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| number = ML13102A296 | | number = ML13102A296 | ||
| issue date = 04/10/2013 | | issue date = 04/10/2013 | ||
| title = | | title = Response to Request for Additional Information (RAIs 53 and 72) Regarding Confirmatory Action Letter Response | ||
| author name = St.Onge R | | author name = St.Onge R | ||
| author affiliation = Edison International Co, Southern California Edison Co | | author affiliation = Edison International Co, Southern California Edison Co | ||
| addressee name = | | addressee name = | ||
Line 14: | Line 14: | ||
| page count = 14 | | page count = 14 | ||
| project = TAC:ME9727 | | project = TAC:ME9727 | ||
| stage = Response to RAI | |||
}} | }} | ||
=Text= | =Text= | ||
{{#Wiki_filter:SOUTHERN CALIFORNIA Richard 1. St. | {{#Wiki_filter:SOUTHERN CALIFORNIA Richard 1. St. Onge EDISONmeDirector, ED SO " | ||
}} | Nuclear Regulatory Affairs and Emergency Planning An EDISON INTERNATIONAL Company April 10, 2013 10 CFR 50.4 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555-0001 | ||
==Subject:== | |||
Docket No. 50-361 Response to Request for Additional Information (RAIs 53 and 72) Regarding Confirmatory Action Letter Response (TAC No. ME 9727) | |||
San Onofre Nuclear Generating Station, Unit 2 | |||
==References:== | |||
: 1. Letter from Mr. Elmo E. Collins (USNRC) to Mr. Peter T. Dietrich (SCE), dated March 27, 2012, Confirmatory Action Letter 4-12-001, San Onofre Nuclear Generating Station, Units 2 and 3, Commitments to Address Steam Generator Tube Degradation | |||
: 2. Letter from Mr. Peter T. Dietrich (SCE) to Mr. Elmo E. Collins (USNRC), dated October 3, 2012, Confirmatory Action Letter - Actions to Address Steam Generator Tube Degradation, San Onofre Nuclear Generating Station, Unit 2 | |||
: 3. Letter from Mr. James R. Hall (USNRC) to Mr. Peter T. Dietrich (SCE), dated March 18, 2013, Second Request for Additional Information (RAI 33-67) | |||
Regarding Response to Confirmatory Action Letter, San Onofre Nuclear Generating Station, Unit 2 | |||
: 4. Letter from Mr. Richard J. St. Onge (SCE) to Document Control Desk (USNRC), dated February 25, 2013, Response to Request for Additional Information (RAIs 2, 3 and 4) Regarding Confirmatory Action Letter Response, San Onofre Nuclear Generating Station, Unit 2 | |||
: 5. Email from Mr. James R. Hall (USNRC) to Mr. Ryan Treadway (SCE), dated March 15, 2013, Request for Additional Information (RAIs 68-72) Regarding Response to Confirmatory Action Letter, San Onofre Nuclear Generating Station, Unit 2 | |||
==Dear Sir or Madam,== | |||
On March 27, 2012, the Nuclear Regulatory Commission (NRC) issued a Confirmatory Action Letter (CAL) (Reference 1) to Southern California Edison (SCE) describing actions that the NRC and SCE agreed would be completed to address issues identified in the steam generator tubes of San Onofre Nuclear Generating Station (SONGS) Units 2 and 3. In a letter to the NRC dated October 3, 2012 (Reference 2), SCE reported completion of the Unit 2 CAL actions and included a Return to Service Report (RTSR) that provided details of their completion. | |||
La P.O. Box 128 San Clemente, CA 92672 q | |||
Document Control Desk April 10, 2013 By letter dated March 18, 2013 (Reference 3), the NRC issued Requests for Additional Information (RAls) regarding the CAL response. Enclosure 1 of this letter provides the response to RAI 53. | |||
SCE provided the response to RAIs 2, 3 and 4 in a letter dated February 25, 2013 (Reference 4). By e-mail dated March 15, 2013 (Reference 5), the NRC issued Requests for Additional Information (RAIs) regarding the response to RAIs 2, 3 and 4. Enclosure 1 of this letter provides the response to RAI 72. | |||
There are no new regulatory commitments contained in this letter. If you have any questions or require additional information, please call me at (949) 368-6240. | |||
Sincerely, | |||
==Enclosure:== | |||
: 1. Response to RAIs 53 and 72 cc: A. T. Howell III, Regional Administrator, NRC Region IV J. R. Hall, NRC Project Manager, SONGS Units 2 and 3 G. G. Warnick, NRC Senior Resident Inspector, SONGS Units 2 and 3 R. E. Lantz, Branch Chief, Division of Reactor Projects, NRC Region IV | |||
ENCLOSURE 1 SOUTHERN CALIFORNIA EDISON RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION REGARDING RESPONSE TO CONFIRMATORY ACTION LETTER DOCKET NO. 50-361 TAC NO. ME 9727 Response to RAIs 53 and 72 | |||
===RAI 53=== | |||
