- Email: [email protected]
Adaptive Optimization Approach for the Supervision of an Irrigation System
Copyright © IFAC Management and Control of Production and Logistics, Carnpinas, SP, Brazil, 1997
ADAPTIVE OPTIMIZATION APPROACH FOR THE SUPERVISION OF AN IRRIGATION SYSTEM
R. M. Faye t*; F. Mora-Camino +t; A. K. Achaibou t
tLAAS du CNRS 7, Avenue du Colonel Roche 31077 Toulouse - France (jaye, mora, [email protected] )Tel: (33) 5 61336470 Fax: (33) 5 61336936 +Ecole Nationale de l'Aviation Civile 7, Avenue Edouard Belin 31055 Toulouse - France Tel: (33) 5 62174358 Fax: (33) 5 62174403 *Ecole Superieure Polytechnique B.P.1O Thies - Senegal ([email protected]) Tel: (221) 5142091514239 Fax: (221) 511476
Abstract: In this communication is considered the problem of the design of an efficient supervision system for a large irrigation system composed of a sequence of reaches which supply water for agricultural, industrial and domestic uses. Here the irrigation system is viewed as a hybrid dynamical system subject to continuous operations broken by discrete events when new goals must be defined on the short term to guarantee an efficient use of the upstream water resource. Here the automation of the supervision of this process is considered and it appears that, until recently, very little has been obtained on methodological grounds to face at the tactical level the large uncertainties that impair the operations of such systems. So in this communication, this problem is coped with through an adaptive optimization approach where the occurrence of significant events leads to the automatic definition of new short term optimization problems to handle new operational situations. Copyright © 1998 IFAC Keywords: Irrigation Systems, Hybrid Dynamics, Intelligent Systems, Optimization, Supervision.
long term goals with the actual operational state of the system while a fault detection system is implemented. At this level, discrete decisions must also be taken to enforce security of operations and equity in deliveries. At the control level effective inflows and deliveries are computed on line to ensure precision of service and measurements are processed to check the operational integrity of the control system and ensure the continuity of the service. In the literature, General Predictive Control has been considered to achieve successfully the control level task (Sawadogo 1992), while at the supervision level empirical solutions for short term resource management have been developed on a case by case approach (Levin 1969).
1. INTRODUCTION Since the origins of History, human ingenuity has been reported to be continuously challenged by the development of new ways and means to master water resources. The Management of water resource systems can be considered to be composed of three levels: a control level , a supervision level and a planning level. At the planning level, irrigation systems are managed on the long term so as to guarantee availability of the resource and efficiency in its use over the whole cycle duration. At the supervision level, reference values and control parameters are optimized on the short run to adequate
363
In this communication, the water resource supervision problem is tackled, considering that irrigation systems are hybrid dynamics systems for which the resource management task of the supervision level must revise its goals dynamically when significant discrete events occur.
The meeting of the above requirements is not at all an easy task and many difficulties can be quoted: - Difficulty to manage in the long term the water resource since forecasts of available global reserves as well as of global demand are often inaccurate, - Difficulty to control efficiently the timing of inflows since transportation delays can change appreciably, - Difficulty to anticipate needs on the short term since the behaviour of users with respect to water demand is not well known, - Difficulty to use quantitative techniques since the water transport phenomenon obeys to complex dynamics, - Difficulty to operate a dense network of sensors and communication devices to get an on line image of the current state of the system.
2. THE MANAGEMENT AND CONTROL OF THE IRRIGATION SYSTEMS The global objective of controVsupervision Iplanning structures (Yacov, et aI., 1973) for irrigation systems is to meet, regardless of uncertainties, water demand (agricultural, industrial and domestic) at each discharge point while maintaining an acceptable level of water all along the reaches and in the reservoirs during any given period. To turn effective the design of these structures, the main characteristics of such systems must be taken into account. Nowadays, a large variety of irrigation systems can be found around the world, from temperate to arid subtropical regions, considering either large river basins with varied geography (relief and vegetation) or multiple isolated micro-regions. However, these systems present some common characteristics which must be taken in consideration for the effective solution of management and control problems related with this resource: - the operation is distributed over space and time, - the transfer dynamics are characterized by hard delays, - the presence of strong operational uncertainties cannot be bypassed, - the estimation of final users demand is a complex task. In general terms, advanced irrigation systems should present desirable properties such as: availability, continuity, equity, precision, security and integrity.
