 Open Access
 Total Downloads : 229
 Authors : Huang Darong, Chu Xiaoyan, Zhao Ling, Tang Jianping
 Paper ID : IJERTV3IS051620
 Volume & Issue : Volume 03, Issue 05 (May 2014)
 Published (First Online): 28052014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
MultipleFault and Degradation Degree Simultaneous Diagnosis Based on Artificial Neural Network and Hidden SemiMarkov Model
Huang Darong, Chu Xiaoyan, Zhao Ling, Tang Jianping
Chongqing Jiaotong University
Institute of Information Science and Engineering Chongqing, China
AbstractBased on the theory of Artificial Neural Networks and Hidden SemiMarkov Model, a hierarchical diagnosis network (ANNHSMM) is proposed with the respect to multiple faults and their degradation degree simultaneous diagnosis. ANNHSMM consists of several subnetworks, and aims at dividing a larger pattern into several smaller subspaces, so that the subnetwork can be trained on the subspace, respectively, and the whole network is capable of multiplefaults and their degradation degree simultaneous diagnosis. The experiment results show that ANNHSMM can not only recognize multiple faults diagnosis, but also achieve the degradation degree diagnosis for the corresponding faults, and is available for real time condition monitoring and diagnosis.
KeywordsMultipleFault; Degradation Degree; ANN; HSMM)

INTRODUCTION
It is the fault diagnosis and the identification for corresponding fault degradation degree that is the basis to maintain the critical transmission parts for machinery and equipment to operation smoothly and steady. In [1], aiming at the problem of fault diagnosis and faulttolerant control for system with delayed measurements and states, an innovative solution is proposed; in [2], a fractal dimension calculation method for discrete signals in the fractal theory was proposed and was applied to extract the fractal dimension feature vectors and classified various fault types; in [3], a new safety performance evaluation of the faultprediction technology was research based on misclassification cost, and the future development trend of the fault prediction technology was discussed.
Meanwhile, Artificial Neural Network (ANN) and Hidden Markov Model (HMM) are applied in the field of the fault diagnosis, and the studies about Hidden SemiMarkov Model (HSMM) are launched subsequently, and the diagnosis accuracy is improved to some extent. Aiming at the problem that the static multiple fault models in existence can not fit the need of the more and more complicated equipments as the development of electron technique, [4] put forward a dynamic multiple fault model which is based on Hidden SemiMarkov Model (HSMM) and make the process simpler, meanwhile the original dynamic multiple fault problems are decomposed into several independent subproblems and the Binary Particle
This work is supported by National Nature Science Foundation under Grant (NO. 61004118, 61304104) and the China Scholarship Council.
Swarm Optimization (BPSO) is utilized to solve this problem; respecting to multiplefaults simultaneous diagnosis for the rotating machine, [5] proposed a hierarchical diagnosis network (HDANN) based on the theory of Artificial Neural Networks; in [6], the work status of pump are divided into five categories, and each kind of the four faults is subdivided into three kinds of health statues respectively, and then Hidden Markov Model (HMM) is used to recognize the real work statues from the thirteen statues, realizing the fault and its degradation degree simultaneous diagnosis. However, the model reveals good recognition performance on faults, but bad for faults degradation degree, which is on account of that the state dwell time probability of various faults degradation degree obeys exponential distribution on the condition of Markov assumption, causing the dwell time for each degraded state can not be reacted in the evolution of equipment failure. In accordance with the theory of HMM, HSMM is proposed on the condition of introducing the dwell time for each degraded state. HSMM, owning rigorous mathematical structure, can make the behavioral characteristics of the entire observation sequence being expressed completely. However, it is difficult to recognize the multiplefaults by means of HSMM due to the characteristics and the maximum likelihood criterion of HSMM. Artificial Neural Network (ANN) not only having good biology basis and data base, but also owning good ability of generality and fault tolerance, which can deal with the problem of multiplefaults diagnosis, but the accuracy for the identification of the faults degraded state is not high. Thus, it is critical to research the model of multiplefault and degradation degree simultaneous diagnosis based on the advantages of Artificial Neural Network and Hidden Semi Markov Model.
This paper presents a new fault diagnosis method using ANN and HSMM, realizing the multiplefault and degradation degree simultaneous diagnosis.

