doolittlecarey_1977

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AN ASSESSMENT OF THE ERFORMANCE OF A CONCEPTUAL ACOUSTIC SURVEILLANCE SYSTEMFOR ANOMALOUS EVEN TS I N LMFBRS

R. D. Doolittle, and W. M . Carey

Prepared fo rIEEE Nuclear Science Symposium

San F ra nc isc o, CAOctober 1 9 - 2 1 , 1977N O T I C E -

This report was fjeptred as an account of worksponsored by the U nited States Government. Neither theUnited States nor the United Stales Department ofEnergy, nor any of their employees, nor any of theircontractors, subcontractors, or theit employees, makesany w arranty, express or implieO, or assumes any leaalliability or responsibility for the accuracy, completenessor usefulness of any information, apparatus, ptoduct orprocess disclosed, or repitsenls that its use would notinfringe privately owned rights.

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QlSTRIQUTiQN Of- iHiS DO CUME NT IS UNUMHE0

ARGONNE NATIONAL LABORATORY, ARGONNE, ILLINOIoperated under contract W-31-109-Eng-38 for theU. S. ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION


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The facilities of Argonne National Laboratory are owned by the United States Govern-ment. Under the terms of a contract (W-31- 109-Eng-38)between the U. S. Energy Research andDevelopment Administration, Argonne Universities Association and The University of Chicago,the University employs tfie staff and operates the Laboratory in accordance with policies andprograms formulated, approved and reviewed by the Association.

MEMBERS OF ARGONNE UNIVERSITIES ASSOCIATIONThe Univers ity of ArizonaCarnegie -Mel lon Univers i tyCase Wes tern Reserve Univers i tyThe Univers ity of Chicago. Univers ity of CincinnatiIllinois Institute of TechnologyUnivers i ty of I l l inoisIndiana UniversityIowa State Univers ityThe Univers ity of Iowa

Kansas State Univers ityThe Univers i ty of KansasLoyola Univers ityMarquette Univers ityMichigan State Univers ityThe Univers ity ofMichiganUnivers i ty of MinnesotaUnivers i ty of M i s s o u r iNorthwes tern Univers i tyUnivers i ty of Notre Dame

The Ohio State UniversityOhio Univers ityThe Pennsylvania State Univers ityPurdue Univers itySaint Louis Univers itySouthern I l l inois Univers ityT h e U n i v e r s i t y of T e x a s at A u s t i nWashington UniversityWayne State UniversityThe University of Wisconsin

NOTICE-This report was prepared as an account of work sponsoredby the United States Government. Neither the United Statesnor the United States'Energy Research and Development Ad-ministration, nor any of their employees, nor any of theircontractors, subcontractors, or their employees, makes anywarranty, express or implied, or assumes any legal liabil-ityor responsibility for the accuracy, completeness or use-fulness of any information, apparatus, product or processdisclosed, or represents that its use would not infringeprivately-owned rights. Mention of commercial products,their manufacturers, or their suppliers in this publicationdoes not imply or connote approval or disapproval of theproduct by Argonne National Laboratory or the U. S. EnergyResearch and Development Administration.


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AN ASSESSMENT OP THE PERFORMANCE OF A CONCEPTUAL ACOUSTIC SURVEILLANCE SYSTEMFOR ANOMALOUS EVENTS IN LMFBRS*

R. D. Doolittle , Woodmont Associates Ltd, Bethesda, Md .an d

K. M. Carey +, Scientific Consultant, Essex, Ct .

A Metho d is developed for calculating t he detect-bility o f anomalous acoustic events. Th e example usedis t h e sodium vspor bubble collapse In th o subcooledregions o f a Liquid Metal Past Breeder Reactor (LMPBK).This method provides a range o f estimates f o r detectionand false alarm.probabilities in acoustic surveillancesystems f o r sodium boiling a n d voiding detection, a swell a s a n y other impulsive events such a s loose-partsmonitoring.The signal excess a t t h e receiver array from a nimpulsive source i s computed b y a n extension o f methodsintroduced b y W . Carey. Assuming a n exponential pul seform f o r t h e signal ( o r i t s envelope) t h e equivalentsource level i s determined from t h e energy flux spec-tral density f o r inclusion i n t h e sonar equation. Th esignal excess (SE) s then given b y t h e source level(SL) minu s t h e noise level (NL) minus t h e transmissionloss (TL) minus t h e detection threshold (DT) plus t h e

