Analysis of time-varying characteristics of signals from borssele reactor

Progress in Nuclear Energy. 1985, Vol. 15, pp. 853-861 0079-6530185 $0.00 + .5[) Printed in Great Britain.

ANALYSIS OF TIME-VARYING CHARACTERISTICS OF SIGNALS FROM

BORSSELE REACTOR

E . TORKCAN AND M . K1TAMURA*

Netherlands Energy Research Foundation, ECN, P.O. Box 1, 1755 ZG Petten, The Netherlands

*Department of Nuclear Engineering, Tohoku University, Aoba, Sendai, 980 Japan

ABSTRACT

A method of random data analysis, based on least squares autoregresslve (AR) modeling, was applied to signals from Borssele reactor. In this method, the model parameters are determined directly from the data without estimating correlation functions, enabling to avoid the modeling errors often encountered when the number of samples is small.

From the estimated AR model, auto power spectral density (APSD) and secondary noise signatures are derived easily. The following secondary signatures were used to quantify the time-variatlon of statistical properties of the signals: - sample variance of the signal, - sample variance of the residual, - resonance frequencies of peaks in the APSD, - amplitudes of the peaks, - magnitude of the APSD at the lowest frequency.

The purpose of this paper is to demonstrate the usefulness of the method as a practical tool for surveillance and diagnostics of a nuclear power plant. The method was implemented into the PDP-|| system of the physics department of ECN, where signals are available taking the advantage of on-line link with Borssele reactor instrumentation. The method was applied to several sets of data in which non-stationary was recognized. Typical ex- amples of them are: the signals obtained while the reactor was undergoing a power level change, the response of vibration sensors to artificial disturbance imposed under cold shut-down conditions and pressure standing wave phenomena observed during the cool-down procedure.

Through the analysis, it was confirmed that the method is highly efficient in detecting changes of

the statistical properties of the signals.

In addition to the detection, information relevant to the cause and extent of the changes was also extractable. Development of diagnosis systems covering not only stationary but also time-varying operation modes of nuclear reactors can be accomplished by proper use of the present method.

KEYWORDS

Borssele reactor; reactor noise; on-llne monitoring; nonstationary signal analysis; least-squares

modeling, time dependent spectra.

INTRODUCTION

A method of random data analysis was applied to signals from Borssele nuclear power plant. The method is a modified version of autoregressive (AR) modeling, in which the model parameters are determined without using correlation functions. Since the method is free from errors in correlation functions, it shows a higher applicability to data with smaller number of samples. This property enables us to analyse signals even when the process behaviour is non-stationary, i.e. stationarity of the signals is maintained only for a highly limited period of time.

Although a nuclear power plant is usually operated at a constant power level, it can experience expected and unexpected transient as well. For an unexpected transient it is an issue of great importance to detect the occurrence of it as soon as possible, hopefully within its incipient phase, and to extract dynamical information from the signals for detailed diagnosis of the phenomena.

...... 853

854 E. TORKCAN and M. KITAMURA

Even when the transient is an expected one, it would be desirable if information relevant to dynamic characteristics of the plant subsystems is extractable by processing the transient data.

The purpose of this report is to demonstrate the applicability of the present method of least squares autoregressive (LSAR) modeling to transient data for pursuing the aforementioned goals. The method was implemented into the PDP-II/24 system at ECN, physics department, and the analysis was carried out taking the advantage of the accessibility of the system to the Borssele nuclear power plant.

METHOD

The data to be analysed were divided into NC segements, each containing N samples. When the whole data (i.e. NC~N samples) are characterized by the non-stationarity, the use of conventional methods tends to be misleading. By the segmentation, the stationarity of the data is improved in each segment. Since the number of samples is small, the nonparametric method such as Fast Fourier Transform (FFT) becomes invalid. The parametric modeling methods, i.e. autoregressive (AR) and autoregressive moving average (ARMA) modeling, allow us to analyse the data. However, when the number of samples becomes further smaller, a numerical difficulty could often take place, preventing the model determination itself as far as the conventional modeling algorithm is utilized. The present method of least squares modeling using Householder transformation is expected to be a more promising technique for alleviating the difficulty without sacrificing the accuracy in the spectral information extracted from the data. The method (Kitagawa and Akaike, 1978; Kitamura andothers,|984) isdescribed briefly in terms of one segment of the data denoted as [y(l),y(2) .... ,y(N)]. An AR model written as

