Mathematical Problems in Engineering

Volume 2015, Article ID 513039, 9 pages

http://dx.doi.org/10.1155/2015/513039

## A Fuzzy Neural Network Based on Non-Euclidean Distance Clustering for Quality Index Model in Slashing Process

^{1}School of Electrical Engineering, Shenyang University of Technology, Shenyang 110870, China^{2}College of Information and Science Engineering, Northeastern University, Shenyang 110003, China

Received 27 November 2014; Revised 9 April 2015; Accepted 12 April 2015

Academic Editor: Jyh-Hong Chou

Copyright © 2015 Yuxian Zhang 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

The quality index model in slashing process is difficult to build by reason of the outliers and noise data from original data. To the above problem, a fuzzy neural network based on non-Euclidean distance clustering is proposed in which the input space is partitioned into many local regions by the fuzzy clustering based on non-Euclidean distance so that the computation complexity is decreased, and fuzzy rule number is determined by validity function based on both the separation and the compactness among clusterings. Then, the premise parameters and consequent parameters are trained by hybrid learning algorithm. The parameters identification is realized; meanwhile the convergence condition of consequent parameters is obtained by Lyapunov function. Finally, the proposed method is applied to build the quality index model in slashing process in which the experimental data come from the actual slashing process. The experiment results show that the proposed fuzzy neural network for quality index model has lower computation complexity and faster convergence time, comparing with GP-FNN, BPNN, and RBFNN.

#### 1. Introduction

The slashing process is a very important procedure in textile manufacturing processes. It can improve the ability of warp to resist the loading of weaving and improve the textile ability, so as to ensure the smooth going of weaving [1, 2]. Size add-on, size moisture regain, and elongation are very important quality indexes in slashing process in which size add-on (the amount of size added) is the key quality index which affects directly product quality in slashing process [3]. Since the slashing process employs complex physical, chemical, and thermal changes, it is difficult to build precise first-principle model that can explain why the desired quality appears in products. Hence, it is a significant task to establish an accurate quality index model and obtain true quality index.

Another option to solve this difficult situation is to use artificial intelligence technology. Nowadays various new technologies such as artificial neural networks and fuzzy system have been accepted as a potentially useful tool for modeling complex nonlinear systems [4, 5]. As a solution, artificial intelligence technology has gained increasing popularity in various industries, like the chemical industry, bioprocess, steel industry, and so forth [6–8]. In the textile industry, most of companies have also built integrated databases to store empirical data from production process. And most popular quality index models were built on the basis of the linear statistical model. However, the applicability of these statistical models to the complicated nonlinear processes such as slashing process is limited.

Recently, some researchers have proposed new technology to solve the above problem. In [9] a neural network model for predicting initial load-extension behavior is presented in which a single hidden layer feed-forward neural network based on a back-propagation algorithm with four input neurons and one output neuron is developed to predict initial modulus in the warp and weft directions. In [10], the predictability of the warp breakage rate from a sizing yarn quality index using a feed-forward back-propagation network is investigated. An eight-quality index (size add-on, abrasion resistance, abrasion resistance irregularity, hairiness beyond 3 mm, breaking strength, strength irregularity, elongation, and elongation irregularity) and warp breakage rates are rated in controlled conditions. A good correlation between predicted and actual warp breakage rates indicates that warp breakage rates can be predicted by artificial neural networks. In [11], the performance of multilayer perceptron (MLP) and multivariate linear regression (MLR) models for predicting the hairiness of worsted-spun wool yarns from various top, yarn, and processing parameters is evaluated. In [12], a predictive model using empirical data is built by a neural network in order to describe complicated nonlinear relationship between operating parameters and quality index in slashing process. However, there are some shortages in the above methods, such as ambiguous physical interpretation for weight and number of layers and neurons in artificial neural networks.

Since Zadeh proposed the fuzzy logic theorem to describe complicated systems, it has become very popular and has been successfully used in various problems [13, 14]. More recently, fuzzy logic has been highly recommended for modeling to solve the inherent imprecision and vagueness characteristics in nonlinear system [15, 16]. On the other hand, a neural network has the ability to learn from input-output pairs, self-organize its structure, and adapt to it in an interactive manner. The integration of fuzzy inference system and neural network will make full use of their advantages and avoid disadvantages [17, 18]. The fuzzy neural network (FNN) is a multilayer feed-forward network which uses neural network learning algorithms and fuzzy reasoning to map an input space to an output space. With the ability to combine the verbal power of a fuzzy system with the numeric power of a neural system adaptive network, fuzzy neural network has been shown to be powerful in modeling numerous processes [19]. Fuzzy neural network has the advantage of allowing the extraction of fuzzy rules from numerical data or expert knowledge and adaptively constructs a rule base [20].

In this paper, a fuzzy neural network based on non-Euclidean distance for quality index model in slashing process is proposed in which the input space is partitioned into many local regions by the fuzzy* c*-means clustering based on non-Euclidean distance, and number of fuzzy rules and membership function are determined so that computation complexity is decreased. Then, the premise and consequent parameters of fuzzy neural network are trained by hybrid learning algorithm, and the convergence condition of consequent parameters is analyzed by Lyapunov function. The experiment shows that the proposed fuzzy neural network modeling method can restrain influence on noise data and decrease computation complexity, and the established size add-on model for slashing quality index has a faster convergence speed and higher accuracy.

The rest of the paper is organized as follows: the structure of fuzzy neural network is introduced in Section 2; the learning algorithm is proposed for fuzzy neural network in Section 3 in which structure identification and parameter estimation are introduced, respectively; a size add-on model is implemented for predicting slashing quality index in Section 4. Finally, the work is concluded in Section 5.

#### 2. Structure of Fuzzy Neural Networks

The fuzzy neural networks are composed of premise part and consequent part. The structure of fuzzy neural networks can be described as a multilayer neural network shown in Figure 1.