Intelligent control for modeling of real-time reservoir
operation, part II: artificial neural network with
operating rule curves
Ya-Ting Chang, Li-Chiu Chang and Fi-John Chang*
Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan
Abstract:
To bridge the gap between academic research and actual operation, we propose an intelligent control system for reservoir operation. The methodology includes two major processes, the knowledge acquired and implemented, and the inference system. In this study, a genetic algorithm (GA) and a fuzzy rule base (FRB) are used to extract knowledge based on the historical inflow data with a design objective function and on the operating rule curves respectively. The adaptive network-based fuzzy inference system (ANFIS) is then used to implement the knowledge, to create the fuzzy inference system, and then to estimate the optimal reservoir operation. To investigate its applicability and practicability, the Shihmen reservoir, Taiwan, is used as a case study. For the purpose of comparison, a simulation of the currently used M-5 operating rule curve is also performed. The results demonstrate that (1) the GA is an efficient way to search the optimal input–output patterns, (2) the FRB can extract the knowledge from the operating rule curves, and (3) the ANFIS models built on different types of knowledge can produce much better performance than the traditional M-5 curves in real-time reservoir operation. Moreover, we show that the model can be more intelligent for reservoir operation if more information (or knowledge) is involved. Copyright 2004 John Wiley & Sons, Ltd. KEY WORDS genetic algorithm; artificial neural network; fuzzy rule base; adaptive network-based fuzzy inference
system; reservoir operation
INTRODUCTION
The main purpose of this paper is to enhance our previous work (Chang and Chang, 2001) through combining fuzzy operating rule curves into our original intelligent control system so that it will involve more knowledge, and to investigate its applicability and practicability for real-time operation of the Shihmen reservoir, Taiwan. Real-time reservoir operation can be very complex because of the inherent variability of natural streamflow and diversified demands. In the last several decades, the development of optimal operating methodologies for reservoir operation has been very active. Yeh (1985) reviewed a number of approaches to reservoir operation and described the state of the art at that time. Since then, dynamic programming (DP) and its variants have been explored and frequently recommended to determine the optimal operating strategy for a multipurpose and/or multireservoir system (Kelman et al., 1990; Thomas et al., 1997; Perera and Codner, 1998; Chang et al., 2002; Chandramouli et al., 2002). More recently, fuzzy logic has been highly recommended for modelling reservoir operation to solve the inherent imprecision and vagueness characteristics in reservoirs. Even though a great number of promising results and considerable progress have been made, the research relating to real-time reservoir operation has still been very slow in finding its way into practice (Yeh, 1985; Russell and Campbell, 1996).
Intelligent control is a state-of-the-art technology that resembles the human thinking process in decision making and strategy learning, and it has been well recognized for its outstanding ability in controlling complex
* Correspondence to: Fi-John Chang, Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan. E-mail: [email protected]
GA for I/O patterns Historical inflows Downstream demands Inference systems Reservoir Operation Objective function & constraints Optimal Input/Output Patterns training sets GA base
Integrated GA&FRB bases FRB base Input vector
Figure 1. The framework of an intelligent control system for reservoir operation
systems, such as aerospace systems (Lin and Su, 2000), dynamic systems (Becerikli et al., 2003), and motor dynamic systems (Davies and Watton, 1995). In order to bridge the gap between academic research and actual operation, we proposed an intelligent control methodology for reservoir operation in our previous study. The intelligent control system combines two major procedures: a genetic algorithm (GA) and an adaptive network-based fuzzy inference system (ANFIS). The GA is used to search the optimal reservoir operating histogram based on a given inflow series, which can be recognized as the base optimal input– output training pattern for the intelligent control system. From these training patterns, the ANFIS is then built to create the fuzzy inference system, construct the suitable structure and parameters of the network, and then estimate the optimal water release according to the current reservoir watermark and inflow situation. In this study, the intelligent control system is enhanced through incorporating knowledge extracted from operating rule curves. The extracted knowledge is implemented as extra input information for the original ANFIS. It is our thought and hope, if the built intelligent control system integrated more knowledge, especially the currently used rules or information, it should be more intelligent and more likely applicable.