P y(k) = ~ a(m)y(k-m) +v(k) (I)

m = l

is determined so that statistical properties of the signal can be transfered to the model as much as possible. The parameters [a(m)~ m=l..p], called AR coefficients, are to be determined to fulfill the requirement. The residual sequence v(k) is assumed to satisfy the condition

E[v(k)v(j)] = o~.6kj,

where

6k~ J = 1 for k=j = 0 otherwise. (2)

Usually, the AR coefficients and the variance of v(k), o 2 are obtained by solving Yule-Walker equation (Box and Jenkins 1970), which sometimes results i~ numerical difficulties as mentioned above. In the present method, the parameters are given by solving a set of overdetermined equa- tions.

Y = A a (3)

where

Y = [y(p+l),y(p+2) ..... y(N)]', (4)

= [a(1),a(2) .... ,a(p)]', (5)

and

A(i,j) = y(p+i-j). (6)

The A(i,j) represents the (i,j)-element of the matrix A.

The Householder transformation technique (Golub, 1965) is so far known to be the most efficient method for solving the eq. (3). By operating an orthogonal transformation matrix to both sides of eq. (3), the matrix A is transformed to an upper-triangular form. After this operation, the determination of the vector a satisfying the equation in the sense of minimum euclidean norm is carried out by backward substitution. The value of the norm is obtained at the same time, from which the variance of residual is easily estimated. Once the model is determined, the estimation of PSD is easily performed through Fourier transformation of the AR coefficients as

Sy(f) = 2o~At/IH(f)] 2 (7) P

H(f) = I -m~ I a(m)exp(-j2~fmAt). (8)

Time-varying characteristics of signals from Borssele reactor 855

This Sy(f) is estimated for each time-segment of data. The time-dependent variation in the PSD can be studied by examining the sequence of Sy(f) in a systematic manner. In order to make this examination efficiently and objectively, following secondary signatures representing the features of the PSD pattern are estimated for each Sy(f). - Variance of the signal, VARy. - Variance of the residual, VARv(= ~2).

Resonance frequencies of peaks in VpSD, FPi(i=],2,...). - Amplitude of the peaks, PKi(iffil,2,...). - Magnitude of the PSD at the lowest frequency, PO.

The signature VARy indicates the overall energy of the fluctuation of signal y, while the VARy the energy of an ur~easurable noise source, i.e. the primal cause of the fluctuation of y. The ratio, VARv/VARy, is a measure of goodness-of-fit of the AR-model to the data. The signatures FPi and PKi characterize the significant peaks in the PSD.

The signature PO is a simple but useful parameter characterizing the overall PSD pattern. The PO, normalized by VARy, takes a small value when the global shape of PSD is similar to the output PSD of a band-pass or high-pass filter driven by a white noise source, and takes a large value when the shape is similar to that of a low-pass filter.

All these signatures are obtained automatically by the program. In addition, trend and correlation analysis are carried out for specified pairs of the FPi and PKi for more detailed examination and characterization of the time-dependent variation of the signals.

DESCRIPTION OF DATA

Example I: Secondary System Transient

The signals were obtained from the Borssele reactor when the reactor was undergoing a transient triggered by a sudden load change. During the turbine transient 32 process signals (dc as well as ac) of the reactor were followed by the on-line monitoring system (T~rkcan, 1982), with 8 samples/s for ac and 1 sample/s for dc. In undergoing transient event the reactor signals have been changed in the following order: - the generator output showed increasing large oscillations, secondary flow was reduced while the steam pressure increased. By the same event (40 s later), through the steam generator, the primary system pressure and the temperature increased 40 s later, while the D- and L-control-rod bank of the reactor came in action. The reactor safety system be- haved correctly, the reactor power was reduced and one hour later the reactor power reached again the previous operational level. The noise signals of turbine generator power G, secondary system flows SFI and SF2 (sensors RA01/ RA02.F001), and secondary system pressure SPI and SP2 (sensors RA01/RA02.P001) are illustrated

in Fig. I.