In Reference 9, Section 4.6.2, "[Tube-to-Tube (TTW)] Growth Model," was the regression fit slope and intercept uncertainty modeled (e.g., as was done for the burst pressure versus voltage model in NRC Generic Letter 95-05)? If not, why is this conservative? Was the data scatter about the regression fit modeled as normally distributed? If so, provide justification for the adequacy of this assumption (i.e., normal distribution) to fully capture the upper tail of the distribution as shown in Figure 4-12 on page 4-25. | |||
===RESPONSE=== | |||
Note: RAI Reference 9 is the Operational Assessment for SONGS Unit 2 Steam Generators for Upper Bundle Tube-to-Tube Wear Degradation at End of Cycle 16," prepared by Intertek APTECH for Areva, Report No. AES 12068150-2Q-1, Revision 0, September 2012. | |||
The Monte-Carlo simulation which was used to perform the SONGS Unit 2 operational assessment (OA) for tube-to-tube wear (TTW) relies on a correlation developed using measured Unit 3 TTW depths. The correlating independent variable is the total wear index. | |||
This work is described in summary form in Section 4.6.2 of RAI Reference 9. Elements of the residual analysis of the TTW growth model development process are shown in Figure 4-12 of RAI Reference 9. The two issues identified in RAI 53 are addressed in this response. | |||
: 1. Regression Model Uncertainty In NRC Generic Letter 95-05 (Reference R1), the implementation consisted of developing a sampling method discussed in References R2 and R3. This approach samples from a prediction interval equation which accounts for several components of uncertainty including those involving the slope of the regression line, the intercept, and the basic error-of-estimate from the data set. The form of the sampling equation is given by: | |||
2 2 Ys = YCor +/- ta/2,N-2 Sy/x[ 1 + 1/N + (X-x') /((N-1)Sx | |||
) 0.5 where: | |||
Y= Sampled value of Y YCor = Value computed from regression line ta/2,N-2 = t-distribution with N-2 degrees of freedom Sy/x = Standard error of estimate from the correlation N = Number of data points X = Value of independent variable x' = Mean of independent variable values Sx2 = Sample variance of independent variable values Examination of the above equation shows that the most important component is the size of the data set (N) from which the correlation was developed. In this case, over 320 data points were used. A simplified estimate of the effect of neglecting these terms yields a multiplier of 1.0031 on the standard error of estimate. The other affected component involves the use of the t-distribution rather than the normal distribution for the probabilistic sampling component. In general for sample sizes greater than approximately 30, the Page 2 of 12 | |||
difference is considered negligible for use in simulation. In the case of the Unit 3 data, the difference at the 9 5 th percentile is negligible being approximately 0.3% (1.6497 vs. 1.645). It was not necessary to explicitly address the uncertainties in slope and intercept variables from the regression analysis since it is inconsequential to the simulation results. | |||
: 2. Statistical Treatment of the Regression Model In Figure 4-12 of RAI Reference 9, the distribution of the residuals is well represented by a normal cumulative distribution function. Deviations from normality are observed only at the lower and upper extremes (outside the 95th percentile bounds). For the lower tail, the deviation is conservative. For the upper tail, the deviation can become non-conservative when sampling beyond the upper 97th percentile level (e.g., when the number of TTW initiations is large so that there is a greater chance in having an extreme value for TTW growth as a sample outcome). | |||
To validate that any deviation from normality from the upper tail does not significantly impact the OA results, the TTW growth model was modified. This was accomplished by separately fitting the upper tail of the residuals with a Beta distribution to give a more precise fit to the residuals above the 95th percentile. This modification was done for the 70% power model and involved changing the logic in the algorithm to select the value for growth rate uncertainty when the standard normal parameter exceeds 1.645 (above the upper 95%). | |||
The results from the re-evaluation are given in the table below: | |||
Allowable Inspection Interval for Probability of Burst (POB) = 5% | |||
(RAI Reference 9, Case I - ETSS Depth Sizing) | |||