In the following sections, the methodology of an intelligent control system and its included theorems, i.e. GA and ANFIS, are first briefly introduced. A presentation of the methodology with different types of knowledge for constructing the inference system for reservoir operation then follows. The framework is shown in Figure 1. This shows that the GA is used to obtain the optimization input– output patterns, and then the inference systems, which include three different types of rule base (i.e. GA, fuzzy rule base (FRB), and an integrated GA with an FRB) are used to estimate the optimal reservoir operation. The results of different types of model are then presented and compared with those of the traditional M-5 rule operating curves. Finally, the study conclusions are given.
INTELLIGENT CONTROL SYSTEM
To build up an intelligent control system, one needs to acquire knowledge or information about the system first. The knowledge could be rules or guidelines that explicitly show the way a system responds to an input.
Unfortunately, in most cases, no strict rules exist to guide the way. One alternative way is to collect the input– output data, and then try to analyse and/or classify the input– output relation. If a solid relation can be found, then it can be used for future operation when we face a similar input situation. In this study, we attempt to build an intelligent control system for reservoir operation through the ANFIS. Because there is no optimal input– output pattern for training the ANFIS, we first use the GA to search the optimal reservoir operation based on a set of series of historical inflow data. ANFIS are introduced as follows.
The GA
The GA, which was invented by Holland (1975), is based on Darwinian natural selection with the mechanisms of population genetics. Now in widespread use for computational evolution, it has also been applied to solve a great number of water resource problems (Wang, 1991; Chang and Chen, 1998; Mantawy
et al., 1999; Cai et al., 2001). Since the GA tends to mimic some of the processes observed in natural evolution,
the variables are first coded as a string (biologically referred to as chromosome) or a solution, and then a set of candidate solutions, called a population, is created. The evolution starts from coded solutions and proceeds from generation to generation through genetic operators: reproduction, crossover and mutation. To evaluate the suitability of the derived solution, an objective function is required. In each generation, we calculate the values of the objective function for each chromosome. Those with a high value of the objective function have high probability of reproducing into the next generation; those with a low value of the objective function do not. As the aforementioned genetic operators proceed, the optimal goal would eventually be achieved.
As mentioned above, the input– output patterns are crucial knowledge for training the intelligent control system. Because historical and/or optimal input– output patterns do not exist, we apply the GA to search the optimal reservoir release based on historical inflow series.
The ANFIS
The ANFIS was proposed by Jang (1993) and has been applied successfully to many problems (e.g. Djukanovic et al., 1997; Altug et al., 1999). This neuro-fuzzy network is a five-layer feedforward network that uses neural network learning algorithms coupled with fuzzy reasoning to map an input space to an output space. The major advantage of this network is that it can tune the complicated conversion of human intelligence to fuzzy systems. We notice that even though artificial neural networks (ANNs) have been quite successfully used in a great number of hydrological problems, there are only a few published works on reservoir operation using the ANN approach (e.g. Raman and Chandramouli, 1996; Jain et al., 1999; Hasebe and Nagayama, 2002). The greatest difficulty is probably due to lack of solid knowledge and/or reliable input– output patterns of reservoir operation.
The optimal input– output patterns obtained from the GA are used to construct the ANFIS framework. The details of the ANFIS algorithm can be found in Jang (1993) or Chang and Chang (2001). The simplified ANFIS architecture is shown in Figure 2, and a brief introduction of the model follows.
Layer 1: input nodes. Every node i in this layer is used to perform a membership function
O1,iDAix for i D1, 2
O1,iDBi2y for i D3, 4
where x and y are the crisp inputs to node i, and Aiand Biare the linguistic labels characterized by appropriate
membership functions Ai and Bi respectively. The outputs O1,i are membership functions of Ai and Bi. Layer 2: rule nodes. T-norm operators are employed to perform the multiplications of the incoming signals
to generate the outputs of this layer. The algebraic product is used and shown as follows: O2,k DwkDAix ð Bjy
A 1 A 2 B 2 B 1 x y x y Z Σ z x y x y x y A1 π π π π A2 B2 B1 N N N N z1 = p1x+q1y+r1 z2 = p2x+q2y+r2 z3 = p3x+q3y+r3 z4 = p4x+q4y+r4
Figure 2. ANFIS architecture for a two-input Sugeno fuzzy model with four rules
Therefore, the outputs O2,k of this layer are the products of the corresponding degrees from layer 1.
