A method of nonstationary noise analysis using instantaneous AR spectrum and its application to borssele reactor noise analysis

Progress in Nuclear Energy,

Printed in Great Britain.

1988,Vol. 21, pp. 707-716

0079-6530/88$0.00 + .50 1988PergamonPressplc

A M E T H O D OF N O N S T A T I O N A R Y NOISE A N A L Y S I S U S I N G I N S T A N T A N E O U S A R S P E C T R U M A N D ITS A P P L I C A T I O N TO B O R S S E L E R E A C T O R N O I S E ANALYSIS K. HAYASHI, Y. SHINOHARAand E. TORKCAN* Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken, 319-11 Japan and *Netherlands Energy Research Foundation, ECN, 1755 ZG, Petten (NH), The Netherlands

ABSTRACT This paper describes the test and demonstration of a method of nonstationary noise analysis using frequency-time spectrum based on instantaneous AR spectra. The frequency-time spectra were estimated by dividing the sample record into a series of very short subrecords which can be considered to be locally stationary and by calculating instantaneous spectrum for each eubrecord using univariate AR modeling. This method was applied to the analysis of Borssele reactor noise data measured during shut-down operation, which shows clear dependence of several signals on the coolant temperature. KE~OHDS Non-stationary analysis; Instantaneous AR spectrum; Frequency-time spectrum; IPITRODNCTION Nonstationary phenomena in reactor noise observed during transient operation such as reactor start-up and shut-down contain very important information sources which are very useful for diagnosis of nuclear power plants. In the field of reactor noise analysis, however, nonstationary noise analysis has seldom b e ~ performed because there is no effective analysis method established for nonstationary noise data J and also because noise data measurement during transient reactor operation is much more difficult than during steady state operation. The analysis of non-stationary data requires a method which is able to deal with the characteristics of its non-stationarity. With regard to the non-stationary data whose characteristics change very slowly, the frequency-time spectrum using normal FFT spectra has been applied for the analysis when the data is considered to be locally stationary. However, the resolution in the time axis by this method decreases for the case of small sample data. An example has also been applied in which the least squares AR method applicable to the_@nalysis of a small size sample data was used for the analysis of rapidly changing transient data . In the method of non-stationary noise analysis described in the following sections, the frequencytime spectrum based on instantaneous spectra is applied. For estimating the instantaneous spectra, AR modeling technique based on least squares method is used because it is possible to analyze a relatively small number of data samples. INSTA~TANEOOS SPECTRAL ANALYSIS OF RON-STATIOIARY DATA Instantaneous Mean S~uares For a stationary signal x(t), the mean squares value is defined as the limit of the time average for an infinite observation time as follows;

1 / T x ( t ) 2 dt. lim T-->~ TJO For a very short time span (t,~T), Eq.(1) is replaced by ~/X2"

707

(I)

708

K. HAYASHI et al.

Wx2(t,~T)-

'~:l-Tx(t) 2

(2)

dt

~TJO which gives an instantaneous mean squares. Both estimates of Eqs.(1) and (2) have bias errors when the signal is non-stationary. However, Eq.(2) gives an unbiased estimate for a limited case where the signal during the time span (t,~T) is locally stationary, although the variance error increases. Instantaneous AR model An AR model of a stationary process x(t) is given by M

x(t)= Z

a(m) x(t-m) + n(t). (3) m=1 For a process which is locally stationary in a very short time span (t,~T), the instantaneous AR model for the k-th time span can be expressed by M(k) x(t)= ~ a(m,M(k),k)x(t-m) + n(t,k) (4) m=1 where [a(~),M(k),k} are AR coefficients, n(t,k) a gaussian white noise having a mean 0 and a variance 6Z(k) and M(k) the order of AR model. Eq.(4) is essentially equivalent to a stationary AR model and both coincide when ~T -->oo. For a time varying AR model which represents systematically some non-stationary characteristics, the white noise term is represented by n(t) and the coefficients of the time varying AR model becomes different from those in Eq.(4). In the present analysis, Eq.(4) is used. Instantaneous spectrum Using the instantaneous AR model, an instantaneous spectrum P(f,k) for the k-th time span is obtained by 2(k)At

