E-Journal of Advanced Maintenance Vol. 6 (2014) 71-85
Japan Society of Maintenology

Diagnostic Agent using Parasitic Discrete Wavelet Transform for theHybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”
Takashi NAGAMATSU1,*, Yuki JOU2, Akio GOFUKU3, Takayuki FUJINO3,†and Zhong
ZHANG41

Graduate School of Maritime Sciences, Kobe University, 5-1-1 Fukae-minami, Higashi-nada, Kobe
658-0022, Japan
2
Faculty of Maritime Sciences, Kobe University, 5-1-1 Fukae-minami, Higashi-nada, Kobe 658-0022,
Japan
3
Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-Naka,
Kita-ku, Okayama 700-8530, Japan
4
Department of Mechanical Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka,
Tenpaku-cho, Toyohashi, Aichi 441-8580, Japan
ABSTRACT
In order to detect anomalies in rotating machines such as pumps at an early stage, we developed a system using
wavelet transform. The pump diagnostic experiment equipment was designed taking into consideration the
structure of the pump used for the water-steam system of the fast breeder reactor “Monju”. For improving
detection capability, it is desirable to use a mother wavelet (MW) whose shape is similar to the anomaly signalthat is required to be detected. We call the constructed MW on the basis of the real signal the real motherwavelet (RMW). The parasitic discrete wavelet transform (P-DWT) that has a large flexibility in design of the
MW and a high processing speed was applied for detecting process signals. The vibration and sound signals
were measured using the pump diagnostic experiment equipment when three types of anomalies (injection of an
object, change of a balance of the impeller, and damage to the axis of the impeller) occur. Complex RMWs wereconstructed on the basis of the measured signals, and subsequently, parasitic filters were constructed. Signal
detection was performed by calculating the fast wavelet instantaneous correlation using the parasitic filter. We
evaluated three types of anomalies, and found that P-DWT is useful for detecting these anomalies. Furthermore,
we developed a diagnostic agent using P-DWT as one of the diagnostic agents of our hybrid diagnostic agent
system, which is intended to work together with the “Monju” distributed diagnostic agent system.
KEYWORDS

ARTICLE INFORMATION

Wavelet transform, parasitic discrete wavelet transform, complex realmother wavelet, Monju

Article history:
Received 27 February 2014
Accepted 20 October 2014

1.

Introduction“Monju” is a sodium-cooled fast-breeder reactor (FBR). Fast-breeder reactor uses liquid sodium
as coolant; therefore, it is necessary to handle liquid sodium carefully due to its chemical
characteristics. This means that some improved diagnostic systems to detect small anomalies insystem components are pivotal.
The Japan Atomic Energy Agency (JAEA) already developed a “Monju” distributed diagnostic
agent system [1] in 2001 to diagnose anomalies that might happen in “Monju”. After several years,
the Japanese government promoted to develop improved diagnostic systems for “Monju” by applying
new and/or developing techniques in signal processing and artificial intelligence. Therefore, theauthors studied a four-year R&D project from December 2009 to March 2013. The purpose of the
project was to develop a hybrid diagnostic technique integrating several diagnostic techniques by the*Corresponding author, E-mail: nagamatu@kobe-u.ac.jp
Present address: Mitsubishi Chemical Engineering Corporation, 1-2-2, Nihonbashi-Hongokucho, Chuo-ku,
Tokyo 103-0021, Japan†