Layer 3: average nodes. The ith node’s output in this layer is the ratio of the ith node’s output from the
previous layer to their total:
O3,iDwiD wi 4 kD1 wk i D1, . . . , 4
Layer 4: consequent nodes. In this layer, the ith node corresponds to the following function:
O4,i Dwifi Dwipix C qiy C ri i D1, . . . , 4
where fpi, qi, rig is the parameter set in the consequent part of the first-order Sugeno fuzzy model (Takagi
and Sugeno, 1983).
Layer 5: output nodes. In this layer, a defuzzification inference is used to transform the fuzzy results of this
model into a crisp output. Hence, the sum of all incoming signals is used to generate the decision crisp output:
O5,1 D 4 iD1 wifiD 4 iD1 wifi 4 iD1 wi
PRESENTATION OF CASE STUDY
Case study: Shihmen reservoir
The Shihmen reservoir, located upstream of the Tahan River (Figure 3), is used as the example for the study. The reservoir operates for the purposes of water supply for irrigation, industrial and domestic uses,
Shihmen reservoir
N
Figure 3. The location of Shihmen reservoir
flood control, hydropower generation, and recreation facilities. The watershed area is 763Ð4 km2and its active storage volume is approximately 2Ð35 ð 108 m3. Inflow data for the past 36 years are obtained. A period of 10 days, which is a traditional reference time frame in the Chinese agricultural society, is used as a time step. According to this scale, each month has three time steps, and every year has 36 steps. Consequently, we have 1296 36 ð 36 inflow records. In the case study, 1Ð2 times the water demand in the year of 2001 is adopted to represent the requirement for the simulation period, a total of 1329 ð 106 m3 year1.
The objective function and constraints
Since water release from the reservoir is used to assess the long-term performance of reservoir operation in this study, we define the objective function of the reservoir operation as follows:
minObjFunc D min 36 iD1 max 0,DiOi Di 2 ðni 1
where Di is the water demand of the ith 10 day period, Oi is the outflow of the ith 10 day period, and ni is
the number of 10 day periods in a continuous deficit in the ith 10 day period. The purpose of the variable ni in the objective function is to enlarge the effect of continuous deficiency and to avoid the occurrence of a
continuous deficiency.
Moreover, the main task of the operator in reservoir operation is to meet the objectives as well as possible while complying with legal and other constraints. The mass balance equation and the physical or boundary conditions for reservoir operation are as follows:
1. The mass balance equation (water balance at reservoir) or continuity equation is Si DSi1CIiOi
where Si is the effective storage of the ith 10 day period and Ii is the inflow of the ith 10 day period.
2. The initial storage S0 D50.
3. The variable Si can vary only between the maximum and the dead storage of the reservoir
0 Si235Ð745
4. The conditions on the final stage of the reservoir storage are 0Ð9S0S361Ð1S0
The prior handling of data
In this study, the 36 years of historical inflow data are divided into three independent sets: training, verification, and testing sets (Figure 4). To derive suitable input– output patterns, the GA and the rule-curves methods are applied.
GA for optimal input–output patterns. The historical inflow data are obtained from the Water Resource
Agency, Taiwan. The GA is first employed to search the optimal release series based on a specific water demand series and the inflow series in each year during the training period (1966– 88). There are several important features in the process of the GA:
1. Real-valued chromosomes are used to group the unknown variables together. The 36 10-day period reservoir releases in each year are the unknown variables.
2. A combination of objective function (Equation (1)) and constraints is set as the fitness function.
3. The GA parameters crossover probability, mutation rate, and population size are 0Ð8, 0Ð1, and 1000 respectively.
4. The terminal conditions are set when the fitness function has reached a value less than 0Ð01, or the process has been executed more than 6000 generations.
Owing to the large domain of searching space and the great number of unknown variables, the GA is difficult to converge to a satisfactory solution. In fact, in most cases it terminates at a minimum. To improve this situation, we designed initial multiple sets of feasible values for these variables. Accordingly, the 1000 initial sets of searching variables were divided into three different searching spaces as follows:
1. 10% of the initial sets are scattered randomly in the neighbourhood of water demand. 2. 10% of the initial sets are scattered randomly in the neighbourhood of inflow. 3. The remainder are scattered randomly in the original feasible solution domain.
