ML20058E350

Excerpt from Calculation MYC-905, Generation of Synthetic Time Histories for Maine Yankee Atomic Power Station, BAO-86132-1

ML20058E350
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Site:	Maine Yankee
Issue date:	11/23/1993
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MYC-905, NUDOCS 9312060272
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GENERATION OF SYNTHETIC TIME HISTORIES I

FOR MAINE YANKEE ATOMIC POWER STATION i

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l INTRODUCTION f

three synthetic time is to present l

The purpose of this report histories to be used to generate Amplified Response Spectra l

All require-for the Maine Yankee Atomic Power Station.

of the time histories, (ARS) ments pertinent to the development i

i f

together with a discussion of methodology and a descr pt on o l

software are provided herein.

DESIGN REQUIREMENTS d in The design requirements for the time histories are provide l

to other documents (Ref. 1).

MYPS-29 explicitly and by reference Some modifications to these requirements occurred during the l

The details course of the work and are noted where applicable.

l are described below:

j the response spectra generated l

is that The basic requirement from the time histories should match as closely as possible l

(GRS) specified for the' site.

l the Ground Response Spectra Digitized data are provided in Attachment B to MYPS-29.

i I

The spectra from two time hist'ories are required to match the to-match the vertical.

The-specified horizontal GRS and one for 7 percent critical 1

specific GRS to be matched is that damping (changed from 3 percent per discussion with W.E.

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Henries of YAEC).

The site spectra are specified over a This was extended range of frequencies from 0.5 to 33 Hz.

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to 0.1 Hz to 100 Hz per discussion with W.E. Henr'ies.

the low frequency range the GRS was held constant from 0.25 to 0.50 Hz, at the value at 0.50 Hz. 'Below 0.25 Hz the GRS was specified as a function of the reciprocal of frequency squared from 0.1 to 0.25 Hz as in Regulatory Guide 1.60 (Ref.

l i

2).

In the high frequency range the Zero Period Acceleration (ZPA) specified at 33 Hz was held constant to 100 Hz.

Upper bound requirements to the match of spectra are spe-l cified in Section 3.2 of MYPS-29.

They are that the calcu-l lated, response should be generally less than 20 percent above l

the specified GRS.

Also, specific requirements are that no response be greater than 30 percent above and the average of

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the highest five responses be no more than 20 percent above the specified GRS in the frequency range from 4 to 25 Hz.

i Per discussion with W.E.

Henries, the five responses are to l

be calculated at those f requencies specified in Table 3.7.1-1

~

l in NUREG-0800 (Ref. 5) reproduced as Table 1 herein.

1 Lower bound requirements to the match of spectra are provided j

ii in NUREG-0800 (Ref. 5).

Specifically, using the frequency sweep specified in Table 1, no more than 5 responses may fall

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below and no more than 10 percent-below the specified GRS.

i Further, it is required that a reduction in the frequency j

interval specified in Table 1 result in no more than a 10 l

percent change in the calculated responses.

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,I Since the ARS will be computed f rom a time history analysis i

where the building will be subjected to the simultaneous 1

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3 of ' i 'j j action of the three earthquake components, a further require-ment is that the time histories (earthquake components) be statistically independent (Ref.

3, 4 and 6).

An acceptable criterion for statistical independence is that the absolute value of the correlation coefficient between any two time histories be less than 0.16 (Ref. 3 and 8).

The above requirements constitute all the design limits appli-cable to the generation of the synthetic time histories.

BASIC PROCEDURE The solution algorithm for the time history generation utilizes an iterative approach whereby the frequency components of the time history are factored by ratios of the specified GRS divided by the calculated response.

First, an initial time history is selected (or generated) which has appropriate characteristics to maintain accuracy and to make the problem tractable.

Then a GRS is computed as well as GRS ratios which are the calculated GRS divided by the specified GRS.

The frequency components.,

of the time history are calculated using the Fourier Transform.

These frequency components are then factored by one over the GRS ratio and a new time history is constructed, again using the Fourier Transform.

Essentially, this process is repeated until the design requirements are met.

Other details affect the basic procedure and they are discussed later in this report. i i

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( INITIAL TIME HISTORIES I

The three synthetic time histories were constructed from the

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three earthquake components of the 1952 Taft-(Kern County) earth-l l

quake.

Digitized data was obtained from the Earthquake

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Engineering Research Laboratory (EERL) (Ref. 10).

The initial f

time histories for use in the solution algorithm were constructed from the digitized data.

The time histories from EERL are digi-3 l tized at a time step of 0.02 sec. which was judged to be too large l to maintain accuracy.