~!SO e(t~~ Reservoir
Qi(t)
I
3. A HYBRID MODELLING APPROACH FOR THE OPERATIONS OF IRRIGATION SYSTEMS The basic irrigation system considered for illustration in this study is of the more common nature and is composed of the following elements (fig. 1): an upstream reservoir with control gates, a sequence of interconnected reaches with downstream control gates and off-take discharge devices, a final exit section with a flow measuring device. It appears that to cope with the management of the water resource in the short run, the operations of an irrigation system must be described in two ways: 1) In terms of continuous transfer relations relating inflows to outflows in each reach and following non-linear dynamics such as:
2i(t) = !(Zi(t), Q/ 1'), Qi +1(t), P;(t), S/t» 't
=1 to N
Reach i
UUHHHUUUUU1...;..i_ _ _ _ llconttOl Gate
~~
(>: •
~""""'7"" " "S::":Pi(t) Si(t)
Fig. 1: Main Components of an Irrigation System
364
Qi+l(t)
(1 )
4. THE PROPOSED APPROACH FOR SUPERVISION AUTOMATION
where N is the number of reaches, Z;(t) is the downstream water level in reach i at time t, Qlt) is the upstream inflow to reach i at time 't, Qi+l(t) is the downstream outflow to reach i at time t, Si(t) is the spilled outflow at time t, Pi(t) is the downstream pumped flow at reach i. These equations can be discretized and linearized with a good approximation (Sawadogo 1992) leading to relations such as:
The above hybrid model of the operations of irrigation systems leads to the definition of a finite set of discrete operational situations, or states, to which can be attached different short term goals. Then it appears that the resource management task at the supervision level is concerned with a stochastic sequence of differentiated situations. It seems quite impossible to attach to this stochastic process a set of state transition probabilities useful for tactical management. So the approach proposed here is to do first an on line detection of state transitions, then to identify the current situation, and finally to reformulate, following an adaptive philosophy, an optimization problem whose goals and constraints are in accordance with the current situation.
.<1
(2)
where ht t are the transfer coefficients associated to the linearized model and cri is a reference area for each reach i (Sawadogo 1992). In this case, the upstream water reserve evolves following relation:
4.1 Definition of the set of discrete operational situations
(3)
where et is the water input rate to the reservoir and QIt the upstream inflow of reach 1 at time t.
The definition of such a set must follow some basic considerations: - only significant events with respect to the management of the water resource must be taken into consideration, - the combinatorial multiplication of cases generated by the different operations states of each subsystems must be contained, - every operational situation must be covered by the set of discrete situations. Relevant discrete events for the operations of this kind of systems are: - saturation events: some effective water levels reach their upper or lower limits at an unexpected time, - failure events: some devices (pumps, gates) present a failure and new ways must be defined to minimize the damage to the service level, - discrete decisions events based on calendar, meteorological or present state considerations. Therefore, these states can be considered to be composed of three complementary components: - a supply component related with the distribution of the resource along the irrigation system and involving mainly water levels in reaches and reservoirs, - a system component related with the operational state of its devices (sensors and actuators), - a demand component related with past deficits and short term predictions (meteorology). So, the different states can be characterized by a triplet (p, q, r) with p E 0, q E S, rED, where 0 is the discrete set of sub-states related to the supply component, S is the set of sub-states related to the
2) In terms of qualitative or logical terms related with the degree of saturation of water levels, the intensity of perturbations (rains or dry periods) and the operational state of downstream control gates, pumps and off-take discharge devices. This description is concerned with : - physical constraints such as: Zmin < Z.(t) < Z~ , I I 0$ Qi(t) $ Qi(t) $ QInaJ< 0$ fl(t) $ P;(t) $ flITWU. 0$ Stet) $ SiITWU.(Zi(t»
Vr!un
$ V(t) $ V~
0$ SOt $ Sgw'(V(t» (4)
i=l to N, where Qmax and pITWU. are nominal flows I I capacities, Qi (t) and ~ (t) are actual capacities. For instance when the pumping devices of reach i are down, ~ (t) =0. - qualitative evaluations of actual water demands in view of past deliveries and current meteorology. Note that .here fuzzy techniques can be of great interest to qualIfy and compose these evaluations (Faye et al. 1996). ' ,
365
system component and D is the set of sub-states related with the demand component.
