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Vibration Fault Diagnosis of Mine Ventilator Based on Intelligent Method

An Baoran

Control Theory and Guarantee Technology Research Center, Harbin Institute of Technology, Harbin, H

eilongjiang 150080 E-mail: baoranan@126.com Abstract: Based on the analysis of the vibration fault features of mine ventilator, the paper establishes a fuzzy wavelet neural network model which can diagnose the faults of mine ventilator. The fuzzy wavelet neural network model unifies fuzzy logic and BP neural network, using wavelet basis function as a membership function. Furthermore, a hybrid learning algorithm with self organized and supervised learning is also proposed. Through training the displacement factors, the parameters and the structure of the network approximate to global optimization. The experimental results show that it not only raised the efficiency and accuracy of fault diagnosis, but also provided a valid approach to protect the safety of mine ventilator. Key Words: Fault Diagnosis, Mine Ventilator, Fuzzy Wavelet Neural Network

1.

INTRODUCTION

Ventilator is the key equipment of mine safety production. It not only transports the fresh air to the underground, but also exhausts the dust and dirty air. Vibration is one of the important factors which affect the safe working of mine ventilator. To ensure mine ventilator work safe and steady, great financial and labor supports are wasted. Therefore, it is necessary to diagnose the parameters of mine ventilator by some effective measures in order to eliminate the vibration and reduce the fault happens. Based on the analysis of the fault feature of mine ventilator, the paper proposed fuzzy wavelet neural network (FWNN) model that unify fuzzy logic and BP neural network. The model using wavelet basis function as membership function can realize the intelligent fault diagnosis of mine ventilator. Furthermore, a hybrid learning algorithm based on self organized and supervised learning is also proposed in the paper. Through training the displacement factors, the dilation factors of wavelet basis function and the connection weight values of fuzzy neural network, the parameters and structure of the network approximate to global optimization. The experiment results show that it not only raised the efficiency and accuracy of fault diagnosis, but also provided a valid approach to protect the safety of mine ventilator by using this intelligent method.

2. MINE

VENTILATOR FAULT MECHANISM

According to the analysis of vibration frequency of mine ventilator, the common faults of mine ventilator are classified into eight types as follows [1]: 1) Imbalance. This fault includes rotor eccentricity and certain parts defect accompanied by a double frequency (DF) as its characteristic frequency. 2) Shaft asymmetry. The installation error, deformation and the settlement uneven of the substructure are the main

reasons caused this fault. The characteristic frequency of this fault is 2 double frequency accompanied by 1 or 3 double frequency. 3) Surge. Surge is one of the most serious and dangerous conditions during the working period. The phenomenon of surge is severe vibration. Its characteristic frequency is ultra-low frequency. 4) Frame loose. It is caused by bolt loose and too large gap. Its characteristic frequency is 2 DF, mixed with other DF or high frequency. 5) Bearing defect. Bearing eccentricity and impact caused by pitting are the most important factors. The characteristic frequency is 1 DF, mixed with ultra-low frequency. 6) Oil-film whirl. Oil-film whirl is self-oscillation caused by oil-film mechanical properties of the sliding bearing. Its characteristic frequency is less than 0.5 DF. 7) Friction between rotor and static parts. The reasons are shaft bending, inconsistent thermal expansion of rotor and static parts, axis asymmetry and so on. Its characteristic frequency consists of high-order or low-order harmonics. 8) Shaft transverse crack. The main reason of this fault is long-time operation. Its characteristic frequency is 2 DF. As described above, one table is established as follow on the basis of reference to vibration signals' distribution in rotating machinery of the American scholar J Sohre. It describes the relationship between the eight fault types and the nine vibration frequency bands of mine ventilator in detail. As shown in table 1, the value represents the possibility of faults happen. If the value is closer to 1, then it shows that the faults are more possible to happen. Conversely, if the value is close to 0, then the faults are seldom happen. The paper define that, if the value is greater than 0.9, then represents the faults exist and seriously; if the value is less than 0.1, then represents the faults are not exist.