MULTIPLEFAULT AND DEGRADATION DEGREE SIMULANEOUS DIAGNOSIS BASED ON ANNHSMM

The Fundamental of ANN
Artificial Neural Network (ANN) [7], a mathematical model which can response the human brain structure and its functions abstractly, is a complex network interconnected by a large number of neurons, and its structure is shown as Fig 1. There are m nodes in the input layer, and the number of output equals to the input; the hidden layer i has q nodes, and
f1 denotes the activation function, ij is the connection

Fundamental of Hidden SemiMarkov
The Hidden Markov Model [8] is a doubly stochastic process: one is a state process. Its nature is a Markov chain that can be used to describe the state transfer, and at the same time it is a basic stochastic process; the other is a process called observation sequence value which can describe the corresponding relations of probability and statistics between every state and its observed values. Because the observation sequence value which is due to the implicit state cannot be acquired directly, and the state existence and properties are obtained by perception through a random process. So it is called Hidden Markov model, which is short for HMM denoted
weights between the input layer j and the hidden layer i ; the by (N, M , , A, B) .
output layer k contains l nodes, and f2 stands for their
Where, A (aij )N N
denotes state probability transition
activation function, ki is the connection weights between the
matrix and a
P(q
 q ),1 i, j N ; B (b ) is
hidden layer i and the output layer k . Firstly, the hidden input,
ij t 1
j t i
ik N N
which is obtained by weighted sum for the input of the input
m
on behalf of the observation value probability matrix and
bik P(Ot Vk  qt i ), 1 j N, 1 k N ; (1,2 ,,N )
layer, can be presented by pk ij y j ,
j 1
k 1, 2,, q .
stands for the initial probability distribution vector and
i P(q1 i ),1 i N ; N presents the state number of the
Secondly, in accordance with the activation of the f1 in hidden
model, and N states are denoted by H (H , H ,, H
) , the
layer, the input of the hidden layer can be expressed
1 2 N
m state at time t is denoted by st ; M is the corresponding
as mk f1 (ij y j k ), k 1, 2,, q . Lastly, the real number of possible observation values for every state, and M
j 1
observation values are denoted by V {v , v ,, v } .
input results can be got by the activation function f2
for the
1 2 M
output layer.
y1
j i k
o1
Probability of model staying for some time in a certain state generally obeys the following exponential distributin P (d ) ad 1 (1 a ) in HMM, so we can get to know that the
i ii ii
probability presents exponentially decreasing trend as time
y2 o2
y
increasing. But according to the actual situation, the state staying time does not obey this distribution function in most instances.
m
input layer
ij
hidden layer
ki
o5
output layer
HSMM [9] is one of the models used to overcome the above HMM disadvantage. Based on the HMM, HSMM could overcome HMM modeling limitation caused by the Hidden
Fig.1. The topology for ANN
The model, which can not only simulate the humans ability about presentation and storage for knowledge, but also imitate the humans reasoning behavior for knowledge, is an information system. The objective function, which is
Markov modeling assumption. In HMM, a state only corresponds to one observation value; but in HSMM, a state corresponds to a sectional observation value, it means that the state staying time is added in and the observation value is connected with both the current state and its staying time when transferring from the current state to the next. The HSMM
established by comparing the actual output with the ideal
output, can be used to revise the interconnection weights
topological structure is shown in Fig.2, in which q
r 1
represents
between the respective neurons by repeated learning, achieving the interconnection weights convergence within the stable
the start point at time r and the staying time is d qr qr 1 .
1
range. The trained and learning algorithm of network, which H
determines the initial weights that connect the related neurons, will adjust the weights automatically with the training patterns
H2 HN
adding. By training the learning algorithm, the network could get the satisfied performance. The common training algorithms include the learning of error correction, competitive learning and so on. And the algorithm of DFP is adopted in this paper.
s1 s2 sq1
o1 o2 oq1
Sq1+1 Sq2
Oq1+1 oq2
SqN1 +1 SqN
oqN1 +1 oqN
The neural network could acquire the knowledge through the connection structure and steady weight distribution in the related neurons. Meanwhile, the neural network itself could filter out the noise and deal with problems in the presence of noise. Therefore the neural network is suitable for online fault detection and diagnosis.
Fig.2. HSMM topological structure
HSMM properties can be described by the initial state distribution vector , state staying time distribution D, and the probability matrix of observation value; so HSMM can be denoted with (N, M , , A, D, B) . In HSMM, transition
among macro states meets with the Markov process, but transition among micro states does not, but the model can be trained by according to the algorithm in [10].