P(f,k)=

(5) 11 - a(f,M(k),k)l

2

where At is a sampling interval, mined by

M(k) a(f,M(k),k)=~a(m,M(k),k) m=1

a(f,M(k),k) the Fourier transform of a(m,M(k),k) which is deter-

exp(-2~fm~t)

(6)

AR Model Fittin~ Method The AR model fitting is a process of determining the order M, the coefficients {a(m);m=1,..,Ml and a variance ~2 characterizing a gaussian white noise using the observed data {x(t);t=1,..,N}, which leads to a problem of determining (M+2) unknown parameters. Four types of AR model fitting algorithms are discussed here for determining each AR parameter from the measured data. They are Yule-Walker, Burg, Marple and Kitagawa-Akaike methods. Yule-Walker Method A linear equation called Yule-Walker normal equation is derived by multiplying Eq.(3) by x(t) and taking the expectation,

(7)

RM AM = ~ M where

R~=

~(1)R(o)

:

,

~-

(~,I)

,ZM-

.

Eq.(7) can also be obtained by determining the coefficients of an AR model, viewed as a linear prediction filter, which minimize the mean squares of prediction error. The (M÷I) unknown parameters, consisting of M A R coefficients and a covariance, are obtained by substituting an estimated correlation function {R(k);k=O, 1,..,M} into Eq.(7). Using Lsvinson recursion algorithm, the solutions for higher order models are obtained efficiently once the AR coefficients for M=I are determined. We will call this procedure as Yule-Walker method for convenience in this paper. The optimal model order M as the final unknown parameter is determined using the AIC. Successful fitting by this method is dependent on the accuracy of estimated correlation function. For a small number of data samples, the correlation function is usually computed using biased lag estimates in order to guarantee a positive-definite correlation matrix. However, the fitting error of the AR model becomes large if the sample size is small.

Instantancous A R spectrum

709

Bur 6 Method This method is an improved one in which a constrained least squares method is applied to determine AR coefficients in order to suppress the bias error of correlation estimates, a disadvantage of the Yule-Walker method. The final AR coefficinent a(M,M), i.e. a reflection coefficient, is directly estimated from data samples by minimizing the sum of the forward and backward linear prediction energies. The Burg formula derived theoretically is used ~n this calculation. If a variance R(O) of data samples and a(1,1) are known, then R(1) and O"= are obtained from Eq.(7). {R(k);k=1 ,..,M} and AR parameters except for a(M,M) in higher order models are also obtained using Levinson equation. Successful fitting by this method depends on the estimation accuracy of R(O). Therefore, ting error by this method is smaller than by the Yule-Walker method.

the fit-

Marple Method . Marple method 3) is an advanced algorithm which expands the idea of the Burg method. The principal idea is to apply the exact least squares method to determine not only the reflection coefficients but also all other AR coefficients. From this idea, the following equation is derived.

RM AM = EM

(8)

where

=Ir(?,O)

HM Lr(M,o)

..

...r(?,M~, .. r(M,M~

AM.Ia(M,1)I, 1 I a(M,M))

EM "

' [~OM1

N-M r(i,j) = ~-~I(x(t+M-j)x(t+M-i)

+ x(t+j)x(t+i)

).

(9)

Eq.(9) is a function defined as the sum of the forward and backward correlation functions without time-mean operation. The AR parameters are obtained as a solution of Eq.(8). For solving Eq. (8), it is impossible to use the Levinson recursion algorithm because RM in Eq.(8) is not a Toeplitz matrix. However, instead of the Levinson algorithm, there exists a recursion algorithm for solution of Eq.(8) which can be computed efficiently though complicated. Furthermore, if initial values for Eq.(9) at M=I are obtained, Eq.(9) for higher order models can be calculated efficiently by use of recursive relationship. Kitagawa-Akaike Method 2 . Kitagawa-Akaike method ,4) provides an algorithm which uses the exact least mean squares method as is the case in the Marple method. The AR coefficients are determined by minimizing the sum of either the forward or the backward prediction error. The problem of determining AR coefficients which minimize the prediction error is reduced to solving the following (N-M) simultaneous linear equations. XtXA = xty

(10)

where fx(M ) x(M-m) ... x( I )I X = ~x(M+X)x!M ) x(.2 )~,


Fa(1)]

x(M+I)I A

x(~-M)J

Using the QR decomposition of a

1,1,I.

la(M)J lx('N )J rectangular matrix

X=QR

(I I )

where Q is a (N-M)xM rectangular matrix consisting of column vectors in the orthonormal system and R is an upper triangular matrix, Eq.(10) i8 rewritten as RA=QtY which can be solved by only backward substitution. Householder transform matrix.

