Energy and Power Engineering, 2009, 07-16
doi:10.4236/epe.2009.11002 Published Online August 2009 (
Copyright © 2009 SciRes EPE
A Novel Real-Time Fault Diagnostic System for Steam
Turbine Generator Set by Using Strata Hierarchical
Artificial Neural Network
Changfeng YAN1,2, Hao ZHANG1, Lixiao WU2
1CIMS Research Center, Tongji University, Shanghai, China
2School of mechanical & Electronical Engineering, Lanzhou University of Technology, Lanzhou, China
Email: {changf_yan, lixiao_wu};
Abstract: The real-time fault diagnosis system is very great important for steam turbine generator set due to
a serious fault results in a reduced amount of electricity supply in power plant. A novel real-time fault diag-
nosis system is proposed by using strata hierarchical fuzzy CMAC neural network. A framework of the fault
diagnosis system is described. Hierarchical fault diagnostic structure is discussed in detail. The model of a
novel fault diagnosis system by using fuzzy CMAC are built and analyzed. A case of the diagnosis is simu-
lated. The results show that the real-time fault diagnostic system is of high accuracy, quick convergence, and
high noise rejection. It is also found that this model is feasible in real-time fault diagnosis.
Keywords: real-time, fault diagnosis, strata hierarchical artificial neural network, fuzzy CMAC
1 Introduction
Steam turbine generator set is a key device in power plant.
The real-time fault diagnosis system is very great impor-
tant for steam turbine generator set due to a serious fault
results in a reduced amount of electricity supply in power
plant. It can detect the incipient failure as early as possible,
determine the location of the fault and identify size and
nature of the faults according to the abnormal conditions
appearing in the diagnosis process.
Presently, one of the widely used and effective methods
for fault detection and diagnosis of rotating machines is
vibration analysis. The subject of vibration generally deals
with methods to determine the vibration characteristics of a
system, its vibratory response to a given excitation and the
means to reduce the vibration [1]. Attempts have been
made towards fault diagnosis, through four steps such as
vibration measurement, signal processing, feature extrac-
tion and fault identification [2].
Many different diagnosis methods have been success-
fully applied for turbine generator set and other rotating
machines in real-time or off-line. A prototype expert sys-
tem has been developed that provides decision support to
condition monitoring experts who monitor British Energy
turbine generators [3]. The expert system automatically
interprets data from strategically positioned sensors and
transducers on the turbine generator by applying expert
knowledge in the form of heuristic rules. An expert system
for the turbine generator diagnosis was modeled to help a
plant operator interpret vibration evolution to diagnose
developing faults and to recognize the observed situation
among a hierarchy of typical situations in dealing with
complex problems [4].
A real-time intelligent multiple fault diagnostic system
for manufacturing systems is proposed by Bae et al. [5].
The expert systems and neural networks to gas turbine
prognostics and diagnostics are reviewed in reference [6].
It presents recent developments in technology and strate-
gies in engine condition monitoring including: application
of statistical analysis and artificial neural network filters to
improve data quality; neural networks for trend change
detection, and classification to diagnose performance
change; expert systems to diagnose, provide alerts and to
rank maintenance action recommendations.
Copyright © 2009 SciRes EPE
The application of neural networks and fuzzy logic to
the diagnosis of 1x faults in rotating machinery is investi-
gated by using the learning-vector-quantization (LVQ)
neural network [7]. Yan and Gao presents a signal decom-
position and feature extraction technique for the health
diagnosis of rolling bearing, based on the empirical mode
decomposition [8].
An on-line condition monitoring and diagnosis system
for feed rolls was developed by Jeng and Wei [9]. This
system measures the bearing vibration signals on-line and
judges the feed roll condition automatically according to
the diagnosis rules stored in the computer. Chen et al. pro-
posed the detecting and predicting early faults of the com-
plex rotating machinery model based on the cyclostation-
ary time series [10]. Wang and Yang applied parallel proc-
essing and distributed artificial intelligence at four different
levels in the fault diagnosis process for the turbine genera-
tor of a 300MW fossil power plant [11].