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

use of “Monju” process signals and implement it as a hybrid diagnostic agent system in the “Monju”
distributed diagnostic agent system. The developed agent system of the project is composed of several
diagnostic agents and a diagnostic result is given by integrating the results of the diagnostic agents. In
this paper, we describe a diagnostic agent by using a wavelet transform (WT).
The WT [2] is widely used for signal analysis, particularly for analysis of non-stationary signals,
and can achieve the simultaneous analysis of time and frequency. The WT is classified into a
continuous wavelet transform (CWT) and a discrete wavelet transform (DWT). The CWT can use any
wavelet functions that satisfy the admissibility condition as a mother wavelet (MW). To satisfy theadmissibility condition is not so difficult; therefore, a signal detection method using a real motherwavelet (RMW), which is constructed based on a real signal, can be used in the case where the CWT
is used. However, there is no generalized fast algorithm for CWT; therefore, the processing time of
the CWT increases as the amount of data in the RMW increases. On the other hand, there are fastalgorithms for DWT, such as a multi-resolution analysis (MRA) and a lifting scheme. However, themother wavelet (MW) in the DWT must satisfy a bi-orthogonal condition. To satisfy the bi-orthogonalcondition is difficult; therefore, the MW cannot be designed freely, i.e., it is difficult to design the
MW on the basis of the real anomaly signals.
For improvement in detection capability, it is desirable to use the MW whose shape is similar tothe signal that is required to be detected. A parasitic discrete wavelet transform (P-DWT) proposed byZhang et al. [3][4] has considerable flexibility in the design of the MW and a high processing speed.
Zhang et al. [5] showed that the signal detection method by the P-DWT could get 30% improvementin speed and obtain sufficient calculation accuracy at the same time compared to the method by using
RMW (that was constructed by the CWT) for the application to car rattle noise source identification.
Therefore, we applied the P-DWT to the detection of anomalies in this study. As for improvement in
detection capability, in our preliminary research [6][7], we confirmed that the detection capability of
the anomaly signals by the P-DWT based on MWs designed from observed signals is higher than thatbased on more conventional wavelets (Morlet’s, Mexican hat, and Harr wavelet).
There are quite a few studies applying wavelet transform to the fault diagnosis [8][9]. Peng andChu [8] presented a summary about the application of the wavelet in machine fault diagnostics, butthey did not refer to design issue of mother wavelet similar to a fault signal. The review by Yan et al.
[9] referred to construction of new wavelet functions using CWT and lifting scheme. P-DWT has anadvantage over the methods using CWT in terms of calculation speed. Furthermore, P-DWT has anadvantage over the methods using lifting scheme, because methods using lifting scheme have thelimitation that should satisfy the bi-orthogonal condition.
As for the studies on Monju, Tamayama’s paper [1] described the system outline of distributed
plant monitoring and diagnosis system at Monju, but they implemented only the subsystem of model
based diagnosis at that time. The subsystem using wavelet transform was included only in the futureplan. On the other hand, they or their colleagues studied on the wavelet transform. For example,
Ikonomopoulos and Endou [10] used wavelet transform for computing the probability density
functions. In the study, they used Daubechies family as mother wavelets. Mitsumoto et al. [11]evaluated the dead times of Monju using the CWT. In the study, a complex Morlet wavelet was usedas the mother wavelet. Thus, they used well known wavelets as the mother wavelet. Therefore, theadvantage of our study is that P-DWT can design the mother wavelet to be similar to given anomaly
signals, which can improve the ability of extracting fault-related features.
Following part of this paper, we explain the P-DWT briefly and experiments to apply the P-DWT
by using pump diagnostic experiment equipment that is designed taking into consideration the
structure of the pumps equipped to “Monju”. After that we explain how to construct the agent that
diagnoses anomalies by the P-DWT for a “Monju” distributed diagnostic agent system.

2.

Detection of Signals Using a Parasitic Discrete Wavelet Transform

2.1. Parasitic discrete wavelet transform
Zhang et al. [3][4] proposed the P-DWT to improve computation speed with the same advantageof the CWT. The P-DWT is produced by adding the parasitic filters that are designed from real signals
to the decomposition result by the DWT.

72

Parasitic filter

u

I
k

d-2,k

d-3,k

cj,k
(RMW)

xkR xkI

cj-1,k+xk
dj-1,kuk(a) Decomposition

Fig. 1. Decomposition tree of the parasitic discrete
wavelet transform (P-DWT) and the parasitic filters.

DWT

d-1,k

ukR

c-3,k

DWT

DWT

c0,k

DWT

c-1,k

c-2,k

DWT

T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

xout(b) Reconstruction

Fig. 2. Design method of the parasitic filters.

