# Presentation: 716145

## Predicting SPE Exposures

**Larry Townsend**
**Professor of Nuclear Engineering**
**University of Tennessee**

## Acknowledgement

- Research supported by NASA LWS program under grant No. NAG5-12477 through GSFC

## Background

- As the duration of a mission in space increases, there is a higher probability that a significant dose will be received
- The objective is to develop a set of artificial neural networks (ANN) and Bayesian Inference techniques that are capable of forecasting the dose-time profiles of SPEs

## Dose Calculations

- Proton fluences from SEC website or CD-ROM
- Parameterize using an exponential rigidity function
- J = J0 * exp(-R/R0)
- J – integral fluence
- R – proton rigidity
- J0, R0 – fitting parameters
- J0 and R0 used to describe the input to BRYNTRN

- Profile is dependent on Al and magnitude of SPE
- Weibull growth curve used to represent dose-time profile
- D(t) = D{1-exp[-(t)]}
- D(t) – organ dose at time t
- D – organ total absorbed dose (cGy)
- ,  – fitting parameters
-  in d-1
-  is dimensionless

## Space Radiation Environment

## Dose-Time Profile – Oct. 1989

- Rise 1: D = 55 cGy
- Rise 2: D = 170 (225)cGy
- 	t0 = 1 d
- Rise 3: D = 103 (328)cGy
- 	t0 = 3.25 d
- Rise 4: D = 51 (379)cGy
- 	t0 = 5.167 d

## Time Delay Neural Networks

- Allows for memory of past inputs
- Network inputs represent past and present data
- Delays are equivalent
- Sliding time delay neural network (STDNN) – delays are variable
- If delay is , then input is D[t-(n-1)]

- STDNN block diagram

## Methodology – Network Arch.

- D Neural Network
- Sliding time delay techniques used on linearly scaled inputs
- Architecture:
- 1 input layer with 5 neurons
- 1 hidden layer with 10 neurons & hyperbolic tangent activation function
- 1 output layer with 1 neuron & linear activation function

-  and  Neural Networks
- Time delay techniques used on linearly scaled inputs
- Architecture:
- 1 input layer with 5 neurons
- For , 2 hidden layers:
- 12/8 neurons & hyperbolic tangent activation function
- For , 2 hidden layers:
- 12/8 neurons & logistic activation function
- 1 output layer with 1 neuron & linear activation function

## Methodology – Training 

- Order of training:
- Simulated dose-time data (perfect data created from Weibull parameters)
- Actual dose-time data using weights and biases from simulated training as initial values

- Training within the NN set:
- Train the DNN using all dose data
- Based on final dose input value, separate corresponding  and  data into 5 distinct categories (>500, 100-500, 20-100,
-   5-20, <5)
- Train the NN in 4 sets using corresponding dose data
- Repeat with the NN

## Event 1 Results – 4 x Aug.1972

- Event 1: 4 x Aug. 1972 (“worst case event”); Al shield thickness – 2 g cm-2
- Actual parameter values: D: 2680 cGy; : 2.5076 d-1; : 2.8089

## Event 3 Results – Oct. 1989

- Event 3: October 1989; Al shield thickness – 2 g cm-2
- Actual parameter values:
- Rise 1 -- D: 55 cGy
- 		-- : 1.8724 d-1
- 		-- : 2.1459
- Rise 2 -- D: 170 cGy
- 		-- : 4.3128 d-1
- 		-- : 0.7302
- Rise 2 starts at 0.7 days and 45.5 cGy.

- Actual parameter values:
- Rise 3 -- D: 103 cGy
- 	-- : 1.3943 d-1
- 	-- : 1.5892
- Rise 4 -- D: 51 cGy
- 	-- : 1.2959 d-1
- 	-- : 1.8348
- Rise 3 starts at 3 days and 222.3 cGy.
- Rise 4 starts at 5 days and 327.8 cGy.

## Event 3 Results – Oct. 1989 1st rise

## Event 3 Results – Oct. 1989 2nd rise

## Bayesian Inference

**p(********|D), the joint posterior distribution, is the parameter distribution after observing new data**
**p(D| ********), the likelihood function, is the probability of the data given the parameters**
**p(********), the prior distribution, is the distribution of the parameters before observing the new data**
**p(D), the marginal distribution, is a normalization constant**

## Bayesian Inference (cont.)

**	****Forecasts use the posterior predictive ****	****density expressed as**

**Integrations are typically not analytical.**

## Methodology/Results

**Methodology/Results**
***Predicting  with Hierarchical Models***
**Dose time profiles assumed the following form:**

**As an example, the Weibull hierarchical model **
**	****assumed the following form:**

## Methodology/Results (cont.)

***Predicting  with Hierarchical Models***
**Historical SPEs categorized according to asymptotic dose and maximum dose rate**
**Categorization of new events determined by dose rate early in the evolution of the SPE**

## Methodology/Results (cont.)

***Predicting  with Hierarchical Models***
***	******Group Number******	******	******Max Dose Rate within***
***	******	******	******	******	******5 hours into event(cGy/hr)***
***	******	******	******	******	******	***
***	******	******1******	******	******	******	******>15***
***	***
***	******	******2******	******	******	******	******0.1-15***
***	******	******3******	******	******	******	******0.05-0.1***
***	******	******4******	******	******	******	******0-0.05***

## Results for

***September 24, 2001 SPE***
***Weibull Predicted Mean Values***

## Predicted profile at 2 hours into event

## Predicted profile at 3 hours into event

**Predicted profile at 3 hours into event**

## Predicted profile at 5 hours into event

## Results for

***Results for***
***November 4, 2001 SPE***
***Gompertz Predicted Median Values***

## Predicted profile at 3 hours into event

## Predicted profile at 5 hours into event

## Predicted profile at 6 hours into event

## Results for

***November 22, 2001 SPE***
***Weibull Predicted Mean Values***

## Predicted profile at 2 hours into event

## Predicted profile at 3 hours into event

## Predicted profile at 5 hours into event

## Conclusions

- A set of neural networks was created to forecast the three unknown parameters of a SPE dose-time profile
- A large set of SPE data was trained followed by testing of three SPEs, both single and multiple-rise events
- Training was slow, but testing was quick and allowed for multiple outputs and selections
- The set of networks has the ability to forecast the parameters
- Most of the time the error between forecast and actual value was within 20 %

## Future Work

- Continued work on training/testing programs
- Faster training time and more specific testing outputs
- Inclusion of more SPE parameters
- Better predictions at the boundaries of the training region
- Addition of other training parameters
- Use of particle fluence would eliminate multiple steps
- Forecasts of dose-rate versus time profiles
- Easier comparison with other works and better judgment when looking at dose effects

## Future Work

**	****Develop models/prediction systems to make ****	****forecasts of **
**integral flux spectra**
**cumulative integral flux spectra**
**Flux spectra fitting parameters**