is of the linear form: to+T N I IAit(Df -p/).t:J.t pi .Q: t+to i=1
min
4.2 The design of the Knowledge Based state transition detection System
(5)
under the restrictions:
Here the State Knowledge Based System is devoted to two different supervision tasks: - identification of present state and consequently detection of state transitions, - diagnosis of the current situation. The identification task can be achieved for each component of the states. In relations with the supply component, the identification function may be realised using crisp or smooth definitions of the boundaries of the discrete state and IF-THEN rules can be used to determine the effective membership of the supply component. The system component state identification can be implemented using an event driven state transition graph. It is of course supposed that at the surveillance level, any significant failure can be promptly detected and informed to the supervision level. For a given set of states, the human operator interference is necessary to define tactics to be followed. For other situations, tactics to be followed can be deduced directly from the current state transition. The state transitions that should be submitted to the human operator must be defined beforehand by expert analysis. With respect to the demand component, short term predictions of demand, based on past statistical data and current deficits are corrected according to external perturbations such as heavy or sustained rains, or such as breakdowns in the distribution network. So, if the subsequent discretization leads to the identification of the current discrete state in relation to water demand, this function provides also another valuable information for the management of the resource: an updated short term prediction of demand to be used in the optimization process. The diagnosis system operates as an alert system for the human operational manager and must be able to submit to him intricate tactical choices.
0:::; Qi(t) :::; Qi(t)
0:::; P;U):::;
(6)
min{p;(t),D:}
(7)
0:::; Sit s; SrlaX(ZiU»
(8)
< 2.(t) < zmax I I
(9)
Z~n I
V~n S; V(t) S; V~
(10)
OS; SOt:::; S;ax(V(t»
(11)
where Df is the predicted or assigned demand rate and
P;t is the delivery rate for period (t, t+t:J.t) at
reach i, {I"it> i = 1 to N, t E [ to, to+T]} is a set of deficit weightings for the objective function (equation 5).
Equation (6) and (7) are flow capacity restrictions, equation (9) and (10) are state restrictions. At the end of the optimization the final time constraints can be such as: ?+T+I ~..,t+T+1 ~..,t+T+1
~rrnx
~mn
Lt
i=ItoN
~:;~V;+T~~
(12) (13)
Note that the optimization objective can be written equivalently as: max
to+T N I IAif(p;f. M ) f=foi=1 (14)
where predicted or assigned demand rates are no more present. So, it becomes clear that to the supply component, sub-states transitions are attached variations in the transfer coefficients of the state (equation 2), to the maximum values of downstream outflows (restriction 6) and spilled outflows (restrictions 8 and 11). To the system component, sub-state transitions are attached variations to the maximum values of downstream outflows (restriction 6) and to the maximum values of downstream pumped flows
4.3 Generation of short term resource optimization problems
(restriction 7), determining P;(t) within the interval [ According to the tactics chosen, a set of relevant objectives and effective constraints is selected to define the current short term optimization problem which defines on line reference values for the control system. An acceptable formulation (Carpentier, et al. 1993) of the standard tactical optimization problem
0, min { p;max, Df }]. Also,
whether or not the
satisfaction of the current demand is postponed until the failed devices are restored, the demand rates appearing in restriction (7) must be modified. To the demand component sub-state transitions, are attached adaptations of the weightings (equation 5)
366
demand module which evaluates uncertain users behaviour and a decision module to face failure of devices. In fig. 3 are displayed water levels in normal operating conditions. Here. a nominal water level is assumed in each reach with a random demand. Fig. 4 displays water level variation with failed pump in reach 2. The strategy adopted in this case consists of stocking water in the second reach and postponing current demand until the failed device is restored. This results in an increase of water level in reach 2. Fig. 5 takes up again the previous case but here. there is saturation in the upper water level in reach 2.
and of the demand rates appearing in restncttons (7). The basic approach proposed in this communication is represented in fig. 2.
