=Paper=
{{Paper
|id=Vol-2740/20200137
|storemode=property
|title=Information Technologies to Estimation the Effectiveness of Water
Supply Systems Control Depending on the Degree of Model Uncertainty
|pdfUrl=https://ceur-ws.org/Vol-2740/20200137.pdf
|volume=Vol-2740
|authors=Sergey Dyadun
|dblpUrl=https://dblp.org/rec/conf/icteri/Dyadun20
}}
==Information Technologies to Estimation the Effectiveness of Water
Supply Systems Control Depending on the Degree of Model Uncertainty==
https://ceur-ws.org/Vol-2740/20200137.pdf
Information Technologies to Estimation
the Effectiveness of Water Supply Systems Control
Depending on the Degree of Model Uncertainty
Sergey Dyadun [0000-0002-1910-8594]
V.N. Karazin Kharkiv National University, Majdan Svobody 4, Kharkiv, Ukraine 61077
daulding@ukr.net
Abstract. The efficiency of implemented control depends on the degree of ade-
quacy of used models of object. The article introduces the criteria characteriz-
ing the degree of closeness of obtained solutions when using different types of
models of control object. The algorithm of estimation of quality and efficiency
of water supply systems control depending on the volume and composition of
operative information about the object under control is presented. Carried out
researches have shown, that for maintenance of optimum values of criteria of
quality and efficiency of water supply systems functioning on a control interval
it is enough to have pressure measurements in all local dictating points of a
network. Further increase in number of measurements does not lead to im-
provement of these criteria values. Researches were carried out with the use of
simulation modeling method of real water supply systems functioning. Infor-
mation technologies for solving the whole range of tasks necessary for getting
the result are described.
Keywords: control, model, criteria, efficiency, water supply system, simula-
tion.
1 Introduction: Problem Topicality and Research Aims
The efficiency of implemented control depends on the degree of adequacy of used
object models. In order to obtain estimates of control efficiency of water supply sys-
tems (WSS) on the time interval [0, T] depending on the degree of uncertainty of the
object model, i.e. on the volume and composition of operational information about its
states, we will use a simulation model of real WSS functioning. Much works is devot-
ed to mathematical modeling of WSS [1-4], theoretical bases of optimization and
operative control of flow distribution in engineering networks are laid in [5-7], there
are many other works on this subject [8-13]. By quality of functioning of WSS is
understood [6] probability of its purpose – to supply water to consumers in necessary
quantity under the set pressure according to requirements on an interval [0, T]. The
efficiency of WSS functioning is understood as [6] the cost of a resource (water, elec-
tric power) for providing the preset quality of its functioning on the interval [0, T].
The purpose of these studies was to develop an algorithm for solving the task of esti-
mating the efficiency of WSS control depending on the volume and composition of
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
operational information about the object under control and carrying out the corre-
sponding analysis.
2 Processes Control Simulation of Water Supply Systems
Creation of imitation models of technological processes of functioning WSS and algo-
rithmization of processes of control of their modes allows in practice to raise quality
and efficiency of functioning of these systems. At designing of the automatized con-
trol systems of technological processes of WSS the most important is a stage of work-
ing out of algorithms of operative control over modes of functioning WSS. At an
estimation of their efficiency it is necessary to consider both characteristics of techno-
logical process of giving and distribution of water, and casual character of influences
to which WSS is exposed. This circumstance makes it necessary to create simulation
models not only of WSS and the environment in which it operates, but also the system
of automatized control of functioning its modes as a whole.
The presence of such simulation models allows to generate and analyze deeper the
processes of flow distribution in real WSS, to play on the models and choose the op-
timal structure of the control system taking into account the peculiarities of a particu-
lar WSS (dimensionality, network configuration, number of active sources), to evalu-
ate the quality and efficiency of the implemented control. Besides, an adequate simu-
lation model allows estimating the state of all WSS elements by actual measurements
of output parameters in a number of them (the measure of proximity of these values is
the main criterion of adequacy of the simulation model to the real process).