However, the real-time fault diagnosis is required to
monitor the abnormal change and to judge the fault reason
as soon as possible. This paper proposes a real-time intel-
ligent fault diagnosis system by using strata hierarchical
artificial neural. In this diagnostic system, it can real-time
diagnose faults according to vibration feature on conditions
of steam turbine generator sets. For the mechanical system,
the fault characteristics can be classified systematically to
be a hierarchical structure according to different levels. An
independent engine module which manages the feature
variables input the diagnostic modules in terms of result of
the threshold value trigger in the higher level, and outputs
the fault to operator by collecting the diagnostic result of
the diagnostic module finally in our model. Because com-
bined the advantage of interpreting the imprecise of fuzzy
set with fast training, guaranteed converge and partial gen-
eralization of CMAC, this model can meet online fault
2 Framework of Fault Diagnosis System
In the viewpoint of system, every system is made up of
components, and any components can be broken down
into smaller components [12]. Therefore the system can
be divided into system, subsystem and component level.
The complex hierarchical diagnostic system generates a
relatively abstract ordering of steps to realize the goal of
diagnostic and then each abstract step is realized with
simpler diagnostic plans. A hierarchical scheme looks
somewhat like a tree structure, where the steps at the
higher level of the tree represent more abstract and com-
plex tasks.
Steam turbine generator sets is made up of mechanical,
electrical, hydraulic, heating and related accessorial units,
even hundreds of components in the mechanical unit.
The mechanical fault includes different level fault such
as unbalance, oil whip, pneumatic torque, misalignment,
radial rub, twin looseness, bad thrust bearing, gasp vi-
bration, unequal stiffness bear, and rotor crack and etc.
Because the vibration is a good image of the machine
health for rotating mechanical unit, it is very important
to monitor the vibration parameters along the shaft
and/or the bear such as amplitude, frequency and orbit
online. In order to identify the fault correctly and quickly,
it is necessary to monitor vibration signals together with
other running parameters such as load, bearing oil tem-
perature, hydrogen pressure, vacuum measure, etc. These
symptoms are grouped into 10 categories [13]. The di-
agnosis of a developing fault is necessary to predict fur-
ther evolution and to anticipate it by taking appropriate
measures. Therefore, this paper focuses on the mechani-
cal faults which are relative to the vibration to express
our idea of the model in order to simplify the problem.
The feature signals which are related to the vibration are
regarded as the symptom to detect the cause of fault.
Both time domain and frequency domain approaches
could also be used to analyze vibration signals.
The flowchart of the real-time fault diagnosis system
is shown as Figure 1. The condition monitor and control
system is developed to capture vibration measurements
and operational parameters from strategically positioned
Copyright © 2009 SciRes EPE
Figure 1. Flowchart of fault diagnosis system
sensors and transducers on the turbine generator online.
The system is configured to trigger an alarm when each
predefined limit is breached. The limits are set on each
channel to monitor the overall vibration magnitude,
first-order and/or second-order vibration magnitude,
phase and sub-harmonic frequency levels. When the
signal data is beyond the predefined threshold, the diag-
nostic system is triggered immediately. Fault feature are
extracted on the basis of the measurements provided by
the turbine supervisory instruments (TSI) signals. Then
the actual diagnostic task is to map the points in the
symptoms space into the set of considered faults by the
fuzzy CMAC diagnostic system. The possible fault
names in steam turbine generator sets will be given by
system identifying. Meanwhile the reason of the fault
and preventive or maintenance measurements will be
listed. The operators can deal with the fault as soon as
possible according these advices. Of course, if the actual
fault need to somewhat identify further, the advice would
be given based on the system analysis.
3 Hierarchical Fault Diagnostic Structure
The human body is organized in a hierarchical structure
as shown in Figure 2. In this structure, the upper levels
efficiently control the lower levels. All information of a
human body is delivered to the brain by use of neurons.
