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Uncertainties in In-Structure Response Spectra Due to Uncertainties in Input Motion Amplitude and Phase Spectra
ML23095A243
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Issue date: 07/16/2023
From: Vladimir Graizer, Jinsuo Nie, Dogan Seber, Jim Xu
NRC/RES/DE/SGSEB
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Jinsuo Nie 301-415-6417
References
PVP2023-105307
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Proceedings of the ASME 202 3 Pressure Vessels & Piping Conference PVP2023 July 16-21, 2023, Atlanta, Georgia USA

PVP2023 -105307

UNCERTAINTIES IN IN-STRUCTURE RESPONSE SPECTRA DUE TO UNCERTAINTIES IN INPUT MOTION AMPLITUDE AND PHASE SPECTRA

Jinsuo R. Nie, Jim Xu, Vladimir Graizer, and Dogan Seber

Division of Engineering Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC, USA

ABSTRACT0F INTRODUCTION

We concluded in PVP2020 -21132 that the four or five time To estimate the mean seismic responses of linear structural histories in the current practice are not sufficient for estimating systems, a common practice is to use multiple response stable mean in-structure response spectra (ISRS), therefore a spectrum (RS)-matched input acceleration time histories in check of their power spectral density functions is necessary. seismic analysis [1, 2]. PVP2020 -21132 examined whether The time histories used in that work were not developed based multiple acceleration time histories can be used to achieve on typical response spectrum (RS) convergence criteria and did stable mean responses by explicitly considering the not consider the uncertainties in Fourier amplitude spectra. uncertainties in the Fourier phase spectra of the input time This paper examines how the uncertainties in both Fourier histories while keeping their Fourier amplitude spectra constant phase spectra and Fourier amplitude spectra of the input [3]. However, constant Fourier amplitude spectra are extremely motions resulting from seed time histories and a new difficult, if not completely infeasible, to achieve in RS-matching algorithm affect the uncertainties in ISRS. This RS-matching algorithms. This paper examines how the study finds that the coefficient of variation in ISRS reached as uncertainties in both Fourier phase spectra and Fourier high as 68%, generally confirming previous results obtained amplitude spectra of the input motions resulting from the using a different RS-matching algorithm. This level of ISRS RS-matching algorithms and seed time histories affect the variation continues to support our conclusions in PVP2020- uncertainties in in-structure response spectra (ISRS). We aim at 21132. Therefore, a check of the power spectral density generally confirming whether the coefficient of variation functions of the multiple input time histories in the current (COV) in ISRS, COVISRS, based on a new RS-matching practice is necessary to ensure the estimated mean ISRS would algorithm is comparable to what was reported in PVP2010-vary on the conservative side, although not as stable as 25919 [4], which used a different RS -matching algorithm. A necessarily required for reasonable confidence levels. These confirmed high level of COV ISRS would indicate that the current results provide the necessary technical bases for consistent practice of using the four or five time histories would not be technical positions between industry standards and regulatory sufficient for estimating stable mean ISRS and therefore, a guide for nuclear power plants. check of the power spectral density (PSD) functions of these Keywords: confidence level; in -structure response input time histories would be necessary to ensure the estimated spectrum; multiple input motions ; power spectral density; mean ISRS would vary on the conservative side, although not wavelet based response spectrum matching as stable as necessarily required for reasonable confidence levels.

DISCLAIMER NOTICEThe findings and opinions expressed in this paper are those of the authors, and do not necessarily reflect the view of the U.S. Nuclear Regulatory Commission.

This material is declared a work of the U.S. Government 1 and is not subject to copyright protection in the United States.

Approved for public release; distribution is unlimited.

It should be noted that Section 3.7.1, Seismic Design affect COVISRS and (2) compare the results with what has been Parameters, of NUREG -0800, Standard Review Plan for the reported in the literature. A finding that the COVISRS is Review of Safety Analysis Reports for Nuclear Power Plants: comparable to or greater than what has been reported would LWR Edition [1], already indicates the necessity of a PSD further affirm that the current practice of using four or five input check in Option 2, Multiple Sets of Time Histories. This time histories may not be sufficient to attain stable ISRS study and PVP2020 -21132 can provide the quantitative estimates.

