpared t
o
o
ther
z
o
ne
s
.
Preliminar
y
calibrati
o
n re
s
ult
s
indicated that the initiall
y
a
ss
igned C-fac-
t
o
r
s
in the
s
e l
o
cati
o
n
s
(defined in Step 1
.
)
w
ere nearl
y
adequate,
w
hich led u
s
t
o
re-
s
trict the variati
o
n range f
o
r the
o
ptimi
s
a-
ti
o
n pr
o
ce
ss
.
F
o
r the
s
ame rea
s
o
n,
o
ne
o
f
the
D
M
A
s
w
a
s
e
x
cluded fr
o
m calibrati
o
n
alt
o
gether
.
F
urtherm
o
re, pipe
s
w
ith diam-
eter
s
s
maller than 100 mm
w
ere
o
mitted
due t
o
their marginal
s
hare in the HP
Z
.
A
nal
y
s
i
s
o
f the calibrati
o
n
o
utc
o
me
s
re-
vealed
s
everal imp
o
rtant trend
s
:
l
A
ll 300 mm pipe
s
w
ere a
ss
igned
a C-fact
o
r
o
f 43, the minimum value
permitted b
y
the alg
o
rithm
.
F
i
g
u
r
e
5
.
A
c
o
mpa
ri
s
on
be
tw
ee
n
t
h
e
f
l
o
w
mea
s
u
r
ed
a
t t
h
e
p
u
mp
i
n
g
st
a
t
i
on
a
n
d
t
h
e
c
a
l
c
u
l
a
t
ed
f
l
o
w
Rys
.
5
.
Po
r
ó
w
n
a
n
i
e
z
m
i
e
r
z
on
eg
o
n
a
t
ę
ż
e
n
i
a
p
r
z
ep
ływ
u
n
a
p
r
z
ep
o
mp
o
w
n
i
z
p
r
z
ep
ływ
em
o
b
li
c
z
o
-
n
y
m
w
m
o
de
l
u
F
i
g
u
r
e
6
.
C
o
rr
e
s
p
on
de
n
c
e
be
tw
ee
n
c
a
l
c
u
l
a
t
ed
a
n
d
mea
s
u
r
ed
v
a
l
u
e
s
,
e
x
emp
li
f
i
ed
a
t
on
e
of
t
h
e
mea
s
u
r
eme
n
t
p
o
i
n
ts
.
P
a
rt
a
)
p
r
e
s
e
n
ts
t
h
e
da
t
a
u
s
ed
fo
r
c
a
li
b
r
a
t
i
on
,
e
x
c
l
u
d
i
n
g
pe
r
i
o
d
s w
h
e
n
t
h
e
p
u
mp
i
n
g
st
a
t
i
on
w
a
s
s
hu
t
d
o
w
n
a
t
n
i
g
h
t
,
w
h
il
e
pa
rt
b
)
ill
u
str
a
-
t
e
s t
h
e
fu
ll
tw
o
-
w
ee
k s
i
m
u
l
a
t
i
on
Rys
.
6
.
K
o
r
e
l
a
c
j
a
m
i
ęd
z
y w
a
rt
o
śc
i
am
i
o
b
li
c
z
on
y
m
i
a
z
m
i
e
r
z
on
y
m
i
w
j
ed
n
y
m
z
p
un
kt
ó
w
p
o
m
i
a
r
o
wyc
h.
C
z
ę
ść
a
)
p
r
z
ed
st
a
w
i
a
da
n
e
wyk
o
r
z
yst
a
n
e
d
o
k
a
li
b
r
a
c
ji,
z
wył
ą
c
z
e
n
i
em
o
kr
e
s
ó
w
,
w kt
ó
r
yc
h
st
a
c
j
a
p
o
mp
b
ył
a
wył
ą
c
z
on
a
w
no
cy
,
n
a
t
o
m
i
a
st c
z
ę
ść
b
)
p
r
z
ed
st
a
w
i
a
pe
ł
n
e
d
w
a
ty
g
o
d
n
i
e
sy
m
u
l
a
c
ji
4410/2025
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl
W
l
There
w
a
s
n
o
clear c
o
rrelati
o
n be-
t
w
een pipe diameter and calibrated
C-fact
o
r value
s
.
