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Difference between revisions of "Basic Statistical Analysis of LWR Pin Power Data"
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Finally, the ''root-mean-square difference'' is a weighted RMS difference determined by the formula below. | Finally, the ''root-mean-square difference'' is a weighted RMS difference determined by the formula below. | ||
− | <math>\sqrt< | + | <math>\sqrt<span style="color: red; text-decoration: line-through;">[2]</span>{\frac{\sum(C^{2}{\cdot}W)}{{\sum}W}}</math> |
The following sections detail how to calculate the above quantities over a variety of dimensions to develop statistical results from pin power differences. | The following sections detail how to calculate the above quantities over a variety of dimensions to develop statistical results from pin power differences. |
Revision as of 14:42, 28 February 2015
This article details the basic mathematical formulas used to statistically compare pin power data sets from a reference and an alternate LWR.
Due to the migration of our articles from MediaWiki to Markdown, the formulas are not showing up properly. Unfortunately, Markdown does not have a lot of support for mathematical characters. We will soon be migrating back to MediaWiki pages, at which point this article will be back to normal.
Contents
Pin Power Dataset Representation
First, let's view the pin power dataset of each LWR as a 4D matrix P(i, j, k, l) where
Variable | Represents |
---|---|
i | pin row |
j | pin column |
k | axial level |
l | assembly number |
In order to compare two of these pin power datasets, we shall define the following 4D pin power datasets:
Variable | Represents |
---|---|
A | reference power data set |
B | alternate power data set |
C | power difference data set |
where
_C = B - A _ (a basic power difference)
or
_C = (B - A) / A _ (a relative power difference)
In addition, each element in C can be weighted by a 4D matrix W.
Derived Quantities
There are four general derived quantities used in pin power analysis. The first is the simple difference which is simply the dataset C. The second is the absolute difference which is the absolute value of C or |C|. The third is the average difference is a weighted average calculated with the following formula.
<math>\frac{\sum(C{\cdot}W)}{{\sum}W}</math>
Finally, the root-mean-square difference is a weighted RMS difference determined by the formula below.
<math>\sqrt[2]{\frac{\sum(C^{2}{\cdot}W)}{{\sum}W}}</math>
The following sections detail how to calculate the above quantities over a variety of dimensions to develop statistical results from pin power differences.
1D Axial Power Results
The axial power difference is defined by the formula below.
<math>C(k) = \sqrt[2]{\frac{\sum_{ijl}(C{\cdot}W)}{{\sum_{ijl}}W}}</math>
The average axial power difference is defined as
<math>\frac{\sum_k[C(k){\cdot}dz]}{{\sum_k}dz}</math>
where the dz, the axial weight, is <math>dz = mesh(k+1) - mesh(k)</math>. Here mesh is a 1D array containing the actual physical distance between each axial level k.
The RMS axial power difference is defined by the formula below.
<math>\sqrt[2]{\frac{\sum_k[C(k)^{2}{\cdot}dz]}{{\sum_k}dz}}</math>