reasoning for this necessity. T he results in this study, PVP2010-25919, and PVP2020- 21132 may provide the necessary This paper uses the same statistical reasoning as PVP2020-technical bases for consistent technical positions between the 21132 [3]. This approach is to use a relatively large number of American Society of Civil Engineers (ASCE)/Structural input acceleration time histories to establish a relatively Engineering Institute (SEI) 4-16, Seismic Analysis of Safety - accurate estimate of the COV of the true mean ISRS, which Related Nuclear Structures [2], and NUREG -0800 [1]. The is then used to determine whether a smaller number of current RS convergence criteria in ASCE 4-16 practically do acceleration time histories (e.g., four or five) can lead to a mean not require a PSD check. estimate of ISRS within +/- 10% of the true mean ISRS.

Previous studies [6, 7] provided support that ISRS are more In our PVP2020-21132 paper [3], we demonstrated that the suitable for determining an adequate number of input time uncertainties in Fourier phase spectra of the input motions histories than the RS-matching criteria, because ISRS can alone, which are considered irreducible, could result in a represent the entire frequency range of interest for the structural maximum coefficient of variation (COV) in in-structure responses, while the RS -matching criteria can only represent response spectra (ISRS) (COVISRS) around 40%. With this level the maximum responses (i.e., the zero-period accelerations of COVISRS, four or five input time histories in the current (ZPA) on the ISRS curves ).

practice were found not able to lead to stable ISRS estimates for reasonable confidence levels. In that paper, the Fourier We emphasize that RS-matching methods may introduce amplitude spectra of the input time histories remained constant, some systematic characteristics or biases to the resultant time and their uncertainties were not considered. However, we histories, which are extremely difficult to determine without a postulated that the uncertainties in Fourier amplitude spectra comprehensive comparison of many RS -matching algorithms.

are expected to increase COVISRS. The input time histories in However, the conclusions in this paper are not expected to be PVP2020- 21132 are designated in this paper as p ower spectral affected by the chosen method because the focus of this work is density (PSD)-based time histories because the constant Fourier on the uncertainties in ISRS, not on the system atic biases that amplitude spectra were calculated from the target PSD individual RS -matching methods may introduce.

functions described in Appendix B, Guidance on Minimum Power Spectral Density for NUREG/CR-6728 Based Design In this paper, we demonstrate how the seed time histories Spectra or Other Spectra, to Section 3.7.1, Revision 4, are modified using the new RS -matching algorithm, summarize Seismic Design Parameters, issued December 2014, of the assumptions and the statistical procedure that were also used NUREG- 0800, Standard Review Plan for the Review of Safety in PVP2020- 21132, assess COVISRS based on RS -matched time Analysis Reports for Nuclear Power Plants: LWR Edition histories, and compare them with the PSD -based time histories (SRP) [1]. On average, the response spectra of the PSD -based that consider only the uncertainties in the Fourier phase spectra.

input time histories were essentially identical to the bin These results are also used to determine the number of time representative response spectra in the SRP. histories required to achieve stable estimates of ISRS. Since the amount of effort for RS matching is relatively large, we This paper (1) assesses the uncertainties in ISRS due to considered only one target RS (TRS), which is the Western U.S.

uncertainties in both Fourier phase spectra and Fourie r RS shape for bin M7+D50- 100, using the mid-bin properties amplitude spectra of the input motions and (2) compares the M = 7.5 and D = 75 kilometers (km), as described in results to those that only considered the uncertainties in Fourier appendix B to SRP s ection 3.7.1 [1]. M and D stand for phase spectra. earthquake magnitude and source -to-site distance, respectively.

A common practice to estimate the mean seismic responses GENERATION OF RS-MATCHED INPUT TIME of linear structural systems is to use multiple response spectrum HISTORIES (RS)-matched input a cceleration time histories to obtain stable This work required many RS-matched time histories; estimates of the responses. The resultant time histories include therefore, we developed a new program based on R eference [5]

uncertainties in their Fourier amplitude and phase spectra, to automatically perform RS matching using parallel which can be strongly influenced by the method used for RS processing. This new program uses the same wavelet form as in matching. The uncertainties in the Fourier amplitude spectra of Reference [5] and the same ove rall scheme to add wavelets at the RS-matched time histories are usually not separable from the times when the maximum responses occur in the RS those of the Fourier phase spectra. In this paper, we use a newly calculation. However, our algorithm adds wavelets in a greedy developed, wavelet-based RS-matching algorithm (based on fashion; each iteration adds only one wavelet at the frequency Reference [5]) to (1) explore how uncertainties in both the at which the calculated RS and the TRS differ the most among Fourier amplitude spectra and the Fourier phase spectra can

