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Nuclear Engineering and Design 240 (2010) 2500–2511

Contents lists available at ScienceDirect

Nuclear Engineering and Design

journa l homepage: www.e lsev ier .com/ locate /nucengdes

eismic response prediction for cabinets of nuclear power plants by using impactammer test

i Young Kooa, Sung Gook Chob, Jintao Cuic, Dookie Kimc,∗

Department of Civil and Structural Engineering, University of Sheffield, Sheffield, UKJACE KOREA, Gyeonggi-do, KoreaDepartment of Civil Engineering, Kunsan National University, Jeonbuk, Korea

r t i c l e i n f o

rticle history:eceived 5 August 2009eceived in revised form 28 April 2010ccepted 4 May 2010

a b s t r a c t

An effective method to predict the seismic response of electrical cabinets of nuclear power plants isdeveloped. This method consists of three steps: (1) identification of the earthquake-equivalent forcebased on the idealized lumped-mass system of the cabinet, (2) identification of the state-space equation(SSE) model of the system using input–output measurements from impact hammer tests, and (3) seismicresponse prediction by calculating the output of the identified SSE model under the identified earthquake-equivalent force. A three-dimensional plate model of cabinet structures is presented for the numericalverification of the proposed method. Experimental validation of the proposed method is carried out on athree-story frame which represents the structure of a cabinet. The SSE model of the frame is accuratelyidentified by impact hammer tests with high fitness values over 85% of the actual frame characteristics.

Shaking table tests are performed using El Centro, Kobe, and Northridge earthquakes as input motionsand the acceleration responses are measured. The responses of the model under the three earthquakes arepredicted and then compared with the measured responses. The predicted and measured responses agreewell with each other with fitness values of 65–75%. The proposed method is more advantageous overother methods that are based on finite element (FE) model updating since it is free from FE modelingerrors. It will be especially effective for cabinet structures in nuclear power plants where conducting

ot be

shaking table tests may n

. Introduction

In a typical way, safety-related equipment of nuclear powerlants are seismically qualified by shake table tests. The entiressembly of the equipment which includes the vertical sectionf electrical cabinet with all the devices or components mountednside may be tested on a large shaking table. Alternatively, dummy

asses may be mounted at indicated locations in the tested equip-ent where the corresponding devices will be installed. Then,

cceleration responses to the table input motions are recordedt these locations and later used for seismic qualification of thendividual devices such as relays, switches, and contactors. Theseualification tests are usually performed in the testing laboratoriesontracted by equipment vendors.

Some types of equipment cannot be qualified only by analysis oresting due to its size or complexity. Furthermore, it may be imprac-ical to test large equipment at full levels due to limitations in theapacity of test facilities. In such cases, modal testing and analy-

∗ Corresponding author.E-mail address: kim2kie@kunsan.ac.kr (D. Kim).

029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2010.05.008

feasible. Limitations of the proposed method are also discussed.© 2010 Elsevier B.V. All rights reserved.

sis can be used as an aid to the seismic qualification of large andcomplex systems. Modal testing is a useful method to determineresonant frequencies, mode shapes, and damping values and maybe performed in a laboratory or in the field (i.e., in situ test). Theanalysis and modal testing methods may be combined to establishinput response requirements at the mounting location of a device.The qualification of the device is performed by testing it to a levelequal to or greater than the established response at the mountinglocation. The earthquake input for the device is defined in termsof an in-cabinet response spectrum (ICRS) which can be calculatedfrom the response at the mounting location of the cabinet. The ICRSis used as the input motion in the seismic qualification of electricalinstruments mounted inside the cabinet.

Vibration tests of equipment in the nuclear industry are per-formed for seismic qualification, modal properties measurements,and FE model validation and verification. The vibration tests ofthe electrical cabinets can be normally performed by shaking table

tests. However, the shaking table test cannot be used for the cabi-nets that have already been installed in operating plants since thecabinets are not permitted to be removed from the plants to bemounted on the shaking table. In situ tests may be performed onan electrical cabinet in the field to obtain its modal properties from

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K.Y. Koo et al. / Nuclear Engineer

hich the ICRS may be calculated. This is a cost-effective alterna-ive compared to de-energizing the equipment, disconnecting theables, and moving the equipment to a laboratory for a full-levelhaking table test.

