Extreme learning machines: a new approach for modeling dissolved oxygen (DO) concentration with and without water quality variables as predictors

Abstract

In this paper, several extreme learning machine (ELM) models, including standard extreme learning machine with sigmoid activation function (S-ELM), extreme learning machine with radial basis activation function (R-ELM), online sequential extreme learning machine (OS-ELM), and optimally pruned extreme learning machine (OP-ELM), are newly applied for predicting dissolved oxygen concentration with and without water quality variables as predictors. Firstly, using data from eight United States Geological Survey (USGS) stations located in different rivers basins, USA, the S-ELM, R-ELM, OS-ELM, and OP-ELM were compared against the measured dissolved oxygen (DO) using four water quality variables, water temperature, specific conductance, turbidity, and pH, as predictors. For each station, we used data measured at an hourly time step for a period of 4 years. The dataset was divided into a training set (70%) and a validation set (30%). We selected several combinations of the water quality variables as inputs for each ELM model and six different scenarios were compared. Secondly, an attempt was made to predict DO concentration without water quality variables. To achieve this goal, we used the year numbers, 2008, 2009, etc., month numbers from (1) to (12), day numbers from (1) to (31) and hour numbers from (00:00) to (24:00) as predictors. Thirdly, the best ELM models were trained using validation dataset and tested with the training dataset. The performances of the four ELM models were evaluated using four statistical indices: the coefficient of correlation (R), the Nash-Sutcliffe efficiency (NSE), the root mean squared error (RMSE), and the mean absolute error (MAE). Results obtained from the eight stations indicated that: (i) the best results were obtained by the S-ELM, R-ELM, OS-ELM, and OP-ELM models having four water quality variables as predictors; (ii) out of eight stations, the OP-ELM performed better than the other three ELM models at seven stations while the R-ELM performed the best at one station. The OS-ELM models performed the worst and provided the lowest accuracy; (iii) for predicting DO without water quality variables, the R-ELM performed the best at seven stations followed by the S-ELM in the second place and the OP-ELM performed the worst with low accuracy; (iv) for the final application where training ELM models with validation dataset and testing with training dataset, the OP-ELM provided the best accuracy using water quality variables and the R-ELM performed the best at all eight stations without water quality variables. Fourthly, and finally, we compared the results obtained from different ELM models with those obtained using multiple linear regression (MLR) and multilayer perceptron neural network (MLPNN). Results obtained using MLPNN and MLR models reveal that: (i) using water quality variables as predictors, the MLR performed the worst and provided the lowest accuracy in all stations; (ii) MLPNN was ranked in the second place at two stations, in the third place at four stations, and finally, in the fourth place at two stations, (iii) for predicting DO without water quality variables, MLPNN is ranked in the second place at five stations, and ranked in the third, fourth, and fifth places in the remaining three stations, while MLR was ranked in the last place with very low accuracy at all stations. Overall, the results suggest that the ELM is more effective than the MLPNN and MLR for modelling DO concentration in river ecosystems.

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