Control of water levels in polder areas using neural ... - CiteSeerX

Published in: Water Industry Systems: Modelling and Optimization Applications, vol.1, D.Savic, G. Walters (eds.). Research Studies Press, Ltd. Baldock, UK, 1999, pp. 509-518

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Control of water levels in polder areas using neural networks and fuzzy adaptive systems A.H. Lobbrecht and D.P. Solomatine

ABSTRACT Modern water management in the Netherlands is characterised by considering water systems in their entirety together with all influencing factors and other related systems. Problems of management are posed more and more as multicriterial problems with the strong accent on optimisation. In order to addres such prolems, a DSS Aquarius was built that is capable of generating several control strategies aimed at optimal control at local (regional) and centralised (interregional) level. One of the problems encountered was the quite high computation time needed to generate an optimal control strategy, and its sensitivity to some of the parameters and input variables. Artificial neural network (ANN) and fuzzy adaptive systems (FAS) appeared to be efficient alternatives to using optimal control algorithms in real-time tasks. The obtained results show that ANN and FAS are able to replicate the behaviour of the Aquarius control component at onetwo time steps (1 hour) ahead with the accuracy in the range 90-97%. This gives the possibility to replace the slow computational components by the fast-running trained intelligent controllers and thus to simplify the use of Aquarius in the realtime control tasks.

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INTRODUCTION

Modern water management is characterised by considering water systems in their entirety together with all influencing factors and other related systems. Problems of management are often posed as multi-criterial problems with the strong accent on optimisation. In the Netherlands the problem of water level management in low-land areas is quite acute and was historically determined by the “battle” against sea and river

2 floods. Regional water control is the responsibility of approximately 65 water boards, and the problem of making optimal decisions in real-time control is taking nowadays a high priority. Water authorities responsible for managing water systems have to cope with various problems ranging from flood prevention to recreation, and to take into account the interests of different groups of users. This makes an optimal control of water resources systems a complex problem. This kind of control problem is being investigated extensively especially for optimal operation of single or multiple reservoir systems Fontane et al (1997), Panigrahi and Mujumdar (1997), Russel and Campbell (1996), Solomatine and Avila Torres (1996). Optimal control of a regional water system, considering all urban and rural water subsystems is elaborated in Lobbrecht (1997). The implemented Decision Support System (DSS) Aquarius is used as an aiding tool for operational management of regional water systems by several water boards of the Netherlands. Deterministic models of water-related processes incorporated in Aquarius system will be further called in short Aquarius model. Aquarius is using two modes of control – centralized control and local control. Normally, centralized control is dynamic. Most important control action is pumping. Within the Aquarius model the simulation and mathematical optimization problem are solved simultaneously in order to derive the optimal control actions – with the associated high running time and requirements to the computational power depending on the model complexity. Objective of this study is to investigate the possibility of using AI techniques, namely artificial neural networks (ANN) and fuzzy adaptive systems (FAS), to replicate the behaviour of a deterministic model controlling the polder water levels. The mentioned techniques provide the opportunities to extend the classical controls and deal with the complex systems in an integrated manner (Harris, 1994). The idea is to replace the control actions determined in Aquarius by centralized control option by building adaptive models with local information of a single regulating structure. 2 WATER SYSTEMS AND THEIR CONTROL Operation and maintenance of regional water resources system concern the optimal resources allocation for various interest groups in the system at the same time. In order to have an accurate overall picture of a water system state, which can be used for optimal operation and maintenance, it is necessary to take the conflicting criteria into account. Water systems can be separated into interacting subsystems such as urban drainage, urban or rural groundwater, urban or rural surface water subsystems. In the optimization problem for determining the control strategy, the requirements of each interest group can be expressed through “damage” functions, normally expressed as dimensionless product of a cost coefficient and an optimization variable, representing the weighted harm to one or more interest groups. The constraints define the limits of physical water variables, which can be

