The Impact of Training Data Sequence on the Performance of Neuro-Fuzzy Rainfall-Runoff Models with Online Learning

Abstract

The learning algorithms in many of conventional Neuro-Fuzzy Systems (NFS) are based on batch or global learning where all parameters of the fuzzy system are optimized off-line. Although these models have frequently been used, they suffer from a reduced flexibility in their architecture as the number of rules need to be predefined by the user. This study uses a Dynamic Evolving Neural Fuzzy Inference System (DENFIS) in which an evolving, online clustering algorithm, the Evolving Clustering Method (ECM), is implemented. This study focused on evaluating the performance of this model in capturing the rainfall-runoff process and rainfall-water level relationship. The two selected study catchments are located in an urban tropical and in a semi-urbanized area, respectively. The first catchment, Sungai Kayu Ara (23.22 km2), is located in Malaysia, with 10-min rainfall-runoff time-series from which 30 major events are used. The second catchment, Dandenong (272 km2), is located in Victoria, Australia, with daily rainfall and river stage (water level) data from which 11 years of data is used. DENFIS results were then compared with two groups of benchmark models: a regression-based data-driven model known as the Autoregressive Model with Exogenous Inputs (ARX) for both study sites, and physical models Hydrologic Engineering Center–Hydrologic Modelling System (HEC–HMS) and Storm Water Management Model (SWMM) for Sungai Kayu Ara and Dandenong catchments, respectively. DENFIS significantly outperformed the ARX model in both study sites. Moreover, DENFIS was found comparable if not superior to HEC–HMS and SWMM in Sungai Kayu Ara and Dandenong catchments, respectively. A sensitivity analysis was then conducted on DENFIS to assess the impact of training data sequence on its performance. Results showed that starting the training with datasets that include high peaks can improve the model performance. Moreover, datasets with more contrasting values that cover wide range of low to high values can also improve the DENFIS model performance.