Fig. 1 shows the decomposition tree of the P-DWT. In this figure, the dashed round rectangles
are conventional DWTs that use an orthogonal (or bi-orthogonal) MW. Terms c j ,k and d j ,k are thewavelet (i.e., high-frequency) and scaling (i.e., low-frequency) coefficients, respectively. Terms { u kR }and { u kI } are the real and imaginary parts of the parasitic filter, and xkR and xkI are the real andimaginary parts of an anomaly signal detected by the parasitic filter, respectively.
The level at which the parasitic filters are added is called the parasitic level. In Fig. 1, theparasitic level is -2. Plural parasitic filters can be added to other levels according to the signal
characteristic.
The parasitic filter is designed using the tree structure shown in Fig. 2. The design procedure is
as follows:(1) Construct the complex RMW using the method shown in reference [12].
(2) Decompose the RMW to the level that the filter parasitizes, and obtain coefficients c j −1,k .
(3) Assume coefficients c j −1,k as the initial parasitic coefficients { u k }.
(4) Set c j −1,k = 0 , d j −1,k = 0 , and xk = δ k ,0 (Kronecker delta), and calculate xout using inverse
transformation.
(5) Optimize { u k } with the following evaluation function:arg min xout − RMW.

(1)

We then obtain the optimized parasitic filter { u k }.
2.2. Detection of signals
In order to detect an anomaly signal, Zhang et al. [3] defined a fast wavelet instantaneous
correlation (F-WIC) and showed it as follows:R(k ) =(x ) + (x ) ,
R 2
k

I 2
k

(2)

where k denotes t = k∆t . It should be noted that ∆t differs depending on the parasitic level j, and∆t = ∆t / 2 j , where ∆τ is the sampling interval.
An anomaly is detected when the calculated F-WIC using parasitic filter exceeds a predeterminedthreshold value.

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T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

3.

Data Acquisition

3.1. Pump diagnostic experiment equipment
The pump diagnostic experiment equipment was designed taking into consideration the structureof the pump used for the water-steam system of the fast breeder reactor “Monju” as shown in Fig. 3.
The dimension of the equipment is about 1,219 mm heigh, 600 mm wide, and 480 mm deep. The
apertures of the motor valves and the pump-driving voltage can be adjusted by the external input froma PC. This equipment consists of two loops. Each loop includes a water tank, manual valve, motor
valve, needle valve, flow meter, and pump as shown in Fig. 3 (b). The pump (IWAKI CO.,LTD.,
MD-15RM-N) operates at 50 Hz. The discharge capacity is 19 L/min. The impeller is a magnetic
drive type. The radius of the impeller is 22.5 mm and the height of the vane is 7 mm as shown in Fig.
Inlet ofobjects
Water Tank

Pump

Pump

Manualvalve

Vibration Sensor

Attachment
for Vibration
SensorFlow meter
Needle valve

Motor valve(a) Overview

9.5mm
16 mm

(b) Piping and instrumentation diagram

22.5mm

20mm

Radius of axis： 2 mm Height of Vane： 7 mm(c) Impeller(d) Changing impeller

Vibration sensor
Microphone

Pump

Attachment(e) Installation of Vibration sensor and microphone
Fig. 3. Pump diagnostic experiment equipment.

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T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

3 (c). The impeller can be changed easily as shown Fig. 3 (d). The vibration sensors (OMRONCorporation, D7F-S03-05) are attached to the pumps using attachments around the pipes as shown in
Fig. 3 (e) and have a frequency range of 10 – 2000Hz (±3 dB). The microphone (Audio-Technica
Corporation, AT9942) is set near the pump to get the sounds as shown in Fig. 3 (e) and have afrequency range of 70 – 15,000Hz. The microphone amplifier (Audio-Technica Corporation,
AT-MA2) have a frequency range of 20 – 20,000Hz. This equipment provides functions that simulate
anomalies such as loose part and damage to the impeller.
3.2. Data acquisition
We acquired data using one of the loops of the pump diagnostic experiment equipment. The
vibration signal was measured for several seconds by the vibration sensor attached to a pump via
LabVIEW [13] with sampling frequency of 48 kHz. In this paper, since 4 kHz was enough to detect
the characteristic portion, we downsampled the signals to 8 kHz to reduce the computational load. Inorder to simulate loose part detection, we injected objects from the “inlet of object” as shown in Fig. 3(a). Furthermore, in order to simulate damage of impeller, we modified the impeller in two ways:
attaching the screw to the impeller and scraping the axis of the impeller.
3.2.1. Injection objects
Four types of objects, namely, a sphere (Fig. 4 a), small sphere (Fig. 4 b), cube (Fig. 4 c), andrectangular parallelepiped (Fig. 4 d), which were made of plastic, were used. Each object was injected
through the “inlet of objects” shown in Fig. 3 (a). Experiments for each object were conducted fivetimes in order to obtain the vibration and sound data.

