Mathematical Problems in Engineering

Volume 2015, Article ID 292197, 8 pages

http://dx.doi.org/10.1155/2015/292197

## Reliability Assessment of CNC Machining Center Based on Weibull Neural Network

School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China

Received 23 July 2015; Revised 24 October 2015; Accepted 28 October 2015

Academic Editor: Marco Mussetta

Copyright © 2015 Zhaojun Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

CNC machining centers, as the key device in modern manufacturing industry, are complicated electrohydraulic products. The reliability is the most important index of CNC machining centers. However, simple life distributions hardly reflect the true law of complex system reliability with many kinds of failure mechanisms. Due to Weibull model’s versatility and relative simplicity and artificial neural networks’ (ANNs) high capability of approximating, they are widely used in reliability engineering and elsewhere. Considering the advantages of these two models, this paper defined a novel model: Weibull neural network (WNN). WNN inherits the hierarchical structure from ANNs which include three layers, namely, input layer, hidden layer, and output layer. Based on more than 3000 h field test data of CNC machining centers, WNN has been successfully applied in comprehensive operation data analysis. The results show that WNN has good approximation ability and generalization performance in reliability assessment of CNC machining centers.

#### 1. Introduction

Common life distributions, like normal distribution, lognormal distribution, and Weibull distribution, usually are simple for system reliability modeling [1, 2]. However, CNC machining centers are complex repairable systems in which reliability distribution could not be responded precisely by these simple life distribution models. Mixture distribution has been used popularly during the development process of modern statistics. The application of mixture distribution could trace back to the late 19th century, while Weibull mixture distribution started in 1950s [3–5]. At present, the most common Weibull mixture distribution is twofold Weibull distribution [6, 7]. Multifold Weibull mixture distribution has been seldom used so far. There are two reasons for this: it is hard to estimate large number of parameters, and its bad generalization performance makes it difficult to avoid overfitting.

With the rapid development of computer technology, artificial neural networks (ANNs), as machine learning model with powerful nonlinear approximation ability, have been developed and get wide applications [8–10]. It is often used to deal with the nonlinear relationship between input and output of complex system [11]. However, ANNs easily bring overfitting phenomenon which is a hot topic and attracts many researchers [12, 13]. Improving the generalization performance of artificial neural networks is a key point to solve overfitting problem.

In this paper, Weibull neural network (WNN) is defined based on some advantages of Weibull mixture distribution and artificial neural networks. In this network, hierarchical structure of radical-basis function network (RBF), which has simple structure and powerful nonlinear approximation performance [14, 15], is adopted. RBF was proposed by Moody and Darken [16, 17] with three layers, namely, input layer, hidden layer, and output layer. The input layer is a series of source nodes that connects the networks to reliability data of CNC machining centers. The hidden layer applies a finite Weibull mixture distribution model connecting the input layer and the output layer. The output layer is the probability density of the data. Finite Weibull mixture distribution [7] is applied as hidden layer nodes function (HLNF). Wide application and multiple distribution curve shape are the main characteristics of finite Weibull mixture distribution which suits not only the life distributions of electronic products, but also the life distributions of mechanical parts.

This paper will be focused on WNN’s two key issues: to develop an efficient learning method and to improve the generalization performance of WNN. And the rest of the paper is organized as follows: a definition of Weibull neural network (WNN) is given in Section 2 with the introduction of basic characteristics of artificial neural networks and Weibull mixture distribution. Section 3 presents the learning process of Weibull neural network (WNN). Section 4 offers field test data of CNC machining centers and applies them into comprehensive simulations and reliability assessment by WNN. For comparison, authors also analyze the data by two-parameter Weibull distribution (TPWD). Finally, conclusions are given in Section 5.

#### 2. Weibull Neural Network

##### 2.1. Artificial Neural Networks

Artificial neural networks (ANNs) [18] are the abstraction and simulation of certain basic characteristics of biological neural networks. As complex nonlinear approximation mathematical models, ANNs rely on the complexity of network structure by adjusting the internal connections between nodes and then achieve the purpose of training and learn any complex nonlinear relationship with strong robustness and fault tolerance [19].

Hierarchical structure is the most common structure of ANNs as BP neural network [20], RBF neural network [14, 15], and so on. Hierarchical structure of ANNs can be divided into several layers by function, such as the input layer, an intermediate layer (also called hidden layer), and the output layer. Each layer is connected in order, as shown in Figure 1. The input layer is responsible for receiving input information from the outside and transfers the information to the neurons of hidden layer. A neutron is an information processing unit which is the fundamental of neural networks. Neuron model constituted different transformation functions with various information processing abilities. The hidden layer is internal information processing layer of neural network, responsible for information conversion. According to required information processing capacity, the hidden layer may be designed as one or more layers. The final one, output layer, supplies the response of neural network to the activation pattern (signal) which is applied to the input layer.