Fault Diagnosis Model Based on ANNHSMM Network
Fault diagnosis is divided into before and after two parts in ANNHSMM network, equals to assign a largescale diagnosis task to many subnetworks. The first network uses ANN model to diagnosis multiplefaults; based on the above diagnosis results, the second network adopts HSMM to analyze and diagnose the measured signals again to get the degradation degree. This model can identify multiplefaults, diagnose fault degradation degree, and improve the network learning efficiency to meet the practical online diagnosis requirements. Suppose the measured faults can be divided into 5
classes{F , F , F , F , F } , in which, exclude from F (normal
The firstclass network
HSMM4
HSMM3
HSMM2
HSMM1
ANN
the input vectors
The secondclass network
Fig.3. ANNHSMM network structure
Every network is trained individually according to its grade level. To the trained networks, the inputs are the extracted fault characteristics vectors from the measured objects and the diagnosis should be executed step by step. First ANN network takes effect, and the second corresponding HSMM is
0 1 2 3 4
0 stimulated by the results of firstclass network, and the
wok condition), the other 4 faults can further be divided into
diagnostic rules are as follows:
three different degradation degree faults
{F11 , F12 , F13} ,

If the first output value of ANN is 0, it indicates no
{F21 , F22 , F23} , {F31 , F32 , F33} and {F41 , F42 , F43} . So the faults are
divided into 13 states and the extracted fault eigenvector equals to Y {y1 , y2 ,, ym } .
The first layer is accomplished by the feedforward single hidden layer neural network; number of the input and output panel points is m and 5 (number of fault kind), every output panel point relates to a certain fault, and if the output value is 1, which means the relative fault exists, otherwise no fault exists. The network training modes are shown in TABLE .
Training mode
Input
Output
Relative fault
0
( y0 , y0 ,, y0 )
1 2 m
0 0 0 0 0
F0 (no fault)
1
( y1 , y1 ,, y1 )
1 2 m
1 1 0 0 0
F1
2
( y2 , y2 ,, y2 )
1 2 m
1 0 1 0 0
F2
3
( y3 , y3 ,, y3 )
1 2 m
1 0 0 1 0
F3
4
1 0 0 0 1
F4
5
1 1 1 0 0
F1F2
6
1 1 0 1 0
F1F3
7
1 1 0 0 1
F1F4
8
1 0 1 1 0
F2F3
9
1 0 1 0 1
F2F4
10
1 0 0 1 1
F3F4
11
1 1 1 1 0
F1F2 F3
12
1 1 1 0 1
F1 F2F4
13
1 1 0 1 1
F1F3F4
14
( y14 , y14 ,, y14 )
1 2 m
1 0 1 1 1
F2F3F4
15
( y15 , y15 ,, y15 )
1 2 m
1 1 1 1 1
F1F2 F3F4
TABLE I. The first network training mode
The second layer exploit HSMM network, and output values of the first layer can stimulate the 2th layer to function, reclassify the measured signals to identify different order of fault severity, and the network structure is shown in Fig.3.
faults exist in the equipment, and its over; otherwise turn to 2th step.

Judge the other output of ANN in order excluded from the first output, then input all the relative serial number that is connected with the state whose output value is greater than 0.5 into empty matrix A; if all the output values of ANN are smaller than 0.5, input the serial number that is connected with the panel point whose output value is maximum into matrix A.

Stimulate the second network in order to function according to the elements in matrix A, in the relative HSMM library which connects with the stimulated faults, the state connects with the maximum output probability is concerned to be the degree to this equipment and its corresponding fault.

The ultimate diagnosis result is due to the output of both the first and second network. The output values of the first layer network those are greater than 0.5 or the maximum output value possibly is the fault class to the measured object. Stimulated by theoutput results of the first layer network, the state connected with the model that has the maximum output probability in HSMM library is the corresponding degradation degree to the related faults.

As the training is independent to the subnetworks of the related grades, so in actual, it only needs to use the practical measured fault samples to retrain the related subnetworks for different grades, and the suitable specific units can be acquired which is easier to be trained and has stronger adaptability.