Diameter = 4.8 mm(a) Sphere

Diameter = 3.2 mm
3.9 × 3.9 × 3.9 mm
3.9 × 5.7 × 2.6 mm(b) Sphere (small)(c) Cube(d) Rectangular parallelepiped
Fig. 4. Injected Objects.

3.2.2. Change of a balance of impeller
We attached a screw to the vane to change a balance of the impeller as shown in Fig. 5. It
simulates the change of a balance of the impeller when something adheres to the impeller or the vane
breaks.
3.2.3. Damage of the axis of the impeller
We scraped the axis of the impeller as shown in the Fig. 6. It simulates the aging degradation.

(a) Normal impeller(b) Impeller with a screw
Fig. 5. Change of the balance of the impeller.

75(a) Impeller with scrapes
Fig. 6. Damage of axis of the impeller

T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

4.

Construction of the complex RMW and parasitic filters

4.1. Complex RMWWhen using wavelet transform analysis, if mother wavelet (MW) is made of real numbers, it is
known that the analysis result is vibrating. However, if we use a complex MW, the analysis result
becomes smooth. Therefore, we use the complex MW.
We call the MW constructed based on a real signal the real mother wavelet (RMW). We now
explain how to construct the complex RMW that is proposed by Zhang et al. [12]. First, we constructa real RMWψ R (t ) . The procedure to construct the real RMW is as follows: (1) clip the characteristic
portion from the signal, (2) multiply the window function that has enough speed of convergence tozero outside of some chosen interval, (3) subtract the average value, and (4) normalize such that thenorm ψ R (t ) is 1:
ψ R (t ) =  ∫ ψ R (t ) dt 
∞

2

 −∞

1/ 2



=1 .

(3)

Next, we construct the complex RMW by first computing the Fourier transform of ψ R (t ) andfinding its frequency spectrumψˆ R ( f ) . In the negative frequency domain, ψˆ R ( f ) is set to 0, and in
the positive frequency domain, ψˆ R ( f ) is set to 2ψˆ R ( f ) . ψˆ r ( f ) and ψˆ i ( f ) denote the real andimaginary parts of ψˆ ( f ) , respectively. Then, ψˆ r ( f ) is set to(ψˆ ( f )) + (ψˆ ( f )) , and ψˆ ( f ) is set
R
r

2

R
i

2

i

to 0 in order to delete the phase component. We can then find the complex RMW
ψ (t ) = ψ r (t ) + iψ i (t ) by computing the reverse Fourier transform. We note that ψ r (t ) and ψ i (t ) aresymmetric.
4.2. Construction of the parasitic filters from real signals
From a signal obtained with the pump diagnostic experiment equipment, we constructed acomplex RMW on the basis of the method described in 4.1. First, we calculated the CWT to seek thecharacteristic portion of the signal. Then, we selected the portion of the signal for constructing thecomplex RMW. After that, we used a window function that passes the characteristic frequency of thesignal. After applying the window function, we constructed parasitic filters for the signal.
In the cases where we injected the objects, we could know when the object collided with thepump and observe high-frequency signals as the characteristic portion by using the CWT. Then, we
decided the center of the characteristic portion. Furthermore, we used the window function that passes
a signal including such high-frequency signal. Then we made complex RMWs and constructedparasitic filters from the complex RMWs.
In the cases where we used the impellers whose balance was changed and whose axis wasdamaged, we could find only the characteristic frequencies by using the CWT, because the signals
included the anomaly all over the signals. We set somewhere as the center of the characteristic portionin order to calculate complex RMW in the same way as the case where we injected the objects. After
that, we used the window function that passes a signal including the characteristic frequency signal.
Then we made complex RMWs and constructed parasitic filters from the complex RMWs.

5.

Anomaly Detection from Signals by parasitic filters

5.1. Detection of the anomaly of collisions of a small object in a pump
Fig. 7 (a) shows real vibration signal in the case where the injected objects were sphere.

76

T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”(a) Real vibration signal(b) F-WIC

Fig. 7. Collision detection from vibration signal (injection of the sphere object).

Real part

Imaginary part(a) Sphere.

Frequency spectrum

Real part

Imaginary part(b) Sphere (small).

Frequency spectrum

Real part

Imaginary part(c) Cube.

Frequency spectrum

Real part

Imaginary part(d) Rectangular parallelepiped.

