Chapter 2 - Bat algorithm optimized extreme learning machine: A new modeling strategy for predicting river water turbidity at the United States

Abstract

Turbidity (TU) is one of the most important water quality variables and despite its great importance, the need to increase the number of monitoring stations is becoming a major issue for many regions of the world. In the absence of direct in situ measurement, alternative methods based on the different modeling approaches can be useful tools for predicting river TU. In this research, a novel modeling strategy for predicting river water turbidity using only measured river discharge (Q) has been proposed. Time series of river TU and Q measured at four United States Geological Survey (USGS) gauging stations located in a different region of the United States of America are employed for calibrating and testing several machine learning models. Specifically, four models were proposed and compared: the hybrid bat algorithm optimized extreme learning machine (Bat-ELM), the standalone feedforward artificial neural network (FFNN), the off-line dynamic evolving neural-fuzzy inference system called DENFIS_F, and the on-line dynamic evolving neural fuzzy inference system called DENFIS_O. The models were developed using the Q as input variables combined with the three components of the Gregorian calendar, i.e., the year, month, and day numbers. The models were evaluated using well-known performance evaluation metrics, i.e., coefficient of correlation (R), Nash-Sutcliffe efficiency (NSE), MAE, and RMSE. In general, the Bat-ELM performed best, more accurate than all other models, exhibiting the high R and NSE indexes with values ranging from 0.898 to 0.971 and from 0.806 to 0.936, respectively. It was also found that the inclusion of the periodicity contributed significantly to the improvement of the models performances. Furthermore, obtained results in the present study were encouraging and can be used a basis for future investigation related to river water turbidity modeling and forecasting.