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Essay: ANN-embedded expert system / Feed Forward Neural Network

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  • ANN-embedded expert system / Feed Forward Neural Network
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ANN-embedded expert system :

Expert systems (ES) are a branch of applied artificial intelligence (AI), and were developed by the AI community in the mid-1960s. The basic idea behind an expert system is simply that expertise, which is the vast body of task-specific knowledge and is transferred from a human to a computer. This knowledge is then stored in the computer and users call upon the computer for specific advice as needed. The computer can make inferences and arrive at a specific conclusion. Then like a human consultant, it gives advices and explains, if necessary, the logic behind the advice. An ANN is arrangement of interconnected computational components working in parallel, arranged in patterns similar to biological neural nets, and modeled after the human brain. The ANN embedded expert system are those in which the learning base is created consequently from training data and the system is equipped for making derivations out of the partial information accessible. The Neural Network perceives comparative examples, foreseeing future qualities or occasions based upon the cooperative memory of the examples it has learned.

2.2 Feed Forward Neural Network:

A feedforward neural network is a biologically inspired classification algorithm. It consist of a (possibly large) number of simple neuron-like processing units, organized in layers. Every unit in a layer is connected with all the units in the previous layer. These connections are not all equal: each connection may have a different strength or weight. The weights on these connections encode the knowledge of a network. Often the units in a neural network are also called nodes.

Data enters at the inputs and passes through the network, layer by layer, until it arrives at the outputs. During normal operation, that is when it acts as a classifier, there is no feedback between layers. This is why they are called feedforward neural networks.

Figure 2. Feed Forward Network

Details of Network Used:

1. Transformation Function used : Sigmoid Function
2. Learning Algorithm : Gradient Descent
3. Data Division : Random (dividerand)
4. Performance Criteria : MSE (Mean Squared Error)

2.3 Radial Basis Function:

The radial basis function is used as the learning algorithm for the ANN used. In this approach, learning is an equivalent to finding a surface in a multidimensional space that provides a best fit to the training data. This is generally known as the curve fitting approximation problem, and the functional approximation paradigm is known as the radial basis function (RBF) network.

The criteria on which the RBF is chosen are:

The RBF network uses basis functions in which the weights are effective over only a small position of the input space. This is in contrast to the multilayered perceptron network where the weights are used in a more global fashion, thereby encoding the characteristics of the training set in a more compact form.

The RBF networks can be rapidly trained (No Back Propagation)

This method could be applied to interpolate functions in spaces of arbitrary dimensions.

Gaussian approximation is helpful in dealing with the large amount of noisy data.

The network can implement spline interpolation and the spline is known to have a large power of approximation. Hence a high degree of approximation can be obtained with just one hidden layer network.

The strategy used in RBF networks consists of approximating an unknown function with a linear combination of nonlinear functions, called basis functions. The basis functions are radial in nature, i.e., they have radial symmetry with respect to a center. We use a gaussian radial basis function in our case.

Figure 3 Schematic representation of RBF network

A non-linear transformation is used between input and hidden layers. Such a network implements a mapping function fr : Rn → R according to,
fr(x) = o + i=1nriexp(||x − Ci ||2)

where, x Rn is the input vector, i, , 0 <= i <= nr are the weights or the parameters, Ci Rn , 1<= i <= nr are known as the RBF centers. In RBF networks the functional form Φ(.) and the centers Ci are assumed to be fixed. By providing a set of input x(t) and the corresponding desired output d(t) for t = 1 to n, the values of weights i can be determined using the linear least square method.

Assuming that there are n input nodes and m output nodes, the overall response function without considering nonlinearity in an output node has the following form:

i=iMW(i). K( (x-z(i))(i) ) = i=iMW(i). g ( ( ||x-z(i)|| )(i) )

Where,

M N the set of natural numbers is the number of kernel nodes in the hidden layer,

W(i) Rm : the vector of weights from the ith kernel node to the output nodes,

x : an input vector (an element of Rr),

K : a radially symmetric kernel function of a unit in the hidden layer,

z(i) and (i) : the centroid and smoothing factor (or width) of the (i)th kernel node, respectively

g : [0,inf) -> R is a function called the activation function, which characterizes the kernel shape

Figure 4. RBF Network

A gaussian function is used as an activation function, and the smoothing factors of kernel nodes may be the same or may vary across nodes.

2.3.1 Fine tuning of Radial Basis Neural Network :

SELECTING CENTERS : Use k-means clustering, intialized at randomly chosen points from the training set

Choose k cluster centers in the input space. (Can choose at random, or choose from among the training points.)

Mark each training point as “captured” by the cluster to which it is closest

Move each cluster center to the mean of the points it captured.

Repeat until convergence.

VARIANCE : Manual tuning (Minimising error on Cross Validation Set).

Performance Parameters : MSE (mean squared errors), Average Error percentage.

2.4 3D Woven Structures[2]

3D woven preforms have well-defined fiber architecture and its repeatability in practical manufacturing. 3D fabric is a single-fabric system one of which component yarns are placed in three mutually perpendicular planes in relation to one another. Basic requirements for actual 3D weaving process –

In order to make the 3D weaving operation effective, the following criteria needs to be fulfilled:

(1) Multi-layer warps arranged in a grid-like manner.

(2) Multiple number of sheds are formed are formed in row-wise and column-wise alternately.

(3) Two perpendicular series of wefts are inserted, of which one is in a horizontal direction and the other is in a vertical direction.

2.4.1 Warp interlock Architectures

3D solid structures refer to those woven architectures that have solid cross-sections either in a broad panel or in a net shaped preform. This structure comprises integrated multiple-walled sections in the directions of fabric-width and thickness defining a cross-sectional shape without.

The distinctive feature of the multilayer 3D fabrics is that they have clear definition of fabric layers in the thickness of the fabric.

Each layer is composed of a set of warp ends and a set of weft yarns. The layers can be connected together through weaving by either the existing yarns (self-stitching) or external sets of yarns (central stitching).

Because of the structural characteristics, all warp and weft yarns in a multilayer fabric are crimped, which leads to low initial modulus along the warp and weft directions.

Figure 5: Warp interlock structure

2.4.2 Orthogonal Woven Architecture

3D orthogonal woven fabric is manufactured with a multi-warp yarn system. In this system we use two series of warp yarns (Ground warp and Binder warp).The warp and weft yarns provide high in-plane stiffness and strength, and the binder yarns run through the thickness direction to stabilize the woven structure. 3D orthogonal woven composites have higher inter-laminar fracture toughness and impact damage resistance than laminated composites.

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