**3. NARX model**

**1. Introduction**

252 Advanced Applications for Artificial Neural Networks

the static one.

**2. Static neural network**

the positive weight accentuates it.

The human brain, like every vital organ, is constituted of a set of cells which are called neurons. It is through this organ that we can learn and reason, reflect and memorize. The geniality of human brain and more particularly of its neurons motivates several researchers to interest to this research and to benefit from its biological aspect. The idea was to reproduce, in an artificial way, the behaviors observed in man. It was in 1943 that the first artificial neural network was created by Warren McCulloch and Walter Pitts. It is a simple elementary processor imitating the structure and the functioning from the biological neuron. Artificial neural network is characterized by its capacity of learning and generalizing. It represents a very powerful tool; it provided multiple solutions to different complex problems. In these recent years, its effectiveness is proved in various researches fields. Artificial neural network are subdivided on two main groups, the static and dynamic neural network. The choice of the one or the other neural network type depends on the application to be processed and the complexity of model. For static neural network, information propagates in a single direction, layer by layer, and from the inlet to the outlet. They are generally used in various applications such as classifications, pattern recognition, and functions approximation. The connectivity between neurons in dynamic neural network is not limited. Each neuron can send and receive information from all other neurons. The dynamic neural network architecture includes frequently one or more cycles which necessarily contain at least one delay connection. This gives rise to the dynamism notion. This neural network type is more complex than the static one, but it is more efficient for some particular applications such as dynamic modeling, monitoring, and process control. In this chapter, nonlinear autoregressive models with exogenous input (NARX) model, as type of dynamic neural network, will be used to the solar radiation prediction. Simulation results will be presented to prove the effectiveness of this model compared to

Static neural network was the first and simplest type. It is a nonlooped network since it does not contain a feedback or delay connection [1]. It is a statistical regression tool which allows the approximation of any nonlinear function sufficiently regular. The neural architecture of this network is presented as shown in **Figure 1**. It imitates the structure of the biological neuron. It is composed of a set of layers. The hidden one allows to receive a variable number of inputs, and information is moved only from inputs directly through hidden layer to the output layer without cycles or loops. Each connection is associated with a synaptic weight w, which represents the strength of each connection. The negative weight inhibits its input, while NARX model is the abbreviation of "nonlinear autoregressive models with exogenous input". It is registered under recurrent dynamic neural networks. It is a nonlinear autoregressive model with exogenous inputs. NARX consists of a linear ARX model with two delays, one for input and the other for output. It is based on the multilayer perceptron and the recurring connections. Its effectiveness has been proven in the research work presented in [2] to predict the PV power. It is also used in other applications such as the electricity prices prediction and the air pollution prediction [3–5]. This model is commonly used for the time series, estimation, and prediction as well as for nonlinear dynamic systems modeling. Compared to other neural network types, NARX model is characterized by a good learning, fast convergence, and better generalization [6]. The PV power prediction results presented in [2] have proven an improvement performance when using NARX model compared to those obtained using the static neural network. NARX model performances are also compared to those of static neural network and radial neural network in the research works presented in [7]. NARX gave also the best prediction results in these studies.