Specifically a 25 Hz (0.04 sec. period) t response would be calculated at only 2 points per cycle at a time j

step of 0.02 sec.

A time step of 0.005 seconds was selected and judged to provide sufficient accuracy at 25 Hz (8 points per cycle) and at 33 Hz (6 points per cycle).

Also, the EERL time j

histories are all longer than 54 seconds which, at a time step of l

0.005 seconds, and considerations to be viscussed later, would j

ll result in a time history containing 32,768 time steps which is i

too many.

A length of time of about 20 seconds is judged to be f

l sufficiently long enough for the various frequency components to I capture low frequency response and the plateau of specified response between 2.1 and 8 Hz.

The solution algorithm requires use of the Fourier Transform thus, to reduce computer expense, the Fast Fourier Transform-l (FFT) method was selected (Ref. 7).

This imposes two additional l

requirements on the time histories.

The first is that the time f'

history be followed by a quiet time, i.e.,

specified time inter-l val where the time history values are zero.

The longer the quiet time the more accurate the inverse transform (frequency to time domain) will be.

This quiet time is necessary because the FFT assumes that the time history signal is periodic (Ref. 7 and 6

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The second requirement, specifically related to FFT, is the total number of time steps must be equal to a whole l

that number power of 2, i.e.,

2N where N is an integer.

1 Given the above considerations, the initial time histories were constructed form the Taft records as follows:

The initial N-S time history was constructed from the N21E Taft record thus:

l 0.01 time step reduced by interpolation from 0.02 to j

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seconds.

t Time step then reset to 0.005 seconds holding the acceleration values constant.

This results in a shift of' frequency content.

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First 4099 time steps selected to be the-non-zero portion of the time history resulting-in a 20.495 f

second record.

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An additional 4,093 zero points were added~resulting l

i in a total record of 8192 points.(213),

The initial E-W time history was constructed from the i

S69E Taf t record by using the first 20.495 seconds with

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the time step reduced from 0.02 to 0.005 records by i

interpolation.

Again the 4,093 zero points were added.

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The initial vertical time history was constructed from l

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the vertical.Taft record in the same manner as the

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construction of the initial N-S time history.

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all three time histories contain 8,192 points of which

Thus, time step of 0.005 seconds for I

4,099 represent the earthquake at a a duration of 20.495 seconds.

These are judged to have the appropriate characteristics to maintain accuracy as well as make 2

the solution tractable.

A SOFTWARE E

the solution.

The Two separate programs were used to carry out 3j first is program INSPEC (Ref. 9) and the second is an FFT program.

Program INSPEC was modified to accept the specified GRS and provide the GR3 ratios as well as the specified GRS at all

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f requencies calculated on a computer file ref erred to as a target file.

The program calculates the absolute acceleration response l

of a simple degree of freedom elastic system for various frequen-cies when the excitation consists of an earthquake acceleration at the base.

z.

3 The equilibrium equation for this case is:

s ur+2 ur +

2ur = -xg(t)

(1)

'9 where ur = relative displacement g

ur = relative velocity ur = relative acceleration 1

3 g = acceleration at the base x

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= frequency in rad /sec l

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= damping ratio 3

The absolute acceleration u(t) is then given by:

I u=u j

r + xg 3

Assuming that the input acceleration varies linearly within a l

J timestep, recurrence relations are established that allow the j

l numerical solution of equation (1).

Reference is made to the l

3 INSPEC User's Manual for further details (Ref.

9)..

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l The FFT program was designed specifically to interface with the modified INSPEC program.

Specifically it reads the time history l

i data, performs a forward transform (time to frequency domain),

l reads the target file, factors the frequency components and per-l j

form an inverse transform (frequency to time domain) and creates l

l a file suitable for input to INSPEC.

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l The program is interactive and provides data manipulation-features necessary to maintain solution stability and/or' hasten l

convengence.

Time domain features include:

Decrease the time step by interpolation.

f

'3 Reset the time step causing a shift in frequency content.

g Reset the number of nonzero time steps and sets the remainder to zero.

l Apply a linear acceleration to cause the last accelera-tion of the nonzero portion to be zero.

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1 Apply a user supplied acceleration increment to all points.

Factor the entire time history to a user specified 2PA value.

i Plotting Creation of an 1NSPEC input file.

l Frequency demain features include:

Factor all frequency components by a user specified l

value.

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Factor individual components by user specified values.

I Apply linear functions of factors over a specified fre-quency range, e.g.,

factor components by 1.1 @ 2 Hz varying to 2.0 @ 8 Hz.

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Read the target file, interpolate GRS ratios to the fre-quencies of the components and apply.

Within this i

feature, functions include:

Specification of frequency range of application.