Frequency spectrum

Fig. 8. Parasitic filters for vibration signals of injected objects.

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T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

Fig. 8 (a) shows the real and imaginary parts and the frequency spectrums of the parasitic filters
constructed based on the vibration signal shown in Fig. 7 (a). For comparison, we show the parasitic
filters for the sphere (small), cube, and rectangular parallelepiped in the Fig. 8 (b)-(d).
In Fig. 7 (a), it is almost impossible to detect the signal when the spherical object collided, but
the F-WIC (Fig. 7 (b)) indicate clearly when the object collided.
Table 1 lists the results for all objects that we evaluated whether the F-WICs at the collision time
were higher than other parts of the signal. The numbers of the first row express the number of trials.
In all the cases, we could detect the anomalies (collisions of objects). In the table, the parentheses
indicate that the signal detections were carried out by the filter made from the same signal. In addition
to this, we checked the effectiveness of filters constructed for other anomalies for several cases. For
example, about whether the filter constructed from a sphere object detects a cubic object, we
confirmed the filter was somewhat effective. In case where we apply this method to a real problem,
we construct filters for representative anomalies. Even if the method does not use the exact filter for
detecting the anomaly, this method performs a function of a subsystem of our hybrid diagnostic
system, because our hybrid diagnostic system makes a decision comprehensively on the basis of thediagnostic results of subsystems.
Table 1 Results of the collision detection from vibration signals (Injection of the objects)

Objects
1
2
3
Sphere(O)OO
Sphere (small)
(O)
O
O
Cube
(O)
O
O
Rectangular parallelepiped(O)OO*( ) indicate that the signal detections were carried out by the filter made from the same signal.

4
O
O
O
O

5
O
O
O
O

Fig. 9 shows (a) real sound signal and (b) F-WIC using parasitic filters constructed with a realsound signal, in the case where the injected objects were sphere. In (a), we easily detect the signal
when the spherical objects collided, and the F-WIC also indicates clearly when the object collided. In
real plants, there are many noises coming from surrounded equipment such as motors, pumps, etc.,
but our pump diagnostic experiment equipment was set in a quiet laboratory. Therefore, by using theparasitic filters constructed from the signals captured in the quiet laboratory, we tried to detectcollisions from noise-added signals. We added the noises whose maximum amplitude is 25, 50, 75, or100% of the maximum amplitude of the real sound signals. The noise signal was produced byrecoding sounds of a motor in a normal operation.
For example, Fig. 10 shows (a) real sound signal added with noise signal of 75 %, and (b) F-WIC
using parasitic filters constructed with a noise-added real sound. Table 2 lists the results for all objects
that we evaluated whether the F-WICs were higher than other pars of the signal; the symbol “O”
means that the system can detect the anomaly, and “X” means that the system cannot detect theanomaly, if the adequate thresholds are set.

(a) Real sound signal(b) F-WIC

Fig. 9. Collision detection from sound signal (injection of the sphere object); with no noise.

78

T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”(a) Real sound signal with nosise signal of 75%(b) F-WIC

Fig. 10. Collision detection from sound signals (injection of the sphere object); with noise signal of 75 %.
Objects
SphereTable 2 Results of the collision detection from sound signals (Injection of the objects)

Noise
1
2
3
0％
(O)
O
O
25％
(O)
O
O
50％
(O)
O
O
75％
(O)
O
X
100％
(X)
X
X
Sphere (small)
0％
(O)
O
O
25％
(O)
O
O
50％
(O)
O
O
75％
(O)
O
X
100％
(X)
X
X
Cube
0％
(O)
O
O
25％
(O)
O
O
50％
(O)
O
O
75％
(O)
O
X
100％
(X)
X
X
Rectangular
0％
(O)
O
O
parallelepiped
25％
(O)
O
O
50％
(O)
O
O
75％
(O)
O
X
100％
(O)
O
X
*( ) indicate that the signal detections were carried out by the filter made from the same signal.