The brain judges this information based on person’s ex-
perience, and gives instruction to the each part of the
body by the distributed neural system.
The hierarchical fault diagnostic structure can be de
Copyright © 2009 SciRes EPE
Figure 2. Hierarchical structure in a human body
Figure 3. Hierarchical fault diagnostic structure
scribed as shown in Figure 3. Feature variables are ex-
tracted from vibration signals and other running parame-
ters firstly. The different features are needed to input for
the different level and the different components. The
fault diagnostic algorithms in three levels are all the
fuzzy CMAC in our model.
An independent engine module in thicker line which
manages the feature variables input the diagnostic mod-
ules in terms of result of the threshold value trigger in
the higher level, and outputs the fault to operator by col-
lecting the diagnostic result of the diagnostic module
finally in our model. The diagnostic cells that actually
fire as a result of various levels of the feature depend on
the threshold levels of the diagnostic cells. Only diag-
nostic cells with enough excitatory inputs to exceed
threshold will fire. This threshold value for diagnostic
cells is regulated by the possibility of decision.
The independent engine module simulates the neural
anatomy structure in the human body. The brain collects
the information by the nervous process and gives in-
structions by nerve fibers to the every part of body based
on the diagnostic results.
The upper level is the mechanical fault diagnosis units,
which can identify the fault which item belongs to in
primarily. The next level is the item fault level which can
be considered several subsystems, for example, the me-
chanical fault including unbalance, oil whip, pneumatic
torque, misalignment, radial rub, twin looseness, bad
thrust bearing, gasp vibration, unequal stiffness bear,
rotor crack fault and so on. The diagnosis of a develop-
ing fault is necessary to predict further evolution and
anticipate it by taking appropriate measures. This paper
focuses on the mechanical faults which are relative to the
vibration to express our idea of model in order to sim-
plify the problem. In fact, people who work with steam
turbine generator sets usually perform vibration diagno-
sis using their field experience and textbook knowledge.
The other diagnostic unit will be investigated further in
the future.
Copyright © 2009 SciRes EPE
The lower level is the detail fault in theory. For in-
stance, it can judge whether the rotor crack is damage,
high-cycle fatigue, low-cycle fatigue, creep, crack and
erosion or not. In this hierarchical system, it can also
classified by more levels to identify the fault in detail
further. However it is not always good use for this kind
of the diagnostic system. The decision of how to parti-
tion the diagnosis system depends on how complex is
each level, and how many and what types of the feature
variables are available at each level, and what methods
are to identify the fault in the steam turbine generator
sets. When we care for the more minute fault, the more
monitoring device must be used, the more signal should
be processed, and also the more experiment should be
taken to obtain the feature of the fault. Despite of avail-
ability of these measurements, such tasks are left to the
diagnostic system and the operator, and thus will result
in overload in real time especially, even lead to errone-
ous decisions in the serious cases.
Figure 4. Neural anatomy structure of engine module
In order to identify the fault further, the trend features
such as relationships between amplitude of the vibration,
the pressure and the load are also required to be given.
4 Mechanism of Fuzzy CMAC Diagnosis
4.1 Introduction of Fuzzy CMAC
Albus presented the CMAC neural network and applied
it to the robotic manipulator control in 1975 [14]. The
CMAC is a kind of memory, or table kook-up mecha-
nism. From a purely structural standpoint, the CMAC
neural network simulates the human being’s cerebrum
which function visual cortex and need process consider-
able feature-detection to generate the appropriate com-
mand signals [15]. The CMAC neural network is shown
as Figure 5 with anatomy.
However there are some disadvantages for the stan-
dard CMAC. The large generalization parameter C will
increase the memory requirement seriously and decrease
the local generalization ability of CMAC, eventually more
expensive calculating time [16][17]. When the small
memory applied for online diagnosis, the insufficient
memory will prevent excessive noise caused by overlap
due to hash coding. Besides, if the training patterns are not
enough to update all weights, there would be some weights
untrained. This will lead to severe decrease the approxi-
mation performance in some certain regions [18].