3 controlled directly or indirectly – such as surface water level, groundwater level, sewer filling, water quality level etc. The optimization problem can be formulated as follows (Lobbrecht, 1997): Minimize: Z ( x , u ), subject to: gi ( x , u ) ≤ 0,

i ∈ 1,..., l; j ∈ 1,..., m; (1) xl , j ≤ x j ≤ xu, j , ui , k ≤ uk ≤ uu , k , k ∈ 1,..., n; where Z ( x , u ) - objective function, gi ( x , u ) - constraints, x - vector of state variables, u -vector of control variables, xl , j , xu , j - lower and upper limits of state variables x, ui , k , uu ,k - lower and upper limits of state variable u. Two levels of control can be distinguished in the water system, in each of which the control actions can be manual and automatic: • local control, that involves a single regulating structure in a water system and is executed on the basis of data gathered in the vicinity of that single structure and the standards that have been set for each subsystem. • centralized dynamic control, in which the actions are based on time varying requirements of interests in the water system, the water system load and the dynamic processes in the water system. The dynamic control mode with or without prediction (of hydrological load) is distinguished. In dynamic control with prediction, an optimization problem is solved and the system state is predicted for specific control horizon on the basis of forecasted hydrological data. In order to implement the mentioned optimisation, Aquarius modelling and optimization system was developed. It is used for management of regional water resources systems in the Netherlands by building models of combined urban and rural water systems that describe water quantity and quality processes. Urban water subsystems in Aquarius model represent fast runoff characteristics, while the rural subsystems are used for slow and delayed runoff processes. The subsystem interactions can be expressed in objects such as storage elements, regulating structures, free flow elements and also in the system description itself by formulating the boundary conditions. Different continuity equations describing hydrological processes are used for simulation of each subsystem states (Lobbrecht, 1997). Aquarius uses a combination of simulation and mathematical optimization to determine the operational control actions and control strategy. To solve a nonlinear optimization problem (eqn. 1), the Successive Linear Programming method using Taylor approximations of non-linear relationships is implemented. In case of a complex water resources system, the size of optimization problem, and subsequently the computational power required increases. For the time series calculation, the matrix where the rows represent the constraints and

4 the columns represent the physical variables defines the optimization problem. The large number of elements to be considered causes the increase of number of non-zero elements in the constraints matrix. The total time needed for one time step simulation for a problem with 95000 variables and the constraint up to 92400 is 1550 s (the control horizon of 12 steps and simulation step of 2 hours used). The results are obtained on a standard PC. In many real-time control situations these high running times are undesirable. It will be shown below how the intelligent controllers based on the ANN and FAS can be trained off-line to reproduce the Aquarius model results. 1.3 Intelligent control Artificial intelligence (AI) techniques are widely used in solving various problems of water management and modelling (Bardossy and Duckstein 1995; Solomatine and Torres 1996; Fontane et al. 1997). AI techniques are also being used nowadays as an alternative approach for conventional controllers – see Miller et al (1990), Omatu et al (1995), Omidvar and Elliot (1997). Such controllers are called intelligent controllers since they employ AI techniques to produce the control actions; being combined with the conventional controllers they enable better handling of complex real-life problems. In this study the artificial neural networks (ANN) and fuzzy adaptive systems (FAS) are used for controlling water level of polders. 3

AI TECHNIQUES USED IN CONTROL

3.1 Neural networks Artificial neural network (ANN) (Tsoukalas and Uhrig, 1997) is an information processing system that roughly emulates the behavior of a human brain by replicating the operations and connectivity of biological neurons. In supervised learning (training), series of connecting weights are adjusted in order to fit the series of inputs to another series of known outputs. Once the training is performed, recall (running ANN to produce an output) is very fast, in a fraction of seconds; this makes ANN applicable for model-based control. In this study only supervised learning algorithms, namely feedforward networks are considered. The feedforward neural networks consist of three or more layers of computing units called also nodes: input layer, output layer and one or more hidden layers. The input vector x passed to the mapping is directly passed to the node activation output of input layer without any computation. After hidden layers provide additional computations, the output layer generates the mapping output vector z. Two types of feedforward networks are used in this study. 3.2

Fuzzy rule-based systems Fuzzy logic approach has been successfully applied for wide range of control problems beginning from the introduction by Zadeh in 1965 of fuzzy-set theory and its applications. In fuzzy logic approach the Boolean logic is extended to