Normal Distribution of Residuals Normal Distribution of Residuals (Full Sample Range) (Adjusted Above 95th Percentile) 1.33(1) (Years at Power) 1.24(2) (Years at Power) | |||
Notes: | |||
: 1) Results from RAI Reference 9 | |||
: 2) Results from modified model The above comparison between the two methods of treating the regression error shows a small difference in the allowable inspection interval calculated from the OA. The change in inspection interval is less than 7%. For the planned inspection interval of 5 months (0.42 years at power), the deviation in the upper tail beyond 95% has a negligible effect on the allowable inspection interval for Unit 2 due to the much shorter operating period. | |||
Page 3 of 12 | |||
==References:== | |||
RI. Generic Letter 95-05: Voltage-Based Repair Criteria for Westinghouse Steam Generator Tubes Affected by Outside Diameter Stress Corrosion Cracking, (August 3, 1995). | |||
R2. Statistics Manual, Crow, Davis, and Maxfield, Dover Press, New York, Page 163. | |||
R3. Applied Regression Analysis, Second Edition, Draper and Smith, John Wiley and Sons, New York, Page 30, 1981. | |||
Page 4 of 12 | |||
===RAI 72=== | |||
Reference 1, Response to RAI 3 - This response did not fully address RAI question 3. What is the sensitivity of the results in Figure 5-4 of Reference 4 to the different formulations of wear index in Equations 1 through 5? | |||
===RESPONSE=== | |||
Note: RAI Reference 1 is SCE's "Response to Request for Additional Information (RAls 2, 3, and 4) Regarding Confirmatory Action Letter Response," dated February 25, 2013. | |||
Note: RAI Reference 4 is the "Operational Assessment for SONGS Unit 2 Steam Generators for Upper Bundle Tube-to-Tube Wear Degradation at End of Cycle 16," prepared by Intertek APTECH for Areva, Report No. AES 12068150-2Q-1, Revision 0, September 2012. | |||
The wear index represents the complete state of wear degradation in a tube due to contact with tube supports. As discussed in the response to RAI 3, the justification of the wear index used in RAI Reference 4 is the ability of the wear index, as a correlating parameter, to describe the SONGS Unit 3 tube-to-tube wear (TTW) in terms TTW depth and maximum depths of TTW after 0.926 years at power. This was accomplished by selecting the correlation equation developed by regression analysis of the Unit 3 data that achieved the best fit. A standard approach in engineering modeling is to apply "goodness of fit" criteria in the selection process. This approach provides a basis for selecting the mathematical combination of wear indices to yield the best correlation. Statistical regression analysis and goodness-of-fit verification (R 2 and standard deviation of the residuals) are the means by which an empirical correlation can be developed that best explains what is physically observed with minimum uncertainty. From this approach, the total wear index based on the summation of anti-vibration bar (AVB) and tube support plate (TSP) wear was established. | |||
The wear index selection process evaluated several alternative definitions and determined the goodness-of-fit for each. Of the five model variations discussed in the response to RAI 3, the first four have similar properties in terms of the fraction of the data variation explained by the regression model (R2 ), and the standard deviation of the residuals (proportional to the standard error of estimate) which is a measure of variance in the prediction ability of the model. For these criteria, it was concluded that Alternatives 1 through 4 are essentially equivalent having similar capability in correlating the observed NDE data to each definition of the wear index. | |||
The wear index definition from Alternative 4 (the summation of AVB and TSP wear) was selected as the definition of the wear index. This alternative resulted in the ability to define the TTW depth prediction model in terms of a single wear related quantity with accuracy comparable to a more complex model of the group. | |||
Alternative 5 redefined the wear index in terms of AVB wear only. As demonstrated in Table 1 of the response to RAI 3, this alternative does not describe wear degradation as well as Alternatives 1 through 4. Because of the greater variance for the AVB wear index model, it was expected that this definition for the wear index would give a more limiting result for probability of burst (POB) than the current total wear index model. | |||