Essential feature of problems of operative control of flow distribution in WSS is
absence, in a general case, analytical dependencies for output parameters of control
and criteria of quality and efficiency of functioning WSS that does practically impos-
sible search of analytical solutions. The only acceptable method of solution is imita-
tion modeling of WSS functioning, which allows to get mathematical expectations of
evaluations of quality criteria of WSS modes control efficiency under observance of
imposed technological restrictions. The software implementation of the corresponding
algorithms meets to the solution of individual tasks [6,15] of the operational control
of WSS in the simulation model.
Simulation model of WSS is a tool for research of efficiency of algorithms at the
decision of practical problems of increase of efficiency and quality of operational
control of modes of functioning WSS. It is expedient to use the simulation model for
training the dispatch service personnel in the pre-launch period of automatized pro-
cess control systems. Also it can be used as a standard at check of adequacy of the
decisions received on more simple, aggregated models WSS.
3 Conceptual Scheme of Information Technology to Support
Operation Control in Water Supply Systems
The process of operational control of WSS is divided into two stages: operational
planning of modes of functioning of WSS and their stabilization.
The solution to the problem of operational control of the functioning of WSS is
achieved by decomposing the original problem into number of hierarchically related
tasks [5-7]. Consider the structure of solving problems of operational control of the
functioning of WSS (Fig.1).
Based on the operational information getting simultaneous data from sensors in-
stalled at controlled points in the network, the task of identification of the state of the
flows distribution in WSS is solve. The multiple solution of this task allows to deter-
mine for each node of WSS model the vector of evaluated water consumptions, which
is then use as a series to predict the water consumption of each of these nodes for the
entire control interval. The solution of the task of predicting the values of nodal water
consumptions for a given time interval is the input source information directly for the
problem of operational planning of the operating modes of WSS. The solution of the
problem of operational planning of the operating modes of WSS is determine as a
result of solving of the sequence of tasks. For each discrete time instant k = 1,2, ...,
K, the task of the optimal load distribution between pumping stations (PS) is solved.
As a result of its solution, for all k = 1,2, ..., K, the values of water consumption and
pressures at WSS outputs are determined, which ensure the pressure in the nodes is
not lower than the set ones. To ensure the obtained parameters at WSS outputs, as a
result of solving for all k = 1,2, ..., K the task of optimization the PS operating mode
for each of them are determine the optimal structure and parameters of its functioning.
However, the solution obtained at the operational planning stage should be invariant
with respect to the predicted level of stochastic environmental disturbances. To study
its effectiveness with a known level of stochastic disturbances, the problem of analyz-
ing the flux distribution in WSS when solving the model of control actions on the PS
is solved. This task is based on a mathematical model of steady flow distribution in
WSS with active elements. The described sequence of solving the operational plan-
ning problem makes it possible to obtain a solution that is invariant with respect to the
predicted level of stochastic disturbances, which guarantees the necessary quality of
WSS operation over the entire control interval at maximum efficiency. The pressure
stabilization at the dictating points of WSS partially compensates for disturbances
acting on the control object in order to prevent the regime parameters from exceeding
the permissible range.
The structure of solving the complex of tasks of operational control of the function-
ing of real WSS is presented (Fig.1).
4 Research Results
Let's denote L - set of pump stations WSS, M - set of trunk sites WSS, N - set of
knots of a network with consumers; E L M N ; hi , qi , i E – pressure loss
and the expense in i-th site WSS, H inp i , qinp i , H out i , qout i , i L – pressure and the
expense on an input and an output i-th PS. Let us introduce the criteria characterizing
the degree of closeness of the obtained solutions when using different types of WSS
model. We will evaluate the effectiveness of solving the problem of controling the
Getting data from sensors installed at controlled points in the network
Identification of the state of water supply system
Getting data from sensors installed at controlled points in the network
Identification of the state of water supply system
Forecast of Forecast of water Forecast of water
water consump- consumption in consumption in
tion in the 1st the 2nd node of the n-th node of
node of WSS WSS WSS
THE STAGE OF OPERATIONAL PLANNING OF THE FUNCTIONING MODES
OF THE WSS
Optimal load distribution between pumping stations
Optimization of Optimization of Optimization
the functioning the functioning of the functioning
mode of the 1st mode of the 2nd mode of the m-th
pumping station pumping station pumping station
Analysis of flow distribution in WSS when implemented on a model of
control actions on pump stations
THE STAGE OF STABILIZATION OF THE FUNCTIONING MODES OF WSS
The pressure stabilization at the dictating points of WSS
The pressure stabilization at the dictating points of WSS
Fig.1. Conceptual scheme of information technology to support
operation control in water supply system
modes of operation of WSS on the basis of an aggregated model with respect to solv-
ing this problem on the basis of a complete WSS model, which is taken as a standard.
