We study the applications of neural nets in the area of fault detection in real vibrational data. The study is one of the first to include a large set of real vibrational data and to illustrate the potential as well as the limitations of neural networks for fault detection

Abdallah, Chaouki T.

Docampo, D.

Heileman, G.L.

Hush, D.R.

English

University of New Mexico

University of New Mexico
UNM Digital Repository
Electrical & Computer Engineering Faculty
Publications Engineering Publications
6-4-1997
Neural networks in fault detection: a case study
Chaouki T. Abdallah
D.R. Hush
G.L. Heileman
D. Docampo
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Recommended Citation
Abdallah, Chaouki T.; D.R. Hush; G.L. Heileman; and D. Docampo. "Neural networks in fault detection: a case study." Proceedings of
the 1997 American Control Conference (1997): 918-921. doi:10.1109/ACC.1997.609660.
Proceedings of the American Control Conference 
Albuquerque, New Mexico June 1997 
0-7803-3832-4/97/$10.00 0 1997 AACC 
NEURAL NETWORKS IN FAULT DETECTION: A Case Study * 
D.R. Hush, C.T. Abdallah, G.L. Heileman, and D. DocamPo* 
EECE Department, University of New Mexico, Albuquerque, NM 87131, USA. 
* Departamento de Tecnologias de las Comunicaciones 
ETSI Telecomunicacion, Universidad de Vigo, 36200-VIGO, SPAIN 
Abstract 
In this paper we study the applications of neural nets 
in the area of fault detection in real vibrational data. The 
study is one of the first to include a large set of real vibra- 
tional data and to illustrate the potential as well as the 
limitations of neural networks for fault detection. 
1. Introduction 
There has been considerable work in the areas of fault 
detection and isolation which were reviewed in [2], [6], [3]. 
There are basically two ways to  approach the analytical 
fault detection problem: The model-based approach and 
the data-based approach. In the model-based approach, 
the engineer has access to a model of the system whose 
behavior is being monitored. In the dataibased approach 
one bypasses the step of obtaining a mathematical model 
and deals directly with the data. This is more appeal- 
ing when the process being monitored is not known to be 
linear or when it is too complicated to be extracted from 
the data. It is this approach which we will concentrate 
on in this paper in order to evaluate the potential of neu- 
ral networks as fault detectors. This paper discusses the 
potential, as well as the limitations, of neural nets usage 
in fault detection and possible accommodation in vibra- 
tional systems. Section 2. provides a study of NN in fault 
detection where our approach to the fault detection and 
isolation problem is presented and our results obtained 
using real data are given. We have also investigated a 
trending approach using Fuzzy ART, the results of which 
are presented in section 3. Finally, our conclusions and 
recommendations are provided in section 4. 
2. Detecting Faulty Bearings 
It is conceivable that a neural net can be used as a 
monitoring device, in order to detect major changes in 
the operation of the system. In some cases, the neural net 
may also be used to accommodate the change of behavior 
as part of hierarchical control system [5]. In others, it is 
used simply as a fault detection device where the cluster- 
ing capabilities of networks such as ART or CMAC are 
called upon. The general idea behind using a NN for fault 
‘The research of D. Hush, C.T. Abdallah, and G .  Heileman was 
supported by a Grant from Chadwick-Helmuth under Contract W- 
300445. The authors are grateful to JP Cain of Chadwick-Helmuth 
for his help in collecting the data. 
detection can be summarized in the following steps: 1) Use 
a signal processing techniques to obtain a figure of merit f 
(Spectrum, Cepstrum, k factor, etc) for the different time 
signals. 2) If the figure of merit is high dimensional, use a 
feature extraction algorithm to reduce its dimensionality 
while keeping most of its information content. The result- 
ing signal is fe. 3) Train the neural network on fe either 
in supervised or unsupervised mode as discussed below. 
The purpose of this study is to explore automated meth- 
ods for detecting faults in the viscous damper bearing of a 
helicopter drive shaft. This portion of the paper describes 
the design of a system that accomplishes this task using 
neural networks. 
Data Description: The data used in this portion of the 
study are t ime series data measured by an accelerometer 
located on the outer bracket housing of the helicopter shaft 
(measured with respect to the shaft 1P). The time series 
were sampled at a rate of 44,100 sps. The bandwidth of 
the anti-aliasing filter was approximately 20 KHz. Spec- 
trograms of the data (shown below) suggest that the sig- 
nals are stationary, and that they were sufficiently over- 
sampled. A total of 21 runs were made using 17 different 
bearings. The duration of the runs varied from 4 to 7 sec- 
onds. Runs 1 and 11 were discarded because they repre- 
sent “start-up” runs from the two different data gathering 
trips, and were both suspect in one way or another. Thus, 
the input data for this portion of the study consists of time 
series data collected from the outer bracket accelerometer 
for Runs 2-10 and 12-21. All experiments described in 
this section used 4 seconds of data from each run. Ap- 
proximately 2.8 seconds (70%) were used for training and 