Figure 5. Anatomy structure of CMAC
Copyright © 2009 SciRes EPE
Figure 6. Scheme of the fuzzy CMAC for diagnosis
In order to overcome these deficiencies, Fuzzy CMAC
is hybrid system that possesses the merits of both the
neural network and the fuzzy rule-based system. In order
to meet the real-time and precision demand for the fault
diagnosis system in steam turbine generator sets, the
detail architecture of a novel fuzzy CMAC shown as
Figure 6 is proposed in the paper.
The fuzzy CMAC network can be applied to approxi-
mate function, in which feature vari-
XR , and fault type, can be real-
ized by three sequential mapping as following.
yY R
:SA, (2 )
Y (3 )
In the first mapping, the feature variables will be
quantized as binary coding. In the second mapping
CMAC uses a fuzzy distributed storage system whereby
the numerical contents of each address are distributed
over a number of physical memory locations. The con-
tents of these physical memory locations are referred to
as weights. Each membership function (MF) in the con-
tents of memory location is represented by a Gaussian
distribution. In the third mapping , the fault types
will be realized by the membership function time weight
sum of contents of an address.
4.2 Step of Diagnosis Mode by Using Fuzzy
Step 1 Input feature signals
The input signals of the fuzzy CMAC in deferent level
might include feature variables such as one or combina-
tion with the frequency feature, phase feature, shaft orbit
feature, even trend feature and so on.
Step 2 Quantize the signals
No matter the testing or training signals, they should
be mapped to quantization output firstly. For the ana-
logue variable, the quantization output can be repre-
sented as following.
min maxmax
,,, ,1,
qQxx xqin, (4)
Copyright © 2009 SciRes EPE
where, min max
ii i
xx is the input, expected maximum
input, expected minimum input respectively. is the
quantization parameter.
Step 3 Segmentation, fired memory addresses coding
The quantization of the signal will be coded
according to binary form. Then we concatenate the quan-
tization signal as a binary string. The combined binary
input maps a set of memory location from a large pool of
memory locations.
In human cerebellar cortex, the mossy rosettes from a
single mossy fiber are widely distributed over several
folia with Gaussian distribution [15]. In order to simulate
the mechanism of the human cerebellar cortex, several
memory addresses near the main memory address will be
activated according to the Gaussian distribution.
(),1, ,
ij iji
wadj jnpnpnp
, (5)
where is the memory address in the j-th column of
i-th group. It can be pointed to addresses in the m layer
in the same time.
()ad x
exp;1, 2,
 
, (6)
where cand
represent respectively the center and the
width of the j-th column of i-th group for input x, k is the
total number of address in each group.
In this structure, the inner layer (Fuzzy CMAC memo-
ries) can be partially activated, allowing the network
output to be smooth. Also the problem that some weights
do not update because of lack of enough training would
be overcome.
Step 4 Calculate output and learning rule
Fuzzy CMAC learns correct output fault by modifying
the contents weight of the selected memory locations.
The actual output of the fuzzy CMAC after mapped can
be described as
, (7)
1, 2,,
where, is the weight of j-th storage hypercube. If
is addressed, then is 1, else is 0. There are
only C storage hypercube has an affection to output
ax ij
Step 5 Learning algorithm
The weight adjusting can be thought as that the teach-
ing and supervised leaning algorithm is described as
kk k
jj jijj
ww kw
 
, (8)
where ()k
is training gain.
In every step of iteration, only those network weights
that participate in output calculation are adjusted. That is,
the weights are determined by a training phase, during
which these values are adjusted to minimize the differ-
ence between the fuzzy CMAC output and its expected
output. So, for Hebbian learning, the cost function
() (()/)
 ij
is minimized.
