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<ul><li><p>Nuclear Engineering and Design 231 (2004) 99107</p><p>Algorithm automation for nuclear power plantLoose Parts Monitoring System</p><p>Young Woo Chang, Jae-Cheon Jung, Poong-Hyun SeongDepartment of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology,</p><p>373-1 Gusung-Dong Yuseong-Gu, Daejeon 305-701, Republic of KoreaReceived 8 November 2002; received in revised form 21 February 2003; accepted 21 February 2003</p><p>Abstract</p><p>Loose Parts Monitoring signals in the control room of the nuclear power plant come in through multiple channels and arepresented as graphs on the display devices. It involves a lengthy and complicated process to determine the size, mass, speed,and impact location of the loose part when the signals are collected and processed. In this work, a simple and efficient modelfor determining the impact location of the loose part using the Least-Sum-of-Square-Errors (LSSEs) method combined withiteration has been developed based on the phase distortion of the impact signal envelopes. The signal peak point shifts to theright on the time axis when the sensor is located farther away from the impact location. This method provides a good estimationof the impact location and can be used as an alternative to existing calculations based on other attributes of the impacting signal.To automate the backend portion of the LPMS algorithm, interpolation was used for compensating the impact attenuation effectand log-log regression was also employed to determine the impacting part size and impact velocity, and the result turned out tobe well in line with the manual calculations. The automated algorithm will improve the efficiency of the LPMS software. 2003 Published by Elsevier B.V.</p><p>1. Introduction</p><p>Loose Parts Monitoring System (LPMS) is a com-puterized monitoring system which provides the sig-nal displays and data to the operating and engineeringpersonnel of the nuclear power plant to assist themin making correct decisions about the loose parts thatcan cause serious damages to the structures of the re-actor vessel, coolant system, and the steam generator.Impact location is one of the major target variablesof concern by the algorithm developers of the LPMS.Other variables include contact time of the impactingloose part, mass, impact speed, size of the loose part,</p><p> Corresponding author. Tel.: +82-42-868-4338;fax: +82-42-861-1488.</p><p>E-mail address: ywchang@kopec.co.kr (Y.W. Chang).</p><p>etc. The typical computation is an involved processcombined with a lookup table and usually impact lo-cation is one of the important variables to be found.From recent research by Lee et al. (1997), it has beendiscovered that the peak point of the impact time datatends to shift to the right when the distance betweenthe impact location and the sensor location increased.Fig. 1 shows the results from test cases.</p><p>The purpose of this research is to review currentlyknown LPMS algorithms for determining the impactlocation of loose parts and their sizes in the steamgenerator of the nuclear power plant. Then a seriesof methods and algorithms are developed so that theLPMS computer can automatically produce the neededinformation on the loose parts.</p><p>In Section 2, the algorithms to be studied in the re-search are described. Section 3 presents a new model,</p><p>0029-5493/$ see front matter 2003 Published by Elsevier B.V.doi:10.1016/j.nucengdes.2003.02.001</p></li><li><p>100 Y.W. Chang et al. / Nuclear Engineering and Design 231 (2004) 99107</p><p>Nomenclature</p><p>KAERI Korea Atomic Energy ResearchInstitute</p><p>LPMS Loose Parts Monitoring SystemLSSE Least-Sum-of-Square-ErrorEPRI Electric Power Research InstituteIAEA International Atomic Energy Agency</p><p>which combines iteration and least-squares methodfor a new impact location algorithm. In Section 4, alog-log regression method is introduced for convert-ing the diameter-and-velocity graph into a curve-fitformula for algorithm automation. Also, impact atten-uation compensation based on the sensor distance isexplained.