1.2 seconds (30%) for testing. Table 1 summarizes the two 
levels of groupings for the data. 
System Design Our focus in this paper is on the Level 
I1 grouping (i.e. good verses bad). It has been our expe- 
rience (as well as others [4]) that there is wide variability 
in the signature produced by both good and faulty bear- 
ings and that the overlap in these signatures is quite large. 
This problem stems from the fact that there are numerous 
factors that contribute to the the variability among bear- 
ing signatures, and the quality of the bearing is only one of 
these factors (and not always the dominate one). The ba- 
sic approach followed here is outlined in Figure 1. This is a 
traditional pattern recognition system consisting of three 
918 
ll Run Level I 
7,12,14 New 
8,13,15,16 Used 
2,9,17,19 Ball Spall 
10,18,20 Inner Race 
5 Outer Race 
6,21 Other 
1 Feature Set I Input Dimension I Projected Dimension 1 
I 
Level 11 ll 
Good 
Good 
Bad 
Bad 
Bad 
Bad 
Spectral 
LPC 
Cepstral 
Plots of one representative spectrogram of the 19 runs 
used in this study is shown in Figure 2. The complete 
runs are described in [l]. 
-10 and 
16 9 
16 13 
16 13 
Pealute Classification Sprctrogram. 4 sreonds o f  Run 2 Extraction Preprocessing 
Figure 1: Pattern Recognition System. 
major components: preprocessing, feature extraction and 
classification. The only preprocessing performed on the 
bearing data was to normalize each of the runs SO that 
it had zero mean and unit standard deviation. The sec- 
ond stage is generally the most difficult to optimize. The 
purpose of feature extraction is “to extract features from 
the preprocessed data which provide the greatest discrim- 
ination between pattern classes”. This is often difficult 
because the “best features” are usually not known ahead 
of time. To this end we settled on the following three 
feature sets: Spectrograms: A time-varying estimate of 
the magnitude of the Fourier Transform of the data. Lin- 
ear Prediction Coeficients (LPC): Coefficients of an opti- 
mal Mth order (FIR) linear predictor for the data. Cep- 
strum: The inverse Fourier transform of the logarithm of 
the magnitude of the Fourier transform of the data. In 
addition to their ability to carry discriminatory informa- 
tion, a good feature set should also have the following 
properties: Invariance: The features should be invari- 
ant to superfluous variations in the data. Dimensional- 
ity Reduction: The training process and generalization 
performance of the classifier (the last stage) suffer from 
the curse of dimensionality. It is therefore important to 
reduce the dimensionality (i.e. the number of features) as 
much as possible at the feature extraction stage. Simpli- 
fied Representation: Ideally, the features should take 
on a representation that permits optimal discrimination 
with the simplest possible classifier. 
We 
investigated a wide variety of classifiers in this study, 
with a focus on the following neural network classifiers: 
Multilayer Perceptrons (MLPs), Radial Basis Functions 
(RBFs), and Fuzzy ARTMAP. In addition to these 
we investigated the traditional linear, quadratic and 
nearest-neighbor classifiers. 
Feature Computation The computational aspects of 
the three feature sets, Spectrograms, LPC coefficients and 
Cepstral coefficients, are described in the full study [l]. 
The final stage in Figure 1 is the classifier. 
Figure 2: Run 2 (Ball Spall) 
Feature Selection The purpose of feature selection is to 
determine which of the individual features in the three fea- 
ture sets are useful for discrimination. The method used 
here forms an estimate of the Bayes Classification Error 
(i.e. the minimum attainable classification error) for each 
individual feature, and discards features with a high (close 
to 50 %) error. 
Dimensionality Reduction After discarding individual 
features, we reduce the dimensionality of the features r e  
tained by projecting them to a lower dimensional space. 
We use a linear method that projects feature vectors onto 
directions with the largest separability The overall projec- 
tions, are summarized in Table 2.. 
Classifier Design All of the training and testing per- 
formed in this section and the next assumes that the oc- 
currence of good and bad bearings is equally likely, i.e. the 
prior probability for both of these events is assumed to be 
0.5. A critical component in the design of the 1-NN, RBF 
and MLP classifiers is the determination of their size. A 
sequential search was performed, starting with the small- 
est possible size and then increasing it until the classifier 
performance began to level off. A specific size (and cor- 
responding performance) must be chosen for the 1-NN, 
RBF and MLP classifiers so that they can be compared 
91 9 
~ Optimal Size Classifiers for Spectral Features - 
Classifier I Size I % Error 
1-NN 1 6  I 27.77126.09 Run3 
Classifier 
Linear (LS) 
Linear (Pocket) 
Quadratic 
RBF (LS) 
RBF (Pocket) 
MLP (BP) 
MLP (Constructive/LS) 
MLP (Constructive/Pocket) 
Fuzzy ARTMAP 
1-NN (LVQ) 
LPC 85.4 14.6 
Cepstrum 14.4 85.6 
SDectrum 32.2 67.8 
% EI 
Traininn 
RBF (LS) 
RBF (Pocket) 
MLP 
24.65 - 
22.07 
24.09 
27.77 
33.75 
27.76 
23.79 
22.56 
21.26 
4.2 
18 33.75/34.44 
18 2 7.761 2 7.39 
10 23.79123.73 
)r 
Test 
24.26 
22.63 
24.56 
26.09 
34.44 
27.39 
23.73 
23.83 
22.15 
27.5 
Run4 
Table 2: Classification Results for Spectral Features. 
1. 
LPC 35.0 65.0 
