The generation of operating rules for an optimal operation of a reservoir system is a very complex task. This complexity arises from a number of sources including from uncertainties in future inflows to the reservoir and demands, and from trade-offs between a wide range of conflicting objectives. The trend in the approaches taken to addressing these complexities of the problem over the last few decades has been towards increased use of sophisticated mathematical formulations and solution techniques, with very little consideration being given to the acceptability or suitability of these methods in practice. As the authors quite correctly point out, this lack of consideration of the practical utility of suitability of the approaches have resulted in very little of the research finding its way into actual practice. The authors are to be complimented for their attempt to introduce Fuzzy Rule Base (FRB) principles to address this problem. Their use of the concept of fuzzy logic presents an innovative and timely approach to bridging the gap between the theory and practice in optimal reservoir operation.

The major strengths of the fuzzy-based approach proposed by the authors lie in its logical simplicity of the technique, its ability to reflect the human thinking and decision making processes, and in the performance of operating policies generated by the technique relative to the performance of operating policies generated by traditional deterministic programming formulation. Furthermore, while the FRB approach retains the capability of incorporating the knowledge and/ or experience of an expert it is easily formulated and implemented within an analytical approaches. There are, however, several issues that warrant further examination. The first relates to the influence of the seasonality of the inflow process and long-term consequences, arising from the variability in inflows inherent in seasonality, associated with release decisions. The second issue relates to the selection of membership function and the development and organisation of the rules used with the membership function.

Before proceeding with an examination of these issues it is important to note that the interpretation of the term ‘consequence’ used in this discussion differs from that used in traditional IF (set of premises) THEN (consequence) rule base terminology. In the IF (set of premises) THEN (consequence) rule base in the reservoir operation problem addressed by the authors, the word ‘consequence’ represents the reservoir release decision to be taken if a set of premises is satisfied or occurs. The terminology ‘consequence’ used in this discussion represents the real-life or practical consequence of adopting a particular decision.

Seasonality and Long-Term Consequence

If the process of representative reservoir operating environment are to realistically incorporated into operating policy for that reservoir, the inherent seasonal variability of the inflow process arising from seasonality must be explicitly considered in the development of fuzzy rule bases.

The FRB developed by the authors appears to be capable of simulating the reservoir operation during the normal operating condition. However, reservoir operating conditions which occur during wet or dry seasons, or other unusual circumstances, may not be able to be simulated adequately. An example on the development of seasonal FRB has been demonstrated in Shrestha et al. (1996). However, the issue related to the long-term consequences of seasonality are still not addressed in that work. Consider the case where two pairs of identical data sets each contain two input variables and one output variable. Consider the input variables include the previous-month inflow and current-period storage volume, and the output variable to be the reservoir release. Now consider the situation where one pair of data relates to a wet season and the other to a dry season. Although the decision, that is, the reservoir release determined for the two data sets might be the same, due to the differences in seasonal characteristics of the environment in which the decision occurs, the consequence of adopting that decision for one set of data may be quite different from that of the other set. For example, during the wet season, longer term (as opposed to immediate) concern may be focused on whether the reservoir volume will increase to unacceptable levels. In this case, precautions against dam overtopping are likely to have a strong influence on the suitability of the decision. During the dry season on the other hand, this longer term concern is more likely to be related to the adequacy of the reservoir volume for the rest of the season. Hedging the release decision will, therefore, becomes a possibility. The fuzzy rule base system such as proposed by the authors does not appear to have the capability of taking into account the environment in which the decision and its different consequences occur.

An underlying requirement for the successful application of any fuzzy reasoning based model is that the system be able to be represented as a bounded function (Cao et al., 1992). This requirement is rarely satisfied in reservoir control problem due, in part, to the nature of inflow process to the reservoir. Inflows to a reservoir are usually has an unconstrained upper bound and for a practical purpose a zero lower bound. In order to apply fuzzy logic theory into reservoir operation problem to comply to the greatest extent possible with the requirement for the bounded functions, the fuzzy reasoning algorithm should be able to recognise different operational conditions, e.g., normal operation, flood season, and drought conditions. One example of FRB application with the explicit consideration on different operational conditions is found in Ikebuchi et al. (1994). The various operational conditions or control levels considered in Ikebuchi et al. (1994) are directed at drought relief management in terms of normal conditions, drought alert, drought, and abnormal drought, but also includes flood warning. Each of the different draught scenarios (control levels) has different operational policy. The operational policies that are defined or adopted in the FRB depend on the control level prevailing during the particular time period. The approach, however, still needs the ‘expert’ to establish the operational policy for each of the operational conditions. As noted in Ikebuchi et al. (1994) there is also a need to incorporate an adaptive operation capability to respond to the different control levels for each operational condition and of the unusual circumstances.

The writers, support the view of the authors that application of fuzzy rule base principles to the problem of optimal reservoir operation should serve as a supplement to conventional optimisation techniques. Further support for this statement lies in the fact that development of any fuzzy rule base policy needs the knowledge of experts or an appropriate data set which is called training data set (Bardossy and Disse, 1993). Unless the experts’ knowledge or the data sets used in the development of the FRB policy are obtained from a situation which is operating at or close to optimality, the generated fuzzy rule base may not result in optimum operation.