Tab. 1: Fault Type and Feature of Mine Ventilator the relative energy between different frequency band 0.01~0.39 0.40~0.49 0.50 0.51~0.99 1 2 high-order odd number extremely high DF DF DF DF DF DF frequencies 0.00 0.00 0.00 0.00 0.90 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.40 0.50 0.10 0.00 0.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.10 0.10 0.10 0.10 0.20 0.10 0.10 0.10 0.10 0.00 0.30 0.10 0.60 0.00 0.00 0.00 0.00 0.00 0.20 0.00 0.00 0.00 0.40 0.20 0.00 0.00 0.20 0.10 0.80 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.30 0.40 0.10 0.00 0.15

Fault Type Imbalance Shaft asymmetry Frame loose Friction Surge Bearing defect Oil-film whirl Shaft transverse crack

3.

FUZZY WAVELET NEURAL NETWORK MODEL

3.1 Fuzzy Wavelet Neural Network Structure

Based on the further analysis of mine ventilator mechanism, considering the characteristics of fuzzy logic, neural network and wavelet transform, the paper builds one 4-layers BP fuzzy wavelet neural network as shown in figure 1. The inputs of the network, denoted by xi （ i =1, 2, ···, n=9）, are the 9 frequency bands of the vibration vector. The outputs of the network, denoted by yi （ i =1, 2, ···, n=8）, are the 8 fault types.

function to overcome the disadvantage of traditional membership function as above. Generally, functions denoted by h(x), meet the allowable condition as shown in equation (1) is named wavelet function (or mother wavelet).

Ch =

+∞

∫

0

h(w) dw < +∞ w

2

(1)

Through dilation transform and displacement transform of h(x), a series of wavelet basic functions can be obtained as shown in equation (2).

? x ?b ? ha ,b ( x ) = h? ? ? a ?

(2)

Equation (3) shows the formula of wavelet basic function: x ?b h(x) = h( ) a (3) ? ( x ? b )2 ? ? x ?b ? ? = cos ? ? ? exp ? ? 2 ? 2 (a ) ? ? 2a ? ? ? , where a is the dilation factor, b is the displacement factor. As shown in equation (3), membership function can be optimized through adjusting parameter a and b. Therefore, as shown in figure 2, the initial membership function can be obtained when a and b are determined by self-organization algorithm.

Fig. 2: the Membership Function Diagram Fig. 1: Structure of FWNN

3.2 Membership Function

Membership function, which describes fuzzy set, influences the accuracy of fault diagnosis. The parameters of traditional membership function are invariant and cannot be optimized [2]. Considering the features of dilation, displacement, local time-frequency characteristic and identical resolution, wavelet function can achieve multi-scales thinning analysis of signal and function [3]. By adjusting the dilation factors and the displacement factors, membership function can be repeated optimized [4]. So, the paper chooses wavelet basis function as membership

3.3 Fuzzy Wavelet Neural Network Model

Fuzzy wavelet neural network is a structure mapping from fuzzy logic to neural network. The modeling method in the paper is as follows: The first layer is input layer. It transports all input variants to the next layer, the input-output relationship is (4) i = 1,2,? ? ?, n Oi(1) = I i(1) = xi The second layer is fuzzification layer. It fuzz the input vectors. According to the theory analysis and experiment results, the paper divides every input into 3 fuzzy subsets (high, normal and low). The output of the nodes is the output

of membership function. Equation (5) describes the relationship between xi and membership function:

( u ij ( x i ) = h aij2 ) ( x i ) ( ? x i ? bij 2 ) ? ? ? =h ? a (2 ) ? ij ? ?