APPLICATION OF SIMULTANEOUS DIAGNOSIS OF MULTIPLEFAULTS AND SEVERITY OF ANNHSMM

Acquirment of Training Samples
The training eigenvector is structured by the energy ratio in vibration signal band of measured equipment and used to divide the fault category to get the fault training model. For the frequency domain features of the vibration signals of the rotating machinery are acquired through the Fourier transform, and time domain signals can be represented by the superposition of multi sinusoidal signals, if a fault exists, it
means that the original time domain signals superpose one or several different sinusoidal signals which have different frequency. f (t) is supposed to be the time domain signal when
the unit has tow singlefrequency faults, as:
f (t) f1 (t) f2 (t) sin(2 f1t 1 ) sin(2 f2t 2 ) (1)
Where, E(Wk ) is the gradient for E plays onWk .
As for the training about HSMMs, the secondorder HSMM with continuous Gaussian density are chosen, and the Markov chain with its status varying from left side to right, which has better effects and high training speed, is selected. The Markov chain with three statuses is selected in this paper, and the initial
According to the linear characteristic of Fourier transform, there can be:
F() F( f1 (t)) F( f1 (t) f2 (t)) F1() F2 () (2)
i i
Multifault eigenvector can be acquired through the superposition of singlefault eigenvector, in order to protect the fault characteristic, doubly fault eigenvector is acquired by two singlefault eigenvector weighting. Suppose y1, y2 is the
Ith relative component of singlefault eigenvector, so the doublyfault eigenvector can be defined as follows:
probability is [1, 0, 0] . The initial value of A can be
obtained by means of uniform choice and B is got randomly. The BaumWelch algorithm is developed on the basis of climbing algorithm so that the initial value has great effects on achieving the best solutions. Therefore, the Kmeans algorithm and clustering algorithm are utilized to obtain the initial values and the BaumWelch [12, 13] with several observation sequences is utilized to train the model to increase the robustness. A couple of initial parameters of HSMM are estimated by the Kmeans algorithm and clustering algorithm, and then the data obtained above is utilized to train the various HSMM.
y1 y2
C. The Test Results and the Analysis for the Network
y1,2 i y1 i y2
(3)
i y1 y2 i
y1 y2 i
i i
i i
The network test is obtained on the trained network ANN
It is the formula (3) that is a filtering process, which can not only maintain the fault characteristics, but also restrain the non fault features. The response component of the multiplefault characteristics vectors can be established similarly to (3), obtaining the standard training samples of the network. Similarly, the statues feature vectors of the various faults degradation degree can be got under different faults status.

The Training for the Network
The feedforward signal hidden layer network is adopted in the firstclass network, and the number of input nodes is m, the output nodes is 5, the hidden layer nodes can be commutated by the formulation the number of hidden layer nodes=2*the number of input nodes+1, that is 2m+1. Then DPF Approach

is adopted to train the first network, and the learning objective function can be defined as below:
HSMM, achieving multiplefault and degradation degree simultaneous diagnosis. The test results are shown as below:

The diagnosis and the classification for the large fault can be realized by means of the firstclass network, and the diagnostic accuracy reaches 95%.

Stimulated by the results of the firstclass network, the second corresponding HSMM starts to work, achieving the faults degradation degree diagnosis. Expected for

the two states S10 , S11 , the other states can be
identified correctly by the hierarchical diagnosis network (ANNHSMM), and the identification accuracy is 90%.
For the same diagnosis problem, the diagnostic performed for the HMM and the ANNHSMM mentioned above is compared, and the comparison results are shown as below:
1 M 2
1 M M 2
J (W ) 2 Ei (W ) 2 (Oj

d j )
TABLE II. The comparison for the recognition rate
i 1 i 1
S0
S 1
S2
S3
S 4
S5
S6
S7
S 8
S9
S10
S11
S12
HMM
85%
75%
75%
90%
75%
70%
70%
100%
100%
85%
65%
60%
75%
ANNHSMM
100%
95%
85%
90%
80%
85%
80%
100%
100%
90%
75%
70%
85%
Where, W denotes the weights vector of the firstclass
network; Ei
is on behalf of the error between the real input
and the ideal input. In accordance with the formula (4), the secondorder polynomial Taylar around the minimum point can be regarded as the objective function approximately, obtaining the estimated value of the minimum point. After obtainingWk 1 , the connection weights for the neural network can be modified according to the following formula (58):
As can be seen from the above table, the diagnosis and the classification for the large faults can be achieved by HMM and ANNHSMM, but for the problem of faults degradation degree diagnosis, the diagnosis accuracy for ANNHSMM are higher than HMM, in other words, the multiplefault and
W W
H E (k) E (W ) /
degradation degree simultaneous diagnosis can be obtained
k 1
k k i i k k
through the hierarchical diagnosis network (ANNHSMM).
H *E(W ) *ET (W ) * H
The test results reveal that for the same diagnosis problem,
k k
H 1[H

k k k k ]
k
(6)
regardless of the diagnosis and the classification for the large fault or the faults degradation degree diagnosis, ANNHSMM is superior to the HMM in conference [6], therefore the
ET (W )* H
*E(W )
(7)
established hierarchical diagnosis network (ANNHSMM) in
k k k k
H1 I (Identity Matrix (8)
this paper is reasonably practicable.


CONCLUSION
Based on the theory of Artificial Neural Networks and Hidden SemiMarkov Model, a hierarchical diagnosis network (ANNHSMM) is proposed with the respect to multiplefaults and their degradation degree simultaneous diagnosis. The experiment results show that comparing with the fault diagnosis method in [6], ANNHSMM can not only recognize multiplefaults diagnosis, but also achieve the degradation degree diagnosis for the corresponding faults, and the diagnostic accuracy is higher, available for realtime condition monitoringand diagnosis.
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