Utilising a bayesian combination m odel to enhance g amma ray detection precision
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Utilising a Bayesian Combination M odel to Enhance G amma-ray Detection Precision. Andrew Parker Lancaster University Engineering Department. Borderline Waste – A Management Problem.

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Utilising a Bayesian Combination M odel to Enhance G amma-ray Detection Precision

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Utilising a bayesian combination m odel to enhance g amma ray detection precision

Utilising a Bayesian Combination Model to Enhance Gamma-ray Detection Precision

Andrew Parker

Lancaster University Engineering Department


Borderline waste a management problem

Borderline Waste – A Management Problem

“...where wastes are borderline between disposal categories the higher standard should be adopted for characterisation purposes.” – Nuclear Decommissioning Authority

Table 1: The disposal cost per-cubic-metre, taken from LLWR at Drigg and NDA budget information

Andrew Parker, Lancaster University Engineering Dept, 2011


Gamma ray detectors

Gamma-ray Detectors

LLW: Waste that has activity ... less than 12 GBq per tonne of gamma radioactivity

Sodium Iodide Scintillator

NaI

Hyper-pure Germanium Semiconductor

HPGe

  • Good energy resolution

  • Insensitive to temperature change

  • Poor detection efficiency relative to NaI.

  • High detection efficiency

  • Cheap to produce

  • Poor energy resolution

Andrew Parker, Lancaster University Engineering Dept, 2011


Bayesian normal normal model

Bayesian Normal-Normal Model

Bayes’ Rule

Likelihood

Posterior Value

Prior

Assuming the detectors’ results are normally distributed with Means and Standard Deviations (M, τ) & (Y,σ) respectively.

Posterior Mean

Posterior Variance

Andrew Parker, Lancaster University Engineering Dept, 2011


Combination of count data

Combination of Count Data

Table 2: Mean and standard deviation of Cs counts with the two detectors

Levenberg-Marquardt fitting method applied to photopeaks.

Example of Cs137 photopeak

Table 3: Shows the Bayesian mean and standard deviation for the selected isotopes, having used all 15 result sets from each detector

Andrew Parker, Lancaster University Engineering Dept, 2011


Precision comparison results

Precision Comparison Results

Coefficient of Variation (CV)

Table 4: CV for single detector results

Table 5: CV for the Bayesian method with varying values of N1 & N2

WhereN1 = Number of sets of data used from Sodium Iodide (NaI)

N2 = Number of sets of data used from Hyper-pure Germanium (HPGe)

Andrew Parker, Lancaster University Engineering Dept, 2011


Visual comparison

Visual Comparison

Bayesian Method

HPGe

NaI

Figure 2: Plot showing the distributions of each detector alone and the plot of the Bayesian method using all available results for Cs 137. Normalised to zero.


Conclusions

Conclusions

  • Under certain conditions the method has shown to reduce the normal distribution dispersion and therefore the precision of the result.

  • By obtaining a higher degree of precision the technique offers lower uncertainty when determining an accurate estimate for the activity of a source.

  • When fewer results were used the model shows higher levels of dispersion compared to that of a single detector.

Thank you for listening, any questions related to the work?

Andrew Parker ([email protected])

Andrew Parker, Lancaster University Engineering Dept, 2011


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