(5)

( ( ? ? ( x ? bij 2 ) ) 2 ? x ? bij2 ) ? ? 0 .5 ? i ? ? exp ? ? i ? = cos ( ( ? ? a ij2 ) ? 2 ( a ij2 ) ) 2 ? ? ? ? ? ( 2) (2) Where aij and bij represents the dilation factor and the

Under the conditions that a set of input sample data xi (i = 1,2,? ? ?, n) , the expected output yi (i = 1,2,? ? ?, m ) , the fuzzy partition ( T (x) and T ( y ) ) and the type of membership function are given, the displacement factor bi and dilation factor a i of membership function can be determined and suitable fuzzy rules can be selected. There are calculation formulas for estimating displacement factor bi according to Kohonen's self-organized learning method.

displacement factor of the number j membership function corresponding xi , respectively. As shown in equation (6) and (7), the input-output relationship of this layer is:

(2) ij ( I ij2) = Oi(1) (1 ) i

? x ( t ) ? bclosest ( t ) = m in { x ( t ) ? bi ( t ) } 1≤ i ≤ k ? ? b clo sest ( t + 1) = bclosest ( t ) + α ( t ) [ x ( t ) ? bclosest ( t ) ] (11) ? ? b (t ) ≠ b w hen bi ( t + 1) = bi ( t ) clo sest ( t ) ? i ? Where bi (t) is a random number starting from zero, bclosest (t ) is the estimated value of the displacement factor, k = T (x)

is the number of the linguistic value of linguistic variable x , α (t ) is a monotone decreasing scalar learning factor. Using the first-order nearest domain method, we can obtain the estimated value of the dilation factor ai by the following formula.

O

=u I

( ) = u (O ), i = 1,? ? ?, n. j = 1, 2,3

(2) ij

(6) (7)

The third layer is fuzzy reasoning layer. Neurons in this layer execute fuzzy logic “and” calculation according to the max-min reasoning rule. The connection weight value (2) between the second and the third layer wij is set as 1. The input-output relationship is:

( ( ( ( Oij3) = I ij3) = min O1( 2) , O22j) ,? ? ?, Onj2) , j = 1,2,3 j

ai = bi ? bclosest / r

(12)

(

)

(8)

The fourth layer is output layer. It clarifies the output of the third layer by de-fuzzification method. The relationship between input and output is shown in equation (9) and (10):

( ( ( ( Oij3) = I ij3) = min O1( 2) , O22j ) ,? ? ?, Onj2 ) , j = 1,2,3 j

(

)

(9) (10)

Where r denotes the overlap degree of membership function. After the factors ( ai and bi ) are determined, the connection ( weight values wij3 ) are determined by competitive learning algorithm. The formula (13) and (14) give the detailed calculating steps for updating the weight values. ( ( (13) ? wij3 ) = O (j4 ) ? wij3) (t ) + Oi( 3 )

[

]

yk = Ok( 4 ) =

I

3

(4) k ( 3) ij

i , j =1

∑O

, k = 1,2,? ? ?, m

( ( ( wij3) (t + 1) = wij3) (t ) + ?wij3) (t )

(14)

Where wij is the connection weight value between the third and the fourth layer that need to be optimized by learning.

(3)

4.

HYBRID LEARNING ALGORITHM

In the fault diagnosis model based on Fuzzy Wavelet Neural Network (FWNN), the dilation factors and the displacement factors of wavelet basis function and the connection weight values of the Fuzzy Neural Network are the key factors to determine the speed, precision of fault diagnosis and the convergence degree of the model. In order to get the parameters approximate to global optimization through off-line training and on-line correction, a hybrid learning algorithm is put forward. The hybrid learning algorithm consists of two portions: self-organized learning and supervised learning [5].

( Where ?wij3) denote the update weight values, O ( 3) denote i the output of the third layer nodes, O (j 4 ) denote the output of ( the fourth layer nodes, wij3) (t )denote the connection weight values between the node i of the third layer and the linguistic ( node j of the fourth layer, wij3) (t + 1) denote the adjusted weight values. The principle of selecting the fuzzy rules is as follows. ( Firstly, calculate the connection weight value wij3) (t + 1) by equation (14); Secondly, preserve the fuzzy rules corresponding to the biggest weight value and delete the other fuzzy rules.