5 handle the concept of partial true which implies the true takes a value between completely true and completely false. The notion of fuzzy sets has to be introduced, which is the collection of the objects that might belong to the set to a degree, taking all values between 0 (full non-belongingness) and 1 (full belongingness), instead of taking crisp value. The indication of intensity of belongingness is expressed in membership function, assigning to each element a number from the unit interval. More on that see e.g., Tsoukalas and Uhrig. (1997) Fuzzy rules consist of arguments coupled by logical operators and verbally formulated, like IF the condition is fulfilled THEN the consequence has to be true. The logical expressions are usually formulated by logical operators AND, OR, NOT and XOR. The truth value corresponding to the fulfillment rule conditions for a given premises is called degree of fulfilment (DOF). The basic structure of fuzzy rule-based system involves four principal components: fuzzification interface, where the values of inputs are measured, fuzzified and the input range is mapped into the suitable universe of discourse , knowledge-base, which involves a numeric ‘database’ section and a fuzzy (linguistic) rule-base section, fuzzy inference mechanism or engine, which constitutes the core of the fuzzy logic control, involves the decision making logic (fuzzy reasoning such as product, max-min composition etc) and defuzzification interface, which maps the range of output variables into corresponding universe of discourse and defuzzifies the results of fuzzy inference mechanism. In a complex system, which is usually the case, the fuzzy rule-base system construction is limited (manipulation and verbalization by expert). Therefore the possibility of inducing and learning the rules from data has been investigated and implemented successfully and those systems are called fuzzy adaptive systems (FAS). Such a method, the weighted counting algorithm is used for this study. For given relevant variables the fuzzy rule based system has to deliver the response close to the observed ones. In other words, on the basis of user defined input membership functions and input-output sets FAS can determine the output membership functions and defuzzified outputs. If all the variables and the responses are continuous then the rules can be constructed by defining the fuzzy set that supports for the fuzzy numbers Ai,k and identifying the corresponding responses. Ai,k is a fuzzy number (αi,k-,αi,k1,αi,k+) where αi,k1 is the mean of all possible ak(s) values which fulfil at least partially the ith rule :

α i1,k =

1 N

∑a

s∈Ri

k

( s)

(2.15)

where N is the number of elements in Ri . Ri is the set of all those premise value vectors that fulfil at least partially ith rule and it forms the subset of a training set. The method chooses the rule responses, which fulfils the certain fuzzy rule at least with specified threshold value of DOF. The value of DOF has to be selected so that the sufficient number of elements of the training set is considered for each rule.

6 3.3 Model-based control Model-based control involves a model of the controlled system or process. A specific example of indirect intelligent control of closed loop control scheme was termed by Saerens (1995) as “model reference adaptive control”. This scheme is used for the considered case of control problem. The scheme involves three main components, namely a reference model, a trainable intelligent controller and the process or system under control. In this scheme the deterministic models are used as a reference and conduct the learning procedure for intelligent controllers. The intelligent controllers are the AI techniques appropriate for adaptive learning. The simulation of a reference model is used for offline adaptive learning of an intelligent controller. At each time step the process or system state target value y(t)d passes through the intelligent controller and gets the control signal u(t). When the process or system results the output y(t), the measured value is passed to the intelligent controller and compared with the target value. As a respond of the intelligent controller the control signal for the next time step should be obtained. The model-based scheme for controlling the polder water level uses Aquarius DSS model as a reference model for the intelligent controller (Figure 1). The desired value is a target water level in the water system, a pumping rate of the drainage station is a control action and the system output is the water level in the polder area. NN and FAS models will be referred as adaptive models onwards. Note that adaptivity here is a property of training and does not characterise the use of the trained system. In fact, the trained ANN or FAS will not automatically adapt well to the changing properties of the controlled system. If the controlled system is changed, they must be re-trained on the basis of the new data. Training Reference model

∆ y(t)

y(t)d

u(t) Intelligent controller

process

y(t)

+ Figure 1. Model-based control

4 CASE STUDY The study has been based on the water resources system model built on one of the areas located in the western part of the Netherlands. The water resources in this

