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ADAPTIVE IDENTIFICATION ALGORITHM FOR THE
HAZEN–WILLIAMS COEFFICIENT (EPANET INTEGRATION)
S. Axmadaliye 1, M. Axmadaliye a2, Z. Axmadaliye 3, I. G’aniye a4,
Doc o al S uden o Tashken A chi ec u e and Ci il Enginee ing Uni e si y1
English Language Teache a School No. 341, Yashnobod Dis ic 2
Elec ical Enginee a he Mode n Design Ins i u e3
Ope a o o he Labo a o y o Physical and Physicochemical Resea ch Me hods, Ins i u e o
Polyme Chemis y and Physics, Academy o Sciences o he Republic o Uzbekis an4
h ps://doi.o g/10.5281/zenodo.17315743
Abs ac . In wa e supply ne wo ks, accu a ely de e mining ic ion losses is o c i ical
impo ance when modeling hyd aulic p ocesses. In p ac ice, wo p ima y o mulas a e widely
used: Hazen–Williams (empi ical and as ) and Da cy–Weisbach (physically based and
uni e sal). Due o i s simplici y, Hazen–Williams is con enien o applica ion in eal ne wo ks;
howe e , i does no ake in o accoun he low egime and pipe oughness. Al hough Da cy–
Weisbach is mo e accu a e, i is mo e challenging o implemen in eal- ime calcula ions. This
s udy p oposes an app oach ha combines hese wo me hods and adap s he pa ame e s in eal-
ime based on p essu e, eloci y, and low measu emen s, he eby imp o ing he accu acy o
hyd aulic modeling in he wa e supply ne wo ks o Nu a shon.
Keywo ds: node in low-ou low balance, e ec i e ic ion, ope a ion (ope a ional
condi ions), p essu e, algo i hm, new coe icien , hazen–williams coe icien , high- equency
noise, low- equency noise.
In oduc ion. Du ing p ac ical ope a ion, signi ican disc epancies exis be ween
calcula ed alues and ac ual measu ed da a, especially due o ac o s such as changes in he numbe
o consume s, empo al luc ua ions in p essu e, and unce ain ies in he hyd aulic g adien . These
ac o s ul ima ely educe he accu acy o calcula ions, which in u n hinde s he e ec i e
managemen o he wa e dis ibu ion sys em. To add ess his issue, a new app oach has been
de eloped. The main idea o he p oposed algo i hm is he in oduc ion o an adap i e coe icien
ha is upda ed based on eal- ime measu emen s. As a esul , he Hazen–Williams o mula
becomes adap i e, aligning he calcula ed low and p essu e alues mo e closely wi h he
measu ed da a. The EPANET so wa e is widely used o modeling wa e supply ne wo ks and
enables he analysis o ne wo k elemen s based on pa ame e s such as p essu e, low, and o he s.
In his s udy, a new algo i hm in eg a ing he EPANET pla o m was de eloped o he adap i e
iden i ica ion o he Hazen–Williams coe icien . This app oach adjus s he coe icien based on
eal- ime measu emen s, aiming o signi ican ly imp o e he accu acy o hyd aulic modeling.
Me hodology. The new coe icien , in o de o ensu e he s able analysis o he sys em, is
exp essed in he ollowing gene al o m:
𝑘(𝑡)=𝑓(𝑃(𝑡),𝑉(𝑡),𝑄(𝑡)) [1,2]
He e, 𝑃(𝑡) ep esen s he p essu e alue o e ime, 𝑉(𝑡)is he low eloci y in he pipes,
and 𝑄(𝑡)deno es he measu ed low a e. The algo i hm p ocesses eal- ime measu emen s coming
om he EPANET sys em and dynamically upda es he Hazen–Williams coe icien 𝐶. The
sequence o he algo i hm begins wi h he inpu o he ini ial wo king pa ame e s. C0 - ini ial
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Hazen–Williams coe icien , D - in e nal pipe diame e (m), L - pipe leng h (m), P - ini ial p essu e,
ini ial eloci y o low speed (m/s), d - ime (s), Senso add esses — inpu s om EPANET o
o he eal- ime measu emen sys ems. In he second s age, senso da a o measu ed alues a e
collec ed and il e ed. Measu emen s a e aken o e ime. The alues 𝑃(𝑡), 𝑉(𝑡), and measu ed
low a e 𝑄(𝑡)a e p ocessed h ough il e ing o educe signal noise. In many cases, eal
measu emen esul s exhibi andom luc ua ions o a iable p essu e and low ( o example, in
low o p essu e alues). To educe p ocess a iabili y, he algo i hm calcula es he a e age o he
las 𝑛measu emen s, ac ing as a il e by ou pu ing he mean o mul iple alues o he sys em.
