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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.

In this study, a comparison between generalized regression neural network (GRNN) and multiple linear regression (MLR) models is given on the effectiveness of modelling dissolved oxygen (DO) concentration in a river. The two models are developed using hourly experimental data collected from the United States Geological Survey (USGS Station No: 421209121463000 [top]) station at the Klamath River at Railroad Bridge at Lake Ewauna. The input variables used for the two models are water, pH, temperature, electrical conductivity, and sensor depth. The performances of the models are evaluated using root mean square errors (RMSE), the mean absolute error (MAE), Willmott's index of agreement (d), and correlation coefficient (CC) statistics. Of the two approaches employed, the best fit was obtained using the GRNN model with the four input variables used.

This article presents a comparison of two adaptive neuro-fuzzy inference systems (ANFIS)-based neuro-fuzzy models applied for modeling dissolved oxygen (DO) concentration. The two models are developed using experimental data collected from the bottom (USGS station no: 420615121533601) and top (USGS station no: 420615121533600) stations at Klamath River at site KRS12a nr Rock Quarry, Oregon, USA. The input variables used for the ANFIS models are water pH, temperature, specific conductance, and sensor depth. Two ANFIS-based neuro-fuzzy systems are presented. The two neuro-fuzzy systems are: (1) grid partition-based fuzzy inference system, named ANFIS_GRID, and (2) subtractive-clustering-based fuzzy inference system, named ANFIS_SUB. In both models, 60 % of the data set was randomly assigned to the training set, 20 % to the validation set, and 20 % to the test set. The ANFIS results are compared with multiple linear regression models. The system proposed in this paper shows a novelty approach with regard to the usage of ANFIS models for DO concentration modeling.

In this study, we present application of an artificial intelligence (AI) technique model called dynamic evolving neural-fuzzy inference system (DENFIS) based on an evolving clustering method (ECM), for modelling dissolved oxygen concentration in a river. To demonstrate the forecasting capability of DENFIS, a one year period from 1 January 2009 to 30 December 2009, of hourly experimental water quality data collected by the United States Geological Survey (USGS Station No: 420853121505500) station at Klamath River at Miller Island Boat Ramp, OR, USA, were used for model development. Two DENFIS-based models are presented and compared. The two DENFIS systems are: (1) offline-based system named DENFIS-OF, and (2) online-based system, named DENFIS-ON. The input variables used for the two models are water pH, temperature, specific conductance, and sensor depth. The performances of the models are evaluated using root mean square errors (RMSE), mean absolute error (MAE), Willmott index of agreement (d) and correlation coefficient (CC) statistics. The lowest root mean square error and highest correlation coefficient values were obtained with the DENFIS-ON method. The results obtained with DENFIS models are compared with linear (multiple linear regression, MLR) and nonlinear (multi-layer perceptron neural networks, MLPNN) methods. This study demonstrates that DENFIS-ON investigated herein outperforms all the proposed techniques for DO modelling.