7 area are managed by one water board. The model represents a complex water resources system of approximately 40 000 ha including the total of 60 polders and correspondingly there are a large number of independent water level areas with 11 pumping stations, 2 weirs and 7 inlets that serve as regulating structures. The water quantity and quality requirements of main interest groups in the modelled area such as flood prevention, ecology, glasshouse horticulture, pasture agriculture and navigation may be in conflict. For example, the navigation requires the maximum depth of water level, while for flood prevention the minimum water level is preferable. The controlled area has the storage basin (SB) which is the main surface water subsystem in the area. Three types of areas are discharging to the SB: lowlying polders, high-lying polders and storage basin land and the SB is drained to the North Sea through the river. If the water level in SB exceeds certain limit, some polders have to stop pumping into the SB. Such policy is applied in situations, when the probability of dike overflow is very high. 5 TRAINING ANN and FAS Adaptive learning of NN and FAS was based on the data sets generated by Aquarius model in both local and centralized dynamic control modes. Water level that represents the state of a certain polder area can be controlled through a control variable - pumping rate of drainage station. For model simulation, the 30 years of real hydrological data was available. The adaptive models built for each pumping station reproduce the pumping rate at time step t. Before training, the correlation analysis for input/output relationships of the pumping station type of control point has been carried out. The most correlated physical variables to the output variable should enable the better model performance. Therefore, the coefficients of linear correlation between output variable and possible input variable sets were identified. The moving average values for water level and precipitation variables and pumping rate at the previous time steps tend to have higher correlation to the output variable. The variables with high correlation to the output are included in the input pattern. Adaptive models were simulated by neural network generator NNN (www.ihe.nl/hi/sol/nnn.htm) and fuzzy adaptive system AFUZ (www.ihe.nl/hi/sol/fuzzy1.htm) developed at IHE. For adaptive models simulation 1-5 years data with time step of one hour and the tolerance target of 5% are used. Mainly, the 50% of data are used for training and another 50% is used for verification. In case of dynamic control with prediction the control horizon of 24 hours is applied. For ANN models from 5000 to 30 000 iterations were needed to accomplish the training. In case of FAS models the triangular shape of membership function, threshold value for DOF of 0.05%, the product inference and centroid defuzzification methods were applied. Several performance indices were used: mean square error (MSE), the percentage of the output data within the tolerance target of 5%; the model

8 accuracy (percentage of examples, where the pumping rates are accurately determined), and the total flow rate difference for the whole range of data set. The best model and data structure for adaptive models was investigated. It was done by including the extreme hydrological events into the training data set, which should have enabled the highest variation in the training data set.

6 RESULTS The adaptive model performances obtained have proved the applicability of AI techniques for this sort of control problems. The extreme events in the training data set included the moving average and moving sum values tend to give the best performances of adaptive models. Also the training by random generated data and verification by natural data enabled reasonable good accuracy of the models. The model structure provided the best results for different control modes are presented below in Table 1 (results for control with prediction were not ready at the moment of publication). The corresponding verification plots are shown in the Figures 3 and 4 for local and dynamic control respectively. a.

local control mode Input variables: 1. Water level at t 2. Water level at t-1 3. Pump status at t-1 Output variable: pump status at t Number of hidden nodes (NNN) 3 Number of rules (AFUZ) 63

b.

Dynamic control without prediction Input variables: 1. Moving average precipitation, t-1 to t-3 2. Moving average water level in SB, t-1 to t-3 3. Moving average water level in SB, t-4 to t-10 4. Moving average pump status, t-1 to t-4 Output variable: pump status, t Number of hidden nodes (NNN) 4 Number of rules (AFUZ) 189

Table 1. Summary of the best results obtained a Tool used NNN MSE 0.096 Accuracy net (%) 81.16 Accuracy overall (%) 92.9 Flow through pump (difference in %) 0.044

AFUZ 0.196 79.34 92.21 0.53

b NNN 0.08 75.25 95.92 4.62

AFUZ 0.24 62.37 82.63 8.97

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60.00 50.00

AFUZ NNN Aquarius

40.00 30.00 20.00 10.00 0.00 0

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time steps, hour

Figure 3. Performance of intelligent controllers for local control strategy Additional analysis was performed in order to assess the performance of adaptive models in case extreme events. It was concluded the adaptive models are able to learn a very specific patterns of control actions. 40.00 35.00 AFUZ NNN Aquarius