I
n
s
o
me ca
s
e
s
,
s
mall-
er-diameter pipe
s
w
ere a
ss
igned high-
er C-fact
o
r
s
than larger
o
ne
s
, a c
o
un-
terintuitive re
s
ult highlighted in
F
igure 7
.
l
O
ut
o
f 27 deci
s
i
o
n variable
s
, 10
w
ere
a
ss
igned the minimum value and 2 the
ma
x
imum,
s
ugge
s
ting the alg
o
rithm
gravitated t
ow
ard
s
b
o
undar
y
s
o
luti
o
n
s
f
o
r a
s
ignificant p
o
rti
o
n
o
f the vari-
able
s
.
T
o
facilitate further anal
y
s
i
s
o
f the rela-
ti
o
n
s
hip bet
w
een r
o
ughne
ss
and pipe di-
ameter, the calibrated C-fact
o
r
s
w
ere c
o
n-
verted int
o
ab
s
o
lute r
o
ughne
ss
(
ε
) and
s
ub
s
equentl
y
int
o
relative r
o
ughne
ss
(
ε
/
D
),
all
ow
ing f
o
r a n
o
rmali
s
ed c
o
mpari
s
o
n
.
Thi
s
tran
s
f
o
rmati
o
n
w
a
s
applied at the lin
k
level
w
ithin the m
o
del, rather than at the level
o
f
deci
s
i
o
n variable
s
, en
s
uring a finer granu-
larit
y
o
f anal
y
s
i
s
.
The
o
utc
o
me
s
o
f thi
s
pr
o
-
ce
ss
are depicted in
F
igure 8
.
,
w
hich
pre
s
ent
s
b
o
x
pl
o
t
s
generated f
o
r each pipe
diameter
.
The calibrated relative r
o
ughne
ss
val-
ue
s
e
x
hibit a clear dependence
o
n pipe
diameter
.
N
o
tabl
y
, t
wo
di
s
tinct trend
s
can
be
o
b
s
erved
:
pipe
s
w
ith a diameter
o
f 300
mm and
s
maller e
x
hibit
s
ignificantl
y
higher
relative r
o
ughne
ss
value
s
c
o
mpared t
o
larger pipe
s
.
Thi
s
o
b
s
ervati
o
n led u
s
t
o
c
o
nclude that the initial pipe r
o
ughne
ss
a
s
-
s
e
ss
ment
w
a
s
s
ufficientl
y
accurate f
o
r larg-
er pipe
s
,
w
hich
w
ere theref
o
re e
x
cluded
fr
o
m the final r
o
ughne
ss
calibrati
o
n u
s
ing
the SC
E
.
The better c
o
nditi
o
n
o
f the
s
e
larger-diameter tran
s
mi
ss
i
o
n main
s
ma
y
be
attributed t
o
m
o
re frequent ren
o
vati
o
n
s
T
ab
l
e
2
.
L
i
st
of
de
c
i
s
i
on
v
a
r
i
ab
l
e
s
de
f
i
n
ed
fo
r
p
i
pe
r
ou
g
hn
e
ss c
a
li
b
r
a
t
i
on.
E
a
c
h
v
a
r
i
ab
l
e
i
s c
h
a
r
a
ct
e
-
r
i
s
ed
b
y
p
i
pe
d
i
ame
t
e
r
a
n
d
l
o
c
a
t
i
on
,
t
h
e
l
a
tt
e
r
de
t
e
r
m
i
n
ed
ba
s
ed
on
DMA
b
oun
da
r
i
e
s
.