Because of the apparent non-stationarity, it was judged invalid to use the standard techniques of noise analysis such as FFT, correlation analysis and the AR method based on the Yule-Walker modeling principle. It was also judged that textbook techniques of non-stationary data handling, i.e. elimination of bias or trend, are not promising in this situation. The use of a novel technique seemed to be necessary.

Example 2: Vibration Test

In order to investigate the dynamic characteristics of the vibration phenomena of main coolant pumps, artificial impacts were imposed to the cold state non-operating pump. One of the time traces of the signal is given in fig. 2; the given impacts can be seen from the time history. Non-stationarity of the signal is apparent and it is very strong that any other conventional

method will not be applicable.

Example 3: Pressure Standing Wave Phenomena

One of the pressure signals of the primary system was measured during the cool-down operation of the reactor fuel cycle I0. Pressure signals are known to be characterized by prominant resonances representing standing wave phenomena, indicated in the paper of T~rkcan (1982). The signal in this case may be regarded as stationary from the point of conventional noise analysis. Time dependent evaluation of this effect was studied by the present method.


RESULTS AND DISCUSSION

Example !

One way of inspecting the time-dependent variation of the signals is to estimate the variance, VARy, as shown in Fig. 3. As expected, the VARy values showed significant increase during the transient. One can use this information for quick detection of transient.

The onset of the transient is detected at case 11 for signal G and at case 13 for other signals. In the present condition of analysis, we could detect it with a time resolution of 32 seconds at most. This value could be reduced further by adopting a smaller number of samples in one case.

Typical PSDs before, during and at the end of the transient are given for G, SFI and SPI in Figs. 4, 5 and 6 respectively. Before the transient, the peaks in PSDs are mostly unclear, without showing any commonly observable structure. Only the PSD of generator signal showed some significant and common peaks around 0.9 Hz and 1.8 Hz. Absolute magnitudes of the peaks are quite small in all PSDs during this phase.

Drastic changes are observed in all PSDs after the onset of the transient. All PSDs are characterized by a sharp resonance at 0.8~0.9 Hz. The resonance frequency changes slightly from case to case. Other peaks are also noticed at higher frequency regions. As will be described later, it appeared that most of them are the higher harmonics of the peak at 0.8-0.9 Hz.

To examine and characterize the time-dependent variation further in detail, trends of the secondary signatures were surveyed. Among them the trends of FPI and PKI, each obtained for SF] and SPI, are shown in Figs. 7 and 8, respectively. Here, FPI and PK| correspond to the frequency and amplitude of the peak at around 0.8 Hz.

For the present example, the PK| was found to be highly useful in detecting the onset of the transient. The characteristic resonance at around 0.8 Hz becomes prominent at case 12 for SF! and SPI. The onset of the transient could be detected about 30 seconds in advance by monitoring PSD compared to monitoring the variance, since the variance increase became significant at case 13 as shown in fig. 3.

Correlation between these trends were also studied. Among the signature pairs which resulted to high values of correlation, only the most significant ones are listed in Table I.

ABLE I. Correlations between the signatures

Signal Signature Pair Correlation

G

G

SP

SP

(FPI, FP2)

(PK2, PK3)

(FPI, FP2)

(PK2, PK3)

0.70

0.82

0.89

0.64

Here, FPi and PKi stand for the frequency and smplitude of peak at around i times of FPI.

No significant correlation was observed for signatures of flow signal. The results in Table 1, particularly the high correlation between (FP|, FP2), indicates that the high frequency compo- nents in the transient PSDs can be regarded as harmonics of the characteristic fluctuation at 0.8-0.9 Hz. Further studies will be needed for better interpretation of the harmonics in terms of non- linearities (e.g. saturation or signal amplitude truncation) dominating in the process.

Example 2

The second example, analysis of the vibration test data, was carried out for examining the applicability of the method to signals with more severe non-stationarlty than the signals in the example I. A total of 2560 samples obtained at a rate of 128 samples/second was analysed after dividing it to 20 segments so that the extent of non-stationarity of the data shown in Fig. 2 could be reduced substantially.

The variance of the signal, showed a significant change during the analysed time span as shown in Fig. 9, reflecting the intermittent occurrence of the impact. Nevertheless, the PSD patterns re- mained roughly the same as illustrated in Fig. I0, where the PSDs corresponding to before, during and after the impacting are compared.