Djordjevic (1992) suggested the amplification factor based on initu modal testing of cabinets and control panels. It is used to scalehe floor response spectra at the base to the amplified responsepectra at the location of the mounted device on the cabinet. U.S.lectric Power Research Institute (EPRI, 1990) developed genericeismic amplification factors for electrical cabinets, bench boards,nd panels that are valid for any location in the cabinets. However,he generic amplification factors are typically very conservative andend to give unrealistic spectra. Simple methods to generate theCRS are needed to reduce the conservatism.

The seismic responses of electrical cabinets can be estimatedfter their dynamic characteristics are identified. The dynamicroperties of cabinets are generally calculated from FE analy-is. In some cases, these dynamic properties are estimated basedn the experimental data obtained from either shaking tableest or in situ modal test. The calculated dynamic properties ofhe cabinets are then used to generate the earthquake input forafety-related instruments. Several researchers have studied theynamic responses of cabinets either analytically or experimen-ally (Stafford, 1975; Llambias et al., 1989; Lee and Abou-Jaoude,992; Katona et al., 1995). Most of the previous studies on theeneration of ICRS focus on evaluating the maximum in-cabinetmplifications and do not attempt to identify significant featuresf the cabinet dynamic behavior. Gupta et al. (1999) and Guptand Yang (2002) presented the Ritz vector approaches to evaluatehe ICRS based on the observations from detailed FE analyses of 16ypical cabinets. These formulations use Rayleigh–Ritz method toalculate the dynamic properties of the significant cabinets, whichre then used for evaluating their ICRS. More recently, Rustogi andupta (2004) verified the Ritz vector approach by using the modalata obtained from shaking table and in situ tests for two differ-nt cabinets. The Ritz vector approach is based on the assumptionhat a single significant cabinet mode is sufficient to calculate theccurate ICRS. More modes should be considered to calculate cor-ectly the dynamic responses of complex structures governed byulti-modal responses.There are mainly two types of evaluation methods to assess the

eismic capacity of electrical equipment: (1) based on experienceata, and (2) based on FE model updating. In the former, the exper-

mental dynamic properties of cabinets are used to evaluate thetructural performances for safety-related instruments subjectedo earthquakes. However, the accuracy of the results rely on thexperience data as they are extrapolated from the experience data.n the second method, the baseline models are to be built based onhe experimental dynamic properties. Even after model updating,here will still be some modeling error. The impact hammer testsata are then expected to be used to predict the seismic responsesy using only the experimental dynamic data and not using thexperience data and FE model.

The main objective of this study is to develop a seismic responserediction algorithm for electrical equipment without using FEnalysis. This paper proposes an algorithm to build the relation-hip between the impact forces and the measured accelerationesponses of the cabinet structures by estimating the state-spaceodel structures. Then the estimated state-space model is uti-

ized to predict the seismic responses to the equivalent earthquakeorces. In this study, a three-dimensional plate model of cabinet

tructures was presented for the numerical verification (Koo et al.,008) and an experimental validation study was carried out onhe seismic response prediction method. For the purpose of thistudy, a small three-story building frame was fabricated by weld-ng steel plates. This paper presents the estimation results of the

d Design 240 (2010) 2500–2511 2501

model structure tested by a shaking table. The paper is organizedas follows: (1) theory of the proposed seismic response predictionfollowed by the theory of stochastic subspace identifications, (2)experimental study of the shear building model structure subjectedto El Centro, Kobe, and Northridge earthquakes on a shaking table,and (3) conclusion with comments on the limitations and furtherresearch directions.

2. Seismic response prediction

The governing equation for the dynamic behavior of a cabinetstructure under a seismic motion ug is given as

Mur + Cur + Kur = −M{1}ug (1)

where M, C, K are the mass, damping and stiffness matrices of thecabinet structure. ur denotes the relative displacement vector tothe base motion ug and 1 is the column vector filled with ones.As shown in Eq. (1)ur is the system response when the load fe =−M

{1}

ug which is so-called the earthquake-equivalent force isapplied to the structure.