5. SIMULATION A three-reach canal with a pumping station is considered for the simulation. Two cases are studied for validation and structuring the approach: • water resource management evaluation with nominal conditions including a strategic resource allocation and a random demand evaluation. • evaluation of the strategy to face device failures. Thus three modules have been implemented: a physical module which describes the system. a
Strategic ManagementiLong term planning~ Long Term Constraints & Choices
Resource Supervision System
,------------------------------------------------- -----------, Calendar Tim.c;.......;--aI
Meteorol~gy I I IL
Formulation and Solution of Short term Water Resource Optimization Problem
Human Supervisor
State Identification (K.B.S)
State Diagnosis
____ _
Reference Values &Thresholds
-------------------------------------------------, :- . .. -_............. . _.... . ............... . . ~
Measurements
Measurement & Control ~ Maintenance
Failures Events
.......... ...... .. ...... .. .. ...... ... .. ..... ...
.... .....
+...... .
-!; Fault Detection & Identification t····· ........;
I..-_ _ _ _ _ _ _ _ _ _ _ _ _
. ........... . .. . . -- . . .. -. . . -_ ... . .. . . _-_ ..... .
Fig. 2: Structure of the proposed Resource Supervision Functions
3.02 fIICI
3.01
m:=
3.02
Wala' atvel in reachl
~ters
3.015
3.015
3.01
3.01
3.005
3.005
3.005
2.995 2.99 2995
2.995
2.985
2.99 2.99 0
20
40
60
80
2985
0
20
2.98 40
Time inbours
60
Time in hours
Fig. 3: Water level in normal operating conditions
367
80
0
40
80 Time In bOlUS
60
4.5 meters
3.06
""Iers
meters
3.04 3.02 3.5 2.95
2.98
2.9
2.5
0
20
40
60
80
0
20
40
Tune in 00urs
60
80
2.96
0
20
40
Time in hours
60 80 Time inooW"S
Fig. 4: Water level in presence of failed device in reach 2 without saturation
).1 . - - - - - - - - - - - - - . Watu itnlin ftac:bl
4.5
).os
3.5 2.95
2.9 L..--.,..20--....:40'---t50~-~80 0
2.50~-----:2~0--40~-~60:----'80
20
4()
Time in
TiffW'. '" hnnr~
60
80
Time in hours
Fig. 5: Water level in presence of failed device in reach 2 with saturation
6. CONCLUSIONS
REFERENCES
In this communication, the design of a water resource supervision function for an irrigation system has been considered. The paper brings out the possibility of treating the automation of this function via two fields of knowledge: Operations Research methods for the generation of short term resource optimization problems and Intelligent Systems techniques for the design of the knowledge based state transition. Considering that subsystems are never uncoupled, adaptive optimization can be a way of tackling the problem avoiding thereby a co-ordination method which is necessary in hierarchical approach (Yacov, et aI., 1973) but difficult to apply to this kind of system. The main advantage of the proposed approach is that it is a global combined approach permitting to evaluate dynamically effective inflows and deliveries. The proposed approach has been already partially validated through a simulation study involving mainly re-optimization in presence of failed devices.
Carpentier, P., and G. Cohen (1993). Applied Mathematics in Water Supply Network Management. Automatica, Volume 29, N° 5, pp. 1215-1250. Faye, R.M., F. Mora-Carnino and K.A. Achaibou (1996). The Contribution of Intelligent Systems to Water Resource Management and Control. ]oumees Hispano-Franfaises, Systemes Intelligents et Controle A vance, Barcelone 12-13 Novembre. Levin, o. (1969). Optimal Control of Storage Reservoir during Flood Season. Automatica, Volume 5, pp. 27-34. Sawadogo, S. (1992) Modelisation, Commande Predictive et Supervision d'un Systeme d'Irrigation. PhD Thesis University Paul Sabatier Toulouse Avril, N° 1161. Yacov, Y. H.and D. Macko (1973) Hierarchical Structures in Water Systems Management. IEEE Transactions on Systems, Man, and Cybernetics, July, pp. 396-402.