To respond to this RAI, a separate and complete operational assessment (OA) model was developed using a wear index based on AVB wear only, to demonstrate the effect of an alternate definition on POB. Comparison of the two wear index models (AVB wear only and the Page 5 of 12 | |||
total wear index as the sum of AVB and TSP) is shown in Figure 1 for Unit 2 and Figure 2 for Unit 3. For Unit 2, the change in definition doesn't appear significant but small differences in indices greater than 60% through-wall (TW) will affect the development of the probability of initiation (POI) model. For Unit 3, the AVB wear index effectively reduces the range of the index from greater than 300%TW to less than 200%TW. This change in definition compresses the scale of both the initiation and TTW growth rate models and affects the shape of the POI model for Unit 2. | |||
Figure 3 shows the existence of TTW in Unit 3 plotted as the presence or non-presence of TTW against the AVB wear index. Logistic regression analysis was used to produce the Unit 3 curve. | |||
Following the same benchmarking procedure in RAI Reference 4, the Unit 3 curve was adjusted to develop the model for Unit 2. The Unit 2 curve transitioned to probability of unity as the AVB wear index approached 200% TW. An acceptable benchmark was achieved when the model produced about two detected indications at the estimated threshold detection level for the | |||
+PointTM probe. This process was discussed in the response to RAI 9. The results from the benchmarking simulation of 1000 trial calculations are shown in the histogram in Figure 4. The benchmarking performed produced similar outcomes as the total wear index model. | |||
The development of the TTW growth model based on the AVB wear index is discussed in the response to RAI 3. The regression line for the TTW maximum depth data is shown in Figure 5 having an intercept of 19.638, a slope of 0.2206 and a standard deviation of the residuals of 12.63. | |||
Figure 6 compares the POB results for the 70% power OA for the two wear index definitions. | |||
The 70% OA in RAI Reference 4 established an allowable inspection interval of 1.33 years at power or 16 months based on the total wear index. For the wear index based on AVB wear, the allowable inspection interval becomes 1.15 years at power or 14 months. The reduction in the inspection interval is about 2 months. This difference is not significant since the more conservative AVB wear index results confirm that significant margin exist for the planned 5 month inspection interval. The more conservative results for the AVB wear index are primarily the result of greater scatter (regression error) evident in the residuals in the regression process. | |||
Based on the goodness-of-fit comparisons discussed in the response to RAI 3, and the response of RAI 72, the total wear index (Alternative 4) is the optimum model (of the alternatives evaluated) for this degradation mechanism. It is expected that the more complex Alternatives 1 through 3 will give similar POB results as the total wear index model (Alternative 4), having nearly identical scatter in the residuals. | |||
Page 6 of 12 | |||
SONGS-2 Wear Index Histogram (after 1.718 Years at Power) 220 u 140 2 | |||
= 120 0 | |||
S100 80 E | |||
z 60 40 20 0 | |||
AVB Wear Index, (%TW) | |||
SONGS-2 Wear Index Histogram (after 1.718 Years at Power) 220 200 *2E-088--j 180 160 u | |||
a 140 U 120 U | |||
0 100 80 z 60 40 20 0 | |||
Total Wear Index, (%TW) | |||
Figure 1- Unit 2 Histograms for AVB Wear Index and Total Wear Index Model Definitions Page 7 of 12 | |||
SONGS-3 Wear Index Histogram (after 0.926 Years at Power) 220 200 - 3E-088 _ | |||
N 3E-089 180 160 U | |||
C 140 | |||
" 120 0 t 6100 | |||
.80-E 2 60-40 20 AVB Wear Index, (%/TW) | |||
SONGS-3 Wear Index Histogram (after 0.926 Years at Power) 220 200 - 3E-088 111312-089 180 - | |||
160 -- | |||
0 U140 - | |||
S120 - | |||
0 100 z 60 40 20-Total Wear Index, (%/,TW) | |||
Figure 2 - Unit 3 Histograms for AVB Wear Index and Total Wear Index Model Definitions Page 8 of 12 | |||
Tube-to-Tube Wear Initiation Model 1.0 0.9 0.8 0.7 | |||
.0 0.6 17 4- 0.5 0 | |||
.0 o.. | |||
0) | |||
J21 0.4 0 | |||
0/ | |||
0U 0.3 0.2 | |||
*SONGS-3Oata-A"B WI | |||
--- SONGS-3 Regression Fit -AVB WI 0.1 -A--SONGS-2 Initiation Model - AVB Wl | |||
-E-SONGS-2 Initiation Model - Total WI | |||
-- ..... ... ._ .II 0.0 0 20 40 60 80 100 120 140 160 180 200 Wear Index, WI (%TW) | |||
Figure 3 - Comparison of Initiation Models for the AVB and Total Wear Index Definitions Page 9 of 12 | |||