However, the application of fuzzy logic in reservoir operation can be extended beyond the FRB approach proposed by the authors. For example, it should be recognised that in practice the actual storage volume in the reservoir rarely, if ever, fall at the grid-point of the discretised variables used to generated an optimal operating policy in stochastic dynamic programming (SDP) formulations. Suharyanto and Goulter (1996) addressed this issue by proposing an approach to assess, in quantitative and rational way, the influence of storage intervals adjacent to the interval within which the actual storage fall on the generated operating policy. The influence of these adjacent intervals was considered through use of overlapping membership function of the adjacent storage intervals. The technique (Suharyanto and Goulter, 1996) uses the by-product of the SDP, namely, the discounted “cost-to-go” or “long-term-consequence”, to guide assessment of the influence of adjacent storage intervals through a fuzzy inferencing principle which they referred to as ‘minimal weighted long-term-consequence’. A further extension of the approach to both optimisation and simulation is presented in Goulter and Suharyanto (1996). The optimal operating policy in this extended approach is generated through the application of the stochastic dynamic programming using a fuzzy membership function for the reservoir storage intervals as originally proposed in Suharyanto and Goulter (1996). As in the original model proposed by Suharyanto and Goulter (1996), the by-product of the optimisation, i.e., “the cost-to-go” or “the long-term consequence”, is then used to guide the operation and to assist in determining an appropriate actual release decision. However, in this extended model the process of identifying the actual release is a rational procedure for determining whether it is necessary to follow or to deviate from the ‘original’ operating policy generated by the stochastic dynamic program. The decision on whether to follow, or to deviate from, the operating decision defined by the dynamic programming solution is determined through ‘minimal weighted long-term-consequence’ inferencing approach. Suharyanto and Goulter (1996) and Goulter and Suharyanto (1996) showed that their approaches generate improved, relative to the policies generated by traditional crisp dynamic programming, solutions and system performances as defined by the reliability, resiliency, and vulnerability measures of the resulting reservoir operation. It is important to note that in these approaches of Suharyanto and Goulter (1996) and Goulter and Suharyanto (1996) used fuzzy reasoning theory as a supplement within, rather than as an alternative to, conventional optimisation techniques.

The Choice of Membership Function and Rules Organisational

The writers recognise that the choice of the membership function, as well as the degree of overlapping of the membership functions of adjacent intervals, the number of fuzzy categories, and the organisational of rules are very complex issues which have to be resolved in the development of any fuzzy rule base. In most cases, these choices tends to be determined a priori, and their suitability and implications are not examined in detail during the formulation of the resulting fuzzy membership functions such as in, e.g., Cao et al. (1992). Subjective choices are not necessarily appropriate, however. The authors use of 0.5 membership level, for example, as a cut-off value for the influence of a data set within adjacent fuzzy categories during the development of the FRB effectively results in no overlapping of adjacent intervals. The influence of adjacent fuzzy categories on a data set does not occur unless the data point has a membership level precisely equal to 0.5, in which case, the data set is influenced by, at most, only two fuzzy categories. The resulting fuzzy categories in this situation will represent a ‘three-valent-logic’, i.e., the influence of a data set can be either {has no influence, has influence on two fuzzy categories, or has influence on only one fuzzy category}, in contrast to ‘multi-valent-logic’ in fuzzy theory. In the FRB proposed by the authors, the choice of this cut-off value has shown to be very crucial.

The choice on the type of membership function affects the outputs and implications of an analysis. Goulter and Suharyanto (1996) and Suharyanto and Goulter (1996) showed that triangular and trapezoidal fuzzy storage intervals represent two extreme ‘minimal weighted long-term-consequence’ inferencing positions, i.e., a triangular fuzzy membership function for the storage intervals results in a more flexible inferencing procedure than the trapezoidal membership function which tend to produce operating policy which resembles more closely to those defined from crisp SDP. Different system performances was evidence in these papers, however, that the membership functions for fuzzy storage intervals within shapes intermediate between triangle and trapezoidal may be worth of further investigation.

An objective procedures in the construction of membership function and the organisation of fuzzy rules can be found in, e.g., Lin (1994). Lin (1994) who uses a ‘bell-shaped’ membership function combined the advantages of fuzzy logic and artificial neural networks modelling to develop a two-phased hybrid learning Fuzzy Neural Network (FNN) Control System. The system was developed specifically to incorporate the learning ability of artificial neural networks (ANN) into a fuzzy control environment to reduce subjective interferencing required in the choice on the membership function and the degree of overlapping.

It should be emphasised, however, that the improvement which might be obtained through the FNN system controller does not overcome the deficiencies, if any, of the training data sets. Additionally, the problem of optimal operation of the generated FNN control system still, being very much dependent on the training data sets, however, would still remain. The writers look forward to hearing further research and discussion on this interesting topic on optimal reservoir operation analysis.

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