As a result of this modification, the solutions have dramatically improved and approximately convergent solutions are achieved for most of the training years. For example, Figure 5 presents the variation of fitness values from generation to generation for the year 2000 to prove its convergence.
The optimal results of the GA and another result of operating by traditional M-5 rule curves (Figure 6) are summarized in Figure 7. It is found that the GA has a much better performance in terms of lower (generalized shortage index GSI; defined in Equation (2)) value than M-5. Consequently, the optimal reservoir operating histogram obtained from the GA can be recognized as the training pattern in the next step.
ten-day period ten-day period ten-day period (a) (b) (c)
Figure 4. Three different procedural inflow time series: (a) the training procedure inflow time series; (b) the verification procedure inflow time series; (c) the testing procedure inflow time series
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0 1000 2000 3000 4000 5000 6000 fitness values generations
Figure 5. The variation of fitness values from generation to generation (year 2000)
1 4 7 10 19 22 25 28 31 34 36 250 200 150 100 50 0 storage (10 6m 3) 13 16 time (ten-day)
Upper limit lower limit Critical lower limit
Figure 6. The M-5 rule curve of Shihmen reservoir
Fuzzified rule curve for reservoir operation. In Taiwan, most reservoirs are operated according to rule
curves, which were obtained through intensity simulation analysis based on inflow data and water demands. Because the rule curve is the official way for guiding the reservoir operation, it is crucial to integrate this knowledge into the intelligent control system. According to the rule curves regulation, reservoir operation is mainly based on the water level and downstream water demand. For example, if time is in the A1 period and
water level L is below the critical lower limit B1, then water release R is equal to 70% of water demand D.
A set of rules can be constructed as follows:
-1000 -600 -200 200 600 1000 1400 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 GSI
GSI from M-5 rule curve GSI from GA
time (year)
Figure 7. Comparison of GSI from the M-5 rule and the GA
Rule 2: IFT D A2 and L B2, THEN R D 0Ð7D2
.. .
Rule k : IFT D Ak and L Bk, THEN R D 0Ð7Dk
Because of the high variability of natural streamflow and the wide range between the curves, it is unlikely to determine the water release precisely according to the above rule alone. A knowledgeable expert with a lifetime of experience in reservoir operation is undoubtedly helpful and crucial for successfully operating the reservoir, especially in an extraordinary situation. However, expert experience and knowledge might not be obtained or be easily transformed.
Fuzzy logic, first introduced by Zadeh (1965), is gaining in popularity for modelling the ambiguity and uncertainty in the decision-making process and control theory. Recently, it has been applied successfully to various water resource problems (e.g. Russell and Campbell, 1996; Shrestha et al., 1996; Dou et al., 1999; Dubrovin et al., 2002). In this study, we attempted to incorporate the M-5 operating rule curves into our intelligent control system. The fuzzy logic provides a feasible way to transfer the rule curves into an FRB model. An FRB model is defined as the set of rules which consist of a set of input variables (such as the time of year and water level) or premises Ai,k in the form of fuzzy sets with membership function Mi,k and a
set of consequence Ri (i.e. water released to meet the various demands) also in the form of a fuzzy set. The
mathematical form of the ith rule is as follows:
If a1 is Ai,1Ða2 is Ai,2Ð. . . Ð ak is Ai,k then Ri
where akis the kth input variable and Ai,k is the kth variable premise condition, which has the form of a fuzzy
set with membership function Mi,k, and Ri is the ith rule’s consequence. Figure 8 shows the membership
function of water level where, for instance, if time is in the ith period and its water level is below the critical lower limit (60), water release Ri is then equal to 70% of water demand Di.
Figure 8. The membership function (sigmoid curve membership function) for water level 30 35 40 45 50 55 60 65 1 6 11 16 21 26 31 36 RMSE num of rule
Figure 9. The relationship between root-mean-square error of the training procedure and the number of fuzzy rules in the GA base
Application of the ANFIS
Given the input– output patterns from (1) the GA and/or (2) the FRB, the ANFIS models are built to create the fuzzy inference system and then to estimate the optimal water release based on given input patterns.