On set L of all WSS inputs we will introduce a measure characterizing the degree of
closeness of the values of the variables determining their states when solving on the
basis of an aggregated and complete WSS model [14, 15]:
2 2
* *
1 Hout i H out i q out i q out i
*
P(U, U ) . (1)
l iL H*out i q*out i
Since the variables H out i , qout i are measured in different units, the use of measure
(1) makes it possible to bring disparate scales to a single, dimensionless one. In addi-
tion, let us introduce a measure characterizing the maximum deviation of the variables
qout i , H out i , i L , that determine the states of the WSS inputs from their optimal
values q*out i , H *out i
2
Hout i H*out i
P0 (Hout i ,H* out i ) max , i L. (2)
iL H*out i
2
*
q out i q*out i
P0 (q out i ,q out i ) max , i L. (3)
iL *
q out i
Let’s consider that among the set of variables, hi , i N , characterizing the state of
the outputs of the complete WSS model, the values of not all are known, but only
some of them, hi , i N0 N , the values of the other variables, hi , i N \ N 0
are noisy. It is shown in [5] that if the observed conditions of the WSS are not met,
an artificial addition of the composition of the observed variables, hi , i N \ N 0 in
the assumption of a uniform law of their distribution, allows us to obtain practically
acceptable results. Therefore, by successively changing the number and composition
of the set variables, hi , i N0 at the network outputs (the values H out i , qout i ,
i L are always known in real conditions of WSS operation), and assuming that the
other variables, hi , i N \ N 0 are distributed according to a uniform law, it is possi-
ble by solving the problem of identification of WSS [5] to obtain estimates of values
of measured and all other functionally related variables characterizing the flow distri-
bution in the network.
The algorithm for estimating the efficiency of WSS control depending on the degree
of uncertainty of the control object model is as follows:
1. Obtaining optimal estimates, further used as a benchmark, when the conditions
for the observation of WSS are met.
1.1 A certain prehistory of implementation of observed variables at time moments
k 0, 1, 2,... preceding the control interval [0, T ] , i.e. information state of the
species, is considered to be given:
P0 Hinp i (k), Hout i (k), qout i (k), h j (k) | i L, j N . (4)
For each k 0, 1, 2,... the task of identification of the water supply network state
~ (н)
is solved, as a result of which the estimations of nodal discharge values q j (k), j N
at each of these moments become known.
~ (c)
1.2 On the basis of these estimations q j (k) at the moments of time
k 0, 1, 2,... for each node j N of the network the forecast of flow rate
^ (c)
qj (k), j є N for the control interval [0, T ] is made. Besides, on the basis of the
prehistory of values, Hinp i (k) , k 0, 1, 2,... i L their values are predicted for
the interval [0, T ] .
1.3 For each moment k 0,1, 2..., K the problem of optimal load distribution
between PS is solved. We receive the reference values H*out i (k), q *out i (k), i L .
1.4 Determining the optimum control actions on the pumps of each PS
k 0,1, 2..., K with the set values H*out i (k), q*out i (k) as well as H*inp i (k), i L
[16]. Calculation of values of efficiency criterions Y2i* (T), Y2* (T) of functioning of
WSS on a control interval [0, T ] .
2. The conditions for the observation of WSS are not fulfilled, so we supplement the
composition of pressure measurements, h j , j N \ N 0 in the network nodes in the
assumption of the uniform law of their distribution.
2.1 In this case, the information state of WSS on the interval [T r ,0] is
P Hinp i (k), Hout i (k), q out i (k), h j (k) | i L, j N0 N . We solve the problem of iden-
tification of the network state k 0, 1, 2,... and calculate the cost estimates
~ (c)
q j (k) .
~ (c)
2.2 Predict the values of nodal costs q j (k), j N , as well as Hinp i (k), i L , the
interval [0, T ] .