Tr
a
n
s
m
i
ss
i
on
ma
i
n
s w
e
r
e
fu
r
t
h
e
r
s
u
bd
i
v
i
ded
i
n
t
o
tw
o
s
epa
r
a
t
e
t
o
p
o
l
o
g
i
c
a
l
r
eg
i
on
s
fo
r c
a
li
b
r
a
t
i
on
p
u
r
p
o
s
e
s
.
T
h
e
t
ab
l
e
i
n
c
l
u
de
s c
a
li
b
r
a
t
ed
v
a
l
u
e
s
of
t
h
e
H
a
z
e
n
–W
illi
am
s C
-
f
a
ct
o
r
,
a
l
on
g
w
i
t
h
t
h
e
m
i
n
i
m
u
m
a
n
d
ma
xi
-
m
u
m
b
oun
d
s
a
ss
i
g
n
ed
t
o
ea
c
h
v
a
r
i
ab
l
e
,
w
h
i
c
h
de
f
i
n
ed
t
h
e
s
ea
rc
h
s
pa
c
e
fo
r t
h
e
S
C
E
a
l
g
o
r
i
t
h
m
T
abe
l
a
2
.
L
i
st
a
z
m
i
e
nn
yc
h
de
cy
z
y
j
n
yc
h
z
de
f
i
n
i
o
w
a
n
yc
h
d
l
a
a
l
g
o
ryt
m
u
k
a
li
b
r
u
j
ą
c
eg
o
c
h
r
o
p
o
w
a
t
o
ść
.
K
a
ż
da
z
m
i
e
nn
a
z
o
st
a
ł
a
o
kr
e
ś
l
on
a
ba
z
u
j
ą
c
n
a
śr
ed
n
i
cy
o
r
a
z
l
o
k
a
li
z
a
c
ji,
wy
z
n
a
c
z
on
e
j
p
r
z
e
z
g
r
a
n
i
c
e
DMA.
S
i
e
c
i
mag
i
st
r
a
l
n
e
z
o
st
a
ły
p
o
d
z
i
e
l
on
a
n
a
d
w
i
e
o
dd
z
i
e
l
n
e
l
o
k
a
c
j
e
.
T
abe
l
a
z
a
w
i
e
r
a
d
o
b
r
a
n
e
w
a
rt
o
śc
i
ws
p
ó
łc
z
y
nn
i
k
a
C H
a
z
e
n
a
-
W
illi
am
s
a
d
l
a
k
a
ż
de
j
z
m
i
e
nn
e
j
wr
a
z
z
e
z
de
f
i
n
i
o
w
a
n
y
m
p
r
z
e
-
d
z
i
a
ł
em
w
a
r
t
o
śc
i,
z
kt
ó
r
eg
o
a
l
g
o
ryt
m
S
C
E
d
o
b
i
e
r
a
ł w
a
rt
o
ść
p
o
d
c
z
a
s k
a
li
b
r
a
c
ji
D
eci
s
i
o
n variable n
o.
D
iameter (
D
), mmL
o
cati
o
nC minimum,
–
C ma
x
imum,
–
C calibrated,
–
1100
A
28 76 36,9
2 125
A
31 78 40,9
3 150
A
34 80 34,0
4 200
A
38 83 83,0
5 250
A
41 85 78,5
6 300
A
43 87 43,0
7 100
B
28 76 53,7
8 150
B
34 80 39,7
9 200
B
38 83 60,1
10 300
B
43 87 43,0
11 400
B
46 93 61,5
12 100 C 28 76 28,0
13 150 C 34 80 34,0
14 200 C 38 83 38,2
15 300 C 43 87 43,0
16 100
D
28 76 48,4
17 150
D
34 80 36,9
18 200
D
38 83 38,0
19 300
D
43 87 43,0
21 500
E
92 109 92,0
22 600
E
94 111 95,6
23 800
E
96 113 102,2
20 1000
E
108 117 117,0
24 400
F
90 108 104,2
25 500
F
92 108 92,0
26 600
F
94 111 95,0
27800
F
9611399,3
F
i
g
u
r
e
7
.
