Journal of Electrical and Computer Engineering

Volume 2018, Article ID 9718951, 9 pages

https://doi.org/10.1155/2018/9718951

## Feedforward Chaotic Neural Network Model for Rotor Rub-Impact Fault Recognition Using Acoustic Emission Method

^{1}School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China^{2}School of Information Engineering, Huzhou University, Huzhou 313000, Zhejiang, China

Correspondence should be addressed to Weidong Liu; moc.361@tmucdwl

Received 26 May 2017; Accepted 12 July 2018; Published 20 September 2018

Academic Editor: Ephraim Suhir

Copyright © 2018 Wei Peng 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 rubbing faults caused by dynamic and static components in large rotatory machine are dangerous in manufacture process. This paper applies a feedforward chaotic neural network (FCNN) to recognize acoustic emission (AE) source in rotor rubbing and diagnose the rotor operational condition. This method adds the dynamic chaotic neurons based on logistic mapping into the multilayer perceptron (MLP) model to avoid the network falling into a local minimum, the delayed and feedback structure for maximum efficiency of recognition performance. The AE data was rotor rubbing process sampled from the test rig of rotatory machine, classification by fault degree. The experimental results indicate that the recognition rate is superior to the traditional BP network models. It is an effective method to recognize the rubbing faults for the machine normal operation.

#### 1. Introduction

Rotor condition monitoring has received considerable attentions as the majority of the rotating machinery problems are caused by the surfaces of dynamic and static components in relative motion [1–5]. Therefore, there is a need in the industry for rotor incipient fatigue detection.

By far, most researches are focused on the different rubbing conditions caused by various damages of the rotor system using vibration and acoustic emission (AE) methods [6–9]. The vibration method is performed based on the changes in stiffness, damping, mode, and other parameters of a rotor system to monitor the rubbing fault statues. Since the vibration response of rotor-stator rubbing is obviously nonlinear and highly depends on the rubbing conditions, it is not sensitive to incipient faults, and the faults are usually masked by background noise caused by mechanical vibration signals from rotating machinery [10–12]. Hence, it is not effective to use the vibration method to recognize rubbing fault diagnosis of the rotor-stator.

AE serving as a significant condition monitoring technology to offer earlier fault detection compared with other more established techniques is the phenomenon of transient elastic wave generation due to a rapid release of strain energy caused by relative motion of small particles under mechanical stresses. At present, some scholars have investigated rubbing fault features through AE signal waveform analysis technology, which are usually described by some characteristic parameters such as hit accumulation, amplitude distribution [13], frequency distribution, and power spectral density (PSD) [14, 15]. Deng et al. [16] researched waveform fractal dimension algorithm and further used the support vector machine (SVM) to recognize the rubbing fault in the rotatory machine. This technology has been demonstrated, and it has beneficial prospects for applications in rubbing fault diagnosis field [17–19].

The hysteretic Hopfield neural network (HHNN) is one of the nondestructive testing methods [20–25], detects defection property by AE signal, and then depends on the pattern recognition to classify the signal. The hysteretic characteristic can help us to enhance the capacity of memory and steadiness of the original states for the neural network, and chaotic characteristic can reflect some perception phenomena or cognitive process of human. Therefore, many neural networks with kinds of nonlinear characteristics such as chaos and hysteretic are proposed to improve the performance of the conventional neural network. However, although HHNN applied the hysteretic neuron into Hopfield neural network, the gradient decent mechanism enabled the network to get easily dragged into local minima as the initial condition is not deal.

CNN is originated from researching dynamic characteristics of nonlinear systems with artificial neural network (ANN) [26–29]. As nonlinear systems, the stability of neural network becomes the important characteristics of the whole system, and it usually needs to use the statistical neural network model instead of the identified model to make the dynamic reconfiguration. Chaos theory is the mathematical model aiming to analyse the unordered, unstable, and unbalanced phenomenon. Unlike back propagation (BP) network, CNN searches out the phase space of chaotic attractors and iterates all the states with its rules unrepeatably, in order to avoid falling into a local minimum effectively [30]. Because chaotic neural network has complex dynamic characteristics, the study on chaos control is the basis for utilizing chaotic neural network to resolve the practical engineering problems [2–4].

In order to achieve a high performance of the rubbing fault recognition algorithm using AE technology, this paper mainly focuses on the design of the improved novel FCNN algorithm, which adds the chaotic neurons based on logistic mapping into the MLP model. FCNN is a kind of dynamic network including delayed and feedback structure by adding the self-feedback gain *α* into the conventional neuron so as to have the associative effect [31]. In this way, it can be seen that hysteretic characteristic and chaotic characteristic are brought into neuron simultaneously. Besides, the context layer with rich chaotic dynamics nodes to make the network parameters from the local minima.

Generally, the function minima problem can be resolved by the feedforward chaotic neural network. In this paper, the uncertain neuron and neural networks are innovatively used to resolve the function optimization problem by the logistic mapping control. The rest of the paper is organized as follows. In Section 2, the logistic mapping is introduced and the relationships between the main parameters are given by numerical simulation. Section 3 presents the chaos control and learning algorithm for FCNN algorithm. Section 4 shows recognition experiments and results of AE source in rotor rubbing and verifies the application performance of the proposed FCNN, and Section 5 gives the final conclusion.

#### 2. Logistic Mapping

In the CNNs, doubling bifurcation is the common method of transferring to chaos states, and logistic mapping is the typical structure to show the multiperiod bifurcation. Logistic mapping also known as the insect population model is a polynomial mapping (equivalently, recurrence relation) of degree 2, and often cited as an archetypal example of how complex chaotic behaviour can arise from very simple nonlinear dynamical equations [32–34] as defined below:where severing as every year’s inspect population represents the ratio of existing population to the maximum possible population. The value of interest for the parameter is those in the interval (0, 4].

indicates different changing trends with different parameters : when , mapping has the tendency to easily attain the stationary state, which is independent of the initial population, and is the motionless point without any other periodic points. When , it has only two motionless points, that is, and , where the population can quickly approach the second motionless points as soon as possible. The system fluctuates at the beginning and returns to the stable state as shown in Figure 1(a). When , the system begins in concrete terms from multiperiod states to go to chaos. Concretely speaking, when , mapping from almost all initial conditions the population can approach the permanent oscillations between two values, and these two values are dependent on . As a result, the system begins to go to chaos with the period as shown in Figure 1(b). When , mapping from almost all initial conditions the population can approach the permanent oscillations among four values as shown in Figure 1(c).