</p><p>2. Criteria for modeling</p><p>Currently known impact point location algorithms(Lee et al., 1997) have their own drawbacks. Ac-cording to Lee et al. (1997), the Wave Method usessignals from three different sensors and each signal</p><p>Distance 0 - 1m 3 m approx. 10 m approx.</p><p>WavePattern</p><p>0 2 0ms</p><p>o o o</p><p>Charactero Fast decrease followed by quick disappearance after around 20ms.</p><p>o o</p><p>Fast increase,Peak of variousFrequencies</p><p>Relatively slowincrease anda few ms to peak.</p><p>Very slowincrease.Peak is notclearly shown.</p><p>Relatively slowdecrease</p><p>Slow decrease.Decrease timetypically islonger than20ms.</p><p>Fig. 1. Impact signal trends based on the sensor-location distances.</p><p>has its own time delay between the fundamental wavemodes of Lamb waves such as quasi-longitudinalwave (So) and bending wave (Ao) according to Fujitaand Tanaka (1982). But it is hard to get an accuratemeasure of wave transition time. Also when usingcurrently known triangulation method based on arrivaltime distinction, three unknowns (sensor distancesfrom the impact point) are to be determined fromtwo equations (signal arrival time differences amongthe three according to Kim et al. (1989)). This doesnot render the solution right away and it takes somegeometric manipulation. In addition, a slight error indetermining the arrival time, for example, 1 ms error,could mean a discrepancy of several meters. Andwith an embedded error, the process of determiningthe signal arrival time can cause significant errors inthe calculated distances. The purpose of this workis to develop a new method to determine the impactpoint on a structure that has been transformed fromthe three-dimensional space to the two-dimensionalplane. It is not a very involved process to trans-form a three-dimensional structure and map it onto atwo-dimensional plane. Typically, when an impact oc-curs, signals from sensors at three different locationsare collected and utilized.</p></li><li><p>Y.W. Chang et al. / Nuclear Engineering and Design 231 (2004) 99107 101</p><p>As shown in Fig. 1, peak points of the signals tendto shift to the right on the time axis when the sen-sor location is farther away from the impact locationcompared with the other sensors. This gives a goodestimate of the sensor distance from the impact point.After a simple algorithm for locating the impact pointis derived, this location is used as a preliminary datain computing other variables, such as, impact mass,speed, or duration of impact, etc.</p><p>3. Impact point location calculation model</p><p>3.1. The model layout for impact point calculation</p><p>The first step of the LPMS algorithm is to developa method to determine the impact point on a structuretransformed from the three-dimensional space (typi-cally, the surface of a vessel or a pipe, in this workthe steam generator) to the two-dimensional plane.An approach reducing complicated computation intoa relatively simpler one is presented in this sec-tion. This method is the Least-Sum-of-Square-Error(LSSE) method combined with iteration.</p><p>To derive the approximate distances from Fig. 1-typedata, a fuzzy weighting method was adopted. Thewhole data of Fig. 4(A), shown later, was sectionedinto 50 intervals then the weighting factor was multi-plied by the distance factor. The interval on the righthand side of the time axis has a higher weightingfactor. This way, the whole graph of each channelcan provide useful approximate distance input. In the</p><p> (0,1) d1 = 2.2 S3 </p><p> d3 = 8 </p><p>(a,b) (10,0) </p><p>d2 = 2.9 </p><p>(0,-2)</p><p>Fig. 2. Impact location determination for the LSSE method.</p><p>test of Fig. 4(A), the farthest sensor was located atapproximately 5 m. And for the sample calculation ofthis and in the following sections, the farthest sensordistance was about 8 m.