## 4 Classification  
RBF neural network [10; 13] is better than BP in convergence rate learning and local approximation performance, because minority weights will locally influence net output in local input sets. Thus, RBF was successful in applying an approximation of nonlinear function, time series analysis, data analysis, pattern recognition, information processing, image processing, system modeling, controlling, and fault diagnosis. The basic idea of RBF is that solved problems are linearized by mapping nonlinear input to high-dimensional space, where the Gaussian function is usually chosen as a transformation function. A simple RBF neural network has a three-layer mapping structure, which includes an input, a hidden layer, and an output layer. The input layer consists of sensing units, which are used to link the outer data and the inner network. The hidden layer is a high-dimensional mapping structure of kernel function, which transforms the nonlinear data to a linearly divisible set. Moreover, the linear output layer fits a curve in the high-dimensional dataset that is optimally equal, to find divisional surfaces in the hidden layer set. Once the central position of the activated distance function is confirmed in the hidden layer, the relationship of input and output is also confirmed, and the output is the linear sum of hidden units. The RBF neural network usually utilizes a distance function (such as Euclidean distance) as the basic function of hidden nodes and adopts a radial basis function (such as Gaussian function) as the activation function. The radial basis function is a radial symmetric about the central point of an \(n\)-dimensional space. Once the input of a neural unit is far away from the central point, the activation degree of this unit is low. This feature is generally named as a local characteristic of the hidden layer. There were 281 artificial defects of broken wires, curling wires, and wide fractures by using the UME. To enhance reliability and generalization, the neural network was trained by a set of 211 randomly selected samples, and the others were used to test the network recognition accuracy. We adopted the MATLAB (2013a, Mathworks Inc. Natick, MA, USA, 2013) neural network toolbox to design an RBF neural network, where \"newmpp\" could quickly establish a classification network. The designed network consisted of three layers, an input with a number of input vectors and the distance function as the activation function. The hidden layer was a competitive layer without threshold values, and the input of this layer was the distance between the input vectors and  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Broken Wires** & \(\sigma\) & \(u_{3}\times 10^{-4}\) & \(U\times 10^{-2}\) & \(e\) & \(M_{1}\) & \(M_{3}\) & \(M_{5}\) & \(M_{7}\) \\ \hline
1 & 5.33 & \(-7.11\) & 6.1446 & 4.3744 & 6.6409 & 30.9157 & 57.4199 & 58.6916 \\
2 & 9.08 & 77.47 & 5.0684 & 4.8489 & 6.6487 & 29.2743 & 55.5046 & 59.2687 \\
3 & 11.03 & 18.17 & 6.3782 & 4.7540 & 6.6390 &  
sample vectors. The probability of each element was calculated by the competitive transfer function. The output of the function was 1, while the maximum probability of the other elements was 0. The radial spread parameter was 0.145, and the hidden nodes adopted the automatic optimization strategy. The activation function of the hidden layer was the \"compet\" function, and the output was a vector of seven elements, where the number of broken wires was only the target element with an output of 1. The network training accuracy was 95.26% and the average training error was 0.0616. The maximum recognition error was three broken wires in the network testing, and with one limited error the recognition accuracy was 91.43%. The testing performance of different parametersis shown in Table 3. The recognition accuracy is low in Table 3. Different diameters of wire rope may cause this result. On the other hand, lift-off distance, magnetization and shaking of detection equipment also would cause singular signal.