4.2 Supervised Learning

In the process of the self-organized learning, the estimated value of the dilation factor ai and the displacement factor bi of membership function, the number of fuzzy rule nodes and the connection weight values are determined. The main task of supervised learning is to realize the optimum adjustment of membership function and network weight values. Meanwhile, it can also support on-line learning of the fuzzy neural network. Under the conditions that training sample data xi , yi the fuzzy partition ( T (x ) and T ( y ) ) and the fuzzy logic decision rules are given, the parameters of membership

4.1 Self-Organized Learning

The main task of self-organized learning is the self-organizing of the fuzzy decision rules and the recognition of membership function parameters in advance. Then, a fuzzy rule which can meet practical requirements and the initial distribution of membership function are obtained. Its learning method is similar to statistical classify.

function (a ( 2 ) and b ( 2 ) ) and the connection weight values of ij ij (3) fuzzy reasoning layer ( wij ) can be adjusted optimally in real time by using the supervised learning algorithm. Expression formula of objective learning function is:

( ( aij2 ) (t + 1) = aij2 ) (t ) ? η ?

?E ( + α ? ?aij2 ) (t ) ( ?aij2 ) (t ) ?E ( + α ? ?bij 2 ) (t ) ( ?bij2 )

(17) (18)

( ( bij2 ) (t + 1) = bij2 ) (t ) ? η ?

1 (15) ∑ ( yid (t ) ? yi (t ))2 m i =1 Where yid (t ) is the expected output, yi (t ) is the actual E=

output of the network. The weight value adjusting law of the network is:

( ( wiji ) (t + 1) = wiji ) (t ) ? η ?

m

5.

SIMULATION RESULTS

Where η is the learning rate,

?E ( + α ? ?wiji ) (t ) (i ) ?wij (t )

(16)

α is momentum factor.

Finally, simulation experiments are carried out to verify the efficiency of the intelligent fault diagnosis method. Before training the network, input samples should be normalized so that make each diagnosis parameter interval is 0～1, equation (19) shows the method of normalization: u (i ) = ui / umax ,0 ≤ u (i ) ≤ 1 (19) In order to ensure the reliability of model, the learning samples should have enough amounts and cover all fault conditions. So, in the paper, learning samples consist of 30 groups of fault parameters. Table 2 just lists a group of learning sample.

( The learning formula of the displacement factor bij2) and the dilation factor a(2) is as follow:

ij

Tab. 2: Learning Sample of FWNN for Faulty Diagnosis of Mine Ventilator 序 号 1 2 3 4 5 6 7 8 9 10 X1 N 0.1 0.5 0.8 0.4 0.1 0.5 0.1 0.1 0.3 0.3 X2 N 0.4 0.1 0.1 0.4 0.1 0.1 0.1 1 1 0.4 FWNN Input Samples X3 X4 N L H N 0.1 0.9 0.9 0.3 0.1 0.3 0.1 0.3 0.1 0.2 0.2 0.1 0.4 0.1 0.1 0.4 0.2 0.1 0.9 0.2 0.1 0.1 0.1 0.3 0.2 0.3 0.1 0.3 1 0.3 0.1 0.38 0.4 0.1 0.1 0.9 0.4 0.1 0.9 0.3 Continue of Tab. 2 序 号 1 2 3 4 5 6 7 8 9 10 X7 N 0.7 0.7 0.2 0.4 0.1 0.2 0.2 0.2 0.4 0.2 FWNN Input Samples X8 L H N L 0.1 0.3 0.1 0.1 0.2 0.3 0.1 0.1 0.2 0.1 0.5 0.1 0.1 0.1 0.4 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.4 0.1 0.1 0.1 0.2 0.1 FWNN Output Samples H 0.2 0.1 0.1 0.1 0.1 0.6 0.1 0.1 0.1 0.1 X9 N 0.1 0.1 0.1 0.4 0.1 0.1 0.2 0.2 0.4 0.2 L 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 y1 0.9 0.3 0.1 0.1 0.1 0.1 0.1 0.14 0.14 0.1 y2 0.1 0.9 0.1 0.1 0.5 0.4 0.2 0.1 0.2 0.1 y3 0.1 0.4 0.8 0.1 0.3 0.1 0.1 0.1 0.2 0.15 y4 0.1 0.1 0.3 0.8 0.2 0.1 0.1 0.1 0.2 0.4 y5 0.3 0.2 0.1 0.1 0.8 0.1 0.1 0.1 0.5 0.7 y6 0.1 0.1 0.1 0.1 0.1 0.8 0.1 0.1 0.6 0.23 y7 0.2 0.2 0.1 0.1 0.1 0.1 0.8 0.2 0.36 0.2 y8 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.9 0.1 0.1 X5 N 1 0.8 0.3 0.6 0.1 0.9 0.3 0.8 0.9 0.4 X6 L 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 H 0.9 0.2 0.1 0.1 0.1 0.8 0.1 0.9 0.1 0.4 N 0.5 0.9 0.2 0.4 0.1 0.3 0.1 0.14 0.4 0.1 L 0.1 0.3 0.1 0.1 0.1 0.1 0.1 0.2 0.3 0.3