Initiation Model Benchmarking Results (1000 Trials) 220 200 - A E Total Wear Index "AVB Wear Index 180 160 140 120 U | |||
0 100 80 60 20-20 Number of TTW Initiations Figure 4 - Unit 2 Benchmarking Results for the AVB and Total Wear Index Model Definitions Page 10 of 12 | |||
Tube-to-Tube Wear Depths - ETSS 27902.2 Sized 100 90 80 70 I 60 | |||
: a. 50 0 | |||
0 40 30 20 10 0 | |||
0 20 40 60 80 100 120 140 160 180 20( | |||
AVB Wear Index, (%TW) | |||
Figure 5 - Unit 3 Tube-to-Tube Wear Depths versus AVB Wear Index Page 11 of 12 | |||
Operational Assessment for TTW for Mid-Cycle 17 for 70% Power Operation 0.16 I I I | |||
--- ETSS 27902.2 Sizing, Total Wear Index Model If | |||
- - - ETSS 27902.2 Sizing, AVB Wear Index Model 0.14- | |||
- - - Mid-Cycle 17 (5 Months at Power) | |||
- -Cycle 17 (1.578 Years at Power) | |||
-SIPC Margin, P09 <= 0.05 0.12 - | |||
0 - - I 0~ | |||
0.10 - S o 0.08 S0.06 0 | |||
0.04- ___ i+---- | |||
0.02 0.00 -. 4 - I- I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Inspection Interval, (Years at Power) | |||
Figure 6 - Probability of Burst Results for the AVB and Total Wear Index Models Page 12 of 12}} |
Latest revision as of 06:45, 6 February 2020
ML13102A296 | |
Person / Time | |
---|---|
Site: | San Onofre ![]() |
Issue date: | 04/10/2013 |
From: | St.Onge R Edison International Co, Southern California Edison Co |
To: | Document Control Desk, Office of Nuclear Reactor Regulation |
References | |
TAC ME9727 | |
Download: ML13102A296 (14) | |
Text
SOUTHERN CALIFORNIA Richard 1. St. Onge EDISONmeDirector, ED SO "
Nuclear Regulatory Affairs and Emergency Planning An EDISON INTERNATIONAL Company April 10, 2013 10 CFR 50.4 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555-0001
Subject:
Docket No. 50-361 Response to Request for Additional Information (RAIs 53 and 72) Regarding Confirmatory Action Letter Response (TAC No. ME 9727)
San Onofre Nuclear Generating Station, Unit 2
References:
- 1. Letter from Mr. Elmo E. Collins (USNRC) to Mr. Peter T. Dietrich (SCE), dated March 27, 2012, Confirmatory Action Letter 4-12-001, San Onofre Nuclear Generating Station, Units 2 and 3, Commitments to Address Steam Generator Tube Degradation
- 2. Letter from Mr. Peter T. Dietrich (SCE) to Mr. Elmo E. Collins (USNRC), dated October 3, 2012, Confirmatory Action Letter - Actions to Address Steam Generator Tube Degradation, San Onofre Nuclear Generating Station, Unit 2
- 3. Letter from Mr. James R. Hall (USNRC) to Mr. Peter T. Dietrich (SCE), dated March 18, 2013, Second Request for Additional Information (RAI 33-67)
Regarding Response to Confirmatory Action Letter, San Onofre Nuclear Generating Station, Unit 2
- 4. Letter from Mr. Richard J. St. Onge (SCE) to Document Control Desk (USNRC), dated February 25, 2013, Response to Request for Additional Information (RAIs 2, 3 and 4) Regarding Confirmatory Action Letter Response, San Onofre Nuclear Generating Station, Unit 2
- 5. Email from Mr. James R. Hall (USNRC) to Mr. Ryan Treadway (SCE), dated March 15, 2013, Request for Additional Information (RAIs 68-72) Regarding Response to Confirmatory Action Letter, San Onofre Nuclear Generating Station, Unit 2
Dear Sir or Madam,
On March 27, 2012, the Nuclear Regulatory Commission (NRC) issued a Confirmatory Action Letter (CAL) (Reference 1) to Southern California Edison (SCE) describing actions that the NRC and SCE agreed would be completed to address issues identified in the steam generator tubes of San Onofre Nuclear Generating Station (SONGS) Units 2 and 3. In a letter to the NRC dated October 3, 2012 (Reference 2), SCE reported completion of the Unit 2 CAL actions and included a Return to Service Report (RTSR) that provided details of their completion.
La P.O. Box 128 San Clemente, CA 92672 q
Document Control Desk April 10, 2013 By letter dated March 18, 2013 (Reference 3), the NRC issued Requests for Additional Information (RAls) regarding the CAL response. Enclosure 1 of this letter provides the response to RAI 53.
SCE provided the response to RAIs 2, 3 and 4 in a letter dated February 25, 2013 (Reference 4). By e-mail dated March 15, 2013 (Reference 5), the NRC issued Requests for Additional Information (RAIs) regarding the response to RAIs 2, 3 and 4. Enclosure 1 of this letter provides the response to RAI 72.
There are no new regulatory commitments contained in this letter. If you have any questions or require additional information, please call me at (949) 368-6240.
