Permite uniformidad en la terminología de las cuentas utilizadas en el

There are several types of ANN (Jang et al. (1997)). They are:  Back Propagation for Feed Forward Network (BPFFN)  Multi Layer Perceptrons (MLP)

 Back Propagation Multilayer Perceptrons (BPMP)  Radial Basis Function Networks (RBFN)

 Self Organized Map (SOM)

All of these types of ANN have been implemented in various fault diagnosis applications.

3.1.3.1 Back Propagation Feed Forward Network (BPFFN)

A typical Back Propagation Feed Forward Network is constructed from several series or successive layers of neurons. In the example shown in Figure 3.1, a typical 3 layer back propagation (BP) feed forward neural network (NN) construction is illustrated.

x₁, x2, … xn are networks inputs, y1, y2, …, ym are outputs. wij represent the connection weightings input layer of neural cell i and the hidden layer neurons layer

y, and v_jt is the connection between hidden layer neurons j and the output neurons layer. Typically, sigmoid-type neurons, neurons with differentiable functions such as the hyperbolic tangent function (Haykin, 1999), are used in the layers as the transfer function of the BP network.

Figure 3.1 Typical three layers of BPFFN network (Galushkin, 2007), (Bin et al. 2012)

Figure 3.1 show the layer configuration of the sigmoid-type neurons which are the building blocks a Feed Forward Neural Network where every neuron in a layer receives inputs from the outputs of all the neurons of the preceding layer.

The term back-propagation is applied to this type of ANN, as during the training or mapping of the input-output relationships of the data, the error is propagated backwards through each internal node. The error information is then used to calculate the weighting adjustment for the corresponding node. This calculation process is the core of the training process during which the information is forwarded from the input layer to the output layer and weighting values are changed until the error value is reduced to an acceptable limit.

The multilayer construction that fully interconnects the feed forward (FF) network uses the ‘delta rule’ to compute the weights between the actual output and the desired output. The desired output is optimised through a least square approach (Alguindigue, 1993). The basic algorithm for back propagation is presented in Rumelhart and McClelland (1986).

The realisation of the arbitrary non-linear mapping between the input and output by using FF a network is useful in areas such as pattern recognition, function approximation, and data compression. The mapping of input data output data is achieved using a multi-layered FF network. This mapping process is carried out by changing the connection weight of each neural neuron in a network. The change of

Chapter 3 – Review of Artificial Intelligence (AI) Systems in Fault Diagnosis 51 weight values aims to ensure that the output generated is consistent with the anticipated one. The process of weight value modifications is known as the training process of the network. The BP NN can be implemented to recognise a non-linear relationship between fault types and fault characteristic parameters of bearings (Bin,

et al. 2012).

Use of either multi layer perceptron (MLP) networks or Radial Basis Function (RBF) networks for the common application of FF networks is optional (Meireles et al. 2003). They are used to map given sets of data points (input-output) using interpolation methods. For the purposes of pattern recognition, adoption of an MLP is preferred since it has a function which produces numerical results of 1 or 0 which are suitable for classification purposes.

In the design of the ANN, determination of the number of processing element within the input-output layers is generally based on the number of variables that are used as input and output entities. The determination of the number of processing elements for the hidden layer is based on the complexity of the problem. Several design criteria for the number of hidden layers of the ANN are presented in Kung and Hwang (1988).

Multi-layer FF networks can be used to map the input and output relationship pattern that exists in the data. Inputs are received by the input layer and are then modified based on the set of weights. The modified results are then sent to the hidden layers. Each hidden layer propagates the modified inputs to the subsequent layers before the modified inputs reach the output layer. The calculation of overall error takes place in the output layer.

3.1.3.2 Recurrent or Recirculation Neural Network (RNN)

The recurrent or recirculation neural network(RNN) and the generic FF networks have similar characteristics, except that the RNN employs additional feedback connections that delay and store information from previous steps (Wang et al. 2004b). The application of these feedback connections means that the training process of an RNN is carried out in cycles. The training is executed iteratively which takes longer for results to be obtained. In general, the RNN has fixed connection

weights of 1, and the dynamic response is achieved by delaying inputs and outputs (Evsukoff and Gentil, 2005). The structure of an RNN is shown in Figure 3.2.

Figure 3.2 Recurrent Recirculation Neural Network structure (Graupe, 1997)

3.1.3.3 Self-Organizing Map (SOM)

The Self-Organizing Map (SOM) network comprises a forward two-layer network that employs a non-linear projection characteristic that maps the input signal, which is of arbitrary dimension, to a one or two-dimensional array of (neurons) nodes in which the array of nodes is related to a discrete map (Kohonen, 1997).

Chapter 3 – Review of Artificial Intelligence (AI) Systems in Fault Diagnosis 53 Figure 3.3 shows the basic configuration of the SOM network which consists of a two layer neural network using full connections between neurons in the output layer.

The SOM provides a mapping process which is based on the sequence of a high- dimensional distribution data on a regular or simplified low dimensional grid. This feature imparts to the SOM the ability to translate complex, nonlinear statistical relationships between data with high dimensions into a simple geometric relationship on a low-dimensional space or simplified graph.

The simplification of relationships is carried out while it preserves the most important structure and metric relationships of the data. This process can also be seen as a type of abstraction. The features of an SOM that provide abstraction and visual information of dimensional data can be used in a number of ways for applications that contain complex tasks such as process monitoring, process analysis and fault diagnosis (Kohonen, et al. 1996), (Zhong et al. 2005).

As an example, the Kohonen SOM network consists of three major learning step attributes: competition, co-operation and adaptation (Yang et al. 2004). In the competition step, the network compares and competes with other neurons based on the output values for a given input vector, modified by a chosen discriminating function. The discriminating function is later used to determine which output is closest to an input pattern. The competition step produces a selection among the output neurons. The neuron with the closest relationship to the input vector will be picked up and labelled as the winning (best-matching) neuron. The cooperation step is where the selected winning neurons are used to predefine a neighbourhood or group of neurons. This will provide the basis for the neighbouring neurons to cooperate by which only the weights of those neurons defined within the topological neighbourhood of the winning neuron will be updated or changed. The synaptic weighting, strength of a connection between two neurons, of neurons outside the neighbourhood will remain unchanged. This is followed by the adaptation step where the winning neuron within the group constantly changes its weight value to adapt to the values of the inputs pattern. This learning strategy provides the ability to evolve the synaptic weight vectors towards the distribution of the input vectors.

3.1.3.4 Radial Basis Function (RBF)

The radial basis function (RBF) network is a forward network with three layers: an input layer, a hidden radial basis layer and an output linear layer (Lei et al. 2009). The input neuron information is transferred to the neurons in the hidden layer. The RBF in the hidden layer responds to the input information, and the network outputs are then generated in the neurons of the output layer.

The RBF was first applied to neural networks by Broomhead and Lowe (1988). The RBF NN is a feed forward network which comprises three layers: an input layer, a hidden radial basis layer and a linear output layer. Information received by neurons in the input layer is sent to neurons in the hidden layer. The RBF neurons in the hidden layer respond to the input information and the output layer generates output.

The advantage of the RBF network is that the hidden neurons will produce non-zero outputs if the outputs values are within the minimum limit of the input values pre- defined range. Otherwise, the output will be zero. This network feature makes the number of active or used neurons small and the time required in training the network is shorter (Lei, et al. 2009).