H 0.1 0.1 0.1 0.1 0.3 0.7 0.1 0.1 0.1 0.1

L 0.3 0.1 0.3 0.1 0.3 0.1 0.5 0.14 4 0.9 0.9

H 0.1 0.1 0.3 0.1 0.7 0.1 0.3 0.1. 9 0.3 0.9

L 0.1 0.3 0.3 0.1 0.3 0.1 1 0.3 0.3 0.1

H 0.3 0.1 0.3 0.1 0.3 0.2 0.1 0.3 0.9 0.9

L 0.1 0.9 0.2 0.1 0.1 0.1 0.1 0.01 0.1 0.1

H 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.1 0.9

H 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

The paper defined 9 linguistic variants and 3 fuzzy subsets, so fuzzification layer has 27 neurons because each linguistic variant corresponding to 3 fuzzy subsets. After repeated optimization by hybrid learning algorithm, finally choose 10 nodes in the third layer. Consequently, the structure of network is 9-27-10-8. In order to increase the convergence speed and avoid falling into local minimum, the paper sets E = 0.0001 , η = 0 . 9 ,

Simulations for trained network are carried out with no disturbance, 2% extra disturbance and 5% extra disturbance, respectively. As shown in table 3, the results have certain error when disturbance exists. However, the accuracy which is higher than 90% can meet the needs of diagnosis. So, the application of fuzzy wavelet neural network to fault diagnosis of mine ventilator is efficiency.

a = 0 .5 .

Tab. 3: the Results of Fault Diagnosis by FWNN Diagnosis Results no disturbance 2% disturbance 5% disturbance Correct Rate 100% 97.2% 94.5% False Alarm Rate 0 2.8% 5.5%

be improved by this method, and a new valid approach to ensure mine ventilator work reliable is provided.

REFERENCES

[1] Z. S. Sheng, Y. L. Yin. Technology and Application of Equipment State Monitoring Fault Diagnosis[M]. Beijing: Chemical Industry Press, 2003. [2] M. J. Zhang. Intelligent Control Technology. Harbin: Harbin Engineering University Press, 2006. [3] W. Sun and Y.N. Wang. "Robot tracking control based on fuzzy wavelet basis neural network," Control Theory and Applications, vo1.20, no. 01, pp, 49~53, 2003. [4] M. P. Jia, F. Y. Xu. "Application of Wavelet Scaling Function to Rotating Machinery Fault Diagnosis," Vibration Test and Diagnosis, vo1.24, no. 1, pp, 6~10, 2004. [5] Z. Q. Fu, X. Y. Wamg. "The Text-Learning Algorithm Based on Kohonen and BP Neural Network,” Computer Engineering and Application, vol. 27, no. 01, pp. 76~78, 2001.

6.

CONCLUSIONS

Based on the analysis of the fault features of mine ventilator, fuzzy wavelet neural network model which integrate the advantages of fuzzy logic, wavelet analysis and neural network is built to diagnose the faults of mine ventilator. Through choose wavelet basis function as membership function and hybrid learning algorithm, the parameters of membership function and the connection weight value of network are optimized and modified. The simulation results prove that the efficiency and accuracy of fault diagnosis can

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