(12) This QR decomposition is realized by use of a

In this method, the solutions are obtained for not only a maximum order Mmax but also for other lower orders at one time of computation of Mmax. However, the fitting by the one time computation is not appropriate for the case of small sample size because the number of data samples used for fitting of lower order models is fixed as (N-Mmax). S]]~LATION STUDY

Tests of Four Fittin~ Methods Four AR methods discussed in the previous section were tested in regard to fitting to a small size

710

K. HAYASHI et al.

samples 5'6j.~ The test data were sampled with a sampling interval of 0.061 sec from a sinusoidal analog signal having a frequency of 1.5 Hz and an amplitude of 2.5. About 12 samples are obtained in a period. When the spectrum of the signal contains line-spectral components, the AR fitting which assumes the white noise source generally becomes difficult. However, in the present test, the condition is slightly better than for purely sinusoidal data because some quantization errors are introduced through AD conversion. Figs. 1 and 2 shows the AR spectra estimated by each method for the model order M=2 and M=3, respectively. The number of the data samples N was 6 or 7. The total number of the data spans which were taken from the original data was 99. In this analysis, each data span overlaps for N-I samples, that is, the length of an updated part is I. From these Figures, it was found that the estimated spectral curves were different for different data spans and also for different fitting methods. It can be explained by the following reasons. When the data spans are taken with a length less than the period of the sinusoidal signal, the mean and variance values cannot be estimated exactly because each truncated sinusoidal data apparently has non-stationary characteristics. The estimation results of the magnitude and the frequency of the original sinusoidal signal are shown in Figs.3 and 4. Note that the results depend on the period rather than the number of data samples. The results shows that both Marple and Kitagawa-Akaike methods, which are based on the exact least squares methods, are superior to other methods for the estimation of the peak frequency but any method can obtain a satisfactory result for the estimation of the peak height. This is due to the assumption of the stationarity which is required in the AR modeling, and for the estimation of statistical parameters, e.g., a mean and a variance, a sufficient number of sample data which can he considered as stationary is required. Non-stationary Case In order to perform estimation tests of the frequency-time spectrum, non-stationary noise data of which stochastic properties change slowly in time was simulated by a system shown in Fig. 5. Three signal sources, a white noise, triangular waves with a fixed base frequency of 8 Hz and a variable base frequency between 15 Hz and 26 Hz, were used. These signals were mixed and then passed through a shaping filter of 2-nd order system having a dumping factor of 0.05 and a cut-off frequency of 5Hz. The output signal was sampled with a sampling interval of 0.01 sec. The total number of the data samples was 4096 and the time length was 40.96 eec. Fig.6 shows the sampled data recordings. The power spectrum estimated using all the sampled data is shown in Fig.7. Three remarkable peaks at 5, 8.5 and 26.5 Hz and trapezoidal components between 17 and 26 Hz are found. Fig. 8. shows the results of the small data span analysis applied to the same data. The length of each data span was selected to be 1024 samples, of which 960 samples overlap with the successive span and 64 samples are updated. The upper graph in Fig. 8 is each data span. It is found served during the initial 13 14-the span whose time range

a frequency-time spectrum and the lower one is the power spectra for from the upper graph that a line spectral component at 27 Hz is obspans, and the form and the location of this component change after is from 8.33 to 18.56 sec.