receiving array gain (AG).Numerical values a r e drawn from recent experimentsat ANL and EBR-II. Signa l exces s valu es a r e computedto b e i n t h e range of 0 to 20 dB, The probability o ffalse alarm associated with high probability o f detec-tion a n d computed signal excess i s excessive f o rreactor instrumentati on. This false alarm rate mustbe reduced b y post processing, i.e., aking advantageof t h e Impulse occurrence statistics a n d b y crosscorrelation with neutronic noise.

IntroductionPrevious wor k 1 introduced t h e concept o f h esonar equation t o t h e field o f sodium boiling detectionand presented a method f o r calculating t h e detectabil-

ity o f sodium vapor bubble collapse b y passive acous-tic means. B y treating t h e bubble a s a single-fre-quency monochromatic source o f sound i n a uniformlydistributed field o f random noise sources, a relation-ship w a s shown between t h e output o f a square-lawdetector a n d t h e power spectral density o f t h e inputsignal a n d noise which determines signal detectability.The detection process w a s then shown t o b e expres-sible a s a n algebraic equation known a s t h e sonarequation i n which each term represents some aspect o fthe signal o r noise generation, transmission o r recep-tion. Th e source o f sound w a s represented b y h eestimated radiated intensity (power p e r unit area a tan arbitrary distance o f 1 meter) known a s t h e sourcelevel.Two points should b e emphasized concerning t h ecomputation o f signal detectabili ty which relate t othe present study. Th e first is that a single f r e -quency steady source o f sound w a s assumed 1 while t h ebubble collapse results i n a n impulsive sound tran-sient. This does n o t negate t h e value o f t h e previouswork since in principle t h e transient c a n b e synthe-sized b y a series o f delta function impulses withcontinuous powe r spectra. However, b y modifying t h etreatment o f R. Urick 2, t h e source energy m a y b e usedto compute t h e "impulsive" source level.

* Work performed under t h e auspices of the U. S. EnergyResearch an d Development Administration* Consultants t o Argonne National Laboratory

The second point h a s t o d o with t h e transmissionloss term. Transmission loss results when t h e soundwavefront spreads with distance or t h e sound intensityis decreased by absorption o r scattering i n t h e sound-conducting medium. Further effects , such a s disper-sion, a r e present f o r t h e finite amplitude (shock)pulse which accompanies bubble collapse. Zero trans-mission loss w a s assumed i n t h e work o f reference 1.It should b e noted that a non-zero value o f transmis-sion loss experienced b y sound transmitted within aworking nuclear reactor i s n o t easy to estimate b u t sexpected t o b e small f o r t h e frequency ranges o finterest. Further work i s underway t o determine t h eactual transmission loss under these conditio ns.The Energy Form o f t h e Sonar Equation

According t o Urick 2 t h e active sonar equation interms o f energy is stated a s :Echo Energy (E) Noise Masking Energy, (NMB) (1)

where the NME:Noise Masking Energy (NME)(NI) x Echo Duration T) . Noise Intensity (2)He then shows that t h o energy form reduces t othe more familiar form o f t h e sonar equation if hosource level is defined a s :SL 1 0 log(E) - 1 0 log(T), ( 3)

where T i s t h e echo duration and I: s the energyflux density o f a plane pressure wave o f 1 dyne/cm 2at 1 meter, i.e., he energy flux/unit area p e rsecond o f signal- dura tion .When w e consider t h e detection b y passive"listening" o f a sodium vapor bubble collap se 1, in ninfinite s e a o f sodium, w e a r e faced with a sharptransient a s a signal in continuous background nois e.Urick h a s stated that f o r t h e passive sonar equation,the difference between t h e energy a n d intensity formis trivial since t he same time integral occ urs o nboth sides o f t h e energy equation. This is undoubtedlytrue f o r continuous sources o f sound b u t f o r transientsit i s n o t necessarily s o. W e will inquire furtherinto this case.