A closer look at the PSDs, however, indicates that some of the peaks are related to the impacting phenomenon. The resonance frequency and the amplitude of the peak detected around 18 Hz are de- picted in Fig. II. The increase in the amplitude of this peak around case 3-6 corresponds well to the occurrence of impacting. It should be noted that the amplitude plots in this figure are given


after normalization by the variance of the signal. In other words, the result implies that the effect of impacting manifests itself more prominently in the amplitude of this peak than in that of the variance.

The observation suggests the possibility of detecting a smaller impact by monitoring the frequency component even when the overall energy of the signal fluctuation remains almost the same. Although further studies are needed to reach a definite conclusion, the example also demonstrates the usefulness of the present approach.

Example 3

The method was also applied to a record of a pressure signal which could be regarded as stationary unless analysed carefully with a special attention to time-evolution of its statistical characteristics. Several resonances in the PSD of the pressure signal have been identified to be caused by so-called standing wave phenomenon. Although the temperature dependence of these resonances has been studied to a certain extent, the data were treated in this study to demonstrate practical advantages of the present method.

Typical PSDs are shown in Fig. 12. Each of them represents 8 seconds of data with 2400 seconds interval between the cases. Though several prominent peaks are noticeable, it is by no means an easy task to find out a systematic tendency just by a visual inspection.

One outcome of application of the present method is shown in Fig. 13, where time-variation of the resonance frequency of the peak at the frequency region of 6.5 through 9.5 Hz is plotted. The resonance frequency tended to increase significantly along with the passage of time, i.e. with the decrease of temperature and pressure.

It should be stressed here that the variance of the signal showed no significant change during this period, as can be seen in the same figure. As far as one is relying on the variance as the only indicator of non-stationarity, this type of phenomena can easily be overlooked, possibly leading to a misinterpretation of the physical process. Trend analysis of various noise signatures, such as the resonance tracking, seems to be an important and indispensable procedure for reliable information extraction from reactor noise.

CONCLUDING REMARKS

Through the results of analysing signals obtained by Borssele reactor on-line monitoring system, it can be concluded that the present method is highly useful in quantifying time-evolution of statistical properties of the signals. The signature tracking of the segmented data by using the LSARmodeling is usable as a technique for detecting occurrence of intermittend anomalies. Moreover, a considerable improvement in time resolution of incipient failure detection is ex- pectable by using the present method.

It would be also reasonable to use the method for identifying characteristic signatures specifi- cally representing certain type of failures, as it allows us to estimate a larger number of signatures than the conventional methods from a given data set. In view of this, development of an efficient procedure for choosing an usable combination of signatures out of a number of candi- dates would be an issue of practical importance for future study.

ACKNOWLEDGEMENT

The authors would like to express their deep thanks to Mr. A.Th.J.M. Overtoom and Mr. W.H.J. Quaadvliet for their assistance in performing the computations. The authors gratefully acknow- ledge the PZEM/KCB for permission of publication of these results. The second author extends his gratitude to Professors K. Sugiyama and K. Kotajima for providing him this opportunity of joint research.

REFERENCES

Box, J.E.P. and G.M. Jenkins (1970). Time Series Analysis, forcasting and control, Holden Day. Golub, G. (1965). Numerisch Math. 7, 206-216. Kitagawa, G. and H. Akaike (1978). Ann. Inst. Statis. Math. 30B, 351-363. Kitamura, M, T. Washio, K. Kotajima and K. Sugiyama (1984). Paper presented at SMORN-4, Dijon. T~rkcan, E. (1982). Progress in Nucl. Energy 9, 437-452.

858 E. TURKCAN and M. KITAMURA

SP2 "

SP1 ...... =llJJJ]~.,~

. . . . . . ' . . : :-", ,; .:"::-I ........... , ~ I ~ . ~ ~

J . . . . ' ,;o ,~o ~,~o' 0 50 100 TIME IN SECONDS

Fig.] . Time trace of the secondary system signals during the transient;

Generaeor output ( G ), Steam Flow (SFI,SF2) and Steam pressure(SP], SP2).