V
a
l
u
e
s
of
c
a
li
b
r
a
t
ed
C
-
f
a
ct
o
r
fo
r
a
ll
de
c
i
s
i
on
v
a
r
i
ab
l
e
s
Rys
.
7
.
Do
b
r
a
n
e
w
a
r
t
o
śc
i
ws
p
ó
łc
z
y
nn
i
k
a
C
d
l
a
ws
z
ystk
i
c
h
z
m
i
e
nn
yc
h
de
cy
z
y
j
n
yc
h
F
i
g
u
r
e
8
.
C
a
li
b
r
a
t
ed
p
i
pe
r
e
l
a
t
i
v
e
r
ou
g
hn
e
ss
.
T
h
e
m
i
n
i
m
u
m
a
n
d
ma
xi
m
u
m
v
a
l
u
e
s w
e
r
e
i
de
n
t
i
f
i
ed
w
i
t
h
i
n
1
.
5 t
i
me
s t
h
e
i
n
t
e
r
q
u
a
rt
il
e
r
a
n
ge
Rys
.
8
.
C
h
r
o
p
o
w
a
t
o
ść w
z
g
l
ęd
n
a
sk
a
li
b
r
o
w
a
n
e
j
s
i
e
c
i
w
o
d
o
c
i
ąg
o
w
e
j
.
M
i
n
i
m
u
m
i
ma
ks
i
m
u
m
z
o
st
a
ł
o
o
kr
e
ś
l
on
e
n
a
p
o
d
st
a
w
i
e
1
,
5
-
kr
o
t
n
e
j
w
a
rt
o
śc
i
r
o
z
st
ęp
u
m
i
ęd
z
ykw
a
rty
l
o
w
eg
o
W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
and replacement
s
, f
o
r
w
hich
s
o
me
s
up-
p
o
rting d
o
cumentati
o
n
w
a
s
available
.
H
ow
ever, thi
s
rea
s
o
ning d
o
e
s
n
o
t appear
t
o
appl
y
t
o
s
maller-diameter pipe
s
,
w
hich
functi
o
n primaril
y
a
s
di
s
tributi
o
n main
s
.
F
urtherm
o
re,
w
hile relative r
o
ughne
ss
i
s
generall
y
e
x
pected t
o
decrea
s
e
w
ith in-
crea
s
ing pipe diameter, the di
s
tributi
o
n
o
f
value
s
f
o
r certain diameter
s
appear
s
s
o
me-
w
hat irregular, particularl
y
f
o
r 100 mm and
200 mm
.
Thi
s
variabilit
y
ma
y
be lin
k
ed t
o
the
s
pecific l
o
cati
o
n
s
o
f the
s
e pipe
s
w
ithin
the net
wo
r
k
,
s
pecific placement
o
f pre
ss
ure
s
en
s
o
r
s
and the net
wo
r
k
’
s
l
oo
ped t
o
p
o
l
o
-
g
y
,
w
hich p
o
s
e
s
challenge
s
f
o
r accurate
calibrati
o
n
.
B
ut it ma
y
al
s
o
indicate that the
calibrati
o
n alg
o
rithm pri
o
riti
s
ed adju
s
t-
ment
s
f
o
r 300 mm pipe
s
w
hile ma
k
ing
minimal m
o
dificati
o
n
s
t
o
the re
s
t
.
C
on
c
l
u
s
i
on
s
O
ur meth
o
d
o
l
o
g
y
integrate
s
a range
o
f data pr
o
ce
ss
ing and anal
y
s
i
s
tech-
nique
s
t
o
en
s
ure the accurac
y
and reliabil-
it
y
o
f the h
y
draulic m
o
del
.