</p><p>In the LSSE method, the target is to calculate theimpact point from the distance data out of the signalshape. For this, the sum-of-square-errors between thecorrect distance and the calculated distance is mini-mized. Then as a result, the correct coordinate of theimpact location, (a, b) is derived as in Fig. 2.</p><p>In the following, a series of equations and logicexplains the algorithm for determining the coordinatesof impact location.</p><p>Let S1, S2, and S3 be the calculated distancesS2i = (xi a)2 + (yi b)2, for i = 1, 2, 3 (1)where (xi, yi) is the coordinate of sensor i.</p><p>Let d1, d2, and d3 be the correct distances. Actu-ally these are observed approximate distances derivedfrom the signal shapes calculated from the method in-troduced in Fig. 1.</p><p>The aim here is to minimize the sum-of-square-errors:</p><p>minimize 2 =</p><p>(Si di)2 (2)where di is the distance between the sensor and impactpoint.</p><p>In this section, the model starts with the known co-ordinate of the sensor. Each sensor-to-impact locationdistance is iteratively calculated and renders the in-terim correct coordinate of the impact point. Initialcoordinate of the impact location is the average (X,</p></li><li><p>102 Y.W. Chang et al. / Nuclear Engineering and Design 231 (2004) 99107</p><p>( a,b)</p><p>S2 (X2C, Y2C) </p><p>d2 (given) </p><p>( x2, y2) </p><p>Fig. 3. Impact location determination from sensor 2. Note: (X2C ,Y2C) is calculated impact point. (x2, y2) is sensor 2 location. S2 iscalculated distance. d2 is known distance from the signal shape.(a, b) are correct point adjusted at each iteration.</p><p>Y) coordinate of three sensors. But in each iteration,as is explained in Section 3.2, since there are threesensors, three different correct impact points are pro-duced. Then, the averages of the three distinct correctpoints are taken as the final impact point in each iter-ation step.</p><p>The errors are newly defined as the discrep-ancies between correct and calculated points. InFig. 3, only the place near sensor 2 is featured. Butthe same algorithm may be applied to sensors 1and 3.</p><p>If d2 < S2, then from a simple geometric relation-ships,X2C x2a x2 =</p><p>d2S2</p><p>= Y2C y2b y2 (3)</p><p>Then, initially, (a, b) is defined from the three sensorlocations:</p><p>aini =</p><p>(xi)</p><p>3(4)</p><p>aini =</p><p>(yi)</p><p>3(5)</p><p>3.2. Algorithm for calculation of theadjusted sensor location using iteration andLeast-Sum-of-Square-Error (LSSE) method</p><p>The adjusted point (a, b) can be calculated usingthe LSSE principle. The sum-of-square-error of thedistances between the adjusted sensor location (a, b)and the calculated impact point should be minimized.The partial differentiation by a and b results in</p><p>Eqs. (6) and (7).</p><p>a</p><p>{(XiC a)2 + (YiC b)2} = 0 (6)</p><p>b</p><p>{(XiC a)2 + (YiC b)2} = 0 (7)</p><p>After rearranging Eqs. (6) and (7), the adjusted pointcan be obtained as,</p><p>a =</p><p>(XiC)</p><p>3(8)</p><p>b =</p><p>(YiC)</p><p>3(9)</p><p>Using Eq. (3), the impact point XiC and YiC can berewritten as Eqs. (10) and (11).</p><p>XiC = (a xi) diSi+ xi, for i = 1, 2, 3 (10)</p><p>YiC = (a yi) diSi+ yi, for i = 1, 2, 3 (11)</p><p>Then, the distance between the impact point locationand the sensor locations can be recalculated usingEq. (1).</p><p>To obtain point (a, b), Si is recalculated and thealgorithm goes back to Eq. (8) then repeats until a andb converge.</p><p>3.3. Iteration results by LSSE method</p><p>The algorithm is programmed and tested using theparameters in Table 1.</p><p>In the above example computation, expected resultis approximately (a, b)= (2, 0) and the LSSE methodshows a good result, and the convergence is reasonablyfast. Fig. 4(A) shows sample signals from the test onthe Ulchin 4 nuclear power plant steam generator, andFig. 