Fig. 9 shows the results for the case where the length of the data spans was set to be 128 samples. Each data span was taken without overlapping from the original data. Although spectral forms are estimated roughly, three main peak components appear clearly. In particular, it is clearly found that the trapezoidal component which appeared in the previous analysis is an afterimage of a line-spectral component with a shifting frequency. The beginning point of the frequency change is the 14-th span. This span number is the same as in the previous analysis but the time range in this case is narrower and is from 16.65 to 17.92 sec. The above result indicates the followings: When the length of data span as an analysis time window is short in consideration of the change speed of the time dependent components, the original component can be well estimated, When the length is long, the magnitude of the estimated spectral component decreases and the spectral distribution spreads if the original signal has frequency shifting components. -

-

APPLICATION TO BORSSELE REACTOR NOISE With respect to the pattern changes in the power spectra of the primary loop pressure signals and the axial vibrations of p r i m a ~ coolant pumps in Borssele reactor, the analysis using normal FFT spectrum was already reported 'j. The analysis was able to follow well the pattern changes in spite of the use of FFT spectrum which requires a large number of data samples because the pattern changes of these signals were very slow.

Instantaneous AR spectrum

711

In this section, we discuss about Borssele reactor noise analysis using an instantaneous AR spectrum from the view point of non-stationary data analysis. Data Records The data were measured during a shut-down operation at the end of 11-th core cycle. Four signals, primary loop pressure (YAOI.PO02), coolant temperature of core exit (XQ33.T01), differential pump pressure (YAOI.POO3) and radial vibration of primary pump (YDOI.VOO3) were selected for this analysis. These data records were divided into 2 files, B11-243 and B11-244, from a reason of limitation of maximum recording time. The recordings of the B11-244 were started after 6 minutes of the end of the B11-243. The DC signal records in each file are shown in Fig.10 (a) and (b). For the B11-243, both coolant temperature and loop pressure are initially constant and decrease after at 21300 sec from 150 to 85 ata and from 262 to 210 C, respectively. The differential pump pressure increases during that time interval from 5.9 to 6.35 ata. The pump vibration signal does not change. Mean Squares Series Fig.11 shows the results of the mean squares series analysis applied to the part of each file data for which appears large changes. The analysis of both files was made for the ranges from 16000 to 24992 sec and from I to 8192 sec, respectively. Each mean squares Fig. 11(a) indicate and then increases time point and the

value was estimated for every 2 that the variance component of the again slowly. The mean component of coolant temperature has a super low

sec (128 samples). The results shown in loop pressure decreases once after 21300 sec the pump vibration increases after the same frequency with a period of 1000 sec.

The results in Fig.11(b) indicate that the variance component of the loop pressure becomes progressively large. The increase of the mean component of pump vibration stops at 4000 sec when the pressure DC signal becomes constant. The period of the super low frequency component appearing in the coolant temperature changes from 1000 to 2000 sec after the time point at 3000 sec. Frequency-Time Spectrum The frequency-time spectra are shown in Figs. 12 to 15. The upper graph (a) in each Figure is the result for the B11-243 for the time range (15800-25008 sec) and each lower graph (b) is the result for the B11-244 for (5200-14208 sec). Each data span was the first 8 sec (1024 samples) taken from each 200 sec segment of the original data. For the case (a) of the loop pressure spectra, the remarkable peaks at 1.5, 6.8, 14 and 16.5 Hz are seen in the initial time span. When the DC components described above changes, the frequencies of two peaks at 6.8 and 14 Hz begin to shift towards higher frequencies. In the initial span for the case (b), the peaks at 1.5, 8, 11.5 and 16.5 Hz are observed. The peak at 8 Hz is the result of shifting of the 6.5 Hz peak in the case (a). The peak at 11.5 Hz is from the 9 Hz peak which was not remarkable in (a). The 15.5 Hz of the peak shifted from 14 Hz of (a) is mixed with the large component of the 16.5 Hz. These frequencies begin to shift again at the time point of 5900 sec and stop at 12000 sec. These time points correspond to the beginning and the end points of the decrease of the coolant temperature. It is found that the shifting lines of the peak frequencies are distorted at 9850 sec by the stop of the decrease of the loop pressure. From Fig.13, it is found that the coolant temperature consists of the colored noise with two sharp peak components at 12 and 25 Hz and that there is no frequency shifting peak. On the other hand, the periodic change of the spectral component at a lower frequency is observed. This indicates a super low frequency oscillation with a period of 1000 sec detected by the mean squares analysis. The differential pump pressure in Fig. 14(a) has remarkable peaks at 11 and 17.5 Hz and a weak peak at 9.6 Hz. When the temperature and pressure begin to change, the peak at 9.6 Hz begins to shift then overlaps with the large peak component at 11 Hz. The peak at 17.5 Hz disappears at the same time. In Fig. 14(b), the shifted frequency component which originated from 9.6 Hz does not clearly appear even when the temperature or pressure changes. The pump vibration in Fig. 15(a) has many remarkable 18 Hz. When the temperature and pressure changes, towards higher frequencies. In Fig. 15(b), a peak at ponent. These peaks shift in a similar manner as in