𝑋𝑓(𝑡)=1
𝑛∑𝑋(𝑡−𝑖∗𝑑𝑡)
𝑛−1
𝑖=0 [3,4]
He e, 𝑋𝑓(𝑡)is he il e ed signal (ou pu alue), 𝑋(𝑡)is he eal measu ed signal (inpu
alue), 𝑛is he numbe o alues used o a e aging, 𝑑𝑡is he ime in e al, and 𝑖is he index
(sequence o he mos ecen alues). A low-pass il e allows slow-changing (smoo h) signals o
pass h ough while educing o comple ely elimina ing high- equency ( apidly luc ua ing, noisy)
componen s. 𝑌(𝑡)=𝑎∗𝑋(𝑡)+(1−𝑎)∗𝑌(𝑡−1)
He e, 𝑋(𝑡)is he inpu signal ep esen ing measu ed p essu e and low, 𝑌(𝑡)is he il e ed
signal, and 𝑎is he smoo hing coe icien (whe e 0<𝑎<1). In wa e ne wo ks, he e m "signal"
in he algo i hm ypically e e s o p essu e, low, o wa e consump ion. These signals a y o e
ime and exhibi wo ypes o dis u bances: high- equency noise— apid luc ua ions occu ing
wi hin seconds (such as senso e o s, elec ical noise, o pump pulsa ions), and low- equency
noise—slowly a ying pa ame e s o e longe pe iods.
Sou ces o low- equency noise include daily luc ua ions in consume demand. Fo
example, p essu e sha ply dec eases in he mo ning (07:00–09:00) and e ening (18:00–21:00),
while emaining ela i ely s able du ing he day ime. Al hough hese luc ua ions occu a a e y
low equency (daily cycle), hey ep esen signi ican sou ces o a ia ion o he sys em.[6]
Changes in he wa e owe o ese oi le el also con ibu e o low- equency luc ua ions.
The g adual ise and all o he wa e le el in he ese oi cause low- equency oscilla ions in he
p essu e signal wi hin he ne wo k. When pumps s a and s op o e ex ended pe iods o a e
au oma ically swi ched o and on mul iple imes pe day, he sys em p essu e expe iences slow
luc ua ions. Addi ionally, he g adual change in he hyd aulic g adien — o example, when
consump ion dec eases in a ce ain a ea—leads o a slow inc ease in p essu e. To allow low-
equency signals o pass and a enua e high- equency signals, he ollowing exp ession is used
o he il e . 𝐻(𝑓)=1
√1+(𝑓
𝑓𝑐)2
He e, 𝐻(𝑓)is he ampli ude coe icien o he ans e unc ion ( he a io o he ou pu signal
ampli ude o he inpu signal ampli ude), 𝑓is he signal equency (Hz),
and 𝑓𝑐=1
2𝜋𝑅𝐶 is he cu o equency.
Resul s. In he algo i hm, he model is selec ed based on he cha ac e is ics o he wa e
supply sys em and he le el o echnological in as uc u e (Case 1, Case 2, Case 3). Depending
on he a ailable sys em da a and he echnologies applied, he algo i hm chooses an app op ia e
compu a ional pa hway.
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Pa h 1 (Case 1) – Linea co ec ion based on p essu e and eloci y.
𝑘=1+𝑎∗𝑃(𝑡)−𝑃𝑝
𝑃𝑝+𝑏∗𝑉(𝑡)−𝑉𝑣
𝑉𝑣
This app oach op imizes he ela i e changes in p essu e and eloci y and inco po a es
hem in o he coe icien .
Pa h 2 (Case 2) – Mul iplica i e co ec ion based on p essu e and eloci y, whe e
empi ical alues a e used. 𝑘=(𝑃(𝑡)𝑎
𝑃𝑣)∗(𝑉(𝑡)𝛽
𝑉𝑣)
He e, 𝛼and 𝛽a e expe imen ally de e mined exponen s ha de ine he in luence o p essu e
and eloci y on he coe icien 𝑘.
Fi s , he heo e ical low is calcula ed using he Hazen–Williams o mula:
𝑄𝐻𝑊 =0,278∗С0∗𝐷2,63∗𝑆0,54
𝑘=𝑄𝑠𝑎𝑟𝑓
𝑄𝐻𝑊
and i is hen adjus ed o a physically easonable limi .
𝑘−€(0,5,1,5)
Upda ing he Hazen–Williams coe icien
𝐶(𝑡)=𝐶0∗𝑘
Calcula ing he slope (g adien ) 𝑆(𝑡)=𝐻𝑏−𝐻𝑓
𝐿
Applica ion o he Hazen–Williams Flow Fo mula
𝑄𝐻𝑊,(𝑡)=0,278∗𝐶(𝑡)∗𝐷2,63∗𝑆0,54
his o mula is used wi h me ic uni s, and he low esul is exp essed in li e s pe second
(L/s).
1-Figu e: Compa ison o eal low and models in he wa e acili y ne wo k.
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2- Figu e: Compa ison o eal p essu e and models in he wa e acili y ne wo k.
Conclusion. In he p oposed algo i hm, measu ed alues o p essu e, eloci y, and low
consump ion a e p ocessed and il e ed (using Mo ing A e age and Low-pass il e s). Based on
hese alues, he coe icien 𝑘(𝑡)is adap i ely upda ed, and he Hazen–Williams o mula is
adjus ed o eal condi ions. Th ee a ian s o he algo i hm (Case 1 – linea co ec ion, Case 2 –
ela i e indica o , Case 3 – low-based adjus men ) we e examined and hei esul s compa ed. In
p ac ice, he highes accu acy was achie ed by Case 3, as i di ec ly adap s o he measu ed low
alues.
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REFERENCES
1. Rossman, L.A. (2000). EPANET 2 Use s Manual. U.S. En i onmen al P o ec ion Agency,
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ime algo i hms).
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