Rainfall-runoff modelling with neuro-fuzzy systems
Date of Issue2013
School of Civil and Environmental Engineering
Intelligent computing tools based on Fuzzy Logic and Artificial Neural Networks (ANN) have been used in hydrological modeling with promising results. A new approach of combining these two powerful artificial intelligence or AI tools, known as Neuro-Fuzzy Systems (NFS), has increasingly attracted researchers in various fields. Although many studies have been carried out using this approach in rainfall-runoff (R-R) applications, relatively few studies have been undertaken to evaluate the fundamental behavior of such models. This study employed NFS for R-R modeling and attempts to address issues related to (i) input selection for NFS in event-based R-R modeling, (ii) Training event selection for NFS in event-based R-R modeling, (iii) adaptability in NFS for R-R modeling, and (iv) interpretability in NFS for R-R modeling. ANFIS was employed for event-based rainfall-runoff modeling and investigations on input selection for ANFIS were conducted by using three input selection methods known correlation analysis (CA), mutual information-correlation analysis (MICA), and stepwise regression (SR). Results revealed that using non-sequential rainfall antecedents are better choices compared to sequential or pruned sequential rainfall antecedents and among the three input selection methods used, MICA is more reliable. The study on training event selection showed that the hydrograph shape is an important consideration in choosing training events. Events with a single peak in the hydrograph were found to be better choices compared to events with multiple peaks for training the ANFIS model. In addition, the lag time was found to be an important factor to be considered in training event selection as well. Based on this study, it is recommended that events with lag times close to the median lag time of the historical events can be chosen as events to be used for training the ANFIS model. Lastly, ANFIS results were found to be comparable with results obtained from the Storm Water Management Model (SWMM) and superior to that of ARX model. A neuro-fuzzy system which uses online learning known as Dynamic Evolving Neural Fuzzy Inference System (DENFIS) was introduced for continuous and event-based rainfall-runoff modeling in different catchment sizes. The results showed that DENFIS was able to capture the rainfall-runoff relationship well when tested for 3 catchments with different sizes. DENFIS results were found comparable when compared with the results obtained from Kinematic Wave Model (KWM), SWMM, and the University of Regina Hydrologic Model (URHM). DENFIS showed superior results to the one obtained by ARX model. Although the improvement in results obtained by the local learning algorithm used in DENFIS over the global offline learning algorithm used in ANFIS were modest, DENFIS had a shorter training time compared to ANFIS. This is because the local learning uses a one pass algorithm, compared to global learning which requires several epochs for training. DENFIS was considered a better model in finding the proper number of membership functions compared to ANFIS, since there is no need to find the suitable number of membership functions by trial. A sensitivity analysis revealed that DENFIS shows less sensitivity to the length of training data while ANFIS was found to be sensitive to the length of the training data used. Significantly, DENFIS required shorter length of training data compared to ANFIS. Lastly, DENFIS was found to be sensitive to the sequence of training data while ANFIS was not. A real time version of DENFIS (RT-DENFIS) which has real time learning capabilities was developed in this study and compared with ANFIS that employs an offline learning algorithm. The results revealed that an ANFIS model which employs batch learning algorithm trained with historical data needed to be retrained periodically in order to maintain reasonably good predictions. RT-DENFIS, however, does not need retraining since the model is constantly being updated when new data is available. A similarity-based neuro fuzzy system known as Pseudo Outer Product Fuzzy Neural Network with Approximate Analogical Reasoning Schema (POPFNN-AARS) was introduced and employed for both event-based and continuous R-R modeling for three different catchment sizes. The results obtained from the POPFNN model were comparable with the results obtained from the physically-based models KWM, SWMM, and URHM. Results obtained by POPFNN were also superior to that of ARX model. POPFNN results were also comparable with the results obtained from an ANFIS model. Although the improvement in results obtained by the rule pruning mechanism used in the POPFNN learning algorithm over ANFIS which has a fixed number of rules was modest, POPFNN has a more flexible rule structure with an optimal number of rules to better capture the association between input and output. Moreover, the Mamdani-type FIS used in POPFNN was found to be able to provide a linguistic understanding for output variable in the consequent part of the rules while the Takagi-Sugeno-type FIS used in ANFIS specifies the rule consequents as quantitative or crisp values. This linguistic nature of the Mamdani-type FIS could be advantageous if a qualitative understanding for the output variable is necessary.
DRNTU::Engineering::Civil engineering::Water resources