)-

i

TIME IN SECONDS

Fig.2 . Time trace of the radial vibration

sensor output mounted on the primary

coolant pump.

E-3

E-E

E-E <~

E-7

E-8

I I

| • •

e SF1 • 6 • S P 1

I I I 5 10 15

CASE No. l -

Fig. 3. Variances of G , SF] and SP! .

20


GENERATOR

1.0"6 l j -6 u r ? 1.o-7 k 111" 7 .LB-O~r

I 0 - 9 ~ | . i , , , . 1 ! l i , , , n l , , , , . d I n ,

FREQUENCY (HZ)

"Fig.4 . Time dependent variation of PSD function of Generator output before,

during and after the transient.

SF1

10"-6 "UI-t~ 10.7 1.11.5 111-4 l i t7

llB--t

IE-81 l i t 71a'6 11 , , , , , , , , , , , , , , , , , , , , , , . , , . . , , . , . .

~e-2 ze-z ~.ee ~eJ. xe-2 ~-x I I# ze z ~-:z ze-.t zsa z.lx

FREQUENCY (HZ)

Fig.5 . Time dependent variation of PSD function of Steam Flow before,


SP1 -IJ-'/~" CASE NO. "7 ,1.0-3f C~,qE N0. 15

111-7 l l r 0

• l . i l Im l -~ z , l l i , i l I I , l l lu l I I imn l ,,,-- ,,,-~L .z~ ~ ,,,,-2 ,,,-1 zee

F~EQUENCY (HZ)

~-~

~-~ I l,ml I I "''~ I i.,.i

Fig.6 . Time dependent variation of PSD function of Steam Pressure before,



to.

/.st ' .6 I ' -

E.z.

SF1

E_5 !

~ E-~

E.-8

E-9

.Irr ~ .Vr • U" . *

#

I i

,i.

.x-

I I 10 15

CASE No. ,,

Fig. 7 .Time variation of FP|(resonance frequency

at 0.8Hz) and PK](amplitude of the peak)

observed for SF].

E O I . *' •

Z E.1 * "I ~ r

[-3

E-~ I 0 5

I i

[YD02. V003]

I I '15

C A S E N o . t

20

~ig.9 , Time dependent variance of the vibra-

tion sensor output.

Fig. ] 0 . PSD function of the vibration

sensor output obtained before

(top),during (middl~ and after

(bottom) the impacting.

.6

E -2

E-3

E-5

I i

4~

t ,

t .K- I

10 15 CASE No.

Fig. 8.Time variation of FPi and PKI

o b s e r v e d f o r S P 1 .

~o-2f c,~ NO. 2

~ 18"

~ 18 .0'

I 18" ~ 10 -7 '1 " , , i , H . l , * l , , ' , , , l

I B B ~ " C ~ E HO. 5

xe-zlr c,~ No. 9

~ ' 2 ~ i 111-3 111-4 IB-S

. L B - 7 ~ i I I I . m l I I i i , ' . . I

FREQUENCY [ Hz] a;-

j

20

Time-varying characteristics of signals trom Borssele reactor 861

Fi~. ]].Time-variation of resonance fre -

quency (top) and amplitude(bottom)

of the peak around 18 Hz.

~ E-I *

E - 2 p

1 0 -

I 5

I , I 10 15

CASE No. m

YD02.VO03

10-3 CA E NO. 5 IB -2~ C~E NO. 6

~ lB... 4 IB ''4 lj..~ ~ llm - 5 1.11-5 10-.6 l.O -5 1 ~ l i - 6 F ~ , , , i , , , , , , . , I , ,,,,,d IB"~t - , ,,,,,d , , , , , ,d ' , ,,,,,~

m -I m a i~ ~=z 1g-1 1~ J.,,J- J.~ m -I I@ I~ m2

FREQ.UENCY [Hz] In,

Fig, ]2. Typical PSDs of the primary pressure signal estimated during the

cool-down operation.

~ E - 3

E - !

I I I

4t 4~

4b q~

I i

! I I I I 2 ~ 6 8 10

CASE No.

= Fig. J3. Time variation of the resonance

frequency of the peak around 6,5

- 9 Hz(top) and the variance of

the signal(bottom).

Documents

Analysis of time-varying characteristics of signals from borssele reactor