4
O
O
O
O
X
O
O
O
X
X
O
O
O
O
X
O
O
O
O
O

5
O
O
O
O
O
O
O
O
O
X
O
O
O
O
O
O
O
O
O
O

5.2. Detection of anomaly of the change of a balance of the impeller
We constructed the parasitic filters based on the real vibration signal in the case where thebalance of the impeller changed. We applied the parasitic filters to the normal signal and the anomaly
signal as shown in Fig.11 and 12. Fig. 11 shows (a) real vibration signal and (b) F-WIC using theparasitic filter in the case where the pump is normal. Fig. 12 shows (a) real vibration signal and (b)F-WIC using parasitic filters in the case where the balance of the impeller changed. Fig. 13 shows thereal and imaginary parts of the filter and the frequency spectrums of the vibration signal constructedfrom the signal shown in Fig. 12 (a).
Most of the F-WIC values in normal condition were under 1.00E-1, but many of the F-WIC
values in anomaly condition were over 1.00E-1. Since there was a difference of F-WIC between
normal and anomaly signals, we have a possibility to detect the anomaly condition. However, it
seemed not easy and needs more effort.
The cases of sound signals, we could observed the signals around 60 Hz as the characteristic
portion by using the CWT. There were small differences of F-WIC between normal and anomaly
signals. However, it seemed not easy to distinguish between normal and anomaly signals.

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T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”(a) Real vibration signal(b) F-WIC

Fig. 11. Result of applying the parasitic filter to the normal signal.

(a) Real vibration signal(b) F-WIC

Fig. 12. Result of applying the parasitic filter to the vibration signal of change of balance of impeller(a) Real part(b) Imaginary part(c) Frequency spectrum
Fig. 13. Parasitic filters for vibration signals of change of balance of impeller.

5.3. Detection of anomaly of the damage of the axis of the impeller
We constructed the parasitic filters based on the real vibration signal in the case where the axis of
the impeller was damaged. We applied the parasitic filters to the normal signal and the anomaly signal
as shown in Fig.14 and 15. Fig. 14 shows (a) real vibration signal and (b) F-WIC using the parasitic
filter in the case where the pump is normal. Fig. 15 shows (a) real vibration signal and (b) F-WIC
using the parasitic filter in the case where the axis of the impeller was damaged. The F-WIC in thiscase shows very similar values with the case where the balance of the impeller changed. Fig. 16
shows the real and imaginary parts of the filter and the frequency spectrums of the vibration signal
constructed from the signal shown in Fig. 15 (a).
Since there was a slight difference of F-WIC between normal and anomaly signals, we have a80

T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

little possibility to detect the anomaly condition. However, it seems not easy and needs more effort.
The cases of sound signals were similar to those of vibration signals. It seemed not easy to
distinguish between normal and anomaly signals.

(a) Real vibration signal(b) F-WIC

Fig. 14. Result of applying the parasitic filter to the normal signal.

(a) Real vibration signal(b) F-WIC

Fig. 15. Result of applying the parasitic filter to the vibration signal with scraped impeller(a) Real part(b) Imaginary part(c) Frequency spectrum
Fig. 16. Parasitic filters for vibration signals with scraped impeller.

5.4. Discussion
We could easily detect anomalies of collisions of small objects in a pump as shown in 5.1. We
confirmed that the P-DWT is good at detecting short characteristic signals. On the other hand, in casesof anomalies of change of a balance of the impeller and damage of the axis of the impeller, detections
are not easy; the anomalies were not detected clearly comparing to the case of object’s collision.
There are conventional signal processing methods such as maximum, RMS, kurtosis, andskewness. Some methods are effective in detecting some anomalies and others are effective otheranomalies. We only considered the method using maximum value of F-WIC in comparing toconventional methods, because our concept of the hybrid diagnostic system is to integrate81

T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

conventional and new diagnostic methods using the advantages of each method. Our aim ofdeveloping subsystems is to add new abilities of detecting small anomalies to the hybrid diagnostic
system and clarify the advantage and disadvantage. In this paper, we evaluated the P-DWT and foundthat the P-DWT is effective in detecting short characteristic signal.
Therefore, when we apply the P-DWT to a diagnostic agent, which is described in the next
section, we should take into account the detection difficulty in some way.

6.

Construction of Agents using P-DWT for the Hybrid Diagnostic Agent
System

In this section, we describe how to combine the detection method by P-DWT to the hybrid
diagnostic agent system. As described in the previous section, the performance of anomaly detection
by the proposed method depends on the type of anomaly. Therefore, we introduce the confidence
value to indicate the self-evaluation of the certainty for a detection result.