1. In the GA case there are five input variables. Since each variable might have several values (in terms of the rule), and each rule includes several parameters of membership function in layer 2, there will be a huge number of parameters to determine as the rule is increased. To solve this problem, subtractive fuzzy clustering is used to establish the rule base relationship between the input and output variables (a detailed explanation can be found in Chang and Chang (2001)). Several clusterings have been evaluated. The results are shown in Figure 9, which indicates that 17 cluster rules can have lowest root-mean-square error. Since
there are only 17 clusters, the inference system becomes quite simple. That is, as we give the five input variables’ values, we can calculate their membership function value for each cluster, and then through the fuzzy inference system the result can be obtained.
2. In the FRB case we attempt to use the knowledge enclosed in the operating rule curves. In the M-5 rule curves, there is only one effective rule in each time step, and we have 36 time steps (10-day periods) in each year. There are 36 if– then rules as built in the previous section. To implement these rules within ANFIS we must have suitable output patterns for given input patterns. Because there is no actual corresponding output pattern for the input pattern, we use the optimal water release obtained from the GA as output patterns. Even though the input– output patterns are the same as the previous GA case, the rules, as is the knowledge, are different. The 36 fuzzy rules are implemented within ANFIS and their corresponding parameters and weights in each layer are systematically adjusted according to the training patterns.
Integrating the GA and FRB rules
In this case, we integrate the rules obtained from the GA (17 cluster rules) and the FRB (36 fuzzy rules) into a whole, so that the knowledge extracted from the input– output patterns by the GA and from operating rule curves by the FRB is all included. Again, there is no actual corresponding output pattern for a given input pattern. To train the ANFIS, we use the same output patterns obtained by the GA.
RESULTS
To construct and test the ANFIS model, the 36 years (1966– 2001) of historical inflow data are divided into three independent sets: training, verification, and testing. The parameters and weights of these models are determined through an optimizing process based on a training data set. The most interesting system structure and corresponding parameters and weights are chosen based on the verification data set. Without any modification, the reliabilities of these systems are investigated using the testing data set.
For comparison, the simulation results of the M-5 curves and the optimal searching results by the GA are also given. The overall results for the M-5 curves, the GA, and different bases of the ANFIS models (namely the GA base, the FRB base, and the integrated GA with FRB base) are presented in Tables I and II. The results show that the ANFIS models could only be trained to obtain similar results to the GA method.
We believe that this is mainly because the optimal result obtained by the GA is based on being given the full series of input patterns to search the optimal operating strategy (output) for the series, whereas the ANFIS model is only based on previous and current (t 1 and t) inflow and water-level information. Consequently, it is reasonable that the ANFIS model could only produce similar results to the GA method. The root-mean-square errors are within the range of 20 to 40 in all cases. To evaluate the model performance in terms of the
Table I. The results of the M-5, the GA and the three ANFIS models at different stages
Set Year M-5 GSI GA GSI ANFISa
GA base FRB base Integrated GA C FRB base
RMSE GSI RMSE GSI RMSE GSI
Training 1966–88 393Ð96 32Ð83 31Ð78 157Ð52 40Ð17 78Ð72 38Ð90 135Ð00
verification 1989–94 981Ð95 54Ð27 27Ð22 237Ð76 34Ð62 297Ð71 36Ð50 185Ð52
Testing 1995–2001 633Ð06 66Ð99 30Ð58 171Ð44 32Ð97 130Ð70 29Ð00 47Ð02
Average 669Ð66 51Ð36 29Ð86 188Ð91 35Ð92 169Ð04 34Ð80 122Ð51
Table II. The results of three ANFIS models and the M-5 rule curves in testing stagea
Year ANFIS M-5 rule curves
GA base FRB base Integrated GA C FRB base (1) (2) GSI
(1) (2) GSI (1) (2) GSI (1) (2) GSI
1995 248Ð81 21 32Ð30 310Ð01 19 40Ð06 263Ð49 21 27Ð26 42Ð44 3 0Ð74 1996 611Ð22 31 417Ð26 648Ð44 32 733 460Ð80 26 143Ð16 601Ð60 32 4256Ð2 1997 358Ð99 21 249Ð08 248Ð00 18 16Ð09 272Ð65 22 37Ð46 218Ð49 12 65Ð95 1998 258Ð42 17 32Ð10 187Ð21 16 5Ð50 229Ð62 19 22Ð19 35Ð29 8 3Ð13 1999 457Ð36 21 378Ð71 372Ð00 21 43Ð76 415Ð49 24 82Ð74 290Ð07 14 49Ð02 2000 329Ð76 24 44Ð69 294Ð21 23 38Ð27 244Ð16 18 9Ð75 119Ð30 13 56Ð32 2001 291Ð90 23 45Ð92 258Ð50 19 38Ð59 164Ð51 16 6Ð59 11Ð46 1 0Ð00 Sum 2556Ð5 2318Ð4 2050Ð7 1318Ð6 Average 23 171Ð4 21Ð14 130Ð70 20Ð86 47Ð02 12 633Ð1
a(1) Total water shortage 106m3. (2) The number of water shortages within the 36 periods of 1 year.
