Neural Computing
Artificial neural networks are non-linear mathematical models capable of learning the arbitrary and complex physico-chemical process of a system from observed input variables and desired outputs of the system. The primary advantage of ANN over phenomenological/conceptual models is that, it does not require information about the complex nature of the underlying process to be explicitly described in mathematical form (Sahoo et al., 2005).
ANNs consists of a system of simple interconnected processing element called neurons. This gives the ability to model any non-linear process through a set of unidirectional weighted connections (Simpson, 1990). Multi-layer perceptron (MLP) belongs to the class of supervised feed-forward networks in which the processing elements are arranged in a multi-layered structure; as an input layer, one or more hidden layers, and an output layer, as illustrated in Figure 1.
Figure 1. Schematic of a multi-layered perceptron
The input layer consists of a set of neurons NI, each representing an input parameter and propagates the raw information to the neuron in the hidden layer (NH), which in turn transmits them, to the neurons in the output layer (NO). Each layer consists of several neurons and the layers are connected by the connection weights (Wij1 and Wij2). The most commonly used transfer function is the sigmoid function that produces output in the range of 0 to 1, as described by;
(1)The back propagation network is the most prevalent supervised ANN learning model (Rumelhart et al., 1986). It uses the gradient descent algorithm to correct the weights between interconnected neurons (Maier and Dandy, 2001). During the learning process of the network, the algorithm computes the error between the predicted and specified target values at the output layer. The error function (E) at the output layer can be defined by;
(2) where, O
d is the desired (experimental) value, and O
p is the model predicted value.
ANNs have already been applied to solve, predict and optimize a variety of environmental and biotechnological problems: wastewater treatment plant performance, effectiveness of riverbank filtration, biodegradation kinetics of organic compounds, and air-pollution related problems.
Wastewater Treatment Processes
According to Qasim (1999), any wastewater treatment plant would necessarily comprise of a number of unit operations and processes in order to achieve the required degree of physico-chemical or biological treatment. The schematic shown in Figure 2 is called a process flow diagram, wherein many unit processes are combined to achieve the desired treatment efficiency of polluted water. Many of these treatment processes, physical, chemical, or biological, however, are used to treat the liquid and solid portions of the wastewater simultaneously. Some typical examples are; stabilization ponds, aerated lagoons, land treatment, and constructed wet lands. The principal types of reactors used for wastewater treatment are; (i) batch reactors, (ii) plug-flow or tubular-flow reactors, (iii) completely mixed or continuous flow stirred tank reactor (CFSTR), and (iv) arbitrary-flow reactors. The basic criteria for developing a process scheme, amongst others, depends on the following factors, (i) characteristics of the wastewater, (ii) requirement of the regulatory authorities, (iii) proximity to the build-up areas, (iv) topography and site characteristics, (v) plant economics (vi) quantity and quality of sludge generated from each process, and (vii) minimal environmental consequence, and maximal environmental benefits/improvements.
Figure 2. Typical treatment scheme for wastewater treatment systems