Specification of a GRS ratio range within which the GRS ratios will not be applied.

Modification of GRS ratios greater than 1.0.

Modification of GRS ratios less than 1.0.

Reset the target file baseline - allows the user to effectively raise or lower portions of the specified GRS.

Consideration of other frequency components - this is the successive application of Bigg's equation-2.41 at each component considering the contribu-tion to response of all other components via SRSS and normalized to user specified ZPA.

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2ero all frequency components above a user specified frequency.

Plotting.

Using the INSPEC and FFT programs alternately allows implemen-tation of the required solution algorithm.

DETAILED PROCEDURE Given the initial time histories and the software described above, each synthetic time history was developed iteratively until compliance with the Design Requirements was achieved.

Using the 8,192 po.ints and a *.ime step of 0.005 seconds results in a fre-quency increment of 0.0244 Hz from the FFT.

The frequency sweep in Table 1 was judged to be too coarse for the solution process so a more detailed frequency sweep (Table 2) was used instead.

However, the design requirements calculations were still carried out using the frequency sweep from Table 1.

At one time or another all of the features of the FFT program were applied to hasten conveygence and the frequency range of application was not always 0.1 to 100.0 Hz.

However, a typical iteration was as follows:

P 1.

Run INSPEC time history and create a target file of GRS ratios.

2.

Run FFT, read in the time history and perform a forward transform to the frequency domain.

l l

3.

Still in FFT, read in the target file and:

apply GRS ratios to all frequency components between 0.1 j

and 33.0 Hz j 0 I

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BOO 262 zero all frequency components above 33 Hz perform inverse transform to time domain l

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apply acceleration correction to bring last non-zero 3

acceleration to zero t

zero all values in the quiet zone f

factor all values to the specified 2PA l

create an INSPEC input file and start again at step 1.

1, Blind application of the above process does not quarantee con-i vengence to the design requirements or, for that matter, produce I

a stable solution algorithm.

So, as previously mentioned some user h

intervention was required.

The process tends to produce as many calculated responses below the GRS as above.

So one correction

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which was always required toward the end of the process was to t

effectively raise the specified GRS using the reset target file l..

baseline feature so that only 5 or less points fell below the l specified GRS using the frequency sweep in Table 1. l:) RESULTS l3 f The resulting records are referred to here as MN7 which' stands i l.] for time. histories for Maine in the North-South direction j l3 developed at 7 percent critical damping; ME7 for East-West, and MV7 for vertical. Graphical data are presented in Figures 1.1 to (

M 1.5 for MN7, 2.1 to 2.5 for ME7 and 3.1 to 3.5 for MV7.

Figures O 1.1 and 1.2 present the time history and its Fourier components. The calculated GRS and specified GRS are shown in Figure 1.3 using the NUREG-0800 frequency sweep (Table 1) plus 2.136 Hz (76 points); in Figure 1.4 at the frequency sweep used in the deve-i I l] lopment (Table 2, 170 points); and Figure.1.5 at an extremely J refined frequency sws;p (Table 3 - 906 points). The same order .3 'a I$. i m i

f BAO-86132-1 1 C11 U 0 0 ')00 ~ 2 l l of presentation is used for Figures 2 and 3. These show that the time histories are unbiased, i.e., do not significantly lie on l either side of zero and that the frequency components are well distributed and have the expected shape, i.e., higher values at low frequency than at high frequency. Further, the data show that the calculated GRS match the specified GRS closely at all frequencies. Numerical data are presented in Tables 4, 5 and 6. Table 4A pro-vides data using the NUREG-0800 frequency sweep (Table 1). The mean of the GRS ratios range from 3.22 to 6.35 percent over the specified because the specified GRS had to be artificially raised so that the five points below criterion could be satisfied. The number of points below the specified GRS range from 3 to 5 with a minimum value of 0.95, hence the lower bound requirements of NUREG-0800 are satisfied. The maximum values vary from 1.104 to 1.170, thus the upper bound of generally less than 20 percent is satisfied. Specific upper bound requirements are provided in l Table 4B. This data shows that between 4 and 25 Hz, the maxima } range from 1.071 to 1.113 which are well within the 30 percent limit, and that the average of the five highest points va'ry from l.060 to 1.109 which is within the specified 20 percent limit. A summary of all lower and upper bound requirements is provided in Table 6. The data in Table 5 provide information regarding the requirement t that a decrease in frequency interval not change the computed spectra by more than ten percent. This data show that the maxima did not change at all, compare Table 4A to 5 and that between j 0.15 and 100 Hz the minima varied from 0.987 to 0.951 for MN7, 1 0.986 to 0.965 for ME7, and 0.950 to 0.939 for MV7. All i _11_ J 1 2 e