, (
is a small positive constant and
an acceptable error), the training process will stop. Be-
cause the fuzzy CMAC tends to generalize over small
neighborhoods in input-space and can approximate a
desired function after a relatively few data points are
stored [17], it does converge rather rapidly compared to
the other artificial neural networks.
Step 6 Test the fuzzy CMAC
Load the diagnosis data which did not used to train the
fuzzy CMAC mode, and test whether diagnostic result
using the fuzzy CMAC mode is correct or not. If the
tolerance is satisfied with the requirement of diagnosis,
then save the mode to the system, else update the weight
value of the memory, until it meet the demand of the
5 Case Study
In order to validate our model, the training samples are
used to test. In fact, one type of fault is often combined
with the other fault no matter which is in incipient or
Copyright © 2009 SciRes EPE
happened, they will interact with each other. Even we
can not identify the major fault immediately. On the
other hand, it is very helpful for operators to find the
fault as early as possible, because the incipient fault or
the earlier fault will cause the lower loss than that fault
which might lead to the machine out of work. The oil
membrane oscillation, unbalance and misalignment
somewhat belong to this condition.
Training sample is combined with oil membrane os-
cillation, unbalance and misalignment. The input vari-
ables are <0.4f, 0.4-0.5f, 1f, 2f, 3f and >3f, which is
shown in Table 1. That is the typical vibration frequency
feature, and the other features are neglected here. The
is 1024 and C is specified 10. The weights in these
memory cell are trained according to the equation 8 until
the tolerance meet the requirement. The results of the
training are shown in the Figures 7, 8 and 9. In these
figures, the desired value is represented by the circle, and
the training value is represented by the star. It can be
shown that the result of the fuzzy CMAC output is very
close to the original value. The error will decrease quite
quickly. Therefore fuzzy CMAC neural network is of
high accuracy, quick convergence, and high noise rejec-
tion for fault diagnosis in steam turbine generator sets.
Table 1. The diagnosis input and output training sample
input feature variable output fault type
<0.4f 0.4-0.5f 1f 2f 3f >3f
Oil membrane
oscillation unbalance Mis-alignment
1 4.7244 67.6934 17.3260 2.38333.14864.72440.7368 0.2677 0.3747
2 6.2277 69.5962 15.4977 3.88871.54983.23990.7703 0.2204 0.3569
3 4.8642 74.1736 16.9309 1.61250.80621.61250.8574 0.2450 0.3603
4 7.9088 67.2246 17.4139 4.91781.72790.80700.7183 0.2559 0.3814
5 7.9706 60.8730 20.2888 4.34762.89713.62300.6835 0.3021 0.4087
6 10 80 10 0 0 0 1.0 0 0
7 1.5804 4.885777.5842 9.48223.30533.16220.2253 0.7138 0.2545
8 3.3843 1.703984.7415 6.77180.85902.53940.2763 0.7568 0.1829
9 0.8574 4.285276.8717 10.27895.99051.71630.1820 0.6937 0.2715
10 0.8178 2.515179.9901 9.17794.99942.49970.2446 0.7186 0.2472
11 1.8393 2.000084.2180 7.32330.95093.66840.2359 0.7560 0.2337
12 0 0 90 5 5 0 0 1.0 0
13 2.2962 8.120076.6193 5.25330.35797.35320.2553 0.6915 0.2216
14 2.1410 1.433929.2606 31.401624.978610.78420.0571 0.2471 0.7608
15 0.6969 1.714839.7991 28.951521.70867.12920.1004 0.3024 0.6222
16 0.6637 2.083727.7821 33.338522.229513.90260.0779 0.2347 0.7759
17 1.3735 0.695030.8176 28.078319.175419.86020.1435 0.2401 0.6437
18 0 0 40 50 10 0 0 0 1.0
19 0.5919 1.185928.0984 28.098422.158019.86730.1194 0.2698 0.6678
Copyright © 2009 SciRes EPE
05 10 1520
le Number
Fault typle 2: Unbalance
Figure 7. Training result of the fault type 1
05 10 1520
Training Sample Number
Fault typle 1: Oil Membrane Osillation
Figure 8. Training result of the fault type 2
05 10 1520
Training Sample Number
Fault typle 3: Misalignment
Figure 9. Training result of the fault type 3
In order to judge whether the fuzzy CMAC model can
be used to diagnose or not, the trained model should be
tested by the experimental data. However, no laboratory
setup can accurately simulate the faulty behavior of the
turbine generator, since it is too expensive to do for the
researcher or the designer of the company. The samples
in Reference [19] is tested in our model, the amplitude of
frequency is 4.42, 6.6, 224.79, 103.31, 29.01, 46.78 re-
spectively in monitoring condition. Because the other
states are not mentioned in it, they are neglected to test.