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all frequencies used for RS calculation. The algorithm in Reference [5] adds wavelets simultaneously at all frequencies in each iteration, weighted using a response matrix that has a 925 Sample RS, size of the number of frequencies for RS matching. Therefore, Overlaid by MRS and the approach in this paper does not need to assemble and invert MRS x (1 +/- COVRS) the response matrix to compute the weights. The new algorithm also include s some other differences to ensure efficiency and stability. Since the algorithm is not the focus of this paper, its details will be introduced in a different publication.

Using the selected TRS (Western U.S. RS with M=7.5, D=75 km [1]), we downloaded from the PEER NGA -West2 database [8] 291 seed acceleration time histories that have the highest similarity between their RS and the TRS. We also used the 1,902 seed time histories in the database associated with NUREG/CR-6728, Technical Basis for Revision of Regulatory Guidance on Design Ground Motions: Hazard-and COV Risk-Consistent Ground Motion Spectra Guidelines, issued October 2001 [9], without assessing their similarity to the TRS.

This was necessary because we need ed many seeds to reach a reasonable number of converged acceleration time histories to develop reliable ISRS statistics. FIGURE 1: DEMONSTRATION OF THE EFFECT OF All seed time histories were set to match the TRS at 301 DETERIORATED RS COMPARISION AFTER CHOPPING THE frequency points from 0.1 hertz (Hz) to 100 Hz, using a +/-5% RESULTANT TIME HISTORIES TO MAINTAIN THE SEED DURATION criterion that is the same as used in Reference [5]. It should be noted that this criterion is much tighter than the [-10%, 30%]

range used for design purposes [1, 2]. Each seed was matched with an initial limit of 2,000 wavelets. If an acceleration time history was not converged to the +/- 5% criterion, Gaussian noises 394 Sample RS, with standard deviations at 5% of instantaneous absolute values Overlaid by MRS and of the time history were added, and the algorithm was rerun for MRS x (1 +/- COVRS) another maximum of 2, 000 wavelets. From the 2,193 seeds, we obtained 1,474 converged acceleration time histories.

One side effect of the wavelet-based time domain methods is that some low-frequency wavelets may be added before the start of some seed time histories. To maintain the same duration as the original seed s, the beginning parts of these added low-frequency wavelets were removed from the resultant time histories. Removing parts of the se wavelets made many converged time histories violate the +/-5% criterion in the RS comparison. Figure 1 shows that after the resultant time histories were chopped to maintain the same duration as the COV seeds, their comparison to the TRA deteri orated. The corresponding COV RS, shown as the thin black curve, increased to about 22% at 0.1 Hz, compared to about 2% at higher frequencies where the agreement between the RS and the TRS is excellent. The COV RS curve decreases from 22% to around FIGURE 2: COMPARISON OF 394 SCREENED-IN TIME 2% at 2 Hz and stays at that level for all higher frequencies. In HISTORIES WITH THE TRS AND THE RESULT ANT NEARLY this figure, the thin gray curves and the thick red curve represent CONSTANT, SMALL COVRS AROUND 2%

the individual RS and the mean RS (M RS), respectively, while the green and blue curves represent M RS x (1 +/- COVRS). The There are ways to avoid adding wavelets before the start of curve for TRS is under the mean curve, not quite visible. N ote the seeds, but the current implementation of our program that this figure was developed in the early stage of this work achieves that manually through a graphical user interface.

and did not use the final 1,474 converged time histories. Therefore, instead of improving the algorithm to automatically achieve that goal, we screened the 1,474 converged time histories using the same +/-5% criterion and obtained 394 final

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time histories, which were then used in this study. Using the 21132 [3], t able 1 lists the Ns calculated using e quation (2) for same colors and line styles as in f igure 1, figure 2 compares the some assumed sample CVISRS. Equation (2) and table 1 can be RS of the 394 screened-in time histories to the TRS and also used to determine N s if the sample COVISRS is known or shows the nearly constant, small COV RS that is between 2% to accurately estimated.