i .\\ ) BAO-86132-1 j C12 I OOO2,3,j i 4, i i variations are well within ten percent of the NUREG-0800 fre-i quency sweep values,-hence, this criteria is satisfied. Visual i confirmation of this conclusion-can also be made by-comparing the plots. The percentage of points below the specified GRS also comply with the intent of NUREG-0800. NUREG-0800 permits 5 of 75 l I } points to lie below or 6.67 percent. Table 5 was generated using 906 points, 636 of which are.below 33 Hz (Table 3). The 8 maximum number of points below is 40 and 40 of 636 is 6.29 per-i 1 cent, which approximately the same as 6.67. In summary, this a data using the refined frequency sweep (Table 5 and Figures 1.5, f 2.5 and 3.5) shows that spectra computed from the time histories-l are stable and that abnormal ARS will not be generated owing to i defects in the-time histories. The final design requirement to be satisfied is that of statisti-h cal independence between the time histories. The correlation coefficients (r) between the records are: MN7 with ME7 r = -0.006 MN7 with MV7 r = -0.044 l ME7 with MV7 r = -0.041 j All absolute values of the coefficients are well within the r accepted limit of 0.16 (Ref. 3 and 8) and the time histories can

1 all be considered statistically independent from one another.

In summary, the three time histories presented comply with-all the design requirements presented above and are therefore suitable to use for the generation of amplified response spectra q for the Maine Yankee Atomic Power Station. j i I] 2

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i REFERENCES _ 1. Yankee Atomic Electric Ccmpany, " Specification for Generation of Amplified Rsponse Spectra for the Maine Yankee Atomic Power Station", Specification No. MYPS-29, May, 1986. !i l! 2. U.S. Nuclear Regulatory Commission, Regulatory Guide 1.60, l " Design Response Spectra for Seismic Design of Nuclear Power f} Plants", Rev. 1, December 1973. l b l., 3. U.S. Nuclear Regulatory Commission, Regulatory Guide 1.92, Ij " Combining Modal Responses and Spatial Components in Seismic Response Analysis", Rev. 1, February 1976. l '1 Nuclear Regulatory Commission, Regulatory Guide 1.122, 4. U.S. y " Development of Floor Design Response Spectra for Seismic j Design of Floor - Supported Equipment or Components", Rev. 1, 4 February 1978. 5. U.S. Nuclear Regulatory Commission, " Standard Review Plan, Section 3.7.1, " Seismic Design Parameters," NUREG-080,0, Rev. 1, July 1981. 6. U.S. Nuclear Regulatory Commission, Standard Review Plan, Section 3.7.2, " Seismic System Analysis", NUREG-0800, Rev. 1, I July 1981. } 7.

Brigham, E.O.,

The Fast Fourier Transform, Prentice-Hall, J 1974. i R-1 1 h 1 4.s '.{ GO .J

E l l i BAO-86132-1 l l C14 J0025s " Definition of Statistically Independent Time 8.

Chen, C.,

Division, ASCE, Vol. Histories," Journal of the Structural 101, ST 2, February, 1975. "INSPEC - A Computer Program for 9. Cygna Energy Services, 3.0, User's & Theoretical Calculating Spectra," Version Manual, October 1986. " Strong Motion

10. Earthquake Engineering Research Laboratory, EERL Earthquake Accelerograms - Index Volume", Report NO.

1976. 76-02, California Institute of Technology, August

11. Hurty, W.C, and Rubinstein, M.F.,

Dynamics of Structures, Prentice-Hall, 1964. l i l l R-2 ^ 1 l

I l e f BAO-86132-1 C15 '.)d h $2 5 7 l NO. FREQUENCIES INCREMENT l FREQUENCY RANGE CUMULATIVE (Hz) (Hz) 29 0.100 0.200 - 3.000 33 0.150 3.150 - 3.600 40 0.200 3.800 - 5.000 52 0.250 5.250 - 8.000 66 0.500 8.500 - 15.000 69 1.000 16.000 - 18.000 71 2.000 20.000 - 22.000 75 3.000 25.000 - 34.000 l 3 d NURG-0800 FREQUENCY SWEEP (75 POINTS) i ? b o TABLE 1 'J i J l 3 1 i

BAO-86132-1 C16 )h h 2,33 INCREMENT NO. FREQUENCIES FREQUENCY RANGE (Hz) (Hz) CUMULATIVE 0.100 - 0.250 0.025 7 0.300 - 2.100 0.100 26 27 2.136 - 2.200 - 3.000 0.100 36 3.150 - 3.600 0.150 40 3.800 - 5.000 0.200 47 5.250 - 34.000 0.250 163 35.000 - 40.000 1.000 169 50.000 - 60.000 5.000 172 70.000 - 100.000 10.000 176 FREQUENCY SWEEP FOR TIME HISTORY GENERATION (176 POINTS) l TABLE 2 i F i:

BAO-86132-1 C17 ' p o m e; .v. INCREMENT NO. FREQUENCIES FREQUENCY RANGE CUMULATIVE (Hz) (Hz) i 7 0.100 - 0.250 0.025 26 0.300 - 2.100 0.100 27 2.136 36 2.200 - 3.000 0.100 636 3.050 - 33.000 0.050 806 33.100 - 50.000 0.100 0.500 906 50.500 - 100.000 i t REFINED FREQUENCY SWEEP (906 POINTS) TABLE 3 l

00026G ~ BAO-86132-1 f C18 l l MN7 l ME7 l MV7 i I 1 I i l 1.0322 l 1.0454 l 1.0635 Mean 1 Sigma O.0235 l 0.0336 l 0.0396 l l 1.104 @ 0.2 Hz l 1.170 0'1.2 Hz l 1.147 @ 2.3 Hz' l F Ave. High 5 1.080 l 1.115 l 1.134 l Max. l l ] Min. 0.987 @ 1.8 Hz l' O.986 @ 0.5 Hz l O'.950'@ 0.5 Hz I 2 No. LT 1.0 4 l 3 l5 I GRS RATIO STATISTICS USING NUREG-0800 FREQUENCY SWEE il (75 POINTS) i r F. TABLE 4A I. lJ i r i ~ MN7 l ME7_ l MV7 H l l i u, ls ' 1.3313 l 1.0355 l 1.~0680 Mean 1 Sigma 0.0195 l 0.0283 ll 0.0295 l l I Max. 1.071 9 7.5 Hz l 1.092 e '11.0 Hz l 1.113 9 4.0 Hz E3 Ave. High 5 1.060 l 1.082 l 1.109 I l l 1.001 9 7. 0 Hz. - l 0.999 8 9.0 Hz l 1.014 9 9.5 Hz Min. ? No. LT 1.0 ,o l 1 l- 0 ,9 !.J QUENCY SWEEP .GRS RATIO STATISTICS USING'NUREG-0800 FRE FROM 4.0 TO 25.0 Hz j (38 POINTS) TABLE 4B_ ) n i .b h --w

9 900261 BAO-86132-1 C19 I f MN7 l ME7 l MV7 I I Mean l 1.0256 l 1.0339 l 1.0432 1 Sigma 0.0225 l 0.0970 l 0.0330 l l Max. 1.104 @ 0.2 Hz l 1.170 0 1.2 Hz l 1.147 @ 2.3 Hz l Min. 0.754 @ 0.125 Hzl 0.965 @ 0.225 Hzl 0.939 @ 0.175 Hz i I f No. LT 1.0 25 l 40 l 11 I I 0.99 - 1.00 1 15 l 22 l 3 0.98 - 0.99 4 l 12 l 3 5 l 3 j i 0.97 - 0.98 3 i i 0.96 - 0.97 0 l 1 l 0 0.95 - 0.96 1+ l 0 l 0 l 0.90 - 0.95 0 l 0 l 2 LT 0.90 2* l 0 l 0 + 0.951 @ 0.15 Hz.

• 0.754 @ 0.125 Hz and 0.825 @ 0.100 Hz.

i l GRS RATIO STATISTICS USING REFINED FREQUENCY SWEEP (906 POINTS) TABLE 5 l

000262 BAO-86132-1 C20 l + 4 I ITEMI l LIMIT' l MN7 l 'ME7 - l MV7-J l l .I I l Min. Using FS1 .GE. 0.90 l 0.987 l 0.986 { 0.950 No. LT. 1.0 Using FS1 .LE. 5 -l 4 l 3 Jl-5 l l 1 - 1 Max. Using FS1 .LT. 1.2 Generally l 1.104 l 1.170 l 1.147 Max. Using FS2 .LE. l.3 l 1.071 l 1.092 l 1.113 Ave. High 5 Using FS2 .LE. 1.2 l 1.060 l 1.082 l 1.109 1

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IN li NOTES: .e j 1 FS1 is the Frequency Sweep specified by NUREG-0800 '(Table 1). l i 1. .g FS2 is FS1 between 4 and 25 Hz inclusive. t !) i i i l l1 GRS RATIO STATISTICS DESIGN REQUIREMENTS lr TABLE 6 a i S b 3 2 ) i 3 \\ O + m

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