Normalizing them into 1.0653, 1.5907, 54.178, 24.899,
6.9919, and 11.275 and inputting to the trained fuzzy
CMAC model, three fault output are 0.2130, 0.5824, and
0.3761 respectively. It is shown that the major fault is the
unbalance and the misalignment is in the early stage.
This result fits the conclusion of bearing house looseness,
unbalance and the misalignment in Reference [19].
6 Discussion
In the viewpoint of practical work, the parameters of
fuzzy CMAC could affect the accuracy of fault detection.
When the generalization parameter C and address num-
ber S are changed, the result of the fuzzy CMAC trained
would also be changed. The conclusion can be made
easily, which the capability of fuzzy CMAC module is
strong as C and S are big. It means that the CMAC can
remember much knowledge while the address number is
large. When the generalization is big, the output of the
fault is smooth. In another words, we can get any value
of the fault when we chose the parameters big enough.
However it is impossible for the fault diagnosis in terms
of limited experimental data. And it is not suitable for
steam turbine generator set to diagnose the fault.
It is observed that the preliminary data is very impor-
tant for the same fault and the training output nearly fits
to the original data very well. Therefore we should use
the high quality data to train the fuzzy CMAC neural
network model. In order to apply to the fault diagnosis of
steam turbine generator sets, for the practical purpose,
experimental data needs to obtain. Furthermore, no
laboratory setup exists that can accurately simulate the
faulty behavior of the turbine generator. Therefore, there
is a little training data available. However the capability
of fault diagnosis will increase with the increase of the
Copyright © 2009 SciRes EPE
causal fault and behavioral knowledge of long-term vi-
bration measurements. Although the fuzzy CMAC diag-
nostic module might not be very correct in the early
stage, it would become more and more precisely to re-
sponse the fault with the training proceeding or the
learning in the application.
7 Conclusions
In this paper, a novel real-time fault diagnostic system is
presented. When the signal is triggered, The TSI signals
are collected and feature extraction is applied. Then the
fault diagnosis system by using strata hierarchical fuzzy
CMAC is used to identify the fault or failure in deferent
level in the steam turbine generator set. This model is
verified by a case of the diagnosis including three faults.
It is found that this model is feasible in real-time fault
diagnostic system. The results show that this model is of
high accuracy, quick convergence, and high noise rejec-
tion for the real-time fault diagnosis.
This work is supported by Program of Shanghai Subject
Chief Scientist (No. 09XD1401900) and Natural Science
Foundation of Shanghai (No. 09ZR1413300).
[1] K. N. Gupta, “Vibration—A tool for machine diagnostics and
condition monitoring,” Sadhana, Vol. 22, No. 3, pp. 393-410,
[2] M. S. Patil, Jose Mathew, and P. K. Rajendra Kumar, “Bearing
signature analysis as a medium for fault detection: A review,”
Journal of Tribology, Vol. 130, pp. 1-7, 2008.
[3] Martin Todd, Stephen D. J. McArthur, J. R. McDonald, and
Sally J. Shaw, “A semiautomatic approach to deriving turbine
generator diagnostic knowledge,” IEEE Transactions on Systems,
Man, and Cybernetics—Part C: Applications and Reviews, Vol.