2.7% across the entire frequency range considered. The number of screened-in time histories is smaller than 500, which was used in PVP2020- 21132; however, we think it can still yield relatively accurate estimate of sample COV ISRS.

RECAP OF THE BASIC ASSUMPTIONS AND THE STATISTICAL PROCEDURE IN PVP2020- 21132 Because input acceleration time histories are often generated using the same procedure or software and meet the same acceptance criteria for RS matching, they generally share some common features and may include systematic biases.

However, the resultant time histories and their RS can be assumed to be statistically independent relative to their common features and biases. Further, the response time histories and the ISRS for the single-degree-of-freedom structures can also be assumed to be statistically independent.

For simplicity, we also assume that ISRS have an identical distribution on a frequency-by-frequency basis. These FIGURE 3: THE REQUIRED NUMBER OF TIME HISTORIES assumptions are considered reasonable because the seeds used INCREASES AS A FUNCTION OF CONFIDENCE LEVEL to generate these time histories are generally uncorrelated. FASTER THAN EXPONENTIALLY

With these assumptions, we can use the sample COV to TABLE 1: THE NUMBER OF INPUT TIME HISTORIES derive the COV for mean quantities. Using a large number ( N) REQUIRED FOR A GIVEN SAMPLE COVISRS TO ACHIEVE A of RS-matched acceleration time histories to estimate an +/-10% CONFIDENCE INTERVAL FOR THE MEAN ISRS accurate sample COV of the input RS and the ISRS ( COVRS and COVISRS, respectively), the COV of the M RS and the COV COVISRS (%) NS (CL = 68%) NS (CL = 95%)

of the mean ISRS (MISRS), COVMRS and COVMISRS can then be 20 4 15 obtained as shown in equation (1) :

22 5 19

= 26 7 26 (1) 30 9 35

=

40 16 61 These quantities are functions of frequency, which is 50 25 96 omitted from the symbols herein for simplicity. In this paper, 70 49 188 we continue to use COV ISRS to determine, for a selected SOURCE: Adapted from table 1 of PVP2020 -21132 [3].

confidence level (CL), how many input time histories are required to achieve a +/-10% confidence interval within which the true M ISRS falls. For two typical levels of CL, the smaller number (Ns) of samples to establish +/-10% confidence interval UNCERTAINTIES IN INPUT RS FOR RS-MATCHED can be calculated as shown in equation (2): INPUT TIME HISTORIES AND THOSE FOR PSD-BASED TIME HISTORIES 100 2, CL=68% Figure 2 shows the RS of the 394 RS -matched input time (2) histories, indicating an excellent agreement with the TRS as 384 2, CL=95% expected due to the tight RS -matching criteria. This figure also shows the COVRS is between 2% and 2.7%, which is about half of the 5% RS-matching criterion. Given this level of COV, the These equations indicate that the required number of input 394 input time histories are judged to be reasonable for acceleration time histories is a quadratic function of the sample producing a good estimate of the sample COVISRS.

CVISRS. Figure 3 shows that Ns increases faster than exponentially as a function of CL. Adopted from PVP2020-

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As a comparison, figure 4 shows the results using the 500 RS-matched time histories. For each oscillator (conceptually, a PSD-based time histories that were used for PVP2020-21132. single-degree-of-freedom structure or a structural mode), t he This figure uses the same colors and line styles as in f igure 1. RS of the 394 response time histories (i.e., the ISRS) were used The average RS of these time histories closely matched the to estimate the sample CVISRS for this oscillator.

same TRS, and the TRS curve is not visible because it is overlaid by the average RS. The Fourier amplitude spectra of Representative oscillators selected from the 151 oscillators these PSD-based time histories are the same, but their Fourier are discussed below, with a focus on how they respond very phase spectra were random. The COVRS was found to be differently to the RS-matched time histories and to the PSD-between 10% and 29%, significantly larger than the COV RS for based time histories.

the RS-matched time histories by a factor of 11 for the maximum values. The COVRS also generally decreases as a Oscillator at 0.49 Hz function of frequency, unlike the COV RS for the RS-matched The top plot in figure 5 shows the ISRS of a 0.49-Hz time histories that stays nearly at a constant value across the oscillator using 394 RS-matched time histories. The thin gray entire frequency range. curves, the thick red curve, and the red dashed curves represent the individual ISRS, their mean M ISRS, and M ISRS x (1 +/-

COVISRS), respectively. The bottom plot shows the 500 Sample RS, frequency-dependent C OVISRS in blue, the C OVRS in red (also Overlaid by MRS and shown in figure 2), and their ratio as the gray dashed line.