Sincerely,
Enclosure:
- 1. Response to RAIs 53 and 72 cc: A. T. Howell III, Regional Administrator, NRC Region IV J. R. Hall, NRC Project Manager, SONGS Units 2 and 3 G. G. Warnick, NRC Senior Resident Inspector, SONGS Units 2 and 3 R. E. Lantz, Branch Chief, Division of Reactor Projects, NRC Region IV
ENCLOSURE 1 SOUTHERN CALIFORNIA EDISON RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION REGARDING RESPONSE TO CONFIRMATORY ACTION LETTER DOCKET NO. 50-361 TAC NO. ME 9727 Response to RAIs 53 and 72
RAI 53
In Reference 9, Section 4.6.2, "[Tube-to-Tube (TTW)] Growth Model," was the regression fit slope and intercept uncertainty modeled (e.g., as was done for the burst pressure versus voltage model in NRC Generic Letter 95-05)? If not, why is this conservative? Was the data scatter about the regression fit modeled as normally distributed? If so, provide justification for the adequacy of this assumption (i.e., normal distribution) to fully capture the upper tail of the distribution as shown in Figure 4-12 on page 4-25.
RESPONSE
Note: RAI Reference 9 is the Operational Assessment for SONGS Unit 2 Steam Generators for Upper Bundle Tube-to-Tube Wear Degradation at End of Cycle 16," prepared by Intertek APTECH for Areva, Report No. AES 12068150-2Q-1, Revision 0, September 2012.
The Monte-Carlo simulation which was used to perform the SONGS Unit 2 operational assessment (OA) for tube-to-tube wear (TTW) relies on a correlation developed using measured Unit 3 TTW depths. The correlating independent variable is the total wear index.
This work is described in summary form in Section 4.6.2 of RAI Reference 9. Elements of the residual analysis of the TTW growth model development process are shown in Figure 4-12 of RAI Reference 9. The two issues identified in RAI 53 are addressed in this response.
- 1. Regression Model Uncertainty In NRC Generic Letter 95-05 (Reference R1), the implementation consisted of developing a sampling method discussed in References R2 and R3. This approach samples from a prediction interval equation which accounts for several components of uncertainty including those involving the slope of the regression line, the intercept, and the basic error-of-estimate from the data set. The form of the sampling equation is given by:
2 2 Ys = YCor +/- ta/2,N-2 Sy/x[ 1 + 1/N + (X-x') /((N-1)Sx
) 0.5 where:
Y= Sampled value of Y YCor = Value computed from regression line ta/2,N-2 = t-distribution with N-2 degrees of freedom Sy/x = Standard error of estimate from the correlation N = Number of data points X = Value of independent variable x' = Mean of independent variable values Sx2 = Sample variance of independent variable values Examination of the above equation shows that the most important component is the size of the data set (N) from which the correlation was developed. In this case, over 320 data points were used. A simplified estimate of the effect of neglecting these terms yields a multiplier of 1.0031 on the standard error of estimate. The other affected component involves the use of the t-distribution rather than the normal distribution for the probabilistic sampling component. In general for sample sizes greater than approximately 30, the Page 2 of 12
difference is considered negligible for use in simulation. In the case of the Unit 3 data, the difference at the 9 5 th percentile is negligible being approximately 0.3% (1.6497 vs. 1.645). It was not necessary to explicitly address the uncertainties in slope and intercept variables from the regression analysis since it is inconsequential to the simulation results.
- 2. Statistical Treatment of the Regression Model In Figure 4-12 of RAI Reference 9, the distribution of the residuals is well represented by a normal cumulative distribution function. Deviations from normality are observed only at the lower and upper extremes (outside the 95th percentile bounds). For the lower tail, the deviation is conservative. For the upper tail, the deviation can become non-conservative when sampling beyond the upper 97th percentile level (e.g., when the number of TTW initiations is large so that there is a greater chance in having an extreme value for TTW growth as a sample outcome).
To validate that any deviation from normality from the upper tail does not significantly impact the OA results, the TTW growth model was modified. This was accomplished by separately fitting the upper tail of the residuals with a Beta distribution to give a more precise fit to the residuals above the 95th percentile. This modification was done for the 70% power model and involved changing the logic in the algorithm to select the value for growth rate uncertainty when the standard normal parameter exceeds 1.645 (above the upper 95%).
The results from the re-evaluation are given in the table below:
Allowable Inspection Interval for Probability of Burst (POB) = 5%
(RAI Reference 9, Case I - ETSS Depth Sizing)
Normal Distribution of Residuals Normal Distribution of Residuals (Full Sample Range) (Adjusted Above 95th Percentile) 1.33(1) (Years at Power) 1.24(2) (Years at Power)
Notes:
- 1) Results from RAI Reference 9
- 2) Results from modified model The above comparison between the two methods of treating the regression error shows a small difference in the allowable inspection interval calculated from the OA. The change in inspection interval is less than 7%. For the planned inspection interval of 5 months (0.42 years at power), the deviation in the upper tail beyond 95% has a negligible effect on the allowable inspection interval for Unit 2 due to the much shorter operating period.