368
ADAPTIVE OPTIMIZATION APPROACH FOR THE SUPERVISION OF AN IRRIGATION SYSTEM
R. M. Faye t*; F. Mora-Camino +t; A. K. Achaibou t
tLAAS du CNRS 7, Avenue du Colonel Roche 31077 Toulouse - France (jaye, mora, [email protected] )Tel: (33) 5 61336470 Fax: (33) 5 61336936 +Ecole Nationale de l'Aviation Civile 7, Avenue Edouard Belin 31055 Toulouse - France Tel: (33) 5 62174358 Fax: (33) 5 62174403 *Ecole Superieure Polytechnique B.P.1O Thies - Senegal ([email protected]) Tel: (221) 5142091514239 Fax: (221) 511476
Abstract: In this communication is considered the problem of the design of an efficient supervision system for a large irrigation system composed of a sequence of reaches which supply water for agricultural, industrial and domestic uses. Here the irrigation system is viewed as a hybrid dynamical system subject to continuous operations broken by discrete events when new goals must be defined on the short term to guarantee an efficient use of the upstream water resource. Here the automation of the supervision of this process is considered and it appears that, until recently, very little has been obtained on methodological grounds to face at the tactical level the large uncertainties that impair the operations of such systems. So in this communication, this problem is coped with through an adaptive optimization approach where the occurrence of significant events leads to the automatic definition of new short term optimization problems to handle new operational situations. Copyright © 1998 IFAC Keywords: Irrigation Systems, Hybrid Dynamics, Intelligent Systems, Optimization, Supervision.
long term goals with the actual operational state of the system while a fault detection system is implemented. At this level, discrete decisions must also be taken to enforce security of operations and equity in deliveries. At the control level effective inflows and deliveries are computed on line to ensure precision of service and measurements are processed to check the operational integrity of the control system and ensure the continuity of the service. In the literature, General Predictive Control has been considered to achieve successfully the control level task (Sawadogo 1992), while at the supervision level empirical solutions for short term resource management have been developed on a case by case approach (Levin 1969).
1. INTRODUCTION Since the origins of History, human ingenuity has been reported to be continuously challenged by the development of new ways and means to master water resources. The Management of water resource systems can be considered to be composed of three levels: a control level , a supervision level and a planning level. At the planning level, irrigation systems are managed on the long term so as to guarantee availability of the resource and efficiency in its use over the whole cycle duration. At the supervision level, reference values and control parameters are optimized on the short run to adequate
363
In this communication, the water resource supervision problem is tackled, considering that irrigation systems are hybrid dynamics systems for which the resource management task of the supervision level must revise its goals dynamically when significant discrete events occur.
The meeting of the above requirements is not at all an easy task and many difficulties can be quoted: - Difficulty to manage in the long term the water resource since forecasts of available global reserves as well as of global demand are often inaccurate, - Difficulty to control efficiently the timing of inflows since transportation delays can change appreciably, - Difficulty to anticipate needs on the short term since the behaviour of users with respect to water demand is not well known, - Difficulty to use quantitative techniques since the water transport phenomenon obeys to complex dynamics, - Difficulty to operate a dense network of sensors and communication devices to get an on line image of the current state of the system.
2. THE MANAGEMENT AND CONTROL OF THE IRRIGATION SYSTEMS The global objective of controVsupervision Iplanning structures (Yacov, et aI., 1973) for irrigation systems is to meet, regardless of uncertainties, water demand (agricultural, industrial and domestic) at each discharge point while maintaining an acceptable level of water all along the reaches and in the reservoirs during any given period. To turn effective the design of these structures, the main characteristics of such systems must be taken into account. Nowadays, a large variety of irrigation systems can be found around the world, from temperate to arid subtropical regions, considering either large river basins with varied geography (relief and vegetation) or multiple isolated micro-regions. However, these systems present some common characteristics which must be taken in consideration for the effective solution of management and control problems related with this resource: - the operation is distributed over space and time, - the transfer dynamics are characterized by hard delays, - the presence of strong operational uncertainties cannot be bypassed, - the estimation of final users demand is a complex task. In general terms, advanced irrigation systems should present desirable properties such as: availability, continuity, equity, precision, security and integrity.