peaks. These are at 2.7, 3.8, 7.4, 9.5, 14 and two peaks at 9.5 and 18 Hz begin to shift 8 Hz newly appears as a shifted frequency comthe loop pressure spectra.

From these results, it is confirmed that the frequency-time spectrum based on instantaneous AR spectra is capable to analyze non-stationary data for a detailed time scale if the change of nonstationary characteristics is slow. The combined use of this spectrum and other time information, i.e., DC signal recordings and instantaneous mean squares series, is very useful for these

712

K. HAYASHIet al.

analyses. CONCLUDING

W~ARk'S

A frequency-time spectrum method based on instantaneous AR spectra was applied to the analysis of non-stationary data whose stochastic characteristics changed slowly. Four fitting methods of AR model were tested in order to investigate their applicability for non-stationary data analysis. From the results,

the following points were confirmed:

Bias errors of estimated peak frequencies are large by both conventional methods of Yule-Walker and Burg method but small by the exact least squares AR methods. They are Marple and KitagawaAkaike methods. For the case of deterministic data such as a sinusoidal wave, the latter methods with the model order of 3 or more can suppress bias errors if the data length is longer than one period. - Variance errors of estimated peak heights are large for all of the methods. To suppress the errors sufficiently, these methods require sufficient number of samples similarly to the estimation of a general statistics. -

The estimation test of the frequency-time spectrum was performed using simulated non-stationary data which change slowly peak frequencies of spectral component. The results indicate: - The number of data samples (the length of time span) determines resolution of the time axis and also bias errors of the estimates. For the data which change the peak frequency or the peak height intermittently, the estimated spectrum seemingly decrease when the span length is long in consideration of the change of characteristics. Finally, the demonstration test of this method was performed using real non-stationary data measured at Borssele reactor during the reactor shut-down operation. It was clearly shown that the stochastic properties of several signals change with decrease of coolant temperature and loop pressure. Furthermore, it was shown that the combined use of the frequency-time spectrum based on AR spectra and the time information functions, i.e. DC signal recordings and the instantaneous mean squares series makes it possible to analyze closely non-stationary data with respect to a time axis. ~K.~CES

I) Bendat J.S. and Piersol A.G. (1971) Random Data : Analysis and Measurement Procedures, John Wiley & Sons,Inc. 2) Kitamura M. et al. (1985) Development of Methods for Analyzing Time-Varying Characteristics of Power Reactor Noise, Prog. Nucl. Energy 15, 57. 3) Marple L. (1980) A New Autoregressive Spectrum Analysis Algorithm, IEEE t ASSP-28, 441. 4) Kitagawa G. and Akaike H. (1979) A Procedure for the Modeling of Non-Stationary Time Series, Ann. Inst. Statist. Math. r 30, Part B, 351. 5) Hayashi K. (1984) JAERI-M 84-127. (In Japanese) 6) Hayashi K. et al. (1982) JAERI-M 82-009. (In Japanese) 7) T~rkcan E. (1985). On-Line Monitoring of a PWR for Plant Surveillance by Noise Analysis, Prog. Nucl. Energy 15, 365.

Instantaneous A R spectrum

713

100

1.0 1

c, >.

i0"2

Marple

Burg

t

y

;.:;,,,;" M=2

Kitagawa-Akai ke ii :' ....... ; . . . . . . .