Page 3 of 12
References:
RI. Generic Letter 95-05: Voltage-Based Repair Criteria for Westinghouse Steam Generator Tubes Affected by Outside Diameter Stress Corrosion Cracking, (August 3, 1995).
R2. Statistics Manual, Crow, Davis, and Maxfield, Dover Press, New York, Page 163.
R3. Applied Regression Analysis, Second Edition, Draper and Smith, John Wiley and Sons, New York, Page 30, 1981.
Page 4 of 12
RAI 72
Reference 1, Response to RAI 3 - This response did not fully address RAI question 3. What is the sensitivity of the results in Figure 5-4 of Reference 4 to the different formulations of wear index in Equations 1 through 5?
RESPONSE
Note: RAI Reference 1 is SCE's "Response to Request for Additional Information (RAls 2, 3, and 4) Regarding Confirmatory Action Letter Response," dated February 25, 2013.
Note: RAI Reference 4 is the "Operational Assessment for SONGS Unit 2 Steam Generators for Upper Bundle Tube-to-Tube Wear Degradation at End of Cycle 16," prepared by Intertek APTECH for Areva, Report No. AES 12068150-2Q-1, Revision 0, September 2012.
The wear index represents the complete state of wear degradation in a tube due to contact with tube supports. As discussed in the response to RAI 3, the justification of the wear index used in RAI Reference 4 is the ability of the wear index, as a correlating parameter, to describe the SONGS Unit 3 tube-to-tube wear (TTW) in terms TTW depth and maximum depths of TTW after 0.926 years at power. This was accomplished by selecting the correlation equation developed by regression analysis of the Unit 3 data that achieved the best fit. A standard approach in engineering modeling is to apply "goodness of fit" criteria in the selection process. This approach provides a basis for selecting the mathematical combination of wear indices to yield the best correlation. Statistical regression analysis and goodness-of-fit verification (R 2 and standard deviation of the residuals) are the means by which an empirical correlation can be developed that best explains what is physically observed with minimum uncertainty. From this approach, the total wear index based on the summation of anti-vibration bar (AVB) and tube support plate (TSP) wear was established.
The wear index selection process evaluated several alternative definitions and determined the goodness-of-fit for each. Of the five model variations discussed in the response to RAI 3, the first four have similar properties in terms of the fraction of the data variation explained by the regression model (R2 ), and the standard deviation of the residuals (proportional to the standard error of estimate) which is a measure of variance in the prediction ability of the model. For these criteria, it was concluded that Alternatives 1 through 4 are essentially equivalent having similar capability in correlating the observed NDE data to each definition of the wear index.
The wear index definition from Alternative 4 (the summation of AVB and TSP wear) was selected as the definition of the wear index. This alternative resulted in the ability to define the TTW depth prediction model in terms of a single wear related quantity with accuracy comparable to a more complex model of the group.
Alternative 5 redefined the wear index in terms of AVB wear only. As demonstrated in Table 1 of the response to RAI 3, this alternative does not describe wear degradation as well as Alternatives 1 through 4. Because of the greater variance for the AVB wear index model, it was expected that this definition for the wear index would give a more limiting result for probability of burst (POB) than the current total wear index model.
To respond to this RAI, a separate and complete operational assessment (OA) model was developed using a wear index based on AVB wear only, to demonstrate the effect of an alternate definition on POB. Comparison of the two wear index models (AVB wear only and the Page 5 of 12
total wear index as the sum of AVB and TSP) is shown in Figure 1 for Unit 2 and Figure 2 for Unit 3. For Unit 2, the change in definition doesn't appear significant but small differences in indices greater than 60% through-wall (TW) will affect the development of the probability of initiation (POI) model. For Unit 3, the AVB wear index effectively reduces the range of the index from greater than 300%TW to less than 200%TW. This change in definition compresses the scale of both the initiation and TTW growth rate models and affects the shape of the POI model for Unit 2.
Figure 3 shows the existence of TTW in Unit 3 plotted as the presence or non-presence of TTW against the AVB wear index. Logistic regression analysis was used to produce the Unit 3 curve.
Following the same benchmarking procedure in RAI Reference 4, the Unit 3 curve was adjusted to develop the model for Unit 2. The Unit 2 curve transitioned to probability of unity as the AVB wear index approached 200% TW. An acceptable benchmark was achieved when the model produced about two detected indications at the estimated threshold detection level for the
+PointTM probe. This process was discussed in the response to RAI 9. The results from the benchmarking simulation of 1000 trial calculations are shown in the histogram in Figure 4. The benchmarking performed produced similar outcomes as the total wear index model.
