Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 354658, 7 pages

http://dx.doi.org/10.1155/2015/354658

## ACO-Initialized Wavelet Neural Network for Vibration Fault Diagnosis of Hydroturbine Generating Unit

^{1}School of Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei 430072, China^{2}Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4

Received 24 November 2014; Accepted 12 January 2015

Academic Editor: Yun-Bo Zhao

Copyright © 2015 Zhihuai Xiao 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

Considering the drawbacks of traditional wavelet neural network, such as low convergence speed and high sensitivity to initial parameters, an ant colony optimization- (ACO-) initialized wavelet neural network is proposed in this paper for vibration fault diagnosis of a hydroturbine generating unit. In this method, parameters of the wavelet neural network are initialized by the ACO algorithm, and then the wavelet neural network is trained by the gradient descent algorithm. Amplitudes of the frequency components of the hydroturbine generating unit vibration signals are used as feature vectors for wavelet neural network training to realize mapping relationship from vibration features to fault types. A real vibration fault diagnosis case result of a hydroturbine generating unit shows that the proposed method has faster convergence speed and stronger generalization ability than the traditional wavelet neural network and ACO wavelet neural network. Thus it can provide an effective solution for online vibration fault diagnosis of a hydroturbine generating unit.

#### 1. Introduction

Nowadays, hydroturbine generating units are becoming larger, more complicated, and more integrated, which not only makes regulation and operation of the hydroturbine generating unit complicated but also increases the probability of occurrence of faults. Therefore, it is of great significance to research effective fault diagnosis methods that give early alert before faults happen or avoid deterioration of existing faults resulting in great economic losses.

About 80% of the hydroturbine generating unit faults reveal characteristics in vibration signals [1]. Vibration signals of a hydroturbine generating unit, a complicated and nonlinear system, are generally influenced by multiple hydraulic, mechanical, and electrical/electronic factors [2]. These factors may interact with each other, which makes it difficult to construct by theoretical analysis a one-to-one relationship between the vibration feature and the cause of the fault. All these factors lead to the difficulty of fault diagnosis for a hydroturbine generating unit.

Taking the characteristics of hydroturbine generating unit vibration signals into consideration, nonlinear diagnosis models are often utilized to realize effective mapping from vibration feature sets to fault sets [3–6]. Neural network [7] has perfect self-organization, adaptive learning, and remembrance abilities. It can realize complicated relationship mapping in nonlinear systems and has become a dominant method in the area of hydroturbine generating unit fault diagnosis. Feedforward neural network trained by back propagation method is one of the most widely used methods [3–5]. However, such a neural network has drawbacks, for example, slow convergence speed and inclination to be trapped in local minima [8]. Wavelet neural network, a kind of feedforward network proposed in 1992 [9] on the basis of wavelet analysis theory by substituting excitation function for wavelet function, has developed fast [10–12]. However, even though by combining time-frequency localization ability of wavelet analysis and self-learning ability of neural network a wavelet neural network has strong approximation, fault tolerance, and classification abilities, it cannot avoid drawbacks of slow convergence speed and high sensitivity to initialization parameters [13]. Therefore, optimizing parameters of wavelet neural networks by heuristic optimization algorithms is becoming an important research topic [14–16].

Ant colony optimization (ACO) algorithm is one kind of the heuristic optimization algorithms. It has perfect global optimization characteristics, strong robust ability, and great distributed computing system. ACO wavelet neural network, which uses ACO to learn parameters of wavelet neural network, preserves the advantages of ACO and does not have the drawbacks of sensitivity to initializing parameters. However, its training speed is still slow according to the information in the literature. Therefore, an ACO-initialized wavelet neural network is proposed in this paper and used in the vibration fault diagnosis of a hydroturbine generating unit. This method employs ACO to train the parameters of a wavelet network and the obtained parameters are taken as the initialization parameters. Vibration frequency features of a hydroturbine generating unit are taken as the inputs and fault types are taken as the outputs of the wavelet neural network. A fault diagnosis model of the hydroturbine generating unit based on ACO-initialized wavelet neural network is constructed. Fault diagnosis results show that, compared with the traditional wavelet neural network and ACO wavelet neural network, not only can the method proposed in this paper increase the speed of convergence but it also has strong generalization ability.

#### 2. Vibration Types and Characteristics of Hydroturbine Generating Units

According to disturbing force types of vibration signals, vibration types can be divided into hydraulic vibration, mechanical vibration, and electrical vibration [2].

##### 2.1. Hydraulic Vibration

Hydraulic vibration is caused by water flow and machinery. There are many factors which lead to this kind of vibration such as hydraulic imbalance, draft tube pressure pulsation, nonuniformity in the path of circulating water flow, nonuniform gap of runner wearing ring, Karman vortex street, clearance jet, cavity erosion, and wrong in cam relationship. The characteristic of this type of vibration is that vibration frequency is different for each vibration source.

##### 2.2. Mechanical Vibration

Mechanical vibration is aroused by improper installation of the unit, drawbacks of the unit structure, or damage in the component of the running unit. There are many factors which lead to this kind of vibration such as imbalance of the rotating part of the unit, misalignment of the axis, defects in the bearing, rotor-to-stator rub, and looseness of the connection. The characteristic of this kind of vibration is that vibration frequency is the rotation frequency or a multiple of the rotation frequency.

##### 2.3. Electrical Vibration

Electrical vibration is caused by nonuniformity of magnetic flux density, unbalance of electromagnetic pull, and stator core looseness. There are many factors which lead to this kind of vibration such as the rotor pole coil turn-to-turn short circuit, nonuniform air gap between rotor and stator, wrong polarity order of the core, out of round of rotor inside or stator outside, and unbalance of current among three phases. The characteristic of this kind of vibration is that vibration frequency is the rotation frequency or the frequency of the polar in the hydropower generator.

It can be seen from the above that vibration signals are the synthesis of results aroused by hydraulic vibration, mechanical vibration, and electrical vibration. It has highly nonlinear characteristic. Hydroturbine generating unit fault diagnosis based on neural network method is used to extract features of these vibration signals and neural network is used to map these features to corresponding fault type in order to realize the fault diagnosis for hydroturbine generating unit.

#### 3. Wavelet Neural Network

Wavelet neural network is a kind of neural network that is constructed based on wavelet analysis theory. As wavelet analysis theory ensures the approximation ability, wavelet function can substitute for excitation function of the neural network to form a new kind of feedforward neural network model.

##### 3.1. Structure of Wavelet Neural Network

Structure of a wavelet neural network is shown in Figure 1, where , , and are number of input layer nodes, hidden layer nodes, and output layer nodes, respectively. (, ), (, ), and (, ) are vectors of input layer, hidden layer, and output layer, respectively. (; ) is weight parameter between input layer and hidden layer. (; ) is weight parameter between hidden layer and output layer. (, ) and (, ) are translation parameters and scaling parameters, respectively. is wavelet function.