~!SO e(t~~ Reservoir
Qi(t)
I
3. A HYBRID MODELLING APPROACH FOR THE OPERATIONS OF IRRIGATION SYSTEMS The basic irrigation system considered for illustration in this study is of the more common nature and is composed of the following elements (fig. 1): an upstream reservoir with control gates, a sequence of interconnected reaches with downstream control gates and off-take discharge devices, a final exit section with a flow measuring device. It appears that to cope with the management of the water resource in the short run, the operations of an irrigation system must be described in two ways: 1) In terms of continuous transfer relations relating inflows to outflows in each reach and following non-linear dynamics such as:
2i(t) = !(Zi(t), Q/ 1'), Qi +1(t), P;(t), S/t» 't
=1 to N
Reach i
UUHHHUUUUU1...;..i_ _ _ _ llconttOl Gate
~~
(>: •
~""""'7"" " "S::":Pi(t) Si(t)
Fig. 1: Main Components of an Irrigation System
364
Qi+l(t)
(1 )
4. THE PROPOSED APPROACH FOR SUPERVISION AUTOMATION
where N is the number of reaches, Z;(t) is the downstream water level in reach i at time t, Qlt) is the upstream inflow to reach i at time 't, Qi+l(t) is the downstream outflow to reach i at time t, Si(t) is the spilled outflow at time t, Pi(t) is the downstream pumped flow at reach i. These equations can be discretized and linearized with a good approximation (Sawadogo 1992) leading to relations such as:
The above hybrid model of the operations of irrigation systems leads to the definition of a finite set of discrete operational situations, or states, to which can be attached different short term goals. Then it appears that the resource management task at the supervision level is concerned with a stochastic sequence of differentiated situations. It seems quite impossible to attach to this stochastic process a set of state transition probabilities useful for tactical management. So the approach proposed here is to do first an on line detection of state transitions, then to identify the current situation, and finally to reformulate, following an adaptive philosophy, an optimization problem whose goals and constraints are in accordance with the current situation.
.<1
(2)
where ht t are the transfer coefficients associated to the linearized model and cri is a reference area for each reach i (Sawadogo 1992). In this case, the upstream water reserve evolves following relation:
4.1 Definition of the set of discrete operational situations
(3)
where et is the water input rate to the reservoir and QIt the upstream inflow of reach 1 at time t.
The definition of such a set must follow some basic considerations: - only significant events with respect to the management of the water resource must be taken into consideration, - the combinatorial multiplication of cases generated by the different operations states of each subsystems must be contained, - every operational situation must be covered by the set of discrete situations. Relevant discrete events for the operations of this kind of systems are: - saturation events: some effective water levels reach their upper or lower limits at an unexpected time, - failure events: some devices (pumps, gates) present a failure and new ways must be defined to minimize the damage to the service level, - discrete decisions events based on calendar, meteorological or present state considerations. Therefore, these states can be considered to be composed of three complementary components: - a supply component related with the distribution of the resource along the irrigation system and involving mainly water levels in reaches and reservoirs, - a system component related with the operational state of its devices (sensors and actuators), - a demand component related with past deficits and short term predictions (meteorology). So, the different states can be characterized by a triplet (p, q, r) with p E 0, q E S, rED, where 0 is the discrete set of sub-states related to the supply component, S is the set of sub-states related to the
2) In terms of qualitative or logical terms related with the degree of saturation of water levels, the intensity of perturbations (rains or dry periods) and the operational state of downstream control gates, pumps and off-take discharge devices. This description is concerned with : - physical constraints such as: Zmin < Z.(t) < Z~ , I I 0$ Qi(t) $ Qi(t) $ QInaJ< 0$ fl(t) $ P;(t) $ flITWU. 0$ Stet) $ SiITWU.(Zi(t»
Vr!un
$ V(t) $ V~
0$ SOt $ Sgw'(V(t» (4)
i=l to N, where Qmax and pITWU. are nominal flows I I capacities, Qi (t) and ~ (t) are actual capacities. For instance when the pumping devices of reach i are down, ~ (t) =0. - qualitative evaluations of actual water demands in view of past deliveries and current meteorology. Note that .here fuzzy techniques can be of great interest to qualIfy and compose these evaluations (Faye et al. 1996). ' ,
365
system component and D is the set of sub-states related with the demand component.