Based on input/output measurements from impact hammertests, the input/output relationship of the structure can be iden-tified in the form of a discrete-time state-space equation (SSE) asfollows:

x(k + 1) = Ax(k) + Bu(k) + Ke(k)y(k) = Cx(k) + Du(k) + e(k)

(2)

where x(k), y(k), u(k) and e(k) are the input force, the responseacceleration, measurement noise and state column vector at timestep k (k = 1, 2, · · · , N; N is the number of time steps), respectively.A, B, C, D, and K are the system matrices. Two types of algorithms areavailable for identification of the discrete-time SSE: (1) predictionerror methods (PEM) which are iterative and (2) stochastic sub-space identifications (SSI) which are non-iterative. In this study, theN4SID (numerical algorithms for subspace state space system iden-tification), a variant of SSI was used which is readily available in theMATLAB system identification toolbox. N4SID has advantages overthe PEM in terms of computation time and convergence. When thediscrete-time SSE is identified from input/output measurements ofthe cabinet structure by impact hammer tests, dynamic responsesunder an arbitrary loading can be obtained by calculating the outputof the identified SSE excited by the arbitrary loading.

Seismic response prediction is carried out straight-forwardly byusing only the earthquake-equivalent force fe as an input to theidentified SSE. The procedure is summarized in Table 1.

3. Stochastic subspace identification

N4SID as a variant of SSI is a better approach than the classicalsystem identification methods concerned with computing polyno-mial models, which are known to typically give rise to numericallyill-conditioned mathematical problems, especially for Multi-InputMulti-Output systems.

The N4SID algorithm was proposed by van Overschee and deMoor (1994, 1997) and is more closely related to linear systemstheory in the engineering literatures. N4SID algorithms require avery simple parametrization on the order of the system while theclassical methods often need various “a priori parametrization” ofthe system. Another major advantage is that N4SID is non-iterativewithout the need of nonlinear optimizations which often causeproblems in convergence, local minima of the objective criterion

and sensitivity to initial estimates. For classical identification, anextra parameterization of the initial state is needed when estimat-ing the state-space system from data measures on a plant with annon-zero initial condition. For N4SID algorithms there is no differ-ence between zero and non-zero initial states.

2502 K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511

Table 1Procedure of the seismic response prediction method of cabinet structures

Step Procedure/description

1 • Idealization of the cabinet structure to a lumped-mass system

• Identification of the earthquake-equivalent load fe = −M{

1}

ug

2 • Identification of the state-space equation by input/output measurements from Impact hammer test

3 • Seismic response prediction by calculating output of the state-space equation when excited by the earthquake-equivalent load

4

ii

. Numerical verification

For the numerical verification, a three-dimensional plate models built as shown in Fig. 1, which is a representative model of cab-net structure. The impact forces were applied at the four points

Fig. 1. Three-dimensional plate model.

from node 2 to node 5 continuously in time, and the accelera-tion responses were also collected at these points. So the impactforces and the acceleration responses in time domain were used asinput–output data to build the state-space model. Fig. 2 shows thenormalized impact forces and the acceleration responses from thenumerical simulation test.

By using a set of the input/output measurements, a state-space equation model was identified by using N4SID. The orderof the state-space equation was selected as 6 by inspecting thesingular values (van Overschee and de Moor, 1994) as shown inFig. 3.

After building the state-space model, the equivalent earthquakeforce fe was calculated by feeding the measured base motion ug

into the SSE model as an input to get earthquake responses. In thenumerical verification, El Centro earthquake (1940) was utilized toverify the accuracy and capability of the proposed algorithm. Thepredicted seismic responses are then compared with the analy-sis results obtained by using MIDAS as shwon in Fig. 4. One cannote that they agree very well with each other for all the fourpoints.

5. Experimental study

5.1. System description

A three-storey framed building structure as a model as shown inFig. 5(a) was used to validate the proposed seismic response pre-

diction method. The structure was composed of three segmentsconnected by bolts as shown in Fig. 5(b). Four accelerometers (PCB393B12) were installed on the three floors of the structure and onthe top of the shaking table. A small-sized shaking table (Quansershaking table II) was used for shaking table tests.

K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511 2503

Fig. 2. Impact forces and acceleration respon

Fig. 3. Model order selection for three-dimensional plate model.

ses for three-dimensional plate model.

5.2. Seismic response prediction by proposed method

5.2.1. Lumped-mass idealizationThe test structure can be idealized by a lumped-mass system as

shown in Fig. 6. Based on the lumped mass matrix M of the ideal-ization, the earthquake-equivalent force fe can be calculated andfeeded into the SSE model identified by the impact hammer testsas explained in the next section.