T
o
ma
x
imi
s
e the
v
o
lume
o
f u
s
able data f
o
r calibrati
o
n,
w
e
empl
oy
ed meth
o
d
s
s
uch a
s
c
o
ncept cl
o
s
-
e
s
t fit and bin
s
m
oo
thing
.
The
s
e appr
o
ach-
e
s
s
ignificantl
y
enhanced data c
o
mplete-
ne
ss
, c
o
ntributing t
o
the
o
verall
s
tr
o
ng fit
o
f
the m
o
del
.
With regard t
o
the SC
E
alg
o
rithm,
o
ur
anal
y
s
i
s
revealed that it pred
o
minantl
y
adju
s
ted r
o
ughne
ss
value
s
f
o
r larger-diam-
eter pipe
s
,
w
hile the calibrati
o
n
o
f
s
maller
pipe
s
remained inc
o
n
s
i
s
tent
.
Thi
s
di
s
crep-
anc
y
s
ugge
s
t
s
that the alg
o
rithm ma
y
have
pri
o
riti
s
ed certain pipe categ
o
rie
s
, p
o
ten-
tiall
y
o
verl
ook
ing finer-
s
cale variati
o
n
s
in
r
o
ughne
ss
acr
o
ss
the net
wo
r
k.
I
n the final
s
tage
o
f calibrati
o
n, pipe
material
w
a
s
n
o
t e
x
plicitl
y
c
o
n
s
idered, a
s
it
s
impact
w
a
s
deemed l
ow
pri
o
rit
y
due t
o
the relativel
y
s
mall pr
o
p
o
rti
o
n
o
f aging
material
s
o
ther than ca
s
t ir
o
n
w
ithin the
HP
Z
.
While inc
o
rp
o
rating material-
s
pecific
r
o
ughne
ss
adju
s
tment
s
c
o
uld have further
impr
o
ved calibrati
o
n accurac
y
, it i
s
al
s
o
nece
ss
ar
y
t
o
e
x
amine additi
o
nal fact
o
r
s
,
including b
o
th h
y
draulic and t
o
p
o
l
o
gical
parameter
s
.
While
o
ur meth
o
d
o
l
o
g
y
s
implified the
data and pr
o
duced a g
oo
d m
o
del fit, it
inevitabl
y
s
acrificed
s
o
me nuance
s
f
o
r the
s
a
k
e
o
f clarit
y.
Theref
o
re, the calibrati
o
n
s
h
o
uld be validated
w
ith additi
o
nal pre
s
-
s
ure and fl
ow
mea
s
urement
s
, p
o
tentiall
y
including h
y
drant di
s
charge te
s
t
s
w
here
fea
s
ible
.
F
urther anal
y
s
i
s
o
f fl
ow
rate
s
c
o
uld help identif
y
area
s
o
f the net
wo
r
k
that
wo
uld benefit fr
o
m
s
uch te
s
t
s
.
I
n addi-
ti
o
n, the ch
o
s
en
o
ne-h
o
ur time
s
tep ma
y
n
o
t
be
o
ptimal, given the d
y
namic nature
o
f
w
ater pre
ss
ure, fl
ow
, and demand
.
F
uture
wo
r
k
c
o
uld c
o
n
s
ider m
o
re detailed mea-
s
urement
s
t
o
refine and impr
o
ve
o
ur ap-
pr
o
ach
.
A
ddre
ss
ing the
s
e challenge
s
w
ill re-
quire further re
s
earch, particularl
y
in de-
vel
o
ping a m
o
re c
o
mprehen
s
ive mathe-
matical frame
wo
r
k
f
o
r defining deci
s
i
o
n
variable
s
in r
o
ughne
ss
calibrati
o
n
.
