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.
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 [
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 [
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 ACOinitialized 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 ACOinitialized 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.
According to disturbing force types of vibration signals, vibration types can be divided into hydraulic vibration, mechanical vibration, and electrical 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.
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, rotortostator 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.
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 turntoturn 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.
Wavelet neural network is a kind of neural network that is constructed based on wavelet analysis theory. As wavelet analysis theory ensures the
Structure of a wavelet neural network is shown in Figure
Structure of wavelet neural network.
Suppose that
Suppose that the error function of a wavelet neural network is
Here,
Generally, the training method of a wavelet neural network is the gradient descent method, for which the equations for parameters adjustment are shown in
Here,
ACO algorithm [
The specific theory of ACOinitialized wavelet neural network is that the parameters waiting to be initialized are treated as the nodes in the seeking traces, and then all of the ants need to choose the nodes to reach the food source. During the food seeking process, error function of the wavelet neural network is taken as the evaluation function to adjust the amount of pheromone and guide the direction of the ants.
The procedure of ACOinitialization of the wavelet neural network is similar to the procedure of ACO wavelet neural network [
Suppose there are
Flowchart of the ACOinitialized wavelet neural network is shown as in Figure
Flowchart of ACOinitialized wavelet network.
(1) Relevant parameters initialization: set pheromone of each element in set
(2) Determine whether the stop condition (the error precision or certain training time) is reached or not. If so, output the optimization solution and stop the iteration; otherwise turn to the third step.
(3) The
(4) After the
(5) After all of the ants finished choosing once, adjust all of the elements in set
Here,
Vibration signals of a hydroturbine generating unit are the synthesized reflection of hydraulic, mechanical, and electric vibration factors and so on. The method, which takes amplitude of vibration signals frequency components as feature vector and employs neural network to realize the mapping from vibration feature set to fault set, is a common method for hydroturbine generating unit fault diagnosis. In this paper, the amplitudes of vibration signals frequency components
Training samples.
Fault types  (0.4–0.5) 
1 
2 
3 
>3 
Object values 








Vortex with eccentric  0.85  0.25  0.06  0.02  0.01  1 
Unbalance  0.04  0.98  0.10  0.02  0.02  2 
Unbalance  0.03  0.96  0.12  0.04  0.03  2 
Misalignment  0.02  0.41  0.43  0.34  0.15  3 
Misalignment  0.02  0.45  0.42  0.28  0.29  3 
Normal  0.01  0.02  0.01  0.05  0.04  4 
Normal  0.10  0.03  0.02  0.03  0.04  4 
Testing samples.
Fault types  (0.4–0.5) 



>3 
Object values 








Unbalance  0.02  0.91  0.08  0.01  0.02  2 
Misalignment  0.01  0.48  0.48  0.36  0.20  3 
Normal  0.10  0.03  0.02  0.03  0.04  4 
In this example, the number of iterations is set as 10, the number of ants in an ant colony is set as 10,
In order to prove the effectiveness of the ACOinitialized wavelet neural network, ACO wavelet neural network and traditional wavelet neural network are chosen as comparison methods in the same computer and with the same parameters. Figures
Training curve of wavelet network.
Training curve of ACOinitialized wavelet network.
Using the testing samples in Table
Diagnosis results of three methods.
Fault types  Wavelet neural network  ACO wavelet neural network  ACOinitialized wavelet neural network  Object values 






Unbalance  1.8307  2.1806  2.0564  2 
Misalignment  2.7499  2.8566  2.9255  3 
Normal  3.9745  3.9700  3.9723  4 
Table
Error and training time of three methods.
Diagnosing methods  Wavelet neural network  ACO wavelet neural network  ACOinitialized wavelet neural network 





Training time/s  2.3438  9.3281  0.6094 
According to Tables
All three kinds of neural networks can recognize fault types of the hydroturbine generating unit.
Compared with the traditional neural network, ACO wavelet neural network has higher generalization ability, but it needs more computer time to finish the training process.
The training time of the ACOinitialized wavelet neural network is 0.6094 s, and its diagnosing error is 0.0093. Compared with the other two types of neural networks, the proposed network not only has higher generalization ability but also increases the convergence speed. Thus, the ACOinitialized wavelet neural network is more suited to online vibration fault diagnosis for hydroturbine generating unit.
Wavelet neural network is sensitive to initial parameters. In other words, when the parameters are initialized improperly, the convergence speed of the neural network will become slower and its generalization ability will become worse. This constrains its application in the hydroturbine generating unit fault diagnosis. In this paper, the advantages of both ACO algorithm and wavelet neural network are combined and the parameters optimized by the ACO algorithm are used as the initialized parameters of the wavelet neural network. The wavelet neural network is trained further and the trained wavelet neural network is applied to vibration fault diagnosis of a hydroturbine generating unit. The method proposed in this paper can determine the initial parameters of the wavelet neural network and also has the timefrequency location property of wavelet neural network and global optimization ability of the ACO algorithm. By using the extracted features of amplitude of frequency components of hydroturbine generating unit vibration signals, the traditional wavelet neural network, the ACO wavelet neural network, and the ACOinitialized wavelet neural network are compared with each other. The results show that the ACOinitialized wavelet neural network has stronger generalization ability and faster convergence speed and thus is more suitable to diagnose the vibration faults of a hydroturbine generating unit online.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors acknowledge the supports from the National Natural Science Foundation of China under Grant no. 51379160.