The development of the TTW growth model based on the AVB wear index is discussed in the response to RAI 3. The regression line for the TTW maximum depth data is shown in Figure 5 having an intercept of 19.638, a slope of 0.2206 and a standard deviation of the residuals of 12.63.
Figure 6 compares the POB results for the 70% power OA for the two wear index definitions.
The 70% OA in RAI Reference 4 established an allowable inspection interval of 1.33 years at power or 16 months based on the total wear index. For the wear index based on AVB wear, the allowable inspection interval becomes 1.15 years at power or 14 months. The reduction in the inspection interval is about 2 months. This difference is not significant since the more conservative AVB wear index results confirm that significant margin exist for the planned 5 month inspection interval. The more conservative results for the AVB wear index are primarily the result of greater scatter (regression error) evident in the residuals in the regression process.
Based on the goodness-of-fit comparisons discussed in the response to RAI 3, and the response of RAI 72, the total wear index (Alternative 4) is the optimum model (of the alternatives evaluated) for this degradation mechanism. It is expected that the more complex Alternatives 1 through 3 will give similar POB results as the total wear index model (Alternative 4), having nearly identical scatter in the residuals.
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SONGS-2 Wear Index Histogram (after 1.718 Years at Power) 220 u 140 2
= 120 0
S100 80 E
z 60 40 20 0
AVB Wear Index, (%TW)
SONGS-2 Wear Index Histogram (after 1.718 Years at Power) 220 200 *2E-088--j 180 160 u
a 140 U 120 U
0 100 80 z 60 40 20 0
Total Wear Index, (%TW)
Figure 1- Unit 2 Histograms for AVB Wear Index and Total Wear Index Model Definitions Page 7 of 12
SONGS-3 Wear Index Histogram (after 0.926 Years at Power) 220 200 - 3E-088 _
N 3E-089 180 160 U
C 140
" 120 0 t 6100
.80-E 2 60-40 20 AVB Wear Index, (%/TW)
SONGS-3 Wear Index Histogram (after 0.926 Years at Power) 220 200 - 3E-088 111312-089 180 -
160 --
0 U140 -
S120 -
0 100 z 60 40 20-Total Wear Index, (%/,TW)
Figure 2 - Unit 3 Histograms for AVB Wear Index and Total Wear Index Model Definitions Page 8 of 12
Tube-to-Tube Wear Initiation Model 1.0 0.9 0.8 0.7
.0 0.6 17 4- 0.5 0
.0 o..
0)
J21 0.4 0
0/
0U 0.3 0.2
- SONGS-3Oata-A"B WI
--- SONGS-3 Regression Fit -AVB WI 0.1 -A--SONGS-2 Initiation Model - AVB Wl
-E-SONGS-2 Initiation Model - Total WI
-- ..... ... ._ .II 0.0 0 20 40 60 80 100 120 140 160 180 200 Wear Index, WI (%TW)
Figure 3 - Comparison of Initiation Models for the AVB and Total Wear Index Definitions Page 9 of 12
Initiation Model Benchmarking Results (1000 Trials) 220 200 - A E Total Wear Index "AVB Wear Index 180 160 140 120 U
0 100 80 60 20-20 Number of TTW Initiations Figure 4 - Unit 2 Benchmarking Results for the AVB and Total Wear Index Model Definitions Page 10 of 12
Tube-to-Tube Wear Depths - ETSS 27902.2 Sized 100 90 80 70 I 60
- a. 50 0
0 40 30 20 10 0
0 20 40 60 80 100 120 140 160 180 20(
AVB Wear Index, (%TW)
Figure 5 - Unit 3 Tube-to-Tube Wear Depths versus AVB Wear Index Page 11 of 12
Operational Assessment for TTW for Mid-Cycle 17 for 70% Power Operation 0.16 I I I
--- ETSS 27902.2 Sizing, Total Wear Index Model If
- - - ETSS 27902.2 Sizing, AVB Wear Index Model 0.14-
- - - Mid-Cycle 17 (5 Months at Power)
- -Cycle 17 (1.578 Years at Power)
-SIPC Margin, P09 <= 0.05 0.12 -
0 - - I 0~
0.10 - S o 0.08 S0.06 0
0.04- ___ i+----
0.02 0.00 -. 4 - I- I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Inspection Interval, (Years at Power)
Figure 6 - Probability of Burst Results for the AVB and Total Wear Index Models Page 12 of 12