Application of experimental design for the optimization of artificial neural network-based water quality model: a case study of dissolved oxygen prediction.

This paper presents an application of experimental design for the optimization of artificial neural network (ANN) for the prediction of dissolved oxygen (DO) content in the Danube River. The aim of this research was to obtain a more reliable ANN model that uses fewer monitoring records, by simultaneous optimization of the following model parameters: number of monitoring sites, number of historical monitoring data (expressed in years), and number of input water quality parameters used. Box-Behnken three-factor at three levels experimental design was applied for simultaneous spatial, temporal, and input variables optimization of the ANN model. The prediction of DO was performed using a feed-forward back-propagation neural network (BPNN), while the selection of most important inputs was done off-model using multi-filter approach that combines a chi-square ranking in the first step with a correlation-based elimination in the second step. The contour plots of absolute and relative error response surfaces were utilized to determine the optimal values of design factors. From the contour plots, two BPNN models that cover entire Danube flow through Serbia are proposed: an upstream model (BPNN-UP) that covers 8 monitoring sites prior to Belgrade and uses 12 inputs measured in the 7-year period and a downstream model (BPNN-DOWN) which covers 9 monitoring sites and uses 11 input parameters measured in the 6-year period. The main difference between the two models is that BPNN-UP utilizes inputs such as BOD, P, and PO43-, which is in accordance with the fact that this model covers northern part of Serbia (Vojvodina Autonomous Province) which is well-known for agricultural production and extensive use of fertilizers. Both models have shown very good agreement between measured and predicted DO (with R2 ≥ 0.86) and demonstrated that they can effectively forecast DO content in the Danube River.

A linear and non-linear polynomial neural network modeling of dissolved oxygen content in surface water: Inter- and extrapolation performance with inputs' significance analysis.

Accurate prediction of water quality parameters (WQPs) is an important task in the management of water resources. Artificial neural networks (ANNs) are frequently applied for dissolved oxygen (DO) prediction, but often only their interpolation performance is checked. The aims of this research, beside interpolation, were the determination of extrapolation performance of ANN model, which was developed for the prediction of DO content in the Danube River, and the assessment of relationship between the significance of inputs and prediction error in the presence of values which were of out of the range of training. The applied ANN is a polynomial neural network (PNN) which performs embedded selection of most important inputs during learning, and provides a model in the form of linear and non-linear polynomial functions, which can then be used for a detailed analysis of the significance of inputs. Available dataset that contained 1912 monitoring records for 17 water quality parameters was split into a "regular" subset that contains normally distributed and low variability data, and an "extreme" subset that contains monitoring records with outlier values. The results revealed that the non-linear PNN model has good interpolation performance (R2=0.82), but it was not robust in extrapolation (R2=0.63). The analysis of extrapolation results has shown that the prediction errors are correlated with the significance of inputs. Namely, the out-of-training range values of the inputs with low importance do not affect significantly the PNN model performance, but their influence can be biased by the presence of multi-outlier monitoring records. Subsequently, linear PNN models were successfully applied to study the effect of water quality parameters on DO content. It was observed that DO level is mostly affected by temperature, pH, biological oxygen demand (BOD) and phosphorus concentration, while in extreme conditions the importance of alkalinity and bicarbonates rises over pH and BOD.

Modeling the BOD of Danube River in Serbia using spatial, temporal, and input variables optimized artificial neural network models.

This paper describes the application of artificial neural network models for the prediction of biological oxygen demand (BOD) levels in the Danube River. Eighteen regularly monitored water quality parameters at 17 stations on the river stretch passing through Serbia were used as input variables. The optimization of the model was performed in three consecutive steps: firstly, the spatial influence of a monitoring station was examined; secondly, the monitoring period necessary to reach satisfactory performance was determined; and lastly, correlation analysis was applied to evaluate the relationship among water quality parameters. Root-mean-square error (RMSE) was used to evaluate model performance in the first two steps, whereas in the last step, multiple statistical indicators of performance were utilized. As a result, two optimized models were developed, a general regression neural network model (labeled GRNN-1) that covers the monitoring stations from the Danube inflow to the city of Novi Sad and a GRNN model (labeled GRNN-2) that covers the stations from the city of Novi Sad to the border with Romania. Both models demonstrated good agreement between the predicted and actually observed BOD values.