The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

Cluster analysis server system using Self-Organizing Maps (SOM)
H.Sakaki, H.Yoshikawa
JAERI Tokai-mura, Naka-gun, lbaraki, 319-1195
Abstract
We analyzed the instability behavior of the accelerator by using the Self-Organizing Maps (SOM)
which Dr. T.Kohonen was advocating. The SOMis
constructed by the neural net-work technique, andthe best method on the pattern recognition.
In this report, the measurement data of the Lband LINAC at Osaka University was used for theSOM analysis. The result of this analysis and thedifferent analysis technic, ARmodel, was extremelycorresponding. Moreover, the SOMis able to be usedfrom the World Wide Web browser on the Internet.

This technique is a suitable tool for automaticallyclassifying and visualizing large-scale data. Thesemethod is one of the Data-mining. Especially, analyzing the similarity grouping is called Cluster analysis.
In this paper, the cluster analysis is done by using
SOM algorithm which Dr. T.Kohonen advocates[3].
--e---sin(2pi*t}+sin(3pi*t)+sin(4pi*t)-+-{J +rand(t)),.sin(.:!pl,..i)+sin{3pi"'ll+sin(4pi*t):#1:#.:!

-B--(I+rand(t))*sin(2pi*t)+sin(3pi*t}+sin(4.1pi*t) :#3--*-{I+randt.t))*sin{2pi*t)+siu(3pi*t)+siu(J.9pi*t) :#4--$-- (1 +rand(t)) *sin(2.1 pi*t)+siu(3pi *t}+sin(4.15pi* t):#54
31INTRODUCTION
2The system analysis using the noise contribution
rate has been shown to an effective way to analyze ofthe accelerator's system[1][2]. But, this is not recommended to beginners. Because, the analysis requires
a lot of know-how to do.
Most the the noise analysis are applied by thepower spectrum analysis using the Fast FourierTransform(FFT). This analysis is simple to understand, so that we use one the first step. On theother hand, if only the similarities of the FFT spectrum are compared by visual observation, a wrong
result is sometimes analysed by one's subjectivity.
In addition, if many disturbance factors are analyzed
using the FFT, clarifying the result becomes so difficult. The problem in the FFT analysis is solved byusing Self-Organizing Map algorithm (SOM) which
Dr. T.Kohonen advocates.
In this report, the data measured at Osaka University is analyzed using the SOM, as one of the applied case to the accelerator. And, to improve convenience, we had this analysis used by the Internet. H
you use the Internet World Wide Web broWser, youcan obtain the result of the SOM from anywhere.

22.1

SELF-ORGANIZING MAPS
AND APPLICATION TO TIMESERIESSIGNAL ANALYSIS
Self-Organizing Masp (SOM)

In general, the neural net-work is used to dothe pattern recognition and system estimation. The
SOM is a category which is called "unsupervised neural net-work", and some models need not be used.

0-I-2-3-···-···-,
050··-···

100

150
time

200Figure 1: Prepared time series data.
sine waves are added each other.

250

300

Three

2.2 Procedure of time series signal analysis
This paragraph outlines the analysis of time-series
signal procedure which uses the SOM.
The data preparation . First of all, the signal data made by the computer is prepared (Fig.1).
These signals were made from the addition of threesine waves, sin(21rt), sin(37rt), andsin(47rt). '#1' is abase waveform. In '#2', the Gauss noise was added
to the amplitude of the sin(21rt). '#3' and '#4'adds the Gauss noise to the amplitude, and changes
the frequency of sin(47rt). In addition, '#5' changes
both frequencies of sin(47rt) and sin(21rt).
Fast Fourier 'fransform(FFT) The FFT isdone to these data. Each spectrum data has three-479-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

spectral-peaks, as shown in Fig.2. And, each spectrum pattern is different little by little.

--&- sin(2pi*t)+sin(3pi*l)+sin(4pi*t)

1.2:#I:#2---G- (I +rand(t))* sin(2pi*t)+sin(3pi *t)+sin(4.1 pi *t) :#3~ { 1+rami{fl)*sin(2pi*t.)+~i:l(3pi*t)-;-sin0.9pi*t):#4~ (l +rand.(t'))*sin{2 ..l.pi*L)+si.n{3pi*t)+sin(4.15pi*t) :fi.5

addition, if each distance is near it is a similar factor.
From Fig.3, we can understand that '#1',......'#4' is asimilar group.
However, '#5' is not in the same white area, so it
is understood to belong to another group.

-~·-·· (l-:-Tand(_t)_)"'sin(2pi*t)+sin(3pi~~<t)+sm(4p1 "'n3...u 0.8~1Jr-0"'..

p,.