5.2.2. Identification of SSE model by impact hammer testsThe test structure was hammered at the three floor locations

as shown in Fig. 5(a) and the structural responses from the threeaccelerometers along with the impact hammer signal were mea-sured for about 1600 s with the sampling frequency Fs = 200 Hz asshown in Fig. 8. Three small sponge pads were attached to the struc-

ture to avoid excessive hammer signals. The tests were repeatedone more time to get validation data. The natural frequencies ofthe structure (the damping values in the bracket, and the modeshapes are shown in Fig. 7) were obtained by using frequencydomain decomposition method based on the impact hammer test

2504 K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511

time h

m

Fig. 4. Comparison of acceleration response

easurements as follows:

f1 = 3.564 Hz(� = 4.62%), f2 = 10.205 Hz(� = 2.56%),

f3 = 14.365 Hz(� = 1.45%)

Fig. 5. Test model structure on the shaking table. (a) Impact hammer

istories for three-dimensional plate model.

The phenomenon that the accelerations measured in a1 was greaterthan that in a2 accelerometer during 500–800 s time interval maybe possible. The structure might vibrate more based on the 2ndmode shape when we hammered at the top floor. This will causethe accelerations measured in a1 greater than that in a2. The similar

ing and accelerometer locations. (b) Dimensions of a segment.

K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511 2505

Fig. 6. Lumped-mass model idealization of the test structure.

p(

sT

B =⎢⎢⎢⎢

−0.0014 0.0001 0.00110.0005 −0.0014 0.00130.0003 −0.0012 0.0005

⎥⎥⎥⎥ , K =⎢⎢⎢⎢

0 0 00 0 00 0 0

⎥⎥⎥⎥

Fig. 7. Schematic view of mode shapes of the test model structure.

henomenon also can be found in the numerical verification partFig. 8).

By using a set of the input/output measurements, atate-space equation model was identified by using N4SID.he order of the state-space equation was selected as

Fig. 8. Impact forces and acceleratio

Fig. 9. Model order selection in stochastic subspace identification.

6 by inspecting the singular values as shown in Fig. 9.The system matrices were identified as follows: A =⎡⎢⎢⎢⎢⎣

0.9508 −0.3059 −0.0041 −0.0061 0.0091 0.01730.3068 0.9483 0.0104 0.0300 −0.0711 −0.00360.0042 −0.0010 0.8999 0.3249 0.2862 −0.0158

−0.0037 −0.0309 −0.3101 0.9403 −0.0878 −0.08760.0114 0.0706 −0.2995 −0.0013 0.9483 0.0674

−0.0163 0.0008 0.0069 0.0887 −0.0683 0.9935

⎤⎥⎥⎥⎥⎦

⎡0.0000 0.0003 0.0002

⎤ ⎡0 0 0

⎤

n responses for one set data.

⎣0.0009 −0.0005 0.00140.0002 0.0002 0.0005

⎦ ⎣0 0 00 0 0

⎦

2506 K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511

Fig. 10. Measured and SSE model responses for an impact hammer measurement.

Fig. 11. Verification of the SSE model for another impact hammer measurement set.

K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511 2507

Fig. 12. Comparison of acceleration response time histories for El Centro earthquake.

Fig. 13. Comparison of acceleration response time histories for Kobe earthquake.

2508 K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511

onse time histories for Northridge earthquake.

C1 69.800557 128.91575

]

D

rd

F

w

r

vdav

thasiOgogp

posed method applies the N4SID method which is more closelyrelated to a linear system theory. However, the actual structureshave some nonlinear characteristics which cannot be considered bythe proposed method. Second, the idealized lumped-mass system

Fig. 14. Comparison of acceleration resp

=[ −303.2742 160.0424 −148.6699 19.2553 14.367

−35.1810 −26.6233 266.4671 −11.0563 −109.04260.5675 −122.9851 −264.5725 225.6425 −92.000

=[

2.0438 −0.0518 0.0188−0.0085 2.0020 −0.0670−0.0711 −0.01267 3.5708

]

Fig. 10 shows the measured impact response and the fittedesponse by using the SSE model along with the fitness valuesefined as follows:

itness =(

1 − ||ym − yf||||ym||

)× 100%. (3)

here ym and yf are the column vectors of measured and fitted

esponse, respectively, and ||y|| =

√√√√ N∑i=1

y2i; N is the length of the

ector y. The fitness values were given here to show how the pre-icted and measured responses match in overall time history nott the peak-values, and they are also in accordance with the con-ention by N4SID function in MATLAB.