M=2

~ 4.0

M=2

'

M=3 4.0 O

I0

Fig. [

Kitagawa-

'

'

20 ' I'0 NUMBER OF DATA SAMPLES

3 Bais

errors

for

the

peak

frequency.

I

100

100

Burg

IO'~~

~

102 IOD

0

2

~=

,....

Kitagawa-Akaike

,'~ ,..

.

r,

:!':~"/''~J~

•..~ ~ . , ;~, , , ~. ;.

:"P::-:" . . . . . . . . .

, ° C

......

4

FREQUENCY(~)

Marple

', .- . . . . . .

/

;'; ,,v;~..; ,

M=2

, ....

wM=2

,;I

,,

. . ,, •

:/-

......

.~,/ M=2 .x

-

P Fig.

I AR s p e c t r a e s t i m a t e d by four methods; M=2.

~ 1O "~ -~ '

,,<,

Ib

'

~0 ~

Ib

:

20

~

IO:

~

20

0.

102

io°

F-

•

iOO 1o-2. l 00 ';

~I

g

;

N~6

1

:

i

t

II

..

" ' ' ' ' "

• "f V ~.: ="~Z"~," ' ' -P ,~" • ~" "1",=},"" ....... ;.,,- . . . . . . . . . . . . . --: - - ~ ,i. . . . . . . . . . . . . -': ,~ ,,;-z Z_ '_'_ _ _ M=3 ' '~ M=3 ..~) M=3 ..

10-2

'

I;

lO-2.

'

2'0 :

l:O

:

20

"'

I0'

' 20

NUMBER OF DATA SAMPLES

~i001 ~

Marple;N=6

(

~

Fig.

4 Bias

errors

for

the

peak

height.

i0-4

Whlte Noi se

~ .~

10°

1

0

-

4

~

f=48Hz = ~ " ~

+k~-~ I v-

I----1

f:eHz ~"

~

Signal am

f:O. ~ Ol D c H Z 0

2 FREQUENCY(Hz)

4

-5V o Fig.

Fig.

2 AR s p e c t r a e s t i m a t e d by four methods; M=3.

_ V C F ~ ISHzN ,

.

=

G(s)~ s2+2E=nS+i =SHz fn

~ =0.05

5 B l o c k d i a g r a m of n o n - s t a t i o n a r y signal generator.

714

K. HAYASH[ et

2.5

al.

~

Fig. -2.5

"l

t

,

,

,

i

,

,",

I0

0

,

i

,

,

,

20 TIME (sec)

POWER SPECTRUM OF CH-( I} NARRLE SPAN( N.409~, OT. ,919900 ( SEC I, M. 50 t9

,

]...~..,

,

,

6 The s i m u l a t e d nons t a t i o n a r y data

.I

30

40

i }

0

19 -2

19 - 6

Fig. 7 P o w e r s p e c t r u m of the simulated non-stationary data; N=4096.

10 -B

i ( 19

89

19

49

39

S9

FREQUENCY ( HZ ) POUER SPECTRUM OF C H , ( I ) MARPLE SPAN( N,102% DT" ,0t0900 ( SEC ), M. S9

10

1 J 47

POUER 5PECTRUR OF CH,( 1) MARPLE

)

N-

128,

,010000

DT,

I:

SPAN( SEC ),

(

32)

10

M*

0

10 -S

u TIME(sec)

:sec)

1~'2-; t0-4

10-4

10"6

Ie-6 -

1(8

,,,,,

. . . . . . . tg

. . . . . . . . . . . . 20

30

40

SO

te -s

'

'

'

e,

Fig, 8 F r e q u e n c y - t i m e the s i m u l a t e d data; N=1024.

s p e c t r u m of non-stationary

'

'

i"' te

FREQUESCY ( HZ )

'

'

,

i",'

,

2e

'

,

i

....

39

"1

,

,

,-'-"

40

SO

FREQUENCY ( HZ 1 Fig.

9

Frequency-time

the s i m u l a t e d data; N=128.

spectrum

of

non-stationary

Instantaneous AR spectrum

Primary Loop Pressure

Primary Loop Pressure

~12o

-~ 40

80

.