6.1. Confidence value
In our plan, our hybrid diagnostic agent system [14] gets the measured data from the “Monju”
distributed diagnostic agent system. Our hybrid diagnostic agent system sends the data to thediagnostic agent by P-DWT. After diagnosing, the diagnostic agent by P-DWT returns the diagnostic
results and the confidence value. The confidence value shows the confidence of the diagnostic agent
by P-DWT. The hybrid diagnostic agent system diagnoses comprehensively considering thediagnostic results and the confidence values from all the agents.
We define the confidence value of the diagnostic agent by P-DWT as follows;

confidence _ value =

C−B
A− B

(4)

where C is the fast wavelet instantaneous correlation, A is determined in advance as the maximum
value of F-WIC when the parasitic filter processed the same series of signals as were used when theparasitic filter produced, and B is also determined in advance as the maximum value of F-WIC when
the parasitic filter processed the normal series of signals. When the confidence value is larger than 1,
the confidence value is set to 1, and when the confidence value is smaller than 0, the confidence value
is set to 0. The parameters A and B are shown in Fig. 17.
Diagnostic agents must be constructed for each signal that we want to detect. When the number of
spiky peaks in F-WIC are many, the smoothing filter must be applied before we decide A and B foreach diagnostic agent.

Fig. 17. A and B that are necessary for calculating the confidence value.

6.2. Diagnostic agent

Our anomaly detection program by P-DWT was constructed in LabVIEW, but our hybrid
diagnostic agent system was constructed in Java language, because it was constructed according to thesoftware specification of the “Monju” distributed diagnostic agent system [1].
Therefore, we constructed a diagnostic agent program in Java (Fig.18, left side), and weconnected the diagnostic agent program with the detector by P-DWT implemented in LabVIEW by
using sockets communication, as shown in Fig.18.

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T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

Agnet
Java

Diagnostic angent
program for P-DWT

serverLabVIEW
sockets

detector by P-DWT

clientFig. 18. Socket communication between the diagnostic agent program and the detector by P-DWT.

An example of anomaly detection is shown in Fig. 19. The signal data was the simulation data
whose sampling rate was 1 Hz, which were generated by NETFLOW++ [15] and added with noises
generated by AR model. Fig.19 (a) shows the received data by LabVIEW, and Fig. 19 (b) shows the
F-WIC.

(a) Received data by the detector by P-DWT implemented in LabVIEW(b) Results of F-WIC by using parasitic filter

Fig. 19. Detection of the anomaly of primary pump by received data from the hybrid diagnostic
agent system

Fig. 20 shows an interface image of our hybrid diagnostic agent system, it shows that diagnosis
result: WT Diagnosis Agent said “Anomaly Primary Pump” occurs and the confidence value is“0.64.” In this time, we implemented only one WT diagnosis agent, but we can add more WT
diagnostic agents by changing the port number of sockets.

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T. Nagamatsu, et al./ Diagnostic Agent using Parasitic Discrete Wavelet Transform
for the Hybrid Diagnostic Agent System for the Fast-breeder Reactor “Monju”

Fig. 20. User interface of the hybrid diagnostic agent system showing the detection of an anomaly of
primary pump by WT diagnosis agent

7.

Conclusion

This paper describes a detection technique for small anomalies in pumps using MWs extracted
from real vibration signals. We introduced the P-DWT proposed by Zhang et al. [3][4] to detect theanomalous signal. The pump diagnostic experiment equipment was designed by taking into
consideration the structure of the pump used for the water-steam system of the fast breeder reactor“Monju.” The vibration and sound signals were measured by the vibration sensor attached to thepump and the microphone set near the pump, respectively.
From the real signals, we constructed complex RMWs and parasitic filters. An anomaly isdetected when the calculated F-WIC using parasitic filter exceeds a predetermined threshold value.
The collision anomalies were detected for all of four types of objects. However, it was difficult to
detect the anomalies of changing a balance of the impeller and damaging to the axis of the impeller.
Furthermore, we developed a diagnostic agent using P-DWT as one of the diagnostic agents ofour hybrid diagnostic agent system, which is intended to work together with the “Monju” distributed
diagnostic agent system.

Acknowledgement
This study includes some of the results from “Anomaly detection agents by advanced hybrid
processing of Monju process data” entrusted to Okayama University by the Ministry of Education,
Culture, Sports, Science and Technology of Japan (MEXT).

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