(c)
2.3 Optimal load distribution between PS WSS k 0,1, 2..., K at values q j (k) ,
~ ~
calculated at stage 2.2. We receive H* out i (k), q* out i (k), i L .
2.4 Determining the optimal structure and parameters of each PS [16]
~ ~ ^
k 0,1, 2..., K at the given values H* out i (k), q* out i (k) as well as Hinp i (k) .
2.5 Analysis of the flow distribution in the WSS at implementation by the model of
control actions on each PS k 0,1, 2..., K and values of node expenditures
(c)
q j (k), j N , received at the stage 1.2 [14].
3. Based on the results of Step 2.5 we calculate the values of the quality criteria
Y0i (T ) , Y1i (T ) , Y1*i (T ) , Y1 (T ) , i N and efficiency Y2i (T ) , Y2 (T ) , i L of
the WSS functioning at the interval [0, T ] [5]. We compare them with the optimal
values of the quality and efficiency criteria of WSS functioning in the interval [0, T ] ,
obtained at stage 1.4.
4. We compare the values of H out i (k), qout i (k), i L , k 0,1, 2..., K , obtained at
stage 2.5, with the reference values of these parameters obtained at stage 1.3 in ac-
cordance with expressions (1) – (3).
5. Change the number or composition of observed variables h j (k ) , j N0 N
k 0, 1, 2,... and return to step 2.1.
Analyzing thus at different number and composition of observed variables h j (k )
j N , k 0, 1, 2,... , we will receive estimations of quality criteria and effi-
ciency of WSS functioning on a control interval [0, Т], and also estimations of criteria
(1)–(3), characterizing a degree of closeness of optimum decisions received at enter-
ing of corresponding value of an error at the expense of incompleteness of composi-
tion of the operative information on operated object. If the corresponding level of
stochastic environmental perturbations is set, this algorithm can be extended to the
calculation of estimates of the efficiency of WSS control depending from the degree
of uncertainty of the models of the control object and the environment.
5 Software for the Implementation of Modeling and Operation
Control Tasks of Water Supply Systems
These studies were carried out by the author on his own, while his own developments
of algorithms and information technologies was used, which are based on the scien-
tific works of professors A.G. Evdokimov and A.D. Tevyashev [1,5-7].
Software for solving some of these tasks began to be developed in the languages of
Fortran, Pascal and others. The basic is the task of hydraulic calculation, on its basis
many optimization tasks are solved. Gradually, scientific developments in this direc-
tion developed, supplemented and improved, they were introduced in many large
cities. Contracts with water supply enterprises, depending on the tasks required and
problems to be solved, dictated what the developed software, databases, etc. should
be. The development of list structures instead of the matrix form of describing the
structure of a network graph was a major breakthrough in software implementation. It
allowed to make hydraulic calculations of city water supply networks in seconds, and
to solve many of optimization tasks listed in the article.
Currently, all software is implemented in C++, some tasks in accordance with
agreements at the request of water supply enterprises are implemented in other pro-
gramming languages and tools, especially using standard software package
EPANET2 [17]. The developed databases were implemented with MS Access DBMS.
6 Conclusions and Future Work
The conducted researches have shown that for maintenance of optimum values of
criteria of quality and efficiency of functioning of WSS on a control interval [0,Т] it is
enough to have pressure measurements only in all local dictating points of a network
[6]. Further increase in the number of measurements does not lead to improvement of
these criteria.
This conclusion is inextricably linked with the problem of optimal placement of
sensors on the network. Obviously, for the preceding and subsequent control intervals
not only the position of local dictating points but even the global dictating point
(GDP) can change [6]. Therefore, it is reasonable to use many GDP subintervals of
some long time interval as a set of control points in the network. In practice, when
determining the points for optimal location of sensors on the network, it is necessary
to first install the devices of temporary control of parameters in the most "suspicious"
points, determined on the basis of expert estimates. After a long interval of time it is
possible to place automatic control devices of parameters in the GDP of its subinter-
vals.