Energy, Intensity a nd Integration TimeIf w e have a signal S(t) a n d i t s Fourier trans-form H(f) , its energy SE is expressible a s h eintegral:SE =/|S(t) | 2d t ( 4)

which, by I'nrxevnrs theorem, IN:SE * j*|H(f)| 2df .In term s o f energy t he sonar equation isstated:

(S) /

Transient Signal Energy = Noise Masking Energy (6)(7)

Noise Masking Energy = Noise Intensity xSignal Duration.I f we h a v e a n o i s e n ( t ) w i t h its F o u r i e r t r a n s -f o r m G ( f ) , w;: h a v e for t o t a l n o i s e e n e r g y :


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NME / |G (f )I2d f / | n ( t ) | 2d t . (8) w h i c h b e c o m e s, b y t h e s a m e arguments as before, letting

' Ho w e v e r, n o t a l l o f t h e n o i s e e n e r g y m a s k s t h esignal if the signal bandwidth is finite. Only that{part of th e noise intensity that lies within the signal(intensity spectral band will mask the noise . If weknow the signal spectrum (and thus the signal wav eform )w e m a y f i l t e r t h e n o i s e t o t ha t b a n d w i d t h. W h i l e i t i s.strictly true that a signal and it s spectrum cannotb o t h b e o f f i n i t e e x t e n t, r es p e c t i v e l y i n t i m e a n d f r e -q u e n c y, i t i s a p p r o xi m a t e l y t r u e f o r m o s t s i g n a l s 3.Th e r e f o r e, w e w i l l a s s u m e t h a t 'Equ a t i o n (8) e x p r e s s e st h e n o i s e m a s k i n g e n e r g y NME w h e n w r i t t e n:

NME - 2/|G (f )| 2d f (9)w h e r e f0 is the effective maximum frequency o f the sig-n a l p o w e r s p e c t ra l d e n s i t y, i f n (t ) i s a n o i s e p r e s -s u r e s i g n a l, t h e n o i s e a c o u s t i c i n t e n s i t y i s g i v e n b yMorse 1*

Nr r+Tr2 f / n ( t ) u ( t } d t-T

(10)

whjtre u( t) is the local particle velo city in the wave.F o r a p l a n e w a v e:

thus, Equation (10) becomes:, + T

(11)

- TIf we use Parseval's theorem in its approximateform, i.e., for T sufficiently long:

2pcTs (18)The "intensity form" of the sonar equation holds forthe case as the receiver integrates for only as longas the signal lasts. It is true, for the sphericalsource in the infinite sea, that the "intensity form"of the equations m ay be used to compute the detectabil-ity of the sodium vapor bubble collapse. This is be-cause the signal energy E is a constant and theintensity I is thus:

(19)the r 2 factor in the divisor results in a spreadingloss term when expressed in decibel s. Thus, by detect-ing the signal power and integrating over signalduration the signal intensity at range is determined.The Effects of Boundaries

The effect of the presence o f boundaries (andinhomogeneities) is to extend the signal in time be-yond that of the signal duration at the source. Asmentioned before, the signal at the receiver is' expressed by a convolution of the signal waveform (forlinear si gnals ), S(t ) , and the impulse response of theStructure. A simple example is that of a free su rface.The impulse response of a semi-infinite medium witha free surface is composed of the initial impulse p lusa time-delayed negative image. The time delay isequal to the path length difference between the directand reflected paths from source to receiver divided bythe propagation velocity C. The geometry is shown inFigure 1.

Li mT + *+T

-T| G ( f ) | 2 d f * 2 j * | 6 ( f ) | 2 d f - N M E (13)

FREE SURFACE

RECEIVERSOU

t h e n w e h a v e t h e r e l a t i o n s h i p b e t w e e n t h e n o i s e a c o u s -t i c i n t e n s i ty a n d t h e n o i s e m a s k i n g e n e r g y, b y s u b s t i -tution into Equation (1 2), and letting T * TN, forc o n v e n i e n c e:NME2pcT (14)N

Ap p l y in g t h e s a m e a r g u m e n t s t o t h e s i g n a l, i n t e n s i t y,Sj, i s g i v e n b y:1S I = fF

+ T

/- Tw h e r e u (t ) i s t h e p a r t i c l e v e l o c i t y o f t h e s i g n a l w a v e.If the signal sou rce is small compared with the obser-v a t i o n r a n g e t h e w a v e m a y b e c o n s i d e r e d t o h e p l a n ef o r w h i c h:

C t ) ; ^as witK the noise. Thus:

(16)

Figure 1. Geometry for Half-Space with Free Surface.Ma t h e m a t i c a l l y, w e h a v e:

\ H t - - p - ( t - - f ) ] s(t) (20)where fi( t-a) is the Dirac delta function. The impulsein time is pictured in Figure 2.

f,/C

r,/C

SI (17)-T Figure 2. Impulse Response of Half-Spacewith Point Source.


