# Presentation: 898355

## Jy-An. John Wang* and  N. S. Rao**wangja@ornl.gov, raons@ornl.gov*Nuclear Science & Technology Division**Computer Science & Mathematics DivisionOak Ridge National LaboratoryOak Ridge, Tennessee 37831ASTM 21th Symposium on Effects of Radiation on MaterialsJune 18-20, 2002Tucson, Arizona

***New Methodologies for Developing Radiation Embrittlement Models and Trend Curves of Charpy Impact Test Data***

## Presentation Outline

**A new methodology for developing radiation embrittlement models**
- Information fusion technique
- New embrittlement models and results
**A new fitting procedure for Charpy impact test data**
- Issue on chemical variability
- New Charpy curve fitting models and results

## Background 	 

**The aging of current in-service**** ****nuclear power plants**** **
**Reliable prediction models for the integrity of aging components**
**Success of nuclear technology depending on effective surveillance**
**Integration of the currently available knowledge to effectively tackle the aging issue**

## Radiation Embrittlement Estimates    

**Aging History**
- Temperature
- Neutron flux &
-    flux spectrum
- Power history

**Material History**
- Process history
- Heat treatment
- Chemistry

**Mechanical Test**
**Results**
- Baseline &
- Irradiated Data

**RPV Embrittlement**
**Prediction Models**

**Guthrie's, Odette's, Fisher's,  B&W Lowe's, French FIM, Eason’s,   ORNL models, etc.,**** **

## Aging Material Modeling

**Modeling of material aging behavior is a very ****difficult task****, due to**
**Complex non-linear dependencies observed in typical material aging data;**
**Large uncertainties and data scatter;**
**Insufficient long term aging data.**
**Approach to material modeling**
**Conventional deterministic approach,**
**Domain model approach,**
**Considering the complexity of the problem,  and as evidenced in previous studies, it is unlikely that a *****single***** method will outperform all others.**

## Data Fission and Data Fusion Processes

**Aging Data.**
**Fission Process**

- 1

- 3

- Sensor 2

- Fusion
- Process

**Information fusion is highly sensitive to factors, such as the specific nature of the individual sensors and how they**_** **_**replicate**** or ****complement**** one another.**

## New Approach for Aging Material Modeling

**Utilize advanced information fusion technique to design the ****projective fuser**** that combines**
**domain models**
**generic models**
**Use the designed projective fuser on **
**chemical compositions**
**mechanical test results**
**service environments**
** ****	****to forecast the material aging behavior.**

## Information Fusion Technique

- Domain
- Modeling

- QA
- Database

- Generic
- Modeling

- Information
- Fusion Modeling

- Predicted Material Aging Response

- Fuser needs to be designed through
- Analysis of the error regressions, and
- Identification of suitable projective space

## Information Fusion

**  ****Background**
**1786 – Condorcet: democracy models**
**Most existing methods require closed form  distributions**

**  ****Our Contributions on Fuser Method**
**Developed methods that do not require distributions by utilizing experimental data**
**Provided computationally efficient solutions**
**Provided performance guarantees  **

## Information Fusion Approach 

***Process Model*****: Measurements (y) depend on parameters (p).**
**	****y = F(p) + e.    Error (e).**

***Prediction Method****** ******M_k*****: Estimates parameters using a number of measurements y_1, ..., y_n**
**	****p_k = M_k (y_1, ..., y_n).**

***Information Fusion*****: Given prediction methods M_1 , ... , M_m, combine them to estimate p**
**	****p_f = F(M_1, ..., M_m, y_1, ..., y_n)**
** **
**The combined estimate is guaranteed to be better than the best individual estimate.**

## Information Fusion Architecture - Every component must be designed based on detailed analysis of underlying system

- Domain
- Model 1

- Domain
- Model N

- Generic
- Model 1

- Generic
- Model M

- Projective Space

- Error Estimation

- Computation
- Method for Fuser

**Projective Fuser Design**

## Class of Projective Fusers

**Project fuser based on lower envelope of error profile**** ****of the estimators**
**Requires detailed knowledge of distribution function**
**Linear projective fuser**
**Projective fuser based on nearest neighbor concept **
**Partitions the space domain into regions based on the nearest to the sample**
**For each region an estimator with the lowest empirical error is used to compute function estimate for all the points in the region**
**the expected error is close to optimal with a high probability, for finite sample and irrespective of the underlying  distributions**

## Embrittlement Model Tasks 

**Create unbiased training and test sets**
**PR-EDB surveillance data was streamlined**
**The data values was scaled to the interval [-1, 1]**
**Transform the input feature space to a dimensionally smaller, new input space**