F
uture
s
tudie
s
w
ill e
x
pl
o
re refined meth
o
d
o
l
o
gie
s
that acc
o
unt f
o
r a br
o
ader
s
et
o
f influenc-
ing fact
o
r
s
, aiming t
o
enhance the preci-
s
i
o
n and r
o
bu
s
tne
ss
o
f the calibrati
o
n pr
o
-
ce
ss
.
A
ck
no
w
l
edgme
n
ts
The m
o
delling
s
o
ft
w
are and relevant
data
w
ere pr
o
vided b
y
M
PWiK
.
I
n the
preparati
o
n
o
f thi
s
article,
w
e utili
s
ed Chat-
G
PT
[
15
]
f
o
r grammar c
o
rrecti
o
n and v
o
-
cabular
y
refinement
.
Thi
s
meth
o
d
o
l
o
g
y
f
o
rm
s
part
o
f the im-
plementati
o
n d
o
ct
o
rate
O
ptimi
s
ati
o
n
o
f
Water Net
wo
r
k
Pre
ss
ure U
s
ing
A
rtificial
I
ntelligence and ma
y
be
s
ubject t
o
further
m
o
dificati
o
n
s
.
The pr
o
ject received addi-
ti
o
nal funding fr
o
m the P
o
li
s
h
M
ini
s
tr
y
o
f
Science and Higher
E
ducati
o
n under the
I
mplementati
o
n
Do
ct
o
rate Pr
o
gramme,
6th editi
o
n
.
H
y
draulic m
o
del devel
o
pment, cali-
brati
o
n, and the vi
s
uali
s
ati
o
n
s
h
ow
n in
F
igure 6
.
w
ere carried
o
ut u
s
ing
M
i
k
e
+
2024, devel
o
ped b
y
D
H
I
.
R
E
F
E
R
E
N C
E
S
[
1
]
B
y
l
k
a J,
B
ałut
A
,
B
r
o
d
z
ia
k
R
,
Z
a
k
r
z
e
w
s
k
i P
.
N
o
dal
D
emand C
o
ntr
o
l
G
enetic
A
lg
o
rithm f
o
r
Water Suppl
y
S
y
s
tem
s
.
I
n
s
tal
.
2022;10
.
d
o
i
:
10
.
36119/15
.
2022
.
10
.
8
[
2
]
Cich
o
ń T, Kr
ó
li
kow
s
k
a J
.
The r
o
le and imp
o
rtan-
ce
o
f
s
mart
w
ater meter
s
in the
w
ater
s
uppl
y
s
y
s
tem
[
in P
o
li
s
h
].
Ro
la i
z
nac
z
enie inteligent-
n
y
ch
wo
d
o
mier
z
y
w
s
y
s
temie
z
a
o
patr
z
enia
wwo
dę
.
I
n
s
tal
.
2024;12
.
d
o
i
:
10
.
36119/15
.
2024
.
12
.
7
[
3
]
D
i Nard
o
A
,
B
o
ccelli
D
L, Herrera
M
, et al
.
Smart Urban Water Net
wo
r
k
s
:
S
o
luti
o
n
s
,
Trend
s
and challenge
s
.
Water
.
2021;13(4)
:
501
.
d
o
i
:
10
.
3390/
w
13040501
[
4
]
Do
dge
Y
.
The
Co
nci
s
e
E
nc
y
cl
o
pedia
o
f Stati-
s
tic
s
.
; 2008
.
d
o
i
:
10
.
1007/978-0-387-
32833-1
[
5
]
D
uan
QY
,
G
upta VK, S
o
r
oo
s
hian S
.
Shuffled
c
o
mple
x
ev
o
luti
o
n appr
o
ach f
o
r effective and
efficient gl
o
bal minimi
z
ati
o
n
.
J
o
urnal
o
f
O
ptimi-
z
ati
o
nThe
o
r
y
and
A
pplicati
o
n
s
.
1993;76(3)
:
501-521
.
d
o
i
:
10
.
1007/
bf00939380
[
6
]
G
r
z
y
mala-
B
u
ss
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