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The signal "duration" a t t h e receiver i s n o w :(21)

From this simple example it is apparent that t h e s i g -nal duration T^ at the receiver depends upon t h e geom-etry o f t h e boundary o r boundaries, o r inhomogeneities.Urick 2 shows t h e influence o f a boundary i n t h e wave-form connected with t h e transmission and echo o f nexplosive source o f sound. This figure, taken fromWrick's Figure 1, is reproduced i n Figure 3.

Detectability o f t h e Pulse SignalIt should b e clear from t h e foregoing argumentsthat t h e sonar equations f o r possible detection o f apulse a r e t h e same expressed either in terms o f intensit y o r energy i f t h e integration times a r e t h e same o neither side o f t h e energy equality expression. Howeveby selective filtering, [a rudimentary matched f i l t e r )the noise energy c a n b e reduced.The previous section showed t h e expressions nece ssary t o solve f o r t h e bandwidth from t h e signal energyat t h e source. W e wish t o apply t h e method t o h edetection o f a sodium vapor bubble collapse such a s

might b e experienced i n t h e subcooled regions o f aworking liquid sodium cooled nuclear reactor (LMFBR).The first step i s t o determine t h e effective maximumfrequency o f t h e source signal power spectral density,f Q. Th e signal envelope t o b e detected is assumed tobe a n exponential pulse o f t h e form:p(t) = Pe - t / t i (22

where-1t\ = time to decay to Pe

This pulse is sketched in Figure 5.

Figure 3. Pulse Waveforms f o r Active Sonar,After Urick 2, Figure 1.The "near source" curve i s t h e pressure-time envelopeo f a shock wave at a sufficient distance from t h esource f o r t h e shock front t o develop. Th e manner inwhich t h e shock wave steepens i s illustrated in Cole 5and reproduced in Figure 4.

Figure 4. Wavefront Steepening into a Shockfront,After Col e 5, Figure 2.1.The velocity o f t h e finite amplitude wave dependsupon t h e amplitude so that point b_ atches u p withpoint a at which time t h e velocity o f t h e frontapproaches acoustic velocity. Th e signal a s received,in t h e absence o f boundaries, appears a s t h e time

inverse o f this waveform; thus, t h e model o f h eexponentially decaying impulse in explosive soundtransmission.We thus arrive at a distinction between t h esource signal duration, Tg, and the received signald r t i n T It is evident that T ^ T It is lduration, T R. It is evident that TR^Tg . It is alsoapparent that t h e noise integration time, T^, is equalt o T R .In orde r t o determine t h e proper value o f T R f o rsodium vapor bubble detection in IMFBRs, it is neces-sary t o determine t h e transmission characteristics(impulse resp onse, transmission loss, etc.) o f t h ereactor geometry, either by modeling or in full scaletests with controlled impulsive sources.

ACE Pe"1(0UJCCa.

\- \ .

1 ~?- f > >TIME

Figure 5. Exponential Pulse Waveform.It h a s a plane wave energy density given b y :

E = j y t)dt (23)where p c i s t h e characteristic acoustic impedance o fthe medium. If pressure is in dynes/cm 2, a n d p c i s ncgs units, E will b e expressed in ergs/cm 2.

The energy flux spectral density is found b y h emagnitude squared Pouricr transform o f p( t) ami isgiven s 6:

B 0( f ) 1+ ( 2 i r t 1f ) 2The corner frequency o f t h e spectrum occurs when t h e

Eo

(24)

ratio ( Eo f f o VEr t( o ) ) is equal to 0.5, from which f oTaking a value of tj from the pulse shown inPeppier 8 of tj 200 jisec, we have:fo - l /2 irti * 7.9 60 kHz.- (25)

Thus, we wi l l use a lowpass f i l t e r at 8 kHz. The


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