Fuzzy Dynamic Wave Models For Flow Routing And Flow Control In Open Channels

Abstract

The dynamic wave model (the complete form of the saint-Venant equations), as applied to flow routing in irrigation canals or flood routing in natural channels, is associated with parameter and model uncertainties. The parameter uncertainty arises due to imprecision in the estimation of Manning’s n used for calculating the friction slope (sf) in the momentum equation of the dynamic wave model. Accurate estimation of n is difficult due to its dependence on several channel and flow characteristics. The model uncertainty of the dynamic wave model arises due to difficulty in applying the momentum equation to curved channels, as it is a vector equation. The one-dimensional form of the momentum equation is derived assuming that the longitudinal axis of the channel is a straight line, so that the net force vector is equal to the algebraic sum of the forces involved. Curved channel reaches have to be discretized into small straight sub-reaches while applying the momentum equation. Otherwise, two- or three-dimensional forms of the momentum equation need to be adopted. A main objective of the study presented in the thesis is to develop a fuzzy dynamic wave model (FDWM), which is capable of overcoming the parameter and model uncertainties of the dynamic wave model mentioned above, specifically for problems of flow routing in irrigation canals and flood routing in natural channels. It has been demonstrated earlier in literature that the problem of parameter uncertainty in infiltration models can be addressed by replacing the momentum equation by a fuzzy rule based model while retaining the continuity equation in its complete form. The FDWM is developed by adopting the same methodology: i.e. By replacing the momentum equation of the dynamic wave model by a fuzzy rule based model while retaining the continuity equation in its complete form. The fuzzy rule based model is developed based on fuzzification of a new equation for wave velocity, to account for the model uncertainty and backwater effects. A fuzzy dynamic wave routing model (FDWRM) is developed based on application of the FDWM to flow routing in irrigation canals. The fuzzy rule based model is developed based on the observation that inertia dominated gravity wave predominates in irrigation canal flows. Development of the FDWRM and the method of computation are explained. The FDWRM is tested by applying it to cases of hypothetical flow routing in a wide rectangular channel and also to a real case of flow routing in a field canal. For the cases of hypothetical flow routing in the wide rectangular channel, the FDWRM results match well with those of an implicit numerical model (INM), which solves the dynamic wave model; but the accuracy of the results reduces with increase in backwater effects. For the case of flow routing in the field canal, the FDWRM outputs match well with measured data and also are much better than those of the INM. A fuzzy dynamic flood routing model (FDFRM) is developed based on application of the FDWM to flood routing in natural channels. The fuzzy rule based model is developed based on the observation that monoclinal waves prevail during floods in natural channels. The natural channel reach is discredited into a number of approximately uniform sub-reaches and the fuzzy rule based model for each sub-reach is obtained using the discharge (q)–area (a) relationship at its mean section, based on the kleitz-seddon principle. Development of the FDFRM and the method of computation are explained. The FDFRM is tested by applying it to cases of flood routing in fictitious channels and to flood routing in a natural channel, which is described in the HEC-RAS (hydrologic engineering center – river analysis system) application guide. For the cases of flood routing in the fictitious channels, the FDFRM outputs match well with the INM results. For the case of flood routing in the natural channel, optimized fuzzy rule based models are derived using a neuro-fuzzy algorithm, to take the heterogeneity of the channel sub-reaches into account. The resulting FDFRM outputs are found to be comparable to the HEC-RAS outputs. Also, in literature, the dynamic wave model has been applied in the inverse direction for the development of centralized control algorithms for irrigation canals. In the present study, a centralized control algorithm based on inversion of the fuzzy dynamic wave model (FDWM) is developed to overcome the drawbacks of the existing centralized control algorithms. A fuzzy logic based dynamic wave model inversion algorithm (FDWMIA) is developed for this purpose, based on the inversion of the FDWM. The FDWMIA is tested by applying it to two canal control problems reported in literature: the first problem deals with water level control in a fictitious canal with a single pool and the second, with water level control in a real canal with a series of pools (ASCE Test Canal 2). In both cases, the FDWMIA results are comparable to those of the existing centralized control algorithms.