It is worthy to note that the two time histories were very closeo each other such that they almost looked as a single line withigh fitness values of over 85%. To verify the identified SSE model,response prediction was carried out by using validation data

et which was not used for identifying the SSE model as shownn Fig. 11. The impact hammer tests were performed similarly.

nly the input for one set of impact hammer measurements wasiven to avoid repetition. Similar fitness values of around 85% werebtained and the two time histories still could not be easily distin-uished from each other. The differences between measured andredicted results may come from several reasons. First, the pro-

117.3464

Fig. 15. Fitness values for predicted earthquake response.

K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511 2509

Fig. 16. Comparison of response spectra for El Centro earthquake.

Fig. 17. Comparison of response spectra for Kobe earthquake.

2510 K.Y. Koo et al. / Nuclear Engineering and Design 240 (2010) 2500–2511

e spec

mstt

5e

apwowSaItvmfi

iwmca

Fig. 18. Comparison of respons

ay cause some prediction errors since the idealization will takeome approximation. Third, measurement noise and time length ofhe record for system identification affects the accuracy of estima-ion results.

.2.3. Seismic response prediction by identified SSE model andarthquake-equivalent force

Shaking table tests were carried out using El Centro, Northridgend Kobe earthquakes to verify the effectiveness of the proposedrocedure. The base motion and three floor response accelerationsere measured with the sampling frequency, Fs = 200 Hz. For each

f the three earthquake cases, the equivalent earthquake force fe

as calculated by feeding the measured base motion ug into theSE model as an input to get earthquake responses. The measurednd predicted earthquake responses are compared in Figs. 12–14.t was found that the predicted response reasonably agrees withhe measured response with fitness values around 70%. The fitnessalues are summarized in Fig. 15. It can be found that the proposedethod predicts the earthquake responses reasonably with high

tness values.Response spectra are very useful tools in earthquake engineer-

ng for analyzing the performance of structures and equipmenthen subjected to earthquakes. The measured and predicted seis-ic response spectra are compared in Figs. 16–18 for two damping

ases (2% and 5%). It can be found that the proposed method canccurately predict the seismic response spectrum. The maximum

tra for Northridge earthquake.

floor acceleration resulting from the motion of a given earthquaketime history was the zero period acceleration (ZPA) of the floorresponse spectrum. If we consider the spectral accelerations at25 Hz frequency as the ZPA values of the floor response spectrums,the peak floor accelerations were almost equal to the ZPA valuesafter a little revision of the response spectra.

6. Conclusions

The seismic response prediction algorithm for cabinet structuresis numerically verified on a three-dimensional plate model andvalidated on a three-storey frame building test structure installedon a small-sized shaking table. The proposed method is especiallyeffective and efficient for the cabinet structures which are now inoperation in nuclear power plants and direct shaking table tests arenot suitable.

From the experimental verification of the test structure, it wasfound that identification of the SSE model by the input/output mea-surement of the structure from the impact hammer test was quitesuccessful achieving high fitness values of about 85%. The predictedseismic responses estimated by the output of the SSE model excited

by the earthquake-equivalent load agree well with the measuredones for all the three earthquake responses to El Centro, Kobe, andNorthridge earthquakes.

However, there is also a possible problem with obtaining thelumped mass matrix since exact weights of a cabinet system may

ing an

ntMcqtr

A

t(ee

R

D

E

511–519.van Overschee, P., de Moor, B., 1994. N4SID: Subspace algorithms for the identifica-

K.Y. Koo et al. / Nuclear Engineer

ot be readily available. It may be necessary to develop a wayo estimate the lumped mass matrix from impact hammer tests.

ore validations are needed to obtain enough evidence for appli-ability to a real cabinet structure since real cabinet structures areuite complex in geometry and nonlinear characteristics. For fur-her study, the experimental tests are expected to be performed oneal cabinet structures.

cknowledgements

This work was supported by the Nuclear Innovation Program ofhe Korea Institute of Energy Technology Evaluation and PlanningKETEP) grant funded by the Korea government Ministry of Knowl-dge Economy (No. 20101620100020). The authors would like toxpress their appreciation for the financial support.

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