is of the linear form: to+T N I IAit(Df -p/).t:J.t pi .Q: t+to i=1
min
4.2 The design of the Knowledge Based state transition detection System
(5)
under the restrictions:
Here the State Knowledge Based System is devoted to two different supervision tasks: - identification of present state and consequently detection of state transitions, - diagnosis of the current situation. The identification task can be achieved for each component of the states. In relations with the supply component, the identification function may be realised using crisp or smooth definitions of the boundaries of the discrete state and IF-THEN rules can be used to determine the effective membership of the supply component. The system component state identification can be implemented using an event driven state transition graph. It is of course supposed that at the surveillance level, any significant failure can be promptly detected and informed to the supervision level. For a given set of states, the human operator interference is necessary to define tactics to be followed. For other situations, tactics to be followed can be deduced directly from the current state transition. The state transitions that should be submitted to the human operator must be defined beforehand by expert analysis. With respect to the demand component, short term predictions of demand, based on past statistical data and current deficits are corrected according to external perturbations such as heavy or sustained rains, or such as breakdowns in the distribution network. So, if the subsequent discretization leads to the identification of the current discrete state in relation to water demand, this function provides also another valuable information for the management of the resource: an updated short term prediction of demand to be used in the optimization process. The diagnosis system operates as an alert system for the human operational manager and must be able to submit to him intricate tactical choices.
0:::; Qi(t) :::; Qi(t)
0:::; P;U):::;
(6)
min{p;(t),D:}
(7)
0:::; Sit s; SrlaX(ZiU»
(8)
< 2.(t) < zmax I I
(9)
Z~n I
V~n S; V(t) S; V~
(10)
OS; SOt:::; S;ax(V(t»
(11)
where Df is the predicted or assigned demand rate and
P;t is the delivery rate for period (t, t+t:J.t) at
reach i, {I"it> i = 1 to N, t E [ to, to+T]} is a set of deficit weightings for the objective function (equation 5).
Equation (6) and (7) are flow capacity restrictions, equation (9) and (10) are state restrictions. At the end of the optimization the final time constraints can be such as: ?+T+I ~..,t+T+1 ~..,t+T+1
~rrnx
~mn
Lt
i=ItoN
~:;~V;+T~~
(12) (13)
Note that the optimization objective can be written equivalently as: max
to+T N I IAif(p;f. M ) f=foi=1 (14)
where predicted or assigned demand rates are no more present. So, it becomes clear that to the supply component, sub-states transitions are attached variations in the transfer coefficients of the state (equation 2), to the maximum values of downstream outflows (restriction 6) and spilled outflows (restrictions 8 and 11). To the system component, sub-state transitions are attached variations to the maximum values of downstream outflows (restriction 6) and to the maximum values of downstream pumped flows
4.3 Generation of short term resource optimization problems
(restriction 7), determining P;(t) within the interval [ According to the tactics chosen, a set of relevant objectives and effective constraints is selected to define the current short term optimization problem which defines on line reference values for the control system. An acceptable formulation (Carpentier, et al. 1993) of the standard tactical optimization problem
0, min { p;max, Df }]. Also,
whether or not the
satisfaction of the current demand is postponed until the failed devices are restored, the demand rates appearing in restriction (7) must be modified. To the demand component sub-state transitions, are attached adaptations of the weightings (equation 5)
366
demand module which evaluates uncertain users behaviour and a decision module to face failure of devices. In fig. 3 are displayed water levels in normal operating conditions. Here. a nominal water level is assumed in each reach with a random demand. Fig. 4 displays water level variation with failed pump in reach 2. The strategy adopted in this case consists of stocking water in the second reach and postponing current demand until the failed device is restored. This results in an increase of water level in reach 2. Fig. 5 takes up again the previous case but here. there is saturation in the upper water level in reach 2.
and of the demand rates appearing in restncttons (7). The basic approach proposed in this communication is represented in fig. 2.