37, No. 5, pp. 979-992, 2007.
[4] Jean-Marc David and Jean-Paul Krivine, “DIVA: Recognition of
typical situations for turbine generator diagnosis,” Journal of In-
telligent and Robotic Systems, Vol. 1, pp. 287-298, 1988.
[5] Yong-Hwan Bae, Seok-Hee Lee, Ho-Chan Kim, Byung-Ryong
Lee, Jaejin Jang, and Jay Lee, “A real-time intelligent multiple
fault diagnostic system,” International Journal of Advanced
Manufacturing Technology, Vol. 29, pp. 590-597, 2006.
[6] H. R. DePold and F. D. Gass, “The application of expert systems
and neural networks to gas turbine prognostics and diagnostics,”
Journal of Engineering for Gas Turbines and Power, Vol. 121, pp.
607-612, 1999.
[7] A. El-Shafei, T. A. F. Hassan, A. K. Soliman, Y. Zeyada, and N.
Rieger, “Neural network and fuzzy logic diagnostics of 1x faults
in rotating machinery,” Journal of Engineering for Gas Turbines
and Power, Vol. 129, pp. 703-710, 2007.
[8] Ruqiang Yan and Robert X. Gao, “Rotary machine health diag-
nosis based on empirical mode decomposition,” Journal of Vi-
bration and Acoustics, Vol. 130, pp. 1-12, 2008.
[9] J. J. Jeng and C. Y. Wei, “An on-line condition monitoring and
diagnosis system for feed rolls in the plate mill,” Journal of
Manufacturing Science and Engineering, Transactions of the
ASME, Vol. 124, pp. 52-57, 2002.
[10] Z. S. Chen, Y. M. Yang, Z. Hu, and G. J. Shen, “Detecting and
predicting early faults of complex rotating machinery based on
cyclostationary time series model,” Journal of Vibration and
Acoustics, Transactions of the ASME, Vol. 128, pp. 666-671,
[11] Xue Wang and Shuzi Yang, “A parallel distributed knowl-
edge-based system for turbine generator fault diagnosis,” Artifi-
cial Intelligence in Engineering, Vol. 10, pp. 335-341, 1996.
[12] Benjamin S. Blanchard and Wolter J. Fabrycky, “Systems engi-
neering and analysis,” Prentice-Hall Inc., 1998.
[13] Chun Cheung Siu, Qiang Shen, and Robert Milne, “A fuzzy
expert system for turbomachinery diagnosis,” Proceedings of the
1st Online Workshop on Soft Computing, pp. 7-12, 1995.
[14] James S. Albus, “A new approach to manipulator control: The
cerebellar model articulation controller (CMAC),” Transaction
of ASME, Journal of Dynamic Systems, Measurement, and
Control, Vol. 97, pp. 220-227, 1975.
[15] James S. Albus, “A theory of cerebellar function,” Mathematical
Biosciences, Vol. 10, No. 1/2, pp. 25-61, 1971.
[16] Daqi Zhu and Min. Kong, “A fuzzy CMAC neural network
model based on credit assignment,” International Journal of In-
formation Technology, Vol. 12, No. 6, pp. 1-8, 2006.
[17] James. S. Albus, “Data storage in the cerebellar model articula-
tion controller (CMAC),” Journal of Dynamic Systems, Meas-
urement, and Control, Transaction of ASME, Vol. 97, No. 3, pp.
228-233, 1975.
[18] Hung-Ren Lai and Ching-Chang Wong, “A fuzzy CMAC struc-
ture and learning method for function approximation,” IEEE In-
ternational Fuzzy Systems Conference, Melbourne, Australia, pp.
436-439, 2001.
[19] Zhengjia He and Shusheng An, “A fuzzy identification of machin-
ery condition,” Mechanical Engineering, Vol. 5, pp. 42-44, 1990.