4(B) shows approximate locations of the impactsensors on the structures of the Ulchin Unit 4 nuclear</p><p>Table 1Computation results by LSSE</p><p>Type in d1, d2, d3d 2.2000000 2.8000000 8.0000000Type in option (1 = asis, 2 = wt, 3 = w2, 4 = stop)iopt = 1iter = 7 a = 1.9816700 b = 6.714041E002iter = 8 a = 1.9805710 b = 5.167026E002</p></li><li><p>Y.W. Chang et al. / Nuclear Engineering and Design 231 (2004) 99107 103</p><p>power plant. A data smoothing method similar to thatof Bevington (1969) was adopted. Table 2 shows thecomputation results from the tested data samples withthe two algorithms showing similar results.</p><p>Although the two methods show close results, LSSEmethod is more efficient since it does not requiregeometric measuring (which is typical of triangula-tion method), and the Wave Mode method involveshard-to-automate signal noises and distortions thatwere added to the signal while propagating through</p><p>Fig. 4. (A) Impact Test Signals from the Ulchin 4 nuclear power plant (four channels). (The test data were produced on the surface of theUlchin Unit 4 steam generator with a hammer during the pre-operational test period.) (B) Typical locations of loose part sensors (locatedon the surface of steam generator, reactor vessel, reactor coolant pump).</p><p>the medium and often requires manual measuring thewave mode change.</p><p>4. Algorithm automation using interpolation andlog-log regression</p><p>The EPRI Note on LPMS improvements (EPRI,1988) and IAEA training course material (IAEA,1993) have many useful tables and some technical</p></li><li><p>104 Y.W. Chang et al. / Nuclear Engineering and Design 231 (2004) 99107</p><p>Fig. 4. (Continued ).</p><p>information that are used in this work. The tables cor-relating the parameters, especially center frequency(explained later), impact (G: multiple of gravitationalacceleration), and impact velocity, etc. together are</p><p>Table 2Distance calculation</p><p>Signal detection channel V-108 V-107 V-106 V-105Time of signal arrival (ms) 14.82 15.64 14.91 17.7Arrival time difference</p><p>(ms)0.86 0.09 2.88</p><p>Relative impact location(m)</p><p>4.26 0.47 2.1</p><p>So wave arrival timestamp (ms)</p><p>14.82 15.68 14.91 270</p><p>Ao wave arrival timestamp (ms)</p><p>15.00 219 593</p><p>So, Ao time stampdifference (ms)</p><p>0.18 0.71 0.28</p><p>Distance from impactlocation (m)</p><p>1.27 5.03 1.99 a</p><p>Iteration-LSQ methodlocation (m)</p><p>1.3 5.0 2.0 b</p><p>a Computation result from the Wave Mode method (Lee et al.,1999).</p><p>b Result from the LSSE method.</p><p>used in the algorithm automation. After a numberof trial and error sessions with different curve-fittingformulas, with an exponential formula as in (12), alog-log regression was performed on the data fromthe four parameter graph shown in Fig. 5 from IAEA(1993).zi = cxri yti (12)</p><p>where c, r, t are constants to be estimated by thelog-log regression; zi is diameter of the impacting part(in.); also in the second set of regression computation,impact velocity (ft/s); xi is governing frequency of thesignal (Hz), which is one distinct frequency of highestenergy or the average of a few distinct frequencies; yiis impact (multiple of acceleration) (G)</p><p>Eq. (12) is valid when the distance between the im-pact point and the sensor is 3 ft. Therefore, the truedistance has to be considered and the adjusted impactbased on attenuation formula is explained in the nextparagraph. Table 3 shows the results of the log-log re-gression on the sample data set from the graph. Twosets of c, r, and t are estimated for loose part diam-eter and impact velocity, respectively. For each case,</p></li><li><p>Y.W. Chang et al. / Nuclear Engineering and Design 231 (2004) 99107 105</p><p>Fig. 5. Center frequencyacceleration (G) graph at 3 ft.</p><p>Fig. 6. Impact attenuation for 2 kHz.</p></li><li><p>106 Y.W. Chang et al. / Nuclear Engineering and Design 231 (2004) 99107</p><p>Table 3The result of log-log re...</p></li></ul>

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