**Develop optimal projective fusers**
**Identify the projective space**
**Develop Linear Projective Fuser**
**Develop Nearest Neighbor Fuser (NN Fuser)**

**Compute a collection of estimators**
**For each method, select a criteria function and optimization routine that consistently produces stable results**
**For statistically estimators, adopt the procedure described in the literature**
**For neural networks, determine the number of hidden layers and the number nodes per layer**

## Development of Fuser Model for GE BWR Surveillance Data

**Eight different models were investigated**
**four neural network models (ANN)**
**two ORNL improved models**
**K-nearest neighbor regression (K-NNR)**
**Eason-Wright-Odette (EWO) - 1998 model**
**Parameters: Cu, Ni, P, Fluence, t****irr****, T****irr**
**Projective Fuser: Linear Fuser and NN Fuser**
**NN fuser indicated that about ****67.3% and 52.4%**** ****reduction**** ****in**** ****uncertainty**** for weld and plate data, respectively, compared to that of  NRC R.G. 1.99/R2’s predictions**

## ORNL Embrittlement Models

- _ORNL Model 1:_

- _ORNL Model 2:_

- Parameter: Cu, Ni, P, Fluence, tirr.

- Parameter: Cu, Ni, P, Fluence.

## Eason-Wright-Odette 1998 Embrittlement Models

- Parameter: Cu, Ni, P, Fluence, Tirr, tirr.

## Uncertainty of Embrittlement Models for GE BWR data 

***Uncertainty of Embrittlement Models for GE BWR data****** ***

## GE-BWR Residual Plots

- _ORNL Model II_

- _E-W-O Model_

- _Plate Materials_

- _Weld Materials_

## ORNL Fuser Model results in 67.3% and 52.4% reduction in uncertainty compared to R.G. 1.99/R2

- _NN Fuser Model_

- _R.G. 1.99 /R2 Model_

- _Plate Materials_

- _Weld Materials_

## Conclusion of Information Fusion Embrittlement Model

- NN-Fuser Model achieved 67.3% and 52.4% reduction in 2-sigma uncertainties compared to that of the Reg. Guide 1.99, Rev. 2’s model for base and weld materials, respectively.

- Future improvements of the proposed method can be made by using the k-fold cross validation method.

- The predictions generated by fuser system have the potential for providing efficient, reliable, and fast results, and can be an essential part of the overall safety assessment of material aging research.

## Development of New Trend Curves for Charpy Impact Test Data

- The purpose of this new fitting procedure are
- To reduce uncertainty of Charpy curve fitting
- To generate a new multi-space topography of Charpy data that can properly reflect the inhomogeneneity of the testing materials, and
- To utilize this multi-space trend surface to link and project the surveillance test results to that of reactor pressure vessel steels.

## Characterization of Surveillance Charpy Impact Test Data 

- General form of Charpy impact energy
*E = f *(* T, ****t, Tirr, Cu, Ni, Material History, **	**	**	**Microstructure,..*.)

- For Charpy data from a single capsule
*E = f *(* T, Cu, Ni, ..*)
*For each individual Charpy data*
*	**E**i** = f ( T**i**, Cu**i**, Ni**i**,...)*

## Charpy Impact Curve Fitting

***The hyperbolic tangent model:   E = f (T)****** ***

***The new Charpy fitting model:   E = f (T, Cu, Ni)****** ***

**A=(USE+LSE)/2,  B=(USE-LSE)/2, C=1/SLOPE, and**
**C****i**** are constant fitting parameters**** **

## Advanced Charpy Impact Curve Fitting

***Advanced Charpy Data Fitting Function ***

## Results of Fitting Procedures 

- The weld Charpy data from capsule 18 of Dresden Unit 3 were used in this study.
- The new advanced fitting procedure achieves a reduction in uncertainty by 27%, compared to that of conventional hyperbolic tangent fit procedure.

- Conventional
- =13.84°C

*E*

- New Model
- =12.09°C

- Advanced =10.05°C

## Applying the New Fitting Procedure for Surrogate Material Research

-  Select a target chemistry
-  Substitute it into adjusted functions  *f**i* (Cu,Ni)
-  Form a new curve from intersect of *fi *and *E*

## Conclusion of New Charpy Curve Fitting Procedures

- This new procedure provides an expedient way to determine trend curve for the surrogate materials of the RPV surveillance program.
- Furthermore, based on this new approach, the new advanced fitting procedure achieves a reduction in uncertainty by 27%, compared to that of conventional hyperbolic tangent fit procedure.** **
- However, due to high-order nonlinearity, caution should be exercised while using these fitting functions.

## Acknowledgments

- This research is sponsored by
- ORNL LDRD Seed Money Program, and
- The Engineering Research Program of the Office of Basic Energy Sciences,
-     U.S. Department of Energy