In real conditions of WSS functioning, if to provide known a priori value of the
minimum allowable one taking into account the value of pressure reserve in the GDP
or other characteristic point of the network, the set quality of WSS functioning at the
maximum efficiency can be achieved also at control on one controlled point on the
basis of use of the aggregated model of object [15]. It is obvious that such aggregated
models can be used to control the technological processes of the functioning of all
real WSS, for which the set of characteristic points located in the zone of joint influ-
ence of all PS working on WSS is not empty.
The use and widespread adoption of information technologies of optimal control
operation of WSS allows in practice to improve the quality and effectiveness of their
functioning by reducing the excess pressure in the networks (and, consequently, re-
ducing unproductive costs of water), reducing electricity costs, reducing the probabil-
ity of occurrence of emergency situations in networks.
References
1. Evdokimov, A.G.: Optimal problems on the engineering networks. - Vishcha Shkola,
Kharkov, 153 p. [in Russian] (1976)
2. Fallside, F., Perry, P.F., Burch, R.H., Marlow, K.C.: The Development of Modelling and
Simulation Techniques Applied to a Computer - Based - Telecontrol Water Supply Sys-
tem. In: Computer Simulation of Water Recourses Systems, No.12, pp. 617-639 (1975)
3. Abramov, N.N.: Theory and Methodology of Calculation of Water Supply and Distribu-
tion Systems. Stroyizdat, Moscow, 288 p. [in Russian] (1985)
4. Merenkov, A.P., Hasilev, V.Y.: Theory of hydraulic circuits. - Nauka, Moscow, 279 p. [in
Russian] (1985)
5. Evdokimov, A.G., Tevyashev, A.D., Dubrovskiy, V.V.: Modeling and optimization of the
flow distribution in the engineering networks. - Stroyizdat, Moscow, 368 p. [in Russian]
(1990)
6. Evdokimov, A.G., Tevyashev, A.D.: Operational control of the flow distribution in the en-
gineering networks. - Vishcha Shkola, Kharkov, 144 p. [in Russian] (1980)
7. Evdokimov, A.G., Tevyashev, A.D., Dubrovskiy, V.V.: Streaming distribution in engi-
neering networks. - Stroyizdat, Moscow, 199 p. [in Russian] (1979)
8. Tevyashev, A.D., Matvienko, O.I.: About one approach to solve the problem of manage-
ment of the development and operation of centralized water– supply systems. In: Econ-
techmod. An International Quarterly Journal. Vol. 3, Issue 3, pp. 61–76 (2014)
9. Reinbold, C., Hart, V.: The search for energy savings: optimization of existing & new
pumping stations. In: Florida Water Resources Journal, pp. 44–52 (2011)
10. Burgschweiger, J., Gnadig, B.B., Steinbach, M.C.: Nonlinear programming techniques for
operative planning in large drinking water networks. In: Konrad–Zuse–Zentrum fur Infor-
mationstechnik Berlin. – Berlin: ZIB-Report. (2005)
11. Pulido–Calvo, I. Gutiérrez–Estrada, J.C.: Selection and operation of pumping stations of
water distribution systems. In: Environmental Research Journal, Nova Science Publishers.
Vol. 5, Issue 3, pp. 1–20 (2011)
12. Lipták, B.: Pumping station optimization. In: Control Promoting Excellence in Process
Automation, pp. 12–19 (2009)
13. Dolinskii, A., Draganov, B., Kozirskii, V.: Nonequilibrium state of engineering systems.
In: Econtechmod. An International Quarterly Journal. Vol. 1, Issue 1, pp. 33–34 (2012)
14. Dyadun, S.V.: Mathematical modeling of the established flow distribution in the water
supply systems. In: Radio electronics and informatics. – Kharkov, KNURE. No. 4. pp. 54-
56 [in Russian] (2000)
15. Dyadun, S.V.: Modeling and rational control of water supply systems with minimum vol-
ume of operative information. In: Radio electronics and informatics. – Kharkov, KNURE,
No. 20, pp. 111-115 [in Russian] (2002)
16. Dyadun, S.V.: Selection of the optimal combinations of the pump station units for the city
water supply system. In: City utilities. – Kiev: Tehnika, Issue 1, pp. 63-70 [in Russian]
(1992)
17. EPANET: Application for Modeling Drinking Water Distribution Systems. Available at:
https ://www.epa.gov/water-research/epanet (accessed on July 17th, 2020)