MRS x (1 +/- COVRS) Figure 6 shows similar plots for the same oscillator subjected to the 500 PSD-based input time histories, which were part of the work for PVP2020-21132 [ 3].

Comparing the se two figures, the COVISRS for the RS-matched time histories has been significantly amplified from the COVRS of the input motions at the oscillator frequency by a factor greater than 8, wh ile that factor is only about 1.3 for the COV PSD-based time histories. Although COV RS for the RS-matched time histories is much smaller than COVRS for the PSD-based time histories, the resultant COVISRS for the former is only slightly lower than that for the latter, 21% versus 30%.

The ZPA effect as reported in PVP2020- 21132 for th e PSD-based input time histories does not occur for the RS-matched time histories. The ZPA effect refers to an observation that COV ISRS maintains the value of COV RS at the oscillator frequency at frequencies higher than the ZPA frequency, after which the spectral acceleration equals ZPA.

FIGURE 4: RS AND COVRS OF THE 500 PSD-BASED INPUT For example, as shown in f igure 6, the COVISRS at frequencies MOTIONS GENERATED FOR W ESTERN U.S. RS FOR BIN higher than 4 Hz stays flat at the value of COV RS at the M7+D50- 100 oscillator frequency of 0.49 Hz.

ASSESSMENT OF COVISRS The significant differences in COVRS between (1) the case of RS-matched time histories that include both amplitude and phase uncertainties and (2) the case of PSD-based time histories that include only phase uncertainties do not translate to COVISRS, as demonstrated in this section.

We used the same approach as in PVP2020-21132 to generate the ISRS for this work. As a summary, for each input time history, 151 single-degree-of-freedom oscillators with a damping ratio of 5% were used to generate response time histories. These oscillators cover a frequency range of 0.1 Hz to 100 Hz and can represent various modes of complex structur es.

The response time histories of an oscillator were generated in the frequency domain through the convolution of the oscillators transfer function and the Fourier spectr a of the 394

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394 Sample ISRS, 500 Sample ISRS, Overlaid by MISRS and Overlaid by MISRS and MISRS x (1 +/- COVISRS) M x (1 +/- COV )

ISRS ISRS

FIGURE 5: ISRS AND COVISRS FOR A 0.49-HZ OSCILLATOR FIGURE 6: ISRS AND COVISRS FOR A 0.49-HZ OSCILLATOR USING 394 RS-MATCHED TIME HISTORIES USING 500 PSD-BASED TIME HISTORIES

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FIGURE 7: ISRS AND COVISRS FOR A 4.97-HZ OSCILLATOR FIGURE 8: ISRS AND COVISRS FOR A 4.97-HZ OSCILLATOR USING 394 RS -MATCHED TIME HISTORIES USING 500 PSD-BASED TIME HISTORIES

Oscillator at 4.97 Hz Figure 7 and figure 8 show similar plots for another oscillator with a frequency of 4.97 Hz for the RS -matched time histories and for the PSD -based time histories, respectively.

Similar to the 0.49-Hz oscillator, this oscillator significantly amplified the COV at the oscillator frequency for the RS-matched time histories. Although the COVRS for the RS-matched time histories is much smaller, the corresponding COVISRS becomes larger than that for the PSD -based time histories at the oscillator frequency.

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FIGURE 9: ISRS AND COVISRS FOR A 9.89-HZ OSCILLATOR FIGURE 10. ISRS AND COVISRS FOR A 9.89 -HZ OSCILLATOR USING 394 RS -MATCHED TIME HISTORIES USING 500 PSD-BASED TIME HISTORIES

Oscillator at 9.89 Hz Figure 9 and figure 10 show an oscillator with a frequency of 9.89 Hz for the RS-matched time histories and for the PSD-based time histories, respectively. Compared to the previous two oscillators, this oscillator amplified the COV even more for the RS-matched time histories by a factor of more than 11. It barely amplified the COV for the PSD -based time histories. Although the COV RS for the RS-matched time histories is still much smaller by a factor of 5 at the oscillator frequency, the corresponding COV ISRS approximately doubles that for the PSD-based time histories.