5. SIMULATION A three-reach canal with a pumping station is considered for the simulation. Two cases are studied for validation and structuring the approach: • water resource management evaluation with nominal conditions including a strategic resource allocation and a random demand evaluation. • evaluation of the strategy to face device failures. Thus three modules have been implemented: a physical module which describes the system. a
Strategic ManagementiLong term planning~ Long Term Constraints & Choices
Resource Supervision System
,------------------------------------------------- -----------, Calendar Tim.c;.......;--aI
Meteorol~gy I I IL
Formulation and Solution of Short term Water Resource Optimization Problem
Human Supervisor
State Identification (K.B.S)
State Diagnosis
____ _
Reference Values &Thresholds
-------------------------------------------------, :- . .. -_............. . _.... . ............... . . ~
Measurements
Measurement & Control ~ Maintenance
Failures Events
.......... ...... .. ...... .. .. ...... ... .. ..... ...
.... .....
+...... .
-!; Fault Detection & Identification t····· ........;
I..-_ _ _ _ _ _ _ _ _ _ _ _ _
. ........... . .. . . -- . . .. -. . . -_ ... . .. . . _-_ ..... .
Fig. 2: Structure of the proposed Resource Supervision Functions
3.02 fIICI
3.01
m:=
3.02
Wala' atvel in reachl
~ters
3.015
3.015
3.01
3.01
3.005
3.005
3.005
2.995 2.99 2995
2.995
2.985
2.99 2.99 0
20
40
60
80
2985
0
20
2.98 40
Time inbours
60
Time in hours
Fig. 3: Water level in normal operating conditions
367
80
0
40
80 Time In bOlUS
60
4.5 meters
3.06
""Iers
meters
3.04 3.02 3.5 2.95
2.98
2.9
2.5
0
20
40
60
80
0
20
40
Tune in 00urs
60
80
2.96
0
20
40
Time in hours
60 80 Time inooW"S
Fig. 4: Water level in presence of failed device in reach 2 without saturation
).1 . - - - - - - - - - - - - - . Watu itnlin ftac:bl
4.5
).os
3.5 2.95
2.9 L..--.,..20--....:40'---t50~-~80 0
2.50~-----:2~0--40~-~60:----'80
20
4()
Time in
TiffW'. '" hnnr~
60
80
Time in hours
Fig. 5: Water level in presence of failed device in reach 2 with saturation
6. CONCLUSIONS
REFERENCES
In this communication, the design of a water resource supervision function for an irrigation system has been considered. The paper brings out the possibility of treating the automation of this function via two fields of knowledge: Operations Research methods for the generation of short term resource optimization problems and Intelligent Systems techniques for the design of the knowledge based state transition. Considering that subsystems are never uncoupled, adaptive optimization can be a way of tackling the problem avoiding thereby a co-ordination method which is necessary in hierarchical approach (Yacov, et aI., 1973) but difficult to apply to this kind of system. The main advantage of the proposed approach is that it is a global combined approach permitting to evaluate dynamically effective inflows and deliveries. The proposed approach has been already partially validated through a simulation study involving mainly re-optimization in presence of failed devices.
Carpentier, P., and G. Cohen (1993). Applied Mathematics in Water Supply Network Management. Automatica, Volume 29, N° 5, pp. 1215-1250. Faye, R.M., F. Mora-Carnino and K.A. Achaibou (1996). The Contribution of Intelligent Systems to Water Resource Management and Control. ]oumees Hispano-Franfaises, Systemes Intelligents et Controle A vance, Barcelone 12-13 Novembre. Levin, o. (1969). Optimal Control of Storage Reservoir during Flood Season. Automatica, Volume 5, pp. 27-34. Sawadogo, S. (1992) Modelisation, Commande Predictive et Supervision d'un Systeme d'Irrigation. PhD Thesis University Paul Sabatier Toulouse Avril, N° 1161. Yacov, Y. H.and D. Macko (1973) Hierarchical Structures in Water Systems Management. IEEE Transactions on Systems, Man, and Cybernetics, July, pp. 396-402.
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