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Modeling Wastewater Treatment Plant (WWTP) constitutes an important tool for controlling the operation of the process and for predicting its performance with substantial influent fluctuations. The purpose of this paper is to apply an artificial neural network (ANN) approach with a feed-forward back-propagation in order to predict the ten-month performance of Touggourt WWTP in terms of effluent Chemical Oxygen Demand (CODeff).

The influent variables such as (pHinf), temperature (TEinf), suspended solid (SSinf), Kjeldahl Nitrogen (KNinf), biochemical oxygen demand (BODinf) and chemical oxygen demand (CODinf) were used as input variables of neural networks. To determine the appropriate architecture of the neural network models, several steps of training were conducted, namely the validation and testing of the models by varying the number of neurons and activation functions in the hidden layer, the activation function in output layer as well as the learning algorithms.

The better results were achieved with an architecture network [6-50-1], hyperbolic tangent sigmoid activation functions at hidden layer, linear activation functions at output layer and a Levenberg – Marquardt method as learning algorithm. The results showed that the ANN model could predict the experimental results with high correlation coefficient 0.89, 0.96 and 0.87 during learning, validation and testing phases, respectively. The overall results indicated that the ANN modeling approach can provide an effective tool for simulating, controlling and predicting the performance of WWTP.

This work is the first of its kind in this region due to the remarkable development in terms of population and agricultural activity in the region, which drove to the increase of water pollutants, so it is necessary to use the modern technologies to modeling and controlling of WWTP.

The purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.

Firstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.

The model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.

Due to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.

The main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.