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Significant amplification More consistent amplification

No amplification

FIGURE 11: ISRS AND COVISRS FOR A 29.99 -HZ OSCILLATOR FIGURE 12: ISRS AND COVISRS FOR A 29.99 -HZ OSCILLATOR USING 394 RS -MATCHED TIME HISTORIES USING 500 PSD-BASED TIME HISTORIES

Oscillator at 29.99 Hz Overall Assessment of the 151 Oscillators Figure 11 and figure 12 show the results for the 29.99-Hz Figure 13 and figure 14 summarize the COVISRS for all 151 oscillator for the RS-matched time histories and PSD-based oscillators for the RS-matched time histories and the time histories, respectively. Compared to the previous cases, PSD-based time histories respectively. There are many this oscillator significantly amplified the COV for the different curves for individual COV ISRS and related statistics, RS-matched time histories by a factor of 27. In contrast, there but our focus is on the two thick, yellow curves that envelop the is essentially no amplification of the COV for the PSD-based COVISRS values at the oscillator frequencies, representing how time histories. The COVRS for the RS-matched time histories is the COVRS gets amplified. These two curves represent how still one-fifth of that for the PSD-based time histories at the the two types of input time histories can result in COV ISRS for oscillator frequency, but the corresponding COV ISRS is about 5 structural modes in the frequency range from 0.1 Hz to 100 Hz.

times that for the PSD-based time histories. For the RS-matched time histories, the COVISRS is around

It is interesting to note that for the RS-matched time 20%, relatively flat between 0.2 Hz and 6 Hz. For a frequency histories, the ISRS of some input time histories do not show any reference, the spectral peak for the TRS is around 4 Hz. After amplification, while others show significant amplification at the 6 Hz, the COVISRS increases quickly, to 40% at 18 Hz, and to oscillator frequency. As a comparison, the ISRS for the around 68% at 60 Hz. COV ISRS appears to be independent of PSD-based time histories have relatively more consistent COVRS, which is nearly a constant value of 2% across the entire amplification at the same oscillator frequency than the frequency range. COVISRS being independent of COVRS reveals RS-matched time histories. that the variation in ISRS is not caused by the variation of the input RS for the RS-matched time histories. We believe COVISRS is actually caused by the PSD variation of the input motions. This is the reason why we have enclosed in quotation marks all terms related to amplification. Reference [6] has shown that (1) ISRS reflect the power distribution of the input motion, and (2) RS is an inadequate descriptor of the input

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motion without particular consideration of PSD. For the RS-matched time histories using the newly developed, greedy, wavelet-based RS-matching algorithm, the relatively flat COVISRS from 0.2 Hz to 6 Hz largely indicat es that the power in this frequency range varies less than other frequency ranges,

while the la rge COVISRS increase above 6 Hz indicates the PSD variation increases greatly. We reiterate that the variation of COVISRS also depends on the method used to generate the RS-matched time histories.

For the PSD-based time histories, the COVISRS gradually COVISRS values at the decreases from 38% to about 8% from 0.1 Hz to 100 Hz. oscillator frequencies Compared to the COVRS shown in f igure 4, the COVISRS has small increases at low er frequencies and gradually approaches the COVRS at higher frequencies. As shown in PVP2020 -21132

[3], COVRS decreases monotonically from 30% to about 7% for the PSD-based time histories, regardless of the TRS shape. This is a great advantage for the PSD-based time histories, because (1) their COVISRS is smaller than those for the RS-matched time histories, (2) their COVISRS is well defined as monot onically decreasing functions of frequency, and (3) the PSD-based time histories contain only uncertainties in Fourier phase spectra, which are considered irreducible. FIGURE 13: COVISRS FOR 151 OSCILLATORS USING 394 RS-MATCHED TIME HISTORIES Overall, even though the RS -matched time histories have a maximum COVRS that is only one-eleventh of that for the PSD-based time histories, their corresponding COVISRS is generally and significantly larger than the latter for frequencies above 2 Hz. For ISRS below 2 Hz, although the shapes of COVISRS are somewhat different between these two cases (as shown in f igure 13 and f igure 14), they represent a similar COV level and similar trend. The screening procedure in this study, which affects mainly low-frequency wavelets, might have made the COVISRS for the RS-matched time histories somewhat COVISRS values at the smaller than that for the PSD-based time histories. oscillator frequencies