30.00 25.00 20.00 15.00 10.00 5.00 0.00 0

50

100

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300

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time steps, hour

Figure 4. Performance of intelligent controllers for centralized dynamic control 7 CONCLUSION The model-based intelligent control schemes were successfully applied for reproducing optimal control actions for polder water level control. ANN and FAS models can reproduce the corresponding control actions with high accuracy. Nevertheless, the adaptive models’ performances are highly dependent on a choice of training data set so that the two different data sets may result in a different level of model performance. Inclusion of variables resulted from the extreme events and

10 also the use of moving average and moving sum values into the training pattern improves the models’ performance. The advantages of intelligent controllers are in their robustness and ability to reproduce the centralised behaviour of control actions by using the easily measurable local information. However, it should be noted that the present control problem is a model specific, consequently ANN and FAS exhibit properties of adaptation during training, but once trained on the basis of one water system model, they cannot represent the hydrologic behaviour in other model areas, and have to be re-trained. REFERENCES Bardossy, A and Duckstein, L., 1995. Fuzzy rule-based modelling with applications in Geophysical, biological and engineering systems, CRC press Inc Bazartseren, B, 1999, Use of neural networks and fuzzy adaptive systems for controlling polder water level in the Netherlands, MSc thesis, IHE, Delft, The Netherlands Dibike, Y., Solomatine, D.P., Abbott, M.B., 1999. On the encapsulation of numerical-hydraulic models in artificial neural network. Journal of Hydraulic Research, No. 2. .pp. 147-161. Fontane, D.G et al., 1997. Planning Reservoir Operations with Imprecise Objectives, Journal of Water Resources Planning and Management, May/June, pp 154-162 Harris, C.J. 1994. Advances in Intelligent control, Taylor & Franscis Ltd, London Jana, A et al. 1996. Real-time Neuro-Fuzzy control of a nonlinear dynamic system, Proceedings of the 1994 Biennial Conference of the North American Fuzzy Information Processing Society, pp 210-214 Krijgsman, A.J. 1993. Artificial intelligence in Real-time control, Proefschrift. TU Delft Lin, C.T. 1994. Neural fuzzy control systems structure and parameter learning, World Scientific Co. Ltd Lobbrecht, A.H. 1997. Dynamic water system control: Design and Operation of Regional Water Resources Systems, Ph.D thesis, TUDelft Miller, W.T et al (ed) 1990. Neural networks for control, The MIT Press, London Omatu, S et al. 1995. Neuro-control and its applications, Springer- Verlag London Limited, London Omidvar, O and Elliot, D.L. 1997. Neural systems for control, Academic Press Limited, London Panigrahi, D.P & Mujumdar, P.P. 1997. Application of Fuzzy logic to Reservoir Operation modelling, National Conference on Fuzzy sets and Their Applications, Madras Raman, H & Chandramouli, Y. 1996. Deriving the general operating policy for Reservoir using neural network, Journal of Water Resources Planning and Management, Sept/Oct pp 342-347

11 Russel, S.O. and Campbell, P.F. 1996. Reservoir Operation Rules with Fuzzy Programming, Journal of Water Resources Planning and Management, May/June pp 165-170 Sarens, M et al. 1995. Neurocontrol based on the Backpropagation algorithm, Intelligent control systems: Theory and applications, Gupta, M.M & Sinba, H.K (ed), IEEE press Shen Y., D.P. Solomatine, H. van den Boogaard, 1998. Improving performance of chlorophyl concentration time series simulation with artificial neural networks. Annual Journal of Hydraulic Engineering, JSCE, vol. 42, February, pp. 751-756. Solomatine, D.P and Avila Torres, L.A, 1996, Neural Network Approximation of a hydrodynamic Model in Optimizing reservoir operation, proceedings of Hydroinformatics ’96 conference, pp 201-206. Tzafestas, S.G and Tzafestas, C.S. 1997. Fuzzy and neural control: Basic principles and architecture, Methods and applications of Intelligent control: Microprocessor-based and intelligent systems engineering, Kluwer Academics, Tzafestas, S.C ed. Tsoukalas L.H. and Uhrig R.E. 1997. Fuzzy and Neural Approaches in Engineering. John Wiley and Sons, N.Y., 587 p.

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