severity and length of water deficit, the GSI (Hsu, 1995) is used:
GSI D 100 N N iD1 DPDi 100 ð DYi k 2
where DPD, the deficit percent 10-day period index, is given by DPD DDDR% ð NDC
DDR is the 10-day period deficit rate, NDC is the number of 10-day periods in a continuous deficit, DY is the number of 10-day periods in a year (i.e. 36), N is the number of sample years, and k is a coefficient, usually taken as 2.
From Table II, it is easy to see that the three ANFIS models produce a much better performance (in terms of small GSI values) than the M-5 curves in all cases. These results demonstrate that this new approach (with different knowledge), in comparison with the traditional M-5 rule curves, has superior performance with regard to the GSI.
From Tables I and II, we find that the results obtained from the GA-based and FRB-based ANFIS models are comparable, whereas the integrated GA and FRB ANFIS model does significantly reduce the GSI values in all cases. These results seem to provide interesting evidence that the ANFIS model has the ability to learn from the GA input– output pattern and from the FRB, and the system can be more intelligent if more information (i.e. integrated different kinds of knowledge) is implemented.
CONCLUSIONS
Intelligent control is a state-of-the-art technology that resembles the human thinking process, and its outstanding ability has been well recognized in controlling complex systems. Real-time reservoir operation is a continuous decision-making process under the inherent variability of natural phenomena. The operators must be based on an operating policy or predefined rules and cannot violate a large number of constraints, then must try to make things satisfactory for all the users. Apparently, this task can be very complex and difficult.
The main purpose of this study is to enhance our previous intelligent control system through incorporating the knowledge extracted from the M-5 operating rule curves. The newly built intelligent control system includes two kinds of knowledge, i.e. the optimal input– output patterns obtained from the GA, and the FRB extracted from the rule curves.
The systems are implemented for the Shihmen reservoir, Taiwan, and its performance based on 36 years of historical streamflow data. The data are divided into three independent sets, namely training, verification, and testing. Three intelligent control systems are constructed through (1) an optimal input– output pattern obtained by the GA, (2) the FRB, and (3) the integrated GA and FRB frameworks. For the purpose of comparison, the simulation results by the traditional M-5 rule curve method were obtained.
The results demonstrate that all the intelligent control systems developed produce a much better performance (in terms of lower GSI values) than the M-5 rule curves. The intelligent control system can learn to make decisions for reservoir operation through (1) the optimal input– output training patterns obtained from the GA, (2) the FRB extracted from the M-5 rule curves regulation, and (3) the integration of these two different types of knowledge. Moreover, we find the models built (1) by the GA patterns and (2) by the FRB knowledge produce comparable performance, whereas the ANFIS model can be significantly improved if both types of knowledge are used to construct the intelligent control system. The results suggest that the ANFIS model has good ability to learn from different sources of knowledge, and the system can be more intelligent for reservoir operation, if more information is involved.
ACKNOWLEDGEMENTS
This paper is based on partial work supported by the National Science Council, R.O.C. (grant no. NSC 90-2313-B-002-323). In addition, we are indebted to the reviewers for their valuable comments and suggestions.
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