.!:l 0.6·II·OilEz 0.4
00.2

ANALYSIS OF UNSTABLEBEHAVIOR IN LINEAR
ACCELERATORThe SOMis used to analyze unstable behavior in
the actual linear accelerator. The data collected fromL-band LINAC at Osaka Universityis shown in Fig.4(4]. The data of the RF phase is shown in the upper
part, and the data of the disturbance factor measured simultaneously is shown in the lower side. Observing these data, we can't understand which factor
contributes to the RF phase.
~ 5 r-,---.-~--..---,--r-.--r-,--r-.--r-,--T

0.15

0.2

0.25
0.3
Freq. (a.u.)

0.35

0.4

~

~

€Figure 2: Power spectrum from fast Fouriertransform.

0"

Cl>

~ -5 1--················+········............H........,~....-+,·'·~·+111a.
LL

a:.
-10 ~~~~--~~~~--~~~~--~~~

These spectra are intentionally made from thewaves which understand the frequency. Therefore,a slight difference of the pattern can be obviously
confirmed from Fig.2. But, if these spectra weremade from the actual measurement data, the analytical person might explain, "Considering the measurement noise, all spectra are the same characters."

105 r--,.-,-----.---,--..---,---.--,----.---,..---,.-,-----.---r 40

~~

~~
~

Cl>

:.5 99

30 g;

~ 96.
~ 93

25~

!!l.

~

90
0200

400

600

800
Series

1000

1200

20-g:
~151400

Figure 4: Time series data collected in Osaka
University L band-Linac. In the upper part,the RF phase data and the lower side are thedisturbance factor data.

Figure 3: Cluster analysis of pseudotime series
data which use the SOM. It can be understood that '#5' is another group.

Analysis using threSOM Finally, The FFTspectrum is analyzed with the SOM. The SOM map
is shown in Fig.3. In the SOM, factors with highsimilarity are displayed in the same white region. InTo tell the truth, this data is being analyzed using
the AR model by Konishi and Isaka(5]. And, they
analyze that the AC Power Line contributes greatly
in the RF phase.
Next, this data was analyzed by the SOM, Fig.5
was obtained. The RF phase and the AC Power Lineare included in a similar group. Moreover, it is understood that other several kinds of fluctuation factor groups are formed. These results agree with theresult of Konishi and Isaka.

4

CLUSTER ANALYSIS SERVERSYSTEM

If you spend many time to install the SOM analysis software or a lot of preprocessings are neces--480-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

Figure 5: SOM map of Osaka University's
LINAC. The AC Power Line was included in
the same group as the RF phase. This is corresponding with the result of obtaining because of the noise contribution analysis.

sary for data analysis, the impression of this analysis might worsen. Then, we enabled you to use thisanalysis handily. In a word, the measurement datais transmitted to our Sever using World Wide Webbrowser, you can get the SOM map easily.
This usage is sequentially explained as follows.
The top page shown with Fig.6 opens, when URLof the server is selected on the browser. You selects
the data file which wants to be analyzed. SOM map,Fig.7, is sent back from our server only by pushing
the transmission button. These operations are verysimple.

Figure 7: The SOM map sent back from thecluster analysis server.

SOM. The effectiveness was confirmed by comparing
this and other analysis technics ; the AR model analysis.
Moreover, everyone from anywhere can easily do"Cluster analysis" by SOM using the World Wide
Web browser for an analytical interface.

6ACKNOWLEDGEME NT

In the SOM analysis in this work, we used the data
which Mr. Konishi and Mr.Isaka at Osaka University
had collected. We wish to express our gratitude.

7REFERENCES(1] H.Sakaki et al: "Statistical Analysis and Control of
the Electron Beam Energy Fluctuation at Linear Accelerator", SICE, 35-10, 1283/1291 (1999).
[2] H.Sakaki et al.: Proc. of THE 25th LINEAR ACCELERATOR MEETING IN JAPAN, 261/263 (2000).
[3] T.Kohonen et a!: "SELF-ORGANIZING MAPS",
Springer-Verlag Japan (1996).
[4] T.Konishi et al: Osaka-univ. master's thesis (2001).
[5] S.Isaka et al.: Proc. of THE 26th LINEAR ACCELERATOR MEETING IN JAPAN, 104/106 (2001).

Top page of cluster _ analysis
Figure 6:
server. To access, World Wide Web browser,
Netscape, is used.

5CONCLUSION

The instability behavior cause in the accelerator
was analyzed by the cluster analysis which used the-481-