Cepstrum 60.1 39.9 - 
with the others in the next section. Table 2. shows the 
sizes chosen for this purpose. Similar results were obtained 
for the LPC and Cepstrum features [l]. Classification 
Results The classification results for the Spectral feature 
set are summarized in Table 2. The best classifier for this 
feature set is the linear classifier trained with the Pocket 
algorithm. Although one of the MLP networks achieved 
slightly better performance, the additional complexity of 
this classifier does not justify its choice given such a small 
increase in performance. The classification results for the 
LPC and Cepstral features may be found in [l]. 
Tests on Unknown Bearings In this section we describe 
the results of tests performed on Runs 3 and 4 whose true 
classifications are unknown (but believed to be “normal”). 
Neither of these runs were used in the training and test- 
ing above. Both runs were processed by the three dif- 
ferent pattern recognition systems (one for each feature 
type). In each system the optimal classifier (determined 
in the previous section) was used, i.e. the linear, MLP 
and RBF classifiers were used for the Spectral, LPC, and 
Cepstral features respectively. The classification results 
are summarized in Table 3. Several observations can be 
made regarding these results. 1) There is a large varia- 
tion across feature sets. 2) There is a large variation in 
the consistency of the results between Run 3 and Run 4. 
3) None of the results are in close agreement with the clas- 
sification error rates predicted in previous sections. The 
explanation for these poor results is that the data used to 
design these systems was not representative of all future 
data. These results tell us that the systems designed here 
are not likely to produce meaningful classifications of fu- 
Run I Feature I % Good I % Bad 
I Spectrum I 25.2 I 74.8 
Table 3: Classification Results for Runs 3 and 4. 
ture data. A more promising approach is investigated in 
the next section. 
3. Trending Using Fuzzy ART 
We next investigated a trending approach to the de- 
tection of faulty bearing. In order to perform a trending 
analysis, it is necessary to monitor the same bearing over 
an extended time period. In four of the runs supplied to 
us, the same bearing was used; these include Runs 13 (nor- 
mal), 16 (normal), 18 (inner race), and 20 (inner race se- 
vere). Note that the last two runs correspond to damaged 
bearing. 
Our experimental setup for the trending analysis con- 
sisting of a single fuzzy ART (clustering) module. The 
spectrogram data computed for Run 13 was supplied as 
input, and the network formed a single cluster. A his- 
togram of the output node value for this cluster, for each 
of the 500 time time segments is shown in Figure 3. Notice 
that the output node produced the same value for all 500 
inputs. At this point the fuzzy ART network weights were 
“frozen”, and the spectrogram data computed for Run 16 
was supplied as input. The histogram for Run 16 is shown 
in Figure 4. This histogram is only slightly different from 
the previous one (i.e., it is nearly flat). The fuzzy ART his- 
togram corresponding to the spectrogram data computed 
for Run 18 is shown in Figure 5. In this (damaged bear- 
ing) case, the histogram is significantly different from the 
previous two. For the final case (severe damage), Run 20, 
the histogram (Figure 6) is extremely “ragged”. This 
experiment suggests that a trending approach, which is 
based on learning the features associated with a normal 
bearing, and monitoring these features over time, may be 
a feasible alternative to the other experiments performed 
in this study. 
4. Conclusions and Future Directions 
We have presented an overview of fault detection and 
isolation techniques with special emphasis on vibrational 
data and the usage of neural networks. We have pre- 
sented applications of these techniques to real vibrational 
data. Based on this study, we have determined that the 
approach which presents the best probability of success is 
the trending approach where a particular system is moni- 
tored over its lifetime and faults are detected as deviation 
920 
Figure 3: Histogram of Fuzzy ART Output Values for 
Spectral Features for Run 13. 
Figure 5: Histogram of Fuzzy ART Output Values for 
Spectral Features for Run 18. 
FnNm V M r  
Figure 4 Histogram of Fuzzy ART Output Values for 
Spectral Features for Run 16. 
Figure 6: Histogram Of fizzy ART Output Values for 
Spectral Features for Run 20. 
from normal behavior. On the other hand, an approach re- 
lying on combining data from different systems is doomed 
to failure as shown in section 2.. As a direction of fu- 
ture research, we intend to study the trending approach 
using different feature sets and different neural networks 
structures. 
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ing Systems ** Morgan Kaufmann, 
[5] M. Polycarpou and A. Vemuri. "Learning method- 
ology for failure detection and accomodation. IEEE 
Contr. Sys. Mag., 15(3):16-24, 1995. 
[6] A.S. Willsky. A survey of design methods for failure 
detection in dynamic systems. Automatica, 12:601- 
611, 1976. 
References 
C.T. Abdallah, D.R. Hush, G.L. Heileman, and D. Do- 
campo. Neural networks results for fault detection 
applications: Survey and implementation. Technical 
Report EECE96-001, University of New Mexico, Al- 
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