.

.

.

.

0

. . . 10000

- , 20000

,

20

r

0

Reactor Core Coolant Temperature

280

i

~240

200

Fig.

IO

,

~140 '

'

'2o~o~

,

loo

10000 TIME (sec)

0

TIME (sec) record;

B11-243.

Fig.

20000

O(b) DO signal record;

B11-244.

Ch.l YAOI.PO02

o.2 ~,~,~dl.b.,,~,L,~L.,.J~.,J~d~W.~ ......t,,.~.......~1,,

0.0

j

20000

180

Ch,1 YAO1 .PO02

0,01610" "°

,

10000

Reactor Core Coolant Temperature

'

10(a) DC signal

O.l

715

............. } '...... ' ""'"201000 . . . .' . . . . . I " ....... ' 24~00"' "

o.5 1 .............. ,J............. L,.,~,_~LL~,,]I o.o i 0.2

Ch.3 ,Xq33 .TOl

-lip,.. -,m~,-- ,,im.,-~m,, --m~ - ~,,m--. -~m, / ' I " " I ' I

16000 20000 Ch. 5 YAO1. PO03

-~,r"

,-:-;

....

4000

:--=i

......

:8o~0

.. Ch.3 XQ33.TO1

t.Lu,,W..~,,Ld,~,h.l~..,,j.u,llU.IL[d.h ..,i h,ILdt1,11,[,,l,ll~l ,dd.~,

.-~ I

'

-~~

0

0.0

!~ ' ~ . ~ m , -

-.--

I

-. .............

'

0

24000

- - .

I

.......

'

, .....

I

'

8000

Ch. 5 YAO1. PO03

10

0 J ] 16000 4

'

'

"~'~"-'~ 20000

'

J

2 -~--0400

16000

Fig.

20000 TIME (sec)

'

I

''

]

'

"1 8000

'

'

'

80dO

4000 Ch.7 YDOI.VO03

4

p

o .

24000

11 a) Instantaneous mean squares series; B11-243.

I

0

YDOI.VO03 ~..Ch.7 ........ ,............. - - " ~ . ~ ~ - - ' ~

:-.~

I

4000

Fig.

0

,

~

'

4oLoo

TIME (sec)

11 (b) Instantaneous mean squares series; B11-244.

K . HAYASHI et al.

716

23800

c

T

21800 19800

10 o

7800

17800 18 -S

zo -~

--

e

--

5

t8 FRE,T~Y < ~

5800

15

~ TIME

)

tO_re

($ec)

15800

IME (sec)

e

5

18

00

15

FREOUEHCY ( HZ )

- 13200

1.oo !

-IIZO0

9200 1

0

~'t",

,',

e

0 ,-'T'~,

.

~ ,

,

..

7200 .

:,

15

FRE~HCY ( HZ

Fig.

, , , , ~

i0

5

12 F r e q u e n c y - t i m e of Y A O I . P O 0 2 .

I, -5-

~

7200

szoo

2B

--5200 10-I(#

.

)

.

.

.

~

.

.

.

.

~

S

.

.

.

.

~

le

spectrum

.

.

.

.

TIME

15

(sec)

20

FREOUEMCV ( HZ )

Fig.

14 F r e q u e n c y - t i m e of Y A O I . P O O 3 . (a)

"

spectrum

"

"

2380O"23800 .21800"21800 -19800"19800 -

10

17800-

0

-17800

-15200-

- 15800

12 2

ze -~ ~

TIME (sec)

TIME (s~) 10i"

S P E

c T R U M

~T YDOI,YO03 - B11-244

]

t~ $ t e-t

11200

If 2

,

Pl

~

if 3

~ . . . .

~ . . . . IB

~ . . . . 20

18 e S~

1

FRE(}UE~CV ¢ HZ )

Fig.

13

Frequency-time of XQ33.T01.

7

2

Z O il~..~.v,~/...-~ e

spectrum

9200

5

0 O

0 e

....

IB

. , ,~.,

I5

, ] TIME (sec)

20

F R E Q - - ' < Hz )

Fig.

15 F r e q u e n c y - t i m e of YD01. VOO3.

spectrum