SUMMARY

The maximum COV ISRS was found to be 68% for the RS-matched time histories, generally confirming the 70% value reported in PVP2010-25919 [4]. A few differences exist between that study and this one. A frequency domain RS-matching method was used for PVP2010- 25919 [4]. The 70% COVISRS value occurred at 10.5 Hz in that study. At that frequency, the COV ISRS was only 28% in this study. Note that PVP2010- 25919 [4] used real structures and soil structure interaction analyses, while this study cons idered only single -

degree-of-freedom systems. Modal combinations are likely to FIGURE 14: COVISRS FOR 151 OSCILLATORS USING 500 increase COVISRS, at least for frequency ranges where the PSD-BASED TIME HISTORIES COVISRS is lower than its neighboring frequency ranges.

To achieve a stable mean estimate of ISRS that is within This work confirms the conclusion in PVP2020- 21132 [3]

+/-10% of the true mean, using equation (2) or t able 1, a that the current practice of using four or five input time histories maximum COVISRS of 70% suggests that the required num ber should be conditioned by explicitly checking their PSD of input time histories is 49 for a confidence level of 68%, and functions for sufficient power contents in the frequency range 188 for a confidence level of 95%. These high numbers of input of interest to the responses. In addition, we have provided time histories would not be practical in most applications. further evidence using RS -matched time histories to support that a check of PSD functions is necessary even using multiple input time histories, because their mean ISRS estimate,

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although not as stable as necessarily required for reasonable Pressure Vessels and Piping Conference (PVP2020-levels of confidence, would tend to vary on the conservative 21132), Minnesota ( virtual).

side. 4. Houston, T.W., G.E. Mertz, M.C. Costantino, and It should be noted that Section 3.7.1, Seismic Design C.J. Costantino (2010). Investigation of the impact of Parameters, of NUREG- 0800 [1] already indicates the seed record selection on s tructural response, American necessity of a PSD check in Option 2, Multiple Sets of Time Society of Mechanical Engineers Pressure Vessels and Histories. This study and PVP2020- 21132 provide the Piping Conference (PVP2010- 25919), Bellevue, quantitative reasoning for this necessity. The results in this Washington.

study, PVP2010 -25919, and PVP2020- 21132 can also serve as 5. Atik, L., and N. Abrahamson (2010). An improved the necessary technical bases for consistent technical positions method for nonstationary spectral matching, Earthquake between the ASCE/SEI 4-16 [2] and NUREG -0800 [1]. The Spectra, 26(3), 601-617.

current RS convergence criteria in ASCE/SEI 4-16 practically 6. Nie, J.R., J. Pires, and D. Seber ( 2019). Understanding the do not require a PSD check. assumptions in d esign response spectra for s eismic time history analyses, Transactions, SMiRT-25, Charlotte, North Carolina.

REFERENCES 7. U.S. Nuclear Regulatory Commission, Research

1. U.S. Nuclear Regulatory Commission, Standard Review Information Letter RIL-20 19- 01 (2019). Assessment of Plan for the Review of Safety Analysis Reports for Nuclear Artificial Acceleration Time History Guidance in Standard Power Plants: LWR Edition, NUREG- 0800, Washington, Review Plan Section 3.7.1, Seismic Design Parameters, DC. Washington, DC. Agencywide Documents Access and
2. American Society of Civil Engineers (ASCE)/Structural Management System Accession No. ML19308A045.

Engineering Institute (SEI) 4-16, Seismic Analysis of 8. PEER NGA-West2 database:

Safety-Related Nuclear Structures, Reston, V irginia. https://ngawest2.berkeley.edu/.

3. Nie, J.R., J. Xu, V. Graizer, and D. Seber (2020). 9. NUREG/CR-6728, Technical Basis for Revision of Estimating stable mean responses for linear str uctural Regulatory Guidance on Design Ground Motions: Hazard -

systems by using a limited number of acceleration time and Risk-consistent Ground Motion Spectra Guidelines